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Design-Based Uncertainty for Quasi-Experiments

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  • Ashesh Rambachan
  • Jonathan Roth

Abstract

Design-based frameworks of uncertainty are frequently used in settings where the treatment is (conditionally) randomly assigned. This paper develops a design-based framework suitable for analyzing quasi-experimental settings in the social sciences, in which the treatment is at least partially determined by idiosyncratic factors but there are concerns about endogenous selection into treatment. In our framework, treatments are stochastic, but units may differ in their probabilities of receiving treatment, thereby allowing for rich forms of selection. We provide conditions under which the estimands of popular quasi-experimental estimators correspond to interpretable finite-population causal parameters. We characterize the biases and distortions to inference that arise when these conditions are violated. These results can be used to conduct sensitivity analyses when there are concerns about selection into treatment. Taken together, our results establish a rigorous foundation for quasi-experimental analyses that more closely aligns with the way empirical researchers discuss the variation in the data.

Suggested Citation

  • Ashesh Rambachan & Jonathan Roth, 2020. "Design-Based Uncertainty for Quasi-Experiments," Papers 2008.00602, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2008.00602
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    References listed on IDEAS

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    Cited by:

    1. Ruonan Xu, 2023. "Difference-in-Differences with Interference," Papers 2306.12003, arXiv.org, revised May 2024.
    2. Jonathan Roth & Pedro H. C. Sant’Anna, 2023. "Efficient Estimation for Staggered Rollout Designs," Journal of Political Economy Microeconomics, University of Chicago Press, vol. 1(4), pages 669-709.
    3. Lea Bottmer & Guido Imbens & Jann Spiess & Merrill Warnick, 2021. "A Design-Based Perspective on Synthetic Control Methods," Papers 2101.09398, arXiv.org, revised Jul 2023.
    4. Ruonan Xu & Jeffrey M. Wooldridge, 2022. "A Design-Based Approach to Spatial Correlation," Papers 2211.14354, arXiv.org.
    5. Lin Winston & Dudoit Sandrine & Nolan Deborah & Speed Terence P., 2024. "From urn models to box models: Making Neyman's (1923) insights accessible," Journal of Causal Inference, De Gruyter, vol. 12(1), pages 1-12.
    6. Roth, Jonathan & Sant’Anna, Pedro H.C. & Bilinski, Alyssa & Poe, John, 2023. "What’s trending in difference-in-differences? A synthesis of the recent econometrics literature," Journal of Econometrics, Elsevier, vol. 235(2), pages 2218-2244.

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