Omitted Variable Bias in Difference-in-Differences Designs
Abstract
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.
Related
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- Geodesic difference-in-differences
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BibTeX
@misc{wang2026omitted,
title = {{Omitted Variable Bias in Difference-in-Differences Designs}},
author = {Juejue Wang and Pedro H. C. Sant'Anna and Victor Chernozhukov and Carlos Cinelli},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19386},
eprint = {2609.19386},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19386},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Omitted Variable Bias in Difference-in-Differences Designs
AU - Juejue Wang
AU - Pedro H. C. Sant'Anna
AU - Victor Chernozhukov
AU - Carlos Cinelli
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.19386
UR - https://arxiv.org/abs/2609.19386
AB - 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.
ER -