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Extending the difference-in-differences (DID) to settings with many treated units and same intervention time: Model and Stata implementation

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  • Giovanni Cerulli

    (IRCrES-CNR, National Research Council of Italy)

Abstract

The difference-in-differences (DID) estimator is popular to estimate average treatment effects in causal inference studies. Under the common support assumption, DID overcomes the problem of unobservable selection using panel, time, and/or location fixed effects, and the knowledge of the pre/post intervention times. New developments of DID have been recently proposed: (i) the Synthetic Control Method (SCM) applies when a long pre- and post-intervention time series is available, only one unit is treated, and intervention occurs in a specific time (implemented in Stata via SYNTH by Hainmueller, Abadie, Dimond, 2014); (ii) an extension to binary time varying treatment with many treated units, have been also proposed and implemented in Stata via TVDIFF (Cerulli and Ventura, 2018). However, a command to accommodate a setting with many treated units and same intervention time is still lacking. In this presentation, I propose a potential outcome model to accommodate this latter setting, and provide a Stata implementation via the new Stata routine FTMTDIFF (standing for fixed-time multiple treated DID). I will finally set some guidelines for future DID developments.

Suggested Citation

  • Giovanni Cerulli, 2019. "Extending the difference-in-differences (DID) to settings with many treated units and same intervention time: Model and Stata implementation," 2019 Stata Conference 26, Stata Users Group.
    • Handle: RePEc:boc:scon19:26
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    References listed on IDEAS

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    1. David H. Autor, 2003. "Outsourcing at Will: The Contribution of Unjust Dismissal Doctrine to the Growth of Employment Outsourcing," Journal of Labor Economics, University of Chicago Press, vol. 21(1), pages 1-42, January.
    2. Abadie, Alberto & Diamond, Alexis & Hainmueller, Jens, 2010. "Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 493-505.
    3. Cerulli, Giovanni, 2019. "A flexible Synthetic Control Method for modeling policy evaluation," Economics Letters, Elsevier, vol. 182(C), pages 40-44.
    4. Giovanni Cerulli & Marco Ventura, 2019. "Estimation of pre- and posttreatment average treatment effects with binary time-varying treatment using Stata," Stata Journal, StataCorp LLC, vol. 19(3), pages 551-565, September.
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