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Group-Heterogeneous Changes-in-Changes and Distributional Synthetic Controls

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  • Songnian Chen
  • Junlong Feng

Abstract

We develop new methods for changes-in-changes and distributional synthetic controls when there exists group level heterogeneity. For changes-in-changes, we allow individuals to belong to a large number of heterogeneous groups. The new method extends the changes-in-changes method in Athey and Imbens (2006) by finding appropriate subgroups within the control groups which share similar group level unobserved characteristics to the treatment groups. For distributional synthetic control, we show that the appropriate synthetic control needs to be constructed using units in potentially different time periods in which they have comparable group level heterogeneity to the treatment group, instead of units that are only in the same time period as in Gunsilius (2023). Implementation and data requirements for these new methods are briefly discussed.

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  • Songnian Chen & Junlong Feng, 2023. "Group-Heterogeneous Changes-in-Changes and Distributional Synthetic Controls," Papers 2307.15313, arXiv.org.
    • Handle: RePEc:arx:papers:2307.15313
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    References listed on IDEAS

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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. 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.
    3. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    4. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    5. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    6. 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.
    7. F. F. Gunsilius, 2023. "Distributional Synthetic Controls," Econometrica, Econometric Society, vol. 91(3), pages 1105-1117, May.
    8. Alberto Abadie & Alexis Diamond & Jens Hainmueller, 2015. "Comparative Politics and the Synthetic Control Method," American Journal of Political Science, John Wiley & Sons, vol. 59(2), pages 495-510, February.
    9. Alberto Abadie, 2021. "Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects," Journal of Economic Literature, American Economic Association, vol. 59(2), pages 391-425, June.
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