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

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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 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," Carleton Economic Papers 16-11, Carleton University, Department of Economics.
  • Handle: RePEc:car:carecp:16-11
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    Cited by:

    1. Stefano Carattini & Suphi Sen, 2019. "Carbon Taxes and Stranded Assets: Evidence from Washington State," International Center for Public Policy Working Paper Series, at AYSPS, GSU paper1910, International Center for Public Policy, Andrew Young School of Policy Studies, Georgia State University.
    2. repec:tsj:stataj:y:17:y:2017:i:3:p:630-651 is not listed on IDEAS
    3. Heiko T. Burret & Lars P. Feld, 2018. "Vertical effects of fiscal rules: the Swiss experience," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 25(3), pages 673-721, June.
    4. Bruno Ferman & Cristine Pinto, 2019. "Inference in Differences-in-Differences with Few Treated Groups and Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 101(3), pages 452-467, July.
    5. 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.
    6. Ferman, Bruno, 2017. "Matching Estimators with Few Treated and Many Control Observations," MPRA Paper 78940, University Library of Munich, Germany.
    7. Ferman, Bruno, 2019. "Inference in Differences-in-Differences: How Much Should We Trust in Independent Clusters?," MPRA Paper 93746, University Library of Munich, Germany.
    8. 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.
    9. 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.
    10. James G. MacKinnon & Matthew D. Webb, 2017. "Pitfalls When Estimating Treatment Effects Using Clustered Data," Working Paper 1387, Economics Department, Queen's University.

    More about this item

    Keywords

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

    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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