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Leverage, influence, and the jackknife in clustered regression models: Reliable inference using summclust

Author

Listed:
  • James G. MacKinnon

    (Queen’s University)

  • Morten Ørregaard Nielsen

    (Aarhus University)

  • Matthew D. Webb

    (Carleton University)

Abstract

We introduce a new command, summclust, that summarizes the cluster structure of the dataset for linear regression models with clustered disturbances. The key unit of observation for such a model is the cluster. We therefore propose cluster-level measures of leverage, partial leverage, and influence and show how to compute them quickly in most cases. The measures of leverage and partial leverage can be used as diagnostic tools to identify datasets and regression designs in which cluster–robust inference is likely to be challenging. The measures of influence can provide valuable information about how the results depend on the data in the various clusters. We also show how to calculate two jackknife variance matrix estimators efficiently as a by-product of our other computations. These estimators, which are already available in Stata, are generally more conservative than conventional variance matrix estimators. The summclust command computes all the quantities that we discuss.

Suggested Citation

  • James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2023. "Leverage, influence, and the jackknife in clustered regression models: Reliable inference using summclust," Stata Journal, StataCorp LLC, vol. 23(4), pages 942-982, December.
    • Handle: RePEc:tsj:stataj:v:23:y:2023:i:4:p:942-982
    DOI: 10.1177/1536867X231212433
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    Cited by:

    1. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Cluster-robust inference: A guide to empirical practice," Journal of Econometrics, Elsevier, vol. 232(2), pages 272-299.
    2. MacKinnon, James G. & Nielsen, Morten Ørregaard & Webb, Matthew D., 2023. "Testing for the appropriate level of clustering in linear regression models," Journal of Econometrics, Elsevier, vol. 235(2), pages 2027-2056.
    3. Daniel Auer & Michaela Slotwinski & Achim Ahrens & Dominik Hangartner & Selina Kurer & Stefanie Kurt & Alois Stutzer, 2024. "Social Assistance and Refugee Crime," CESifo Working Paper Series 11051, CESifo.
    4. Richard K. Crump & Nikolay Gospodinov & Ignacio Lopez Gaffney, 2024. "A New Jackknife Variance Estimator for Time-Series and Panel Regressions," Staff Reports 1133, Federal Reserve Bank of New York.
    5. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2023. "Fast and reliable jackknife and bootstrap methods for cluster‐robust inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(5), pages 671-694, August.
    6. Wang, Wenjie & Zhang, Yichong, 2024. "Wild bootstrap inference for instrumental variables regressions with weak and few clusters," Journal of Econometrics, Elsevier, vol. 241(1).
    7. Pettersson-Lidbom, Per, 2022. "Exit, Voice and Political Change: Evidence from Swedish Mass Migration to the United States. A Comment on Karadja and Prawitz (Journal of Political Economy, 2019)," Journal of Comments and Replications in Economics (JCRE), ZBW - Leibniz Information Centre for Economics, vol. 1, pages 1-13.
    8. Bruce E. Hansen, 2025. "Standard Errors for Difference‐in‐Difference Regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 40(3), pages 291-309, April.
    9. MacKinnon, James G., 2023. "Using large samples in econometrics," Journal of Econometrics, Elsevier, vol. 235(2), pages 922-926.
    10. Johannes W. Ligtenberg, 2023. "Inference in clustered IV models with many and weak instruments," Papers 2306.08559, arXiv.org, revised Oct 2025.
    11. Sebastian Kranz, 2024. "From Replications to Revelations: Heteroskedasticity-Robust Inference," Papers 2411.14763, arXiv.org, revised Dec 2024.

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    Keywords

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • 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
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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