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Randomization inference for difference-in-differences with few treated clusters

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  • MacKinnon, James G.
  • Webb, Matthew D.

Abstract

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 overreject, and different variants of the wild cluster bootstrap can either overreject or underreject dramatically. We study two randomization inference (RI) procedures. A procedure based on estimated coefficients may be unreliable when clusters are heterogeneous. A procedure based on t-statistics typically performs better (although by no means perfectly) under the null, but at the cost of some power loss. An empirical example demonstrates that RI procedures can yield inferences that differ dramatically from those of other methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:218:y:2020:i:2:p:435-450
    DOI: 10.1016/j.jeconom.2020.04.024
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    More about this item

    Keywords

    Cluster-robust inference; CRVE; Grouped data; Clustered data; Wild cluster bootstrap; Randomization inference; Difference-in-differences; DiD;
    All these keywords.

    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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