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Interpreting the coefficients in dynamic two-way fixed effects regressions with time-varying covariates

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  • Lin, Lihua
  • Zhang, Zhengyu

Abstract

This paper discusses the causal interpretation of event study coefficients in a dynamic two-way fixed effects regression with time-varying covariates under a conditional parallel trends assumption. In addition to the “cross-lag contamination” problem noted by Sun and Abraham (2021), we find a new source of bias induced by the time-varying effect of the covariates. This covariate effect bias will not be eliminated even under treatment effect homogeneity and will remain in the canonical two-period difference-in-differences setting unless one makes more restrictive assumptions on the effects of covariates.

Suggested Citation

  • Lin, Lihua & Zhang, Zhengyu, 2022. "Interpreting the coefficients in dynamic two-way fixed effects regressions with time-varying covariates," Economics Letters, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:ecolet:v:216:y:2022:i:c:s0165176522001823
    DOI: 10.1016/j.econlet.2022.110604
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    References listed on IDEAS

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    1. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    2. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    3. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    4. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 1-19.
    5. 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.
    6. Athey, Susan & Imbens, Guido W., 2022. "Design-based analysis in Difference-In-Differences settings with staggered adoption," Journal of Econometrics, Elsevier, vol. 226(1), pages 62-79.
    7. 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.
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    Keywords

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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