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Testing many restrictions under heteroskedasticity

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  • Anatolyev, Stanislav
  • Sølvsten, Mikkel

Abstract

We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F statistic to a critical value that corrects for many restrictions and conditional heteroskedasticity. This correction uses leave-one-out estimation to correctly center the critical value and leave-three-out estimation to appropriately scale it. The large sample properties of the test are established in an asymptotic framework where the number of tested restrictions may be fixed or may grow with the sample size, and can even be proportional to the number of observations. We show that the test is asymptotically valid and has non-trivial asymptotic power against the same local alternatives as the exact F test when the latter is valid. Simulations corroborate these theoretical findings and suggest excellent size control in moderately small samples, even under strong heteroskedasticity.

Suggested Citation

  • Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    • Handle: RePEc:eee:econom:v:236:y:2023:i:1:s0304407623001677
    DOI: 10.1016/j.jeconom.2023.03.011
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    3. Anna Mikusheva & Liyang Sun, 2024. "Weak identification with many instruments," The Econometrics Journal, Royal Economic Society, vol. 27(2), pages -28.
    4. Michal Koles'ar & Ulrich K. Muller & Sebastian T. Roelsgaard, 2023. "The Fragility of Sparsity," Papers 2311.02299, arXiv.org, revised Jan 2024.

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    More about this item

    Keywords

    Linear regression; Ordinary least squares; Many regressors; Leave-out estimation; Hypothesis testing; High-dimensional models;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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