Marcelo Ortiz-Villavicencio, Pedro H. C. Sant'Anna
arXiv 15 May 2025 · Econometrics
arXiv:2505.09942 · PDF · DOI · OpenAlex · Extracted main text
Triple Differences (DDD) designs are widely used in empirical work to relax parallel trends assumptions in Difference-in-Differences (DiD) settings. This paper highlights that common DDD implementations -- such as taking the difference between two DiDs or applying three-way fixed effects regressions -- are generally invalid when identification requires conditioning on covariates. In staggered adoption settings, the common DiD practice of pooling all not-yet-treated units as a comparison group can introduce additional bias, even when covariates are not required for identification. These insights challenge conventional empirical strategies and underscore the need for estimators tailored specifically to DDD structures. We develop regression adjustment, inverse probability weighting, and doubly robust estimators that remain valid under covariate-adjusted DDD parallel trends. For staggered designs, we demonstrate how to effectively utilize multiple comparison groups to obtain more informative inferences. Simulations and three empirical applications highlight bias reductions and precision gains relative to standard approaches. A companion R package is available.
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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 | Olden and Men (2022) The triple difference estimator | 1.000 | 8 | 4 | 100% |
| 2 | Strezhnev (2023) Decomposing Triple-Differences Regression under Staggered Adoption | 1.000 | 5 | 3 | 100% |
| 3 | Callaway and Sant’Anna (2021) Difference-in-differences with multiple time periods | 0.985 | 22 | 7 | 95% |
| 4 | Sant'Anna and Zhao (2020) Doubly Robust Difference-in-Differences Estimators | 0.909 | 12 | 5 | 75% |
| 5 | Hansen and Wingender (2023) National and Global Impacts of Genetically Modified Crops | 0.874 | 17 | 2 | 100% |
| 6 | Cui, Zhang and Zheng (2018) Carbon Pricing Induces Innovation: Evidence from China's Regional Carbon Market Pilots | 0.874 | 15 | 2 | 100% |
| 7 | Cai (2016) The Impact of Insurance Provision on Household Production and Financial Decisions | 0.874 | 14 | 2 | 100% |
| 8 | Abadie (2005) Semiparametric Difference-in-Difference Estimators | 0.737 | 3 | 2 | 100% |
| 9 | Baker, Callaway, Cunningham, Goodman-Bacon and Sant'Anna (2025) Difference-in-Differences Designs: A Practitioner's Guide self | 0.737 | 3 | 2 | 100% |
| 10 | Borusyak, Jaravel and Spiess (2024) Revisiting Event-Study Designs: Robust and Efficient Estimation | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 50 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Three’s a crowd: Identification challenges in the triple difference model with spillover effects | 0.956 | 16 | 6 |
| 2 | Stacked Triple Differences | 0.928 | 5 | 4 |
| 3 | Triple Difference Designs with Heterogeneous Treatment Effects | 0.644 | 4 | 1 |
| 4 | Difference-in-Differences Designs: A Practitioner's Guide | 0.585 | 3 | 1 |
| 5 | 2606.24785 | 0.511 | 2 | 1 |
| 6 | 2606.17977 | 0.405 | 1 | 1 |