arXiv 6 Feb 2023 · Econometrics
arXiv:2302.03131 · PDF · DOI · OpenAlex · Extracted main text
In settings with few treated units, Difference-in-Differences (DID) estimators are not consistent, and are not generally asymptotically normal. This poses relevant challenges for inference. While there are inference methods that are valid in these settings, some of these alternatives are not readily available when there is variation in treatment timing and heterogeneous treatment effects; or for deriving uniform confidence bands for event-study plots. We present alternatives in settings with few treated units that are valid with variation in treatment timing and/or that allow for uniform confidence bands.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Conley, T. G. and Taber, C. R (2011) Inference with Difference in Differences with a Small Number of Policy Changes | 1.000 | 14 | 4 | 100% |
| 2 | Ferman, B. and Pinto, C (2019) Inference in differences-in-differences with few treated groups and heteroskedasticity self | 1.000 | 10 | 3 | 100% |
| 3 | Callaway, B. and Sant'Anna, P. H (2021) Difference-in-differences with multiple time periods | 1.000 | 5 | 3 | 100% |
| 4 | Goodman-Bacon, A (2021) Difference-in-differences with variation in treatment timing | 0.644 | 2 | 2 | 100% |
| 5 | de Chaisemartin, C. and D'Haultfoeuille, X (2020) Two-way fixed effects estimators with heterogeneous treatment effects | 0.644 | 2 | 2 | 100% |
| 6 | Freyaldenhoven, S., Hansen, C., Pérez, J. P., and Shapiro, J. M (2021) Visualization, identification, and estimation in the linear panel event-study design | 0.644 | 2 | 2 | 100% |
| 7 | Montiel Olea, J. L. and Plagborg-Moller, M (2019) Simultaneous confidence bands: Theory, implementation, and an application to svars | 0.644 | 2 | 2 | 100% |
| 8 | Sun, L. and Abraham, S (2020) Estimating dynamic treatment effects in event studies with heterogeneous treatment effects | 0.644 | 2 | 2 | 100% |
| 9 | Borusyak, K., Jaravel, X., and Spiess, J (2021) Revisiting event study designs: Robust and efficient estimation | 0.585 | 3 | 1 | 100% |
| 10 | Ben-Michael, E., Feller, A., and Rothstein, J (2021) The augmented synthetic control method | 0.405 | 1 | 1 | 100% |
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