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Rank Tests for Instrumental Variables Regression with Weak Instruments

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Abstract

This paper considers tests in an instrumental variables (IVs) regression model with IVs that may be weak. Tests that have near-optimal asymptotic power properties with Gaussian errors for weak and strong IVs have been determined in Andrews, Moreira, and Stock (2006a). In this paper, we seek tests that have near-optimal asymptotic power with Gaussian errors and improved power with non-Gaussian errors relative to existing tests. Tests with such properties are obtained by introducing rank tests that are analogous to the conditional likelihood ratio test of Moreira (2003). We also introduce a rank test that is analogous to the Lagrange multiplier test of Kleibergen (2002) and Moreira (2001).

Suggested Citation

  • Donald W.K. Andrews & Gustavo Soares, 2006. "Rank Tests for Instrumental Variables Regression with Weak Instruments," Cowles Foundation Discussion Papers 1564, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1564
    Note: CFP 1250.
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    Cited by:

    1. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "Applications of subsampling, hybrid, and size-correction methods," Journal of Econometrics, Elsevier, vol. 158(2), pages 285-305, October.
    2. Andrews, Donald W.K. & Marmer, Vadim, 2008. "Exactly distribution-free inference in instrumental variables regression with possibly weak instruments," Journal of Econometrics, Elsevier, vol. 142(1), pages 183-200, January.
    3. Leandro M. Magnusson, 2010. "Inference in limited dependent variable models robust to weak identification," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 56-79, October.
    4. Joel L. Horowitz, 2017. "Non-asymptotic inference in instrumental variables estimation," CeMMAP working papers CWP46/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Cattaneo, Matias D. & Crump, Richard K. & Jansson, Michael, 2012. "Optimal inference for instrumental variables regression with non-Gaussian errors," Journal of Econometrics, Elsevier, vol. 167(1), pages 1-15.
    6. Purevdorj Tuvaandorj, 2021. "Robust Permutation Tests in Linear Instrumental Variables Regression," Papers 2111.13774, arXiv.org, revised Jul 2024.
    7. Murray Michael P., 2017. "Linear Model IV Estimation When Instruments Are Many or Weak," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-22, January.
    8. Joel L. Horowitz, 2017. "Non-asymptotic inference in instrumental variables estimation," CeMMAP working papers 46/17, Institute for Fiscal Studies.
    9. Joel L. Horowitz, 2018. "Non-Asymptotic Inference in Instrumental Variables Estimation," Papers 1809.03600, arXiv.org.
    10. Elise Coudin & Jean-Marie Dufour, 2010. "Finite and Large Sample Distribution-Free Inference in Median Regressions with Instrumental Variables," Working Papers 2010-56, Center for Research in Economics and Statistics.
    11. Horowitz, Joel L., 2021. "Bounding the difference between true and nominal rejection probabilities in tests of hypotheses about instrumental variables models," Journal of Econometrics, Elsevier, vol. 222(2), pages 1057-1082.
    12. Joel L. Horowitz, 2018. "Non-asymptotic inference in instrumental variables estimation," CeMMAP working papers CWP52/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    Keywords

    Asymptotically similar tests; Conditional likelihood ratio test; Instrumental variables regression; Lagrange multiplier test; Power of test; Rank tests; Thick-tailed distribution; Weak instruments;
    All these keywords.

    JEL classification:

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

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