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A simple distributional difference-in-differences estimator for univariate and bivariate outcomes

Author

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  • Iv'an Fern'andez-Val
  • Jonas Meier
  • Aico van Vuuren
  • Francis Vella

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 untreated outcome distribution does not exhibit an interaction effect of group 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 the Card and Krueger (1994) study of the impact of minimum wages on employment to illustrate the utility of our approach.

Suggested Citation

  • Iv'an Fern'andez-Val & Jonas Meier & Aico van Vuuren & Francis Vella, 2024. "A simple distributional difference-in-differences estimator for univariate and bivariate outcomes," Papers 2409.02311, arXiv.org, revised May 2026.
    • Handle: RePEc:arx:papers:2409.02311
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    References listed on IDEAS

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    1. Doruk Cengiz & Arindrajit Dube & Attila Lindner & Ben Zipperer, 2019. "The Effect of Minimum Wages on Low-Wage Jobs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 134(3), pages 1405-1454.
    2. Brantly Callaway & Tong Li, 2019. "Quantile treatment effects in difference in differences models with panel data," Quantitative Economics, Econometric Society, vol. 10(4), pages 1579-1618, November.
    3. 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.
    4. Card, David & Krueger, Alan B, 1994. "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania," American Economic Review, American Economic Association, vol. 84(4), pages 772-793, September.
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    Cited by:

    1. Dominik Wied, 2026. "A Synthetic Control Approach to Conditional Distributional Treatment Effects," Papers 2606.09625, arXiv.org.

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