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Distribution Regression Difference-in-Differences

Author

Listed:
  • Fernández-Val, Iván

    (Boston University)

  • Meier, Jonas

    (Swiss National Bank)

  • van Vuuren, Aico

    (University of Groningen)

  • Vella, Francis

    (Georgetown University)

Abstract

We provide a simple distribution regression estimator for treatment effects in the difference-in-differences (DiD) design. Our procedure is particularly useful when the treatment effect differs across the distribution of the outcome variable. Our proposed estimator easily incorporates covariates and, importantly, can be extended to settings where the treatment potentially affects the joint distribution of multiple outcomes. Our key identifying restriction is that the counterfactual distribution of the treated in the untreated state has no interaction effect between treatment and time. This assumption results in a parallel trend assumption on a transformation of the distribution. We highlight the relationship between our procedure and assumptions with the changes-in-changes approach of Athey and Imbens (2006). We also reexamine two existing empirical examples which highlight the utility of our approach.

Suggested Citation

  • Fernández-Val, Iván & Meier, Jonas & van Vuuren, Aico & Vella, Francis, 2024. "Distribution Regression Difference-in-Differences," IZA Discussion Papers 17264, IZA Network @ LISER.
    • Handle: RePEc:iza:izadps:dp17264
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    References listed on IDEAS

    as
    1. Goodman-Bacon, Andrew & Schmidt, Lucie, 2020. "Federalizing benefits: The introduction of Supplemental Security Income and the size of the safety net," Journal of Public Economics, Elsevier, vol. 185(C).
    2. Biewen, Martin & Fitzenberger, Bernd & Rümmele, Marian, 2022. "Using Distribution Regression Difference-in-Differences to Evaluate the Effects of a Minimum Wage Introduction on the Distribution of Hourly Wages and Hours Worked," IZA Discussion Papers 15534, IZA Network @ LISER.
    3. Arindrajit Dube, 2019. "Minimum Wages and the Distribution of Family Incomes," American Economic Journal: Applied Economics, American Economic Association, vol. 11(4), pages 268-304, October.
    4. Douglas Almond & Hilary W. Hoynes & Diane Whitmore Schanzenbach, 2011. "Inside the War on Poverty: The Impact of Food Stamps on Birth Outcomes," The Review of Economics and Statistics, MIT Press, vol. 93(2), pages 387-403, May.
    5. Andrew Goodman-Bacon, 2021. "The Long-Run Effects of Childhood Insurance Coverage: Medicaid Implementation, Adult Health, and Labor Market Outcomes," American Economic Review, American Economic Association, vol. 111(8), pages 2550-2593, August.
    6. Jonathan Roth & Pedro H. C. Sant'Anna, 2023. "When Is Parallel Trends Sensitive to Functional Form?," Econometrica, Econometric Society, vol. 91(2), pages 737-747, March.
    Full references (including those not matched with items on IDEAS)

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    Keywords

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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