Brantly Callaway, Andrew Goodman-Bacon, Pedro H. C. Sant'Anna
arXiv 6 Jul 2021 · Econometrics · 235 citations (OpenAlex)
arXiv:2107.02637 · PDF · DOI · OpenAlex · Extracted main text
This paper analyzes difference-in-differences designs with a continuous treatment. We show that treatment effect on the treated-type parameters can be identified under a generalized parallel trends assumption that is similar to the binary treatment setup. However, interpreting differences in these parameters across different values of the treatment can be particularly challenging due to selection bias that is not ruled out by the parallel trends assumption. We discuss alternative, typically stronger, assumptions that alleviate these challenges. We also provide a variety of treatment effect decomposition results, highlighting that parameters associated with popular linear two-way fixed-effects specifications can be hard to interpret, even when there are only two time periods. We introduce alternative estimation procedures that do not suffer from these drawbacks and show in an application that they can lead to different conclusions.
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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 | Acemoglu, Daron, Finkelstein, Amy (2008) Input and technology choices in regulated industries: Evidence from the health care sector | 1.000 | 9 | 4 | 100% |
| 2 | Chen, Xiaohong, Christensen, Timothy, Kankanala, Sid (2025) Adaptive estimation and uniform confidence bands for nonparametric structural functions and elasticities | 0.950 | 7 | 4 | 86% |
| 3 | D'Haultfoeuille, Xavier (2020) Two-way fixed effects estimators with heterogeneous treatment effects | 0.928 | 4 | 4 | 100% |
| 4 | Fricke, Hans (2017) Identification based on difference-in-differences approaches with multiple treatments | 0.811 | 4 | 2 | 100% |
| 5 | Callaway, Brantly, Sant'Anna, Pedro HC (2021) Difference-in-differences with multiple time periods self | 0.737 | 5 | 3 | 40% |
| 6 | Angrist, Joshua D, Imbens, Guido W (1995) Two-stage least squares estimation of average causal effects in models with variable treatment intensity | 0.737 | 3 | 2 | 100% |
| 7 | Ai, Chunrong, Chen, Xiaohong (2007) Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables | 0.644 | 2 | 2 | 100% |
| 8 | Angrist, Joshua D, Pischke, Jorn-Steffen (2008) Mostly Harmless Econometrics: An Empiricist's Companion | 0.644 | 2 | 2 | 100% |
| 9 | Blandhol, Christine, Bonney, John, Mogstad, Magne, Torgovitsky, Alex… (2025) When is TSLS actually LATE? | 0.644 | 2 | 2 | 100% |
| 10 | Goodman-Bacon, Andrew (2021) Difference-in-differences with variation in treatment timing self | 0.644 | 2 | 2 | 100% |
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