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A Modified Randomization Test for the Level of Clustering

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  • Yong Cai
Abstract
Suppose a researcher observes individuals within a county within a state. Given concerns about correlation across individuals, it is common to group observations into clusters and conduct inference treating observations across clusters as roughly independent. However, a researcher that has chosen to cluster at the county level may be unsure of their decision, given knowledge that observations are independent across states. This paper proposes a modified randomization test as a robustness check for the chosen level of clustering in a linear regression setting. Existing tests require either the number of states or number of counties to be large. Our method is designed for settings with few states and few counties. While the method is conservative, it has competitive power in settings that may be relevant to empirical work.

Suggested Citation

  • Yong Cai, 2021. "A Modified Randomization Test for the Level of Clustering," Papers 2105.01008, arXiv.org, revised Jan 2022.
    • Handle: RePEc:arx:papers:2105.01008
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Rustam Ibragimov & Ulrich K. Müller, 2016. "Inference with Few Heterogeneous Clusters," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 83-96, March.
    4. Hansen, Bruce E. & Lee, Seojeong, 2019. "Asymptotic theory for clustered samples," Journal of Econometrics, Elsevier, vol. 210(2), pages 268-290.
    5. Alberto Abadie & Susan Athey & Guido W Imbens & Jeffrey M Wooldridge, 2023. "When Should You Adjust Standard Errors for Clustering?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 138(1), pages 1-35.
    6. Ivan A. Canay & Andres Santos & Azeem M. Shaikh, 2018. "The wild bootstrap with a "small" number of "large" clusters," CeMMAP working papers CWP27/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Uri Gneezy & John A. List & Jeffrey A. Livingston & Xiangdong Qin & Sally Sadoff & Yang Xu, 2019. "Measuring Success in Education: The Role of Effort on the Test Itself," American Economic Review: Insights, American Economic Association, vol. 1(3), pages 291-308, December.
    8. 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.
    9. Ivan A. Canay & Joseph P. Romano & Azeem M. Shaikh, 2017. "Randomization Tests Under an Approximate Symmetry Assumption," Econometrica, Econometric Society, vol. 85, pages 1013-1030, May.
    10. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(1), pages 249-275.
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    Cited by:

    1. 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.
    2. Yong Cai, 2021. "Panel Data with Unknown Clusters," Papers 2106.05503, arXiv.org, revised Jan 2022.

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