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A Specification Test for Instrumental Variables Regression with Many Instruments

Author

Listed:
  • Yoonseok Lee

    (Dept. of Economics, University of Michigan)

  • Ryo Okui

    (Institute of Economic Research, Kyoto University)

Abstract

This paper considers specification testing for instrumental variables estimation in the presence of many instruments. The test proposed is a modified version of the Sargan (1958, Econometrica 26(3): 393-415) test of overidentifying restrictions. The test statistic asymptotically follows the standard normal distribution under the null hypothesis of correct specification when the number of instruments increases with the sample size. We find that the new test statistic is numerically equivalent up to a sign to the test statistic proposed by Hahn and Hausman (2002, Econometrica 70(1): 163-189). We also assess the size and power properties of the test.

Suggested Citation

  • Yoonseok Lee & Ryo Okui, 2009. "A Specification Test for Instrumental Variables Regression with Many Instruments," Cowles Foundation Discussion Papers 1741, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:1741
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d17/d1741.pdf
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    References listed on IDEAS

    as
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    3. Andrews, Donald W.K. & Stock, James H., 2007. "Testing with many weak instruments," Journal of Econometrics, Elsevier, vol. 138(1), pages 24-46, May.
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    7. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
    8. Jinyong Hahn & Jerry Hausman, 2002. "A New Specification Test for the Validity of Instrumental Variables," Econometrica, Econometric Society, vol. 70(1), pages 163-189, January.
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    Cited by:

    1. Walter Beckert, 2020. "A Note on Specification Testing in Some Structural Regression Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(3), pages 686-695, June.
    2. Chao, John C. & Hausman, Jerry A. & Newey, Whitney K. & Swanson, Norman R. & Woutersen, Tiemen, 2014. "Testing overidentifying restrictions with many instruments and heteroskedasticity," Journal of Econometrics, Elsevier, vol. 178(P1), pages 15-21.
    3. Walter Beckert, 2019. "A Note on Specification Testing in Some Structural Regression Models," CeMMAP working papers CWP22/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Lee, Yoonseok & Okui, Ryo, 2012. "Hahn–Hausman test as a specification test," Journal of Econometrics, Elsevier, vol. 167(1), pages 133-139.
    5. C. J. Krizan & Adela Luque & Alice Zawacki, 2014. "The Effect Of Employer Health Insurance Offering On The Growth And Survival Of Small Business Prior To The Affordable Care Act," Working Papers 14-22, Center for Economic Studies, U.S. Census Bureau.

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    More about this item

    Keywords

    Instrumental variables estimation; Many instruments; Overidentifying restrictions test; Specification test;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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