Nicholas L. Brown, Qiushi Bu
arXiv 5 Oct 2026 · Statistics — Methodology
arXiv:2610.05705 · PDF · Extracted main text
We study difference-in-differences (DID) estimation of average treatment effects on the treated when the researcher is uncertain about which pre-treatment periods satisfy the parallel trends assumption. Roth (2022) shows that pre-trend testing can induce bias, complementing the statistical literature on post-selection inference. We propose the model averaged difference-in-differences (MADID) estimator, a weighted average of the candidate $2\times2$ DID estimators. The weights are normalized exponential functions of the candidate residual sums of squares, so implementation requires no specification test. We derive MADID's asymptotic properties under conditions that make invalid comparisons detectably more variable than at least one valid comparison. Under these conditions, MADID is consistent when the parallel trends assumption holds for at least one pre-treatment period. Although its joint limiting distribution across post-treatment periods is generally non-Gaussian, inference can be conducted by subsampling or simulation.
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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 | Schenk, Timo (2025) Time-Weighted Difference-in-Differences in Short Panels with Common Shocks | 1.000 | 5 | 4 | 100% |
| 2 | Wang, Miaomiao and Zhang, Xinyu and Wan, Alan TK and Zou, Guohua (2019) On the asymptotic distribution of model averaging based on information criterion | 1.000 | 5 | 4 | 100% |
| 3 | Dench, Daniel and Pineda-Torres, Mayra and Myers, Caitlin (2024) The effects of post-Dobbs abortion bans on fertility | 0.874 | 5 | 2 | 100% |
| 4 | Politis, Dimitris N and Romano, Joseph P (2010) K-sample subsampling in general spaces: The case of independent time series | 0.843 | 4 | 3 | 75% |
| 5 | Roth, Jonathan (2022) Pretest with caution: Event-study estimates after testing for parallel trends | 0.843 | 3 | 3 | 100% |
| 6 | Arkhangelsky, Dmitry and Athey, Susan and Hirshberg, David A and Imb… Synthetic difference-in-differences | 0.737 | 3 | 2 | 100% |
| 7 | Athey, Susan and Imbens, Guido and Qu, Zhaonan and Viviano, Davide (2026) Triply Robust Panel Estimators | 0.644 | 2 | 2 | 100% |
| 8 | Buckland, Steven T and Burnham, Kenneth P and Augustin, Nicole H (1997) Model selection: an integral part of inference | 0.644 | 2 | 2 | 100% |
| 9 | Callaway, Brantly and Sant'Anna, Pedro H.C (2021) Difference-in-Differences with Multiple Time Periods | 0.644 | 2 | 2 | 100% |
| 10 | Lu, Xun (2015) A covariate selection criterion for estimation of treatment effects | 0.644 | 2 | 2 | 100% |
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