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Unbiased Estimation of the Average Treatment Effect in Cluster-Randomized Experiments

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  • Middleton Joel A.

    (Department of Political Science, University of California Berkeley, Berkeley, CA, USA)

  • Aronow Peter M.

    (Department of Political Science, Yale University, New Haven, CT, USA)

Abstract

Many estimators of the average treatment effect, including the difference-in-means, may be biased when clusters of units are allocated to treatment. This bias remains even when the number of units within each cluster grows asymptotically large. In this paper, we propose simple, unbiased, location-invariant, and covariate-adjusted estimators of the average treatment effect in experiments with random allocation of clusters, along with associated variance estimators. We then analyze a cluster-randomized field experiment on voter mobilization in the US, demonstrating that the proposed estimators have precision that is comparable, if not superior, to that of existing, biased estimators of the average treatment effect.

Suggested Citation

  • Middleton Joel A. & Aronow Peter M., 2015. "Unbiased Estimation of the Average Treatment Effect in Cluster-Randomized Experiments," Statistics, Politics and Policy, De Gruyter, vol. 6(1-2), pages 39-75, December.
    • Handle: RePEc:bpj:statpp:v:6:y:2015:i:1-2:p:39-75:n:1
    DOI: 10.1515/spp-2013-0002
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    References listed on IDEAS

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    1. King, Gary & Roberts, Margaret E., 2015. "How Robust Standard Errors Expose Methodological Problems They Do Not Fix, and What to Do About It," Political Analysis, Cambridge University Press, vol. 23(2), pages 159-179, April.
    2. Hansen, Ben B. & Bowers, Jake, 2009. "Attributing Effects to a Cluster-Randomized Get-Out-the-Vote Campaign," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 873-885.
    3. Middleton, Joel A., 2008. "Bias of the regression estimator for experiments using clustered random assignment," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2654-2659, November.
    4. Luke W. Miratrix & Jasjeet S. Sekhon & Bin Yu, 2013. "Adjusting treatment effect estimates by post-stratification in randomized experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 369-396, March.
    5. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    6. Green, Donald P. & Vavreck, Lynn, 2008. "Analysis of Cluster-Randomized Experiments: A Comparison of Alternative Estimation Approaches," Political Analysis, Cambridge University Press, vol. 16(2), pages 138-152, April.
    7. Samii, Cyrus & Aronow, Peter M., 2012. "On equivalencies between design-based and regression-based variance estimators for randomized experiments," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 365-370.
    8. Donald B. Rubin, 2005. "Causal Inference Using Potential Outcomes: Design, Modeling, Decisions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 322-331, March.
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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. Joel A. Middleton, 2021. "Unifying Design-based Inference: On Bounding and Estimating the Variance of any Linear Estimator in any Experimental Design," Papers 2109.09220, arXiv.org.

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