Please join us for a UW Data Science Seminar featuring UW Statistics Ph.D. student Juejue Wang on Wednesday, April 8th from 4:30 to 5:20 p.m. PT. The seminar will be held in IEB G109.

“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 may be of independent interest. We show how the ATT bias is governed by the strength of confounding in the treatment-selection 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. We additionally consider DiD designs using linear regressions with two-way fixed effects and show how the OVB simplifies in such settings. 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. 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 two empirical examples.

Speaker Bio: Juejue Wang is a fourth-year Ph.D. student in Statistics at the University of Washington, advised by Professor Carlos Cinelli. Her research focuses on sensitivity analysis in causal inference, with applications to difference-in-differences designs and instrumental variables.