arXiv 8 Jul 2026 · Econometrics
arXiv:2607.07524 · PDF · DOI · OpenAlex · Extracted main text
Researchers often conduct inference on weighted estimands, defined as weighted averages of group-level effects. Example settings include event studies with cohort-level effects and experiments with site-level effects. Under heterogeneous effects, different weighting schemes yield estimands with distinct empirical and policy interpretations, leading to ambiguity and disagreement over the choice of weights. I establish bounds on differences between weighted estimands and confidence bounds on effect heterogeneity, which I use to construct estimators that minimize worst-case bias and confidence intervals that are uniformly valid over classes of weighted estimands. I apply these methods to an event study in Lakdawala, Nakasone, and Kho (2023), which studies the effects of school-based internet access on test scores. I find that results are robust to broad classes of weights. I then apply the methods to Tennessee's Project STAR experiment and find that results are sensitive to small departures from baseline weights.
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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 | Sun, Liyang and Abraham, Sarah (2021) Estimating dynamic treatment effects in event studies with heterogeneous treatment effects | 1.000 | 15 | 5 | 100% |
| 2 | Callaway, Brantly and Sant’Anna, Pedro HC (2021) Difference-in-differences with multiple time periods | 1.000 | 11 | 4 | 100% |
| 3 | Goldsmith-Pinkham, Paul and Hull, Peter and Kolesár, Michal (2024) Contamination bias in linear regressions | 1.000 | 6 | 3 | 100% |
| 4 | Lakdawala, Leah K and Nakasone, Eduardo and Kho, Kevin (2023) Dynamic impacts of school-based internet access on student learning: Evidence from Peruvian public primary schools | 1.000 | 5 | 4 | 100% |
| 5 | Allcott, Hunt (2015) Site selection bias in program evaluation | 1.000 | 5 | 3 | 100% |
| 6 | Roth, Jonathan and Sant’Anna, Pedro HC and Bilinski, Alyssa and Poe,… (2023) What’s trending in difference-in-differences? A synthesis of the recent econometrics literature | 1.000 | 5 | 3 | 100% |
| 7 | Schanzenbach, Diane Whitmore (2006) What have researchers learned from Project STAR? | 0.874 | 6 | 2 | 100% |
| 8 | Wing, Coady and Freedman, Seth M and Hollingsworth, Alex (2024) Stacked difference-in-differences | 0.843 | 3 | 3 | 100% |
| 9 | De Chaisemartin, Clément and d’Haultfoeuille, Xavier (2020) Two-way fixed effects estimators with heterogeneous treatment effects | 0.811 | 4 | 2 | 100% |
| 10 | Goodman-Bacon, Andrew (2021) Difference-in-differences with variation in treatment timing | 0.811 | 4 | 2 | 100% |
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