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Two-way Fixed Effects Estimators with Heterogeneous Treatment Effects


  • Clément de Chaisemartin
  • Xavier D'Haultfoeuille


Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they identify weighted sums of the average treatment effects (ATE) in each group and period, with weights that may be negative. Due to the negative weights, the linear regression estimand may for instance be negative while all the ATEs are positive. In two articles that have used those regressions, half of the weights are negative. We propose another estimator that solves this issue. In one of the articles we revisit, it is of a different sign than the linear regression estimator.

Suggested Citation

  • Clément de Chaisemartin & Xavier D'Haultfoeuille, 2019. "Two-way Fixed Effects Estimators with Heterogeneous Treatment Effects," NBER Working Papers 25904, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:25904

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    References listed on IDEAS

    1. Timothy G. Conley & Christopher R. Taber, 2011. "Inference with "Difference in Differences" with a Small Number of Policy Changes," The Review of Economics and Statistics, MIT Press, vol. 93(1), pages 113-125, February.
    2. Andrew Goodman-Bacon, 2018. "Difference-in-Differences with Variation in Treatment Timing," NBER Working Papers 25018, National Bureau of Economic Research, Inc.
    3. Sarah Abraham & Liyang Sun, 2018. "Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects," Papers 1804.05785,
    4. Brantly Callaway & Pedro H. C. Sant'Anna, 2018. "Difference-in-Differences with Multiple Time Periods and an Application on the Minimum Wage and Employment," Papers 1803.09015,, revised Aug 2018.
    5. Athey, Susan & Imbens, Guido W., 2018. "Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption," Research Papers 3712, Stanford University, Graduate School of Business.
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    1. Maurer, Stephan E., 2019. "Oil discoveries and education provision in the Postbellum South," Economics of Education Review, Elsevier, vol. 73(C).
    2. Giorgetti, Isabella & Picchio, Matteo, 2018. "One Billion Euro Program for Early Childcare Services in Italy," IZA Discussion Papers 11689, Institute of Labor Economics (IZA).
    3. Thomas Dee & Emily Penner, 2019. "My Brother’s Keeper? The Impact of Targeted Educational Supports," NBER Working Papers 26386, National Bureau of Economic Research, Inc.
    4. Anja Rösner & Justus Haucap & Ulrich Heimeshoff, 2020. "The Impact of Consumer Protection in the Digital Age: Evidence from the European Union," CESifo Working Paper Series 8081, CESifo Group Munich.
    5. Batut, Cyprien & Maurin, Eric, 2019. "From Ultima Ratio to Mutual Consent: The Effects of Changing Employment Protection Doctrine," IZA Discussion Papers 12440, Institute of Labor Economics (IZA).
    6. Gautam Gowrisankaran & Keith A. Joiner & Jianjing Lin, 2019. "How do Hospitals Respond to Payment Incentives?," NBER Working Papers 26455, National Bureau of Economic Research, Inc.
    7. Macchiavello, Rocco & Miquel-Florensa, Josepa, 2019. "Buyer-Driven Upgrading in GVCs: The Sustainable Quality Program in Colombia," CEPR Discussion Papers 13935, C.E.P.R. Discussion Papers.
    8. Isaiah Andrews & Matthew Gentzkow & Jesse M. Shapiro, 2020. "Transparency in Structural Research," NBER Working Papers 26631, National Bureau of Economic Research, Inc.

    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models


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