Juejue Wang, Pedro H. C. Sant'Anna, Victor Chernozhukov, Carlos Cinelli
arXiv 16 Sep 2026 · Statistics — Methodology
arXiv:2609.19386 · PDF · Extracted main text
We study the omitted variable bias (OVB) problem in canonical difference-in-differences (DiD) designs when unobserved confounding induces departures from the parallel trends assumption. Our results provide a novel characterization of the OVB formula for the average treatment effect on the treated (ATT), which is of independent interest. We show how the ATT bias is mainly governed by the strength of confounding in the treatment assignment mechanism and provide alternative ways of quantifying this strength, such as (i) changes in the average odds of treatment among the treated, (ii) confounding imbalance between treated and control units, or (iii) variation explained in treatment odds among the untreated. Building on these results, we offer sensitivity statistics for routine reporting, describing the minimum strength of confounding required to overturn the conclusions of a DiD study, as well as formal bounds on the strength of confounders based on comparisons to observed covariates or pre-trends. Finally, we provide flexible and efficient statistical inference methods for the bounds on ATT, which can leverage modern machine learning algorithms for estimation. We demonstrate the utility of our approach in an empirical example that estimates the effects of minimum wage on teen employment.
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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 | Baker, A., Callaway, B., Cunningham, S., Goodman-Bacon, A., and Sant… (2025) Difference-in-differences designs: A practitioner's guide self | 0.928 | 4 | 3 | 100% |
| 2 | Cinelli, C. and Hazlett, C (2020) Making sense of sensitivity: Extending omitted variable bias self | 0.855 | 8 | 7 | 62% |
| 3 | Cinelli, C. and Hazlett, C (2025) An omitted variable bias framework for sensitivity analysis of instrumental variables self | 0.855 | 8 | 7 | 62% |
| 4 | Callaway, B. and Sant’Anna, P. H (2021) Difference-in-differences with multiple time periods | 0.855 | 8 | 5 | 62% |
| 5 | Rambachan, A. and Roth, J (2023) A more credible approach to parallel trends | 0.855 | 8 | 4 | 62% |
| 6 | Chernozhukov, V., Cinelli, C., Newey, W., Sharma, A., and Syrgkanis, V (2026) Long story short: Omitted variable bias in causal machine learning self | 0.843 | 20 | 7 | 60% |
| 7 | Huang, M. and Pimentel, S. D (2025) Variance-based sensitivity analysis for weighting estimators results in more informative bounds | 0.814 | 13 | 3 | 54% |
| 8 | Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C… (2018) Double/debiased machine learning for treatment and structural parameters self | 0.794 | 8 | 3 | 50% |
| 9 | Imbens, G. W (2003) Sensitivity to exogeneity assumptions in program evaluation | 0.644 | 2 | 2 | 100% |
| 10 | Imbens, G. W. and Rubin, D. B (2015) Causal inference in statistics, social, and biomedical sciences | 0.644 | 2 | 2 | 100% |
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