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Fuzzy Differences in Differences


  • Clément de Chaisemartin

    () (PSE, CREST)


Difference in differences (DID) require that the treatment rate is equal to 0% in the control group and during period 0 (no "always takers") and to 100% in the treatment group in period 1 (no "never takers"). Sometimes, treatment rate increases more in the treatment than in the control group but there are never or always takers. This paper derives identification results applying to such settings. They only require one common trend assumption on the outcome of interest (Y) whereas the standard instrumental variable result usually invoked also requires common trend on treatment rate. When there are never takers but no or few always takers, common trend on Y is sufficient to identify exactly an ATT or at least its sign.

Suggested Citation

  • Clément de Chaisemartin, 2011. "Fuzzy Differences in Differences," Working Papers 2011-10, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2011-10

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    References listed on IDEAS

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    Cited by:

    1. de Chaisemartin, Clement & D'Haultfoeuille, Xavier, 2015. "Fuzzy Differences-in-Differences," The Warwick Economics Research Paper Series (TWERPS) 1065, University of Warwick, Department of Economics.
    2. Bhalotra, Sonia R. & Karlsson, Martin & Nilsson, Therese & Schwarz, Nina, 2016. "Infant Health, Cognitive Performance and Earnings: Evidence from Inception of the Welfare State in Sweden," IZA Discussion Papers 10339, Institute for the Study of Labor (IZA).
    3. de Chaisemartin, Clement & D'Haultfoeuille, Xavier, 2015. "Supplement to Fuzzy Differences-in-Differences," The Warwick Economics Research Paper Series (TWERPS) 1066, University of Warwick, Department of Economics.

    More about this item


    Differences in differences; heterogeneous treatment effect; imperfect compliance; partial identification; smoking cessation;

    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
    • I19 - Health, Education, and Welfare - - Health - - - Other


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