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Hypothesis Testing in Linear Regression when K/N is Large

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  • Calhoun, Gray

Abstract

This paper derives the asymptotic distribution of the F-test for the significance of linear regression coefficients as both the number of regressors, k, and the number of observations, n, increase together so that their ratio remains positive in the limit. The conventional critical values for this test statistic are too small, and the standard version of the F-test is invalid under this asymptotic theory. This paper provides a correction to the F statistic that gives correctly-sized tests under both this paper's limit theory and also under conventional asymptotic theory that keeps k finite. This paper also presents simulations that indicate the new statistic can perform better in small samples than the conventional test. The statistic is then used to reexamine Olivei and Tenreyro's results from "The Timing of Monetary Policy Shocks" (2007, AER) and Sala-i-Martin's results from "I Just Ran Two Million Regressions" (1997, AER).

Suggested Citation

  • Calhoun, Gray, 2010. "Hypothesis Testing in Linear Regression when K/N is Large," Staff General Research Papers Archive 32216, Iowa State University, Department of Economics.
    • Handle: RePEc:isu:genres:32216
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    File URL: http://www2.econ.iastate.edu/papers/p12216-2010-12-20.pdf
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    References listed on IDEAS

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    Cited by:

    1. Cattaneo, Matias D. & Jansson, Michael & Newey, Whitney K., 2018. "Alternative Asymptotics And The Partially Linear Model With Many Regressors," Econometric Theory, Cambridge University Press, vol. 34(2), pages 277-301, April.
    2. Calhoun, Gray, 2014. "Out-Of-Sample Comparisons of Overfit Models," Staff General Research Papers Archive 32462, Iowa State University, Department of Economics.
    3. Abhimanyu Gupta & Myung Hwan Seo, 2023. "Robust Inference on Infinite and Growing Dimensional Time‐Series Regression," Econometrica, Econometric Society, vol. 91(4), pages 1333-1361, July.
    4. Koen Jochmans, 2023. "Testing random assignment to peer groups," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 321-333, April.
    5. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    6. 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.
    7. Richard, Patrick, 2019. "Residual bootstrap tests in linear models with many regressors," Journal of Econometrics, Elsevier, vol. 208(2), pages 367-394.

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    More about this item

    Keywords

    Dimension Asymptotics; F-Test; Ordinary Least Squares;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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