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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 LP, 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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    as
    1. MacKinnon, James G. & Webb, Matthew D., 2020. "Randomization inference for difference-in-differences with few treated clusters," Journal of Econometrics, Elsevier, vol. 218(2), pages 435-450.
    2. Matias Busso & Sebastian Galiani, 2019. "The Causal Effect of Competition on Prices and Quality: Evidence from a Field Experiment," American Economic Journal: Applied Economics, American Economic Association, vol. 11(1), pages 33-56, January.
    3. Guido W. Imbens & Michal Kolesár, 2016. "Robust Standard Errors in Small Samples: Some Practical Advice," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 701-712, October.
    4. 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.
    5. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2021. "Wild Bootstrap and Asymptotic Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 505-519, March.
    6. Djogbenou, Antoine A. & MacKinnon, James G. & Nielsen, Morten Ørregaard, 2019. "Asymptotic theory and wild bootstrap inference with clustered errors," Journal of Econometrics, Elsevier, vol. 212(2), pages 393-412.
    7. 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.
    8. Andrew V. Carter & Kevin T. Schnepel & Douglas G. Steigerwald, 2017. "Asymptotic Behavior of a t -Test Robust to Cluster Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 99(4), pages 698-709, July.
    9. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    10. James G. MacKinnon & Matthew D. Webb, 2017. "Pitfalls When Estimating Treatment Effects Using Clustered Data," Working Paper 1387, Economics Department, Queen's University.
    11. Cameron, A. Colin & Gelbach, Jonah B. & Miller, Douglas L., 2011. "Robust Inference With Multiway Clustering," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(2), pages 238-249.
    12. David Roodman & James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2019. "Fast and wild: Bootstrap inference in Stata using boottest," Stata Journal, StataCorp LP, vol. 19(1), pages 4-60, March.
    13. A. Colin Cameron & Douglas L. Miller, 2015. "A Practitioner’s Guide to Cluster-Robust Inference," Journal of Human Resources, University of Wisconsin Press, vol. 50(2), pages 317-372.
    14. Timothy Conley & Silvia Gonçalves & Christian Hansen, 2018. "Inference with Dependent Data in Accounting and Finance Applications," Journal of Accounting Research, Wiley Blackwell, vol. 56(4), pages 1139-1203, September.
    15. James G. MacKinnon & Matthew D. Webb, 2018. "The wild bootstrap for few (treated) clusters," Econometrics Journal, Royal Economic Society, vol. 21(2), pages 114-135, June.
    16. 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.
    17. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, Decembrie.
    18. Hansen, Bruce E. & Lee, Seojeong, 2019. "Asymptotic theory for clustered samples," Journal of Econometrics, Elsevier, vol. 210(2), pages 268-290.
    19. James G. MacKinnon & Matthew D. Webb, 2019. "Wild Bootstrap Randomization Inference for Few Treated Clusters," Advances in Econometrics, in: The Econometrics of Complex Survey Data, volume 39, pages 61-85, Emerald Group Publishing Limited.
    20. James G. MacKinnon & Matthew D. Webb, 2017. "Wild Bootstrap Inference for Wildly Different Cluster Sizes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(2), pages 233-254, March.
    21. Chang Hyung Lee & Douglas G. Steigerwald, 2018. "Inference for clustered data," Stata Journal, StataCorp LP, vol. 18(2), pages 447-460, June.
    22. James E. Pustejovsky & Elizabeth Tipton, 2018. "Small-Sample Methods for Cluster-Robust Variance Estimation and Hypothesis Testing in Fixed Effects Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(4), pages 672-683, October.
    23. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    24. Bester, C. Alan & Conley, Timothy G. & Hansen, Christian B., 2011. "Inference with dependent data using cluster covariance estimators," Journal of Econometrics, Elsevier, vol. 165(2), pages 137-151.
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    Cited by:

    1. 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.
    2. 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.
    3. Johannes W. Ligtenberg, 2023. "Inference in IV models with clustered dependence, many instruments and weak identification," Papers 2306.08559, arXiv.org, revised Mar 2024.
    4. 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.
    5. 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(2022-3), pages 1-13.
    6. MacKinnon, James G., 2023. "Using large samples in econometrics," Journal of Econometrics, Elsevier, vol. 235(2), pages 922-926.

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    More about this item

    Keywords

    summclust; clustered data; cluster–robust variance estimator; CRVE; grouped data; high-leverage clusters; influential clusters; jackknife; partial leverage; robust inference;
    All these keywords.

    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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