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Exactly Distribution-free Inference in Instrumental Variables Regression with Possibly Weak Instruments

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Abstract

This paper introduces a rank-based test for the instrumental variables regression model that dominates the Anderson-Rubin test in terms of finite sample size and asymptotic power in certain circumstances. The test has correct size for any distribution of the errors with weak or strong instruments. The test has noticeably higher power than the Anderson-Rubin test when the error distribution has thick tails and comparable power otherwise. Like the Anderson-Rubin test, the rank tests considered here perform best, relative to other available tests, in exactly-identified models.

Suggested Citation

  • Donald W.K. Andrews & Vadim Marmer, 2005. "Exactly Distribution-free Inference in Instrumental Variables Regression with Possibly Weak Instruments," Cowles Foundation Discussion Papers 1501, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1501
    Note: CFP 1253.
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    Cited by:

    1. Purevdorj Tuvaandorj, 2021. "Robust Permutation Tests in Linear Instrumental Variables Regression," Papers 2111.13774, arXiv.org, revised Jul 2024.
    2. Nicholas Bloom & Benn Eifert & Aprajit Mahajan & David McKenzie & John Roberts, 2013. "Does Management Matter? Evidence from India," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(1), pages 1-51.
    3. Kazuhiko Hayakawa, 2006. "Efficient GMM Estimation of Dynamic Panel Data Models Where Large Heterogeneity May Be Present," Hi-Stat Discussion Paper Series d05-130, Institute of Economic Research, Hitotsubashi University.
    4. Guggenberger, Patrik & Smith, Richard J., 2008. "Generalized empirical likelihood tests in time series models with potential identification failure," Journal of Econometrics, Elsevier, vol. 142(1), pages 134-161, January.
    5. Joel L. Horowitz, 2017. "Non-asymptotic inference in instrumental variables estimation," CeMMAP working papers 46/17, Institute for Fiscal Studies.
    6. 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.
    7. 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.
    8. Joel L. Horowitz, 2018. "Non-Asymptotic Inference in Instrumental Variables Estimation," Papers 1809.03600, arXiv.org.
    9. Purevdorj Tuvaandorj, 2024. "A Combinatorial Central Limit Theorem for Stratified Randomization," Papers 2402.14764, arXiv.org, revised Apr 2024.
    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. Anand Acharya & Lynda Khalaf & Marcel Voia & Myra Yazbeck & David Wensley, 2021. "Severity of Illness and the Duration of Intensive Care," Working Papers 2021-003, Human Capital and Economic Opportunity Working Group.
    13. Donald W.K. Andrews & James H. Stock, 2005. "Inference with Weak Instruments," Cowles Foundation Discussion Papers 1530, Cowles Foundation for Research in Economics, Yale University.
    14. Aviv Nevo & Adam M. Rosen, 2012. "Identification With Imperfect Instruments," The Review of Economics and Statistics, MIT Press, vol. 94(3), pages 659-671, August.
    15. Kikuta,Kyosuke, 2022. "The drowning-out effect: voter turnout, uncertainty, and protests," IDE Discussion Papers 867, Institute of Developing Economies, Japan External Trade Organization(JETRO).
    16. 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.
    17. Jens Klooster & Mikhail Zhelonkin, 2024. "Outlier robust inference in the instrumental variable model with applications to causal effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 86-106, January.
    18. Leandro M. Magnusson & Sophocles Mavroeidis, 2014. "Identification Using Stability Restrictions," Econometrica, Econometric Society, vol. 82(5), pages 1799-1851, September.
    19. 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.
    20. Michela Giorcelli & Bo Li, 2022. "Technology Transfer and Early Industrial Development: Evidence from the Sino-Soviet Alliance," CESifo Working Paper Series 9552, CESifo.
    21. Guggenberger, Patrik & Ramalho, Joaquim J.S. & Smith, Richard J., 2012. "GEL statistics under weak identification," Journal of Econometrics, Elsevier, vol. 170(2), pages 331-349.

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    More about this item

    Keywords

    Aligned ranks; Anderson-Rubin statistic; categorical covariates; exact size; normal scores; rank test; weak instruments; Wilcoxon scores;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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