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Partial identification of average treatment effects on the treated through difference-in-differences

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  • Yanqin Fan
  • Carlos A. Manzanares

Abstract

The difference-in-differences (DID) method is widely used as a tool for identifying causal effects of treatments in program evaluation. When panel data sets are available, it is well-known that the average treatment effect on the treated (ATT) is point-identified under the DID setup. If a panel data set is not available, repeated cross sections (pretreatment and posttreatment) may be used, but may not point-identify the ATT. This paper systematically studies the identification of the ATT under the DID setup when posttreatment treatment status is unknown for the pretreatment sample. This is done through a novel application of an extension of a continuous version of the classical monotone rearrangement inequality which allows for general copula bounds. The identifying power of an instrumental variable and of a ‘matched subsample’ is also explored. Finally, we illustrate our approach by estimating the effect of the Americans with Disabilities Act of 1991 on employment outcomes of the disabled.

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  • Yanqin Fan & Carlos A. Manzanares, 2017. "Partial identification of average treatment effects on the treated through difference-in-differences," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 1057-1080, October.
    • Handle: RePEc:taf:emetrv:v:36:y:2017:i:6-9:p:1057-1080
    DOI: 10.1080/07474938.2017.1308036
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    References listed on IDEAS

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    Cited by:

    1. Xiaoguang Zhou & Yadi Cui, 2019. "Green Bonds, Corporate Performance, and Corporate Social Responsibility," Sustainability, MDPI, vol. 11(23), pages 1-27, December.
    2. Yanqin Fan & Marc Henry, 2020. "Vector copulas," Papers 2009.06558, arXiv.org, revised Apr 2021.
    3. Augustine Denteh & D'esir'e K'edagni, 2022. "Misclassification in Difference-in-differences Models," Papers 2207.11890, arXiv.org, revised Jul 2022.
    4. Fan, Yanqin & Henry, Marc, 2023. "Vector copulas," Journal of Econometrics, Elsevier, vol. 234(1), pages 128-150.

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