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Fuzzy Changes-in Changes

Author

Listed:
  • de Chaisemartin, Clement

    (University of Warwick)

  • D'Haultfoeuille, Xavier

    (CREST)

Abstract

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. Simple plug-in estimators of treatment effects are proposed. We show that they are asymptotically normal, and that the bootstrap is valid. Finally, we use our results to reanalyze findings in Field (2007) and Duo (2001).

Suggested Citation

  • de Chaisemartin, Clement & D'Haultfoeuille, Xavier, 2014. "Fuzzy Changes-in Changes," CAGE Online Working Paper Series 184, Competitive Advantage in the Global Economy (CAGE).
    • Handle: RePEc:cge:wacage:184
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    File URL: https://www2.warwick.ac.uk/fac/soc/economics/research/centres/cage/manage/publications/184-2014clement.pdf
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    References listed on IDEAS

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    1. Anders Akerman & Ingvil Gaarder & Magne Mogstad, 2015. "The Skill Complementarity of Broadband Internet," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 130(4), pages 1781-1824.
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    9. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
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    Citations

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    Cited by:

    1. C de Chaisemartin & X D’HaultfŒuille, 2018. "Fuzzy Differences-in-Differences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(2), pages 999-1028.
    2. de Chaisemartin, Clement & D'Haultfoeuille, Xavier, 2014. "Fuzzy Changes-in Changes," CAGE Online Working Paper Series 184, Competitive Advantage in the Global Economy (CAGE).
    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.

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    More about this item

    Keywords

    differences in differences; changes in changes; imperfect compliance; instrumental variables; quantile treatment effects; partial identication.;
    All these keywords.

    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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