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Fuzzy Differences-in-Differences

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  • C de Chaisemartin
  • X D’HaultfŒuille

Abstract

Difference-in-differences (DID) is a method to evaluate the effect of a treatment. In its basic version, a “control group” is untreated at two dates, whereas a “treatment group” becomes fully treated at the second date. However, in many applications of the DID method, the treatment rate only increases more in the treatment group. In such fuzzy designs, a popular estimator of the treatment effect is the DID of the outcome divided by the DID of the treatment. We show that this ratio identifies a local average treatment effect only if the effect of the treatment is stable over time, and if the effect of the treatment is the same in the treatment and in the control group. We then propose two alternative estimands that do not rely on any assumption on treatment effects, and that can be used when the treatment rate does not change over time in the control group. We prove that the corresponding estimators are asymptotically normal. Finally, we use our results to reassess the returns to schooling in Indonesia.

Suggested Citation

  • C de Chaisemartin & X D’HaultfŒuille, 2018. "Fuzzy Differences-in-Differences," Review of Economic Studies, Oxford University Press, vol. 85(2), pages 999-1028.
  • Handle: RePEc:oup:restud:v:85:y:2018:i:2:p:999-1028.
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    File URL: http://hdl.handle.net/10.1093/restud/rdx049
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    Cited by:

    1. Esther Delesalle, 2019. "The Effect of the Universal Primary Education Program on Labor Market Outcomes: Evidence from Tanzania," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2019010, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    2. Dany Bahar & Andreas Hauptmann & Cem Özgüzel & Hillel Rapoport, 2018. "Let their Knowledge Flow: The Effect of Returning Refugees on Export Performance in the Former Yugoslavia," CESifo Working Paper Series 7371, CESifo Group Munich.
    3. Cook, Jason B., 2018. "Race-Blind Admissions, School Segregation, and Student Outcomes: Evidence from Race-Blind Magnet School Lotteries," IZA Discussion Papers 11909, Institute of Labor Economics (IZA).
    4. Bahar, Dany & Özgüzel, Cem & Hauptmann, Andreas & Rapoport, Hillel, 2019. "Migration and Post-Conflict Reconstruction: The Effect of Returning Refugees on Export Performance in the Former Yugoslavia," IZA Discussion Papers 12412, Institute of Labor Economics (IZA).

    More about this item

    Keywords

    Differences-in-differences; Control group; Local average treatment effects; Changes-in-changes; Partial identification; Returns to education;

    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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