IDEAS home Printed from
   My bibliography  Save this paper

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 a cluster-robust variance estimator (CRVE) severely over-reject, different variants of the wild cluster bootstrap can over-reject or under-reject dramatically, and procedures based on randomization inference show promise. We demonstrate that randomization inference (RI) procedures based on estimated coefficients, such as the one proposed by Conley and Taber (2011), fail whenever the treated clusters are atypical. We propose an RI procedure based on t statistics which fails only when the treated clusters are atypical and few in number. We also propose a bootstrap-based alternative to randomization inference, which mitigates the discrete nature of RI P values when the number of clusters is small. Two empirical examples demonstrate that alternative procedures can yield dramatically different inferences.

Suggested Citation

  • James G. MacKinnon & Matthew D. Webb, 2016. "Randomization Inference for Difference-in-Differences with Few Treated Clusters," Working Papers 1355, Queen's University, Department of Economics.
  • Handle: RePEc:qed:wpaper:1355

    Download full text from publisher

    File URL:
    File Function: First version 2016
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Hui Kai-Lung & Png Ivan, 2003. "Piracy and the Legitimate Demand for Recorded Music," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 2(1), pages 1-24, September.
    2. Mortimer, Julie Holland & Nosko, Chris & Sorensen, Alan, 2012. "Supply responses to digital distribution: Recorded music and live performances," Information Economics and Policy, Elsevier, vol. 24(1), pages 3-14.
    3. Ram D. Gopal & G. Lawrence Sanders, 2006. "Do Artists Benefit from Online Music Sharing?," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1503-1534, May.
    4. Connolly, Marie & Krueger, Alan B., 2006. "Rockonomics: The Economics of Popular Music," Handbook of the Economics of Art and Culture, Elsevier.
    5. Sylvain Dejean, 2009. "What Can We Learn from Empirical Studies About Piracy?," CESifo Economic Studies, CESifo, vol. 55(2), pages 326-352, June.
    6. Brett Danaher & Michael D. Smith & Rahul Telang & Siwen Chen, 2014. "The Effect of Graduated Response Anti-Piracy Laws on Music Sales: Evidence from an Event Study in France," Journal of Industrial Economics, Wiley Blackwell, vol. 62(3), pages 541-553, September.
    7. Seung‐Hyun Hong, 2013. "Measuring The Effect Of Napster On Recorded Music Sales: Difference‐In‐Differences Estimates Under Compositional Changes," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 297-324, March.
    8. Marie Connolly & Alan Krueger, 2005. "Rockonomics: The Economics of Popular Music," Working Papers 878, Princeton University, Department of Economics, Industrial Relations Section..
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    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.
    3. repec:tsj:stataj:y:17:y:2017:i:3:p:630-651 is not listed on IDEAS
    4. Timothy J. Bartik & Nathan Sotherland, 2015. "Migration and Housing Price Effects of Place-Based College Scholarships," Upjohn Working Papers and Journal Articles 15-245, W.E. Upjohn Institute for Employment Research.
    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

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:qed:wpaper:1355. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mark Babcock). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.