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The Fragility of Sparsity

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  • Michal Koles'ar
  • Ulrich K. Muller
  • Sebastian T. Roelsgaard

Abstract

We show, using three empirical applications, that linear regression estimates which rely on the assumption of sparsity are fragile in two ways. First, we document that different choices of the regressor matrix that do not impact ordinary least squares (OLS) estimates, such as the choice of baseline category with categorical controls, can move sparsity-based estimates by two standard errors or more. Second, we develop two tests of the sparsity assumption based on comparing sparsity-based estimators with OLS. The tests tend to reject the sparsity assumption in all three applications. Unless the number of regressors is comparable to or exceeds the sample size, OLS yields more robust inference at little efficiency cost.

Suggested Citation

  • Michal Koles'ar & Ulrich K. Muller & Sebastian T. Roelsgaard, 2023. "The Fragility of Sparsity," Papers 2311.02299, arXiv.org, revised Mar 2025.
  • Handle: RePEc:arx:papers:2311.02299
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    References listed on IDEAS

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    1. John J. Donohue III & Steven D. Levitt, 2001. "The Impact of Legalized Abortion on Crime," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(2), pages 379-420.
    2. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2018. "Inference in Linear Regression Models with Many Covariates and Heteroscedasticity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1350-1361, July.
    3. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
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    Cited by:

    1. Achim Ahrens & Christian B. Hansen & Mark E. Schaffer & Thomas Wiemann, 2025. "Model Averaging and Double Machine Learning," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 40(3), pages 249-269, April.
    2. Laurent Davezies & Guillaume Hollard & Pedro Vergara Merino, 2024. "Revisiting Randomization with the Cube Method," Papers 2407.13613, arXiv.org, revised Mar 2025.

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