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When and How to Deal with Clustered Errors in Regression Models

Author

Listed:
  • James G. MacKinnon

    (Queen's University)

  • Matthew D. Webb

    (Carleton University)

Abstract

We discuss when and how to deal with possibly clustered errors in linear regression models. Specifically, we discuss situations in which a regression model may plausibly be treated as having error terms that are arbitrarily correlated within known clusters but uncorrelated across them. The methods we discuss include various covariance matrix estimators, possibly combined with various methods of obtaining critical values, several bootstrap procedures, and randomization inference. Special attention is given to models with few treated clusters and clusters that vary a lot in size, where inference may be problematic. Two empirical examples illustrate the methods we discuss and the concerns we raise, and a simulation experiment illustrates the consequences of over-clustering and under-clustering.

Suggested Citation

  • James G. MacKinnon & Matthew D. Webb, 2020. "When and How to Deal with Clustered Errors in Regression Models," Working Paper 1421, Economics Department, Queen's University.
  • Handle: RePEc:qed:wpaper:1421
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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/wpaper/qed_wp_1421.pdf
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    References listed on IDEAS

    as
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    Cited by:

    1. Federico Bugni & Ivan Canay & Azeem Shaikh & Max Tabord-Meehan, 2022. "Inference for Cluster Randomized Experiments with Non-ignorable Cluster Sizes," Papers 2204.08356, arXiv.org, revised Apr 2024.
    2. Sarah Schneider-Strawczynski & Jérôme Valette, 2021. "Media Coverage of Immigration and the Polarization of Attitudes," PSE Working Papers halshs-03322229, HAL.
    3. Matthew D. Webb, 2023. "Reworking wild bootstrap‐based inference for clustered errors," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 56(3), pages 839-858, August.
    4. Yamazaki, Akio, 2022. "Environmental taxes and productivity: Lessons from Canadian manufacturing," Journal of Public Economics, Elsevier, vol. 205(C).
    5. Bruno Ferman, 2019. "Assessing Inference Methods," Papers 1912.08772, arXiv.org, revised Oct 2022.
    6. Paul Heaton & Caleb Flint, 2021. "Medicaid coverage expansions and liability insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(1), pages 29-51, March.

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    More about this item

    Keywords

    clustered data; cluster-robust variance estimator; CRVE; wild cluster bootstrap; robust inference;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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