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Fuzzy differences in differences

Author

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  • Clément De Chaisemartin

    (PSE - Paris School of Economics, PSE - Paris-Jourdan Sciences Economiques - ENS Paris - École normale supérieure - Paris - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique)

Abstract

Difference in differences require that 0% of observations are treated in the control group and during period 0 (no "always takers") and 100% in the treatment group in period 1 (no "never takers"). Sometimes, the treatment rate increases more in the treatment than in the control group but there are never or always takers. This paper develops results to identify treatment effects in such settings. They only require one common trend assumption on the outcome of interest Y whereas the standard instrumental variable result also requires common trend on treatment D. I derive bounds for treatment effects which are tight when there are no or few always takers. This can be the case in applications considering the effect of an innovation, where by definition no observations are treated in period 0. I derive other bounds that are tight when the treatment rate does not change much between the two periods in the control group, which can be the case in applications considering the extension of a program to a group previously not eligible. I use my results to measure the efficacy of a new drug for smoking cessation.

Suggested Citation

  • Clément De Chaisemartin, 2012. "Fuzzy differences in differences," PSE Working Papers halshs-00671368, HAL.
  • Handle: RePEc:hal:psewpa:halshs-00671368
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00671368
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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

    Keywords

    Difference 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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