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Inference with a single treated cluster

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  • Andreas Hagemann

Abstract

I introduce a generic method for inference about a scalar parameter in research designs with a finite number of heterogeneous clusters where only a single cluster received treatment. This situation is commonplace in difference-in-differences estimation but the test developed here applies more generally. I show that the test controls size and has power under asymptotics where the number of observations within each cluster is large but the number of clusters is fixed. The test combines weighted, approximately Gaussian parameter estimates with a rearrangement procedure to obtain its critical values. The weights needed for most empirically relevant situations are tabulated in the paper. Calculation of the critical values is computationally simple and does not require simulation or resampling. The rearrangement test is highly robust to situations where some clusters are much more variable than others. Examples and an empirical application are provided.

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  • Andreas Hagemann, 2020. "Inference with a single treated cluster," Papers 2010.04076, arXiv.org.
    • Handle: RePEc:arx:papers:2010.04076
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    References listed on IDEAS

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    1. Bruno Ferman & Cristine Pinto, 2019. "Inference in Differences-in-Differences with Few Treated Groups and Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 452-467, July.
    2. 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.
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    Cited by:

    1. Hao Yu & Olesya Baker, 2022. "Do noneconomic damage caps reduce medical malpractice insurance premiums? Evidence from North Carolina," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 25(2), pages 201-218, June.
    2. Billy Ferguson & Brad Ross, 2020. "Assessing the Sensitivity of Synthetic Control Treatment Effect Estimates to Misspecification Error," Papers 2012.15367, arXiv.org, revised Feb 2021.
    3. Alexander James & Nathaly M. Rivera & Brock Smith, 2022. "Cash Transfer and Voter Turnout," Working Papers wp536, University of Chile, Department of Economics.
    4. Luis Alvarez & Bruno Ferman, 2023. "Extensions for Inference in Difference-in-Differences with Few Treated Clusters," Papers 2302.03131, arXiv.org.
    5. Wang, Wenjie & Zhang, Yichong, 2024. "Wild bootstrap inference for instrumental variables regressions with weak and few clusters," Journal of Econometrics, Elsevier, vol. 241(1).
    6. Roth, Jonathan & Sant’Anna, Pedro H.C. & Bilinski, Alyssa & Poe, John, 2023. "What’s trending in difference-in-differences? A synthesis of the recent econometrics literature," Journal of Econometrics, Elsevier, vol. 235(2), pages 2218-2244.

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