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Bootstrap inference in a linear equation estimated by instrumental variables

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  • Russell Davidson

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales, CIREG - Centre interuniversitaire de recherche en économie quantitative - Université de Montréal, Department of Economics - McGill University)

  • James Mackinnon

    () (Department of Economics - Queen's University [Kingston])

Abstract

We study several tests for the coefficient of the single right-hand-side endogenous variable in a linear equation estimated by instrumental variables. We show that writing all the test statistics—Student's t, Anderson-Rubin, the LM statistic of Kleibergen and Moreira (K), and likelihood ratio (LR)—as functions of six random quantities leads to a number of interesting results about the properties of the tests under weakinstrument asymptotics. We then propose several new procedures for bootstrapping the three non-exact test statistics and also a new conditional bootstrap version of the LR test. These use more efficient estimates of the parameters of the reduced-form equation than existing procedures. When the best of these new procedures is used, both the K and conditional bootstrap LR tests have excellent performance under the null. However, power considerations suggest that the latter is probably the method of choice.

Suggested Citation

  • Russell Davidson & James Mackinnon, 2009. "Bootstrap inference in a linear equation estimated by instrumental variables," Working Papers halshs-00442713, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00442713
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00442713
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    References listed on IDEAS

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    1. Marcelo J. Moreira & Jack R. Porter & Gustavo A. Suarez, 2004. "Bootstrap and Higher-Order Expansion Validity When Instruments May Be Weak," Harvard Institute of Economic Research Working Papers 2048, Harvard - Institute of Economic Research.
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    4. Kleibergen, Frank, 2007. "Generalizing weak instrument robust IV statistics towards multiple parameters, unrestricted covariance matrices and identification statistics," Journal of Econometrics, Elsevier, vol. 139(1), pages 181-216, July.
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    7. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 95(2), pages 375-389, April.
    8. Davidson, Russell & MacKinnon, James G., 2010. "Wild Bootstrap Tests for IV Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 128-144.
    9. 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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    13. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-529, October.
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    16. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
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    Citations

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    Cited by:

    1. Wenjie Wang, 2012. "Bootstrapping Anderson-Rubin Statistic and J Statistic in Linear IV Models with Many Instruments," KIER Working Papers 810, Kyoto University, Institute of Economic Research.
    2. Simon A. Broda & Raymond Kan, 2016. "On distributions of ratios," Biometrika, Biometrika Trust, vol. 103(1), pages 205-218.
    3. repec:eee:ecolet:v:157:y:2017:i:c:p:107-111 is not listed on IDEAS
    4. Davidson, Russell & MacKinnon, James G., 2010. "Wild Bootstrap Tests for IV Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 128-144.
    5. Corinna Ghirelli, 2015. "Scars of early non-employment for low educated youth: evidence and policy lessons from Belgium," IZA Journal of European Labor Studies, Springer;Forschungsinstitut zur Zukunft der Arbeit GmbH (IZA), vol. 4(1), pages 1-34, December.
    6. 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.
    7. Chau, Tak Wai, 2014. "On the equivalence of indirect inference and bootstrap bias correction for linear IV estimators," Economics Letters, Elsevier, vol. 123(3), pages 333-335.
    8. Russell Davidson & James G. MacKinnon, 2015. "Bootstrap Tests for Overidentification in Linear Regression Models," Econometrics, MDPI, Open Access Journal, vol. 3(4), pages 1-39, December.
    9. Wenjie Wang & Qingfeng Liu, 2015. "Bootstrap-based Selection for Instrumental Variables Model," Economics Bulletin, AccessEcon, vol. 35(3), pages 1886-1896.
    10. Corinna GHIRELLI, 2015. "Scars of early non-employment in a rigid labour market," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2015008, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    11. 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.
    12. James G. MacKinnon, 2007. "Bootstrap Hypothesis Testing," Working Papers 1127, Queen's University, Department of Economics.
    13. Noud P.A. van Giersbergen, 2011. "Bootstrapping Subset Test Statistics in IV Regression," UvA-Econometrics Working Papers 11-08, Universiteit van Amsterdam, Dept. of Econometrics.
    14. Corinna.Ghirelli, 2014. "The scarring effect of early non-employment," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 14/895, Ghent University, Faculty of Economics and Business Administration.
    15. Keith Finlay & Leandro M. Magnusson, 2014. "Bootstrap Methods for Inference with Cluster-Sample IV Models," Economics Discussion / Working Papers 14-12, The University of Western Australia, Department of Economics.

    More about this item

    Keywords

    bootstrap; weak instruments; IV estimation;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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