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Fuzzy Changes-in-Changes


  • Clément de Chaisemartin

    () (Warwick University)

  • Xavier d'Haultfoeuille

    () (CREST-LMI)


The changes-in-changes model extends the widely used difference-in-differences to situations where outcomes may evolve heterogeneously. Contrary to difference-in-differences, this model is invariant to the scaling of the outcome. This paper develops an instrumental variable changes-in-changes model, to allow for situations in which perfect control and treatment groups cannot be defined, so that some units may be treated in the "control group", while some units may remain untreated in the "treatment group". This is the case for instance with repeated cross sections, if the treatment is not tied to a strict rule. Under a mild strengthening of the changes-in-changes model, treatment effects in a population of compliers are point identified when the treatment rate does not change in the control group, and partially identified otherwise. We show that simple plug-in estimators of treatment effects are asymptotically normal and that the bootstrap is valid. Finally, we use our results to reanalyze findings in Field (2007) and Duflo (2001).

Suggested Citation

  • Clément de Chaisemartin & Xavier d'Haultfoeuille, 2014. "Fuzzy Changes-in-Changes," Working Papers 2014-18, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2014-18

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    Cited by:

    1. repec:oup:restud:v:85:y:2018:i:2:p:999-1028. is not listed on IDEAS
    2. C de Chaisemartin & X D’HaultfŒuille, 2018. "Fuzzy Differences-in-Differences," Review of Economic Studies, Oxford University Press, vol. 85(2), pages 999-1028.
    3. Daniel Herrera‐Araujo, 2016. "Folic acid advisories: a public health challenge?," Health Economics, John Wiley & Sons, Ltd., vol. 25(9), pages 1104-1122, September.

    More about this item


    differences-in-differences; changes-in-changes; imperfect compliance; instrumental variables; quantile treatment effects; partial identification;

    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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