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Randomization Inference for Difference-in-Differences with Few Treated Clusters


  • James G. MacKinnon

    () (Queen's University)

  • Matthew D. Webb

    () (Carleton University)


Inference using difference-in-differences with clustered data requires care. Previous research has shown that, when there are few treated clusters, t tests based on cluster-robust variance estimators (CRVEs) severely over-reject, different variants of the wild cluster bootstrap can either over-reject or under-reject dramatically, and procedures based on randomization inference show promise. We study two randomization inference (RI) procedures. A procedure based on estimated coefficients, which is essentially the one proposed by Conley and Taber (2011), has excellent power but may not perform well when the treated clusters are atypical. We therefore propose a new RI procedure based on t statistics. It typically performs better under the null, except when there is just one treated cluster, but at the cost of some power loss. Two empirical examples demonstrate that alternative procedures can yield dramatically different inferences.

Suggested Citation

  • James G. MacKinnon & Matthew D. Webb, 2018. "Randomization Inference for Difference-in-Differences with Few Treated Clusters," Working Papers 1355, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:1355

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    Cited by:

    1. Ferman, Bruno & Pinto, Cristine, 2015. "Inference in Differences-in-Differences with Few Treated Groups and Heteroskedasticity," MPRA Paper 67665, University Library of Munich, Germany.
    2. James G. MacKinnon & Matthew D. Webb, 2017. "Pitfalls when Estimating Treatment Effects Using Clustered Data," Working Papers 1387, Queen's University, Department of Economics.
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    5. Christopher S. Carpenter & Emily C. Lawler, 2017. "Direct and Spillover Effects of Middle School Vaccination Requirements," NBER Working Papers 23107, National Bureau of Economic Research, Inc.
    6. Masayoshi Hayashi, 2017. "Do Central Grants Affect Welfare Caseloads? Evidence from Public Assistance in Japan," CIRJE F-Series CIRJE-F-1064, CIRJE, Faculty of Economics, University of Tokyo.

    More about this item


    CRVE; grouped data; clustered data; panel data; randomization inference; difference-in-differences; wild cluster bootstrap;

    JEL classification:

    • 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

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