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Synthetic difference-in-differences estimation with staggered treatment timing

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  • Porreca, Zachary

Abstract

This note formalizes the synthetic difference-in-differences estimator for staggered treatment adoption settings, as briefly described in Arkhangelsky et al. (2021). To illustrate the importance of this estimator, I use replication data from Abrams (2012). I compare the estimators obtained using SynthDiD, TWFE, the group time average treatment effect estimator of Callaway and Sant’Anna (2021), and the partially pooled synthetic control method estimator of Ben-Michael et al. (2021) in a staggered treatment adoption setting. I find that in this staggered treatment setting, SynthDiD provides a numerically different estimate of the average treatment effect. Simulation results show that these differences may be attributable to the underlying data generating process more closely mirroring that of the latent factor model assumed for SynthDiD than that of additive fixed effects assumed under traditional difference-in-differences frameworks.

Suggested Citation

  • Porreca, Zachary, 2022. "Synthetic difference-in-differences estimation with staggered treatment timing," Economics Letters, Elsevier, vol. 220(C).
    • Handle: RePEc:eee:ecolet:v:220:y:2022:i:c:s0165176522003482
    DOI: 10.1016/j.econlet.2022.110874
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    1. Dmitry Arkhangelsky & Susan Athey & David A. Hirshberg & Guido W. Imbens & Stefan Wager, 2021. "Synthetic Difference-in-Differences," American Economic Review, American Economic Association, vol. 111(12), pages 4088-4118, December.
    2. Eli Ben‐Michael & Avi Feller & Jesse Rothstein, 2022. "Synthetic controls with staggered adoption," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 351-381, April.
    3. Alberto Abadie & Javier Gardeazabal, 2003. "The Economic Costs of Conflict: A Case Study of the Basque Country," American Economic Review, American Economic Association, vol. 93(1), pages 113-132, March.
    4. Erickson, Timothy & Whited, Toni M., 2002. "Two-Step Gmm Estimation Of The Errors-In-Variables Model Using High-Order Moments," Econometric Theory, Cambridge University Press, vol. 18(3), pages 776-799, June.
    5. Guojun He & Shaoda Wang, 2017. "Do College Graduates Serving as Village Officials Help Rural China?," American Economic Journal: Applied Economics, American Economic Association, vol. 9(4), pages 186-215, October.
    6. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    7. Sun, Liyang & Abraham, Sarah, 2021. "Estimating dynamic treatment effects in event studies with heterogeneous treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 175-199.
    8. David S. Abrams, 2012. "Estimating the Deterrent Effect of Incarceration Using Sentencing Enhancements," American Economic Journal: Applied Economics, American Economic Association, vol. 4(4), pages 32-56, October.
    9. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    10. 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.
    11. Jonathan Roth, 2022. "Pretest with Caution: Event-Study Estimates after Testing for Parallel Trends," American Economic Review: Insights, American Economic Association, vol. 4(3), pages 305-322, September.
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    Cited by:

    1. Yoann Morin, 2024. "Synthetic Difference in Differences for Repeated Cross-Sectional Data," Papers 2409.20199, arXiv.org.
    2. Porreca, Zachary, 2023. "Gentrification, gun violence, and drug markets," Journal of Economic Behavior & Organization, Elsevier, vol. 207(C), pages 235-256.
    3. Moscelli, G.; & Sayli, M.; & Blanden, J.; & Mello, M.; & Castro-Pires, H.; & Bojke, C.;, 2023. "Non-monetary interventions, workforce retention and hospital quality: evidence from the English NHS," Health, Econometrics and Data Group (HEDG) Working Papers 23/13, HEDG, c/o Department of Economics, University of York.
    4. Carmen Villa, 2024. "The effects of youth clubs on education and crime," IFS Working Papers W24/51, Institute for Fiscal Studies.
    5. Li, Rui & Fang, Debin & Xu, Jiajun, 2024. "Does China's carbon inclusion policy promote household carbon emissions reduction? Theoretical mechanisms and empirical evidence," Energy Economics, Elsevier, vol. 132(C).
    6. Moscelli, Giuseppe & Sayli, Melisa & Blanden, Jo & Mello, Marco & Castro-Pires, Henrique & Bojke, Chris, 2023. "Non-monetary Interventions, Workforce Retention and Hospital Quality: Evidence from the English NHS," IZA Discussion Papers 16379, Institute of Labor Economics (IZA).

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