Xiaohong Chen, Pedro H. C. Sant'Anna, Haitian Xie
arXiv 21 Jun 2025 · Econometrics
arXiv:2506.17729 · PDF · Extracted main text
This paper investigates efficient Difference-in-Differences (DiD) and Event Study (ES) estimation using short panel data sets within the heterogeneous treatment effect framework, free from parametric functional form assumptions and allowing for variation in treatment timing. We provide an equivalent characterization of the DiD potential outcome model using sequential conditional moment restrictions on observables, which shows that the DiD identification assumptions typically imply nonparametric overidentification restrictions. We derive the semiparametric efficient influence function (EIF) in closed form for DiD and ES causal parameters under commonly imposed parallel trends assumptions. The EIF is automatically Neyman orthogonal and yields the smallest variance among all asymptotically normal, regular estimators of the DiD and ES parameters. Leveraging the EIF, we propose simple-to-compute efficient estimators. Our results highlight how to optimally explore different pre-treatment periods and comparison groups to obtain the tightest (asymptotic) confidence intervals, offering practical tools for improving inference in modern DiD and ES applications even in small samples. Calibrated simulations and an empirical application demonstrate substantial precision gains of our efficient estimators in finite samples.
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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 | Arkhangelsky, Athey, Hirshberg, Imbens and Wager (2021) Synthetic Difference-in-Differences | 1.000 | 24 | 4 | 100% |
| 2 | Sun and Abraham (2021) Estimating dynamic treatment effects in event studies with heterogeneous treatment effects | 1.000 | 14 | 4 | 100% |
| 3 | Callaway and Sant’Anna (2021) Difference-in-Differences with multiple time periods | 1.000 | 13 | 7 | 100% |
| 4 | Baker, Larcker and Wang (2022) How much should we trust staggered difference-in-differences estimates? | 1.000 | 10 | 3 | 100% |
| 5 | Wooldridge (2021) Two-Way Fixed Effects, the Two-Way Mundlak Regression, and Difference-in-Differences Estimators | 1.000 | 9 | 5 | 100% |
| 6 | Gardner (2021) Two-stage differences in differences | 1.000 | 6 | 4 | 100% |
| 7 | de Chaisemartin and D'Haultfœuille (2020) Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects | 0.965 | 10 | 6 | 90% |
| 8 | Borusyak, Jaravel and Spiess (2024) Revisiting Event Study Designs: Robust and Efficient Estimation | 0.946 | 13 | 6 | 85% |
| 9 | Dobkin, Finkelstein, Kluender and Notowidigdo (2018) The economic consequences of hospital admissions | 0.874 | 8 | 2 | 100% |
| 10 | Chen and Santos (2018) Overidentification in Regular Models | 0.843 | 5 | 4 | 60% |
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