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Placebo inference on treatment effects when the number of clusters is small

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  • Hagemann, Andreas

Abstract

I introduce a general, Fisher-style randomization testing framework to conduct nearly exact inference about the lack of effect of a binary treatment in the presence of very few, large clusters when the treatment effect is identified across clusters. The proposed randomization test formalizes and extends the intuitive notion of generating null distributions by assigning placebo treatments to untreated clusters. I show that under simple and easily verifiable conditions, the placebo test leads to asymptotically valid inference in a very large class of empirically relevant models. Examples discussed explicitly are (i) least squares regression with cluster-level treatment, (ii) difference-in-differences estimation, and (iii) binary choice models with cluster-level treatment. A simulation study and an empirical example are provided. The proposed inference procedure is easy to implement and performs well with as few as three treated and three untreated clusters.

Suggested Citation

  • Hagemann, Andreas, 2019. "Placebo inference on treatment effects when the number of clusters is small," Journal of Econometrics, Elsevier, vol. 213(1), pages 190-209.
  • Handle: RePEc:eee:econom:v:213:y:2019:i:1:p:190-209
    DOI: 10.1016/j.jeconom.2019.04.011
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    Cited by:

    1. 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.
    2. Kevin Lang & Kaiwen Leong & Huailu Li & Haibo Xu, 2019. "Lending to the Unbanked: Relational Contracting with Loan Sharks," NBER Working Papers 26400, National Bureau of Economic Research, Inc.
    3. Kevin Lang, 2020. "Effort and wages: Evidence from the payroll tax," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(1), pages 108-139, February.
    4. James G. MacKinnon & Matthew D. Webb, 2020. "When and How to Deal with Clustered Errors in Regression Models," Working Paper 1421, Economics Department, Queen's University.
    5. Andreas Hagemann, 2019. "Permutation inference with a finite number of heterogeneous clusters," Papers 1907.01049, arXiv.org.

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    More about this item

    Keywords

    Cluster-robust inference; Randomization; Permutation;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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