A Nonparametric Framework for Universal Difference-in-Differences

Difference-in-differences (DiD) is a popular approach to evaluate treatment effects in settings where both pre- and post-treatment measurements of the outcome are available. Despite its popularity, existing methods face important limitations. Specifically, they either: (i) only apply to continuous outcomes and the average treatment effect on the treated; (ii) are sensitive to the transformation of the outcome; (iii) rely on a no unmeasured confounding assumption given pre-treatment covariates and outcome; (iv) lack semiparametric efficiency theory. In this paper, we introduce a novel framework for causal identification and inference in DiD settings that overcomes limitations (i)-(iv), making it the only existing framework that simultaneously satisfies these properties. Key to our framework is an odds ratio equi-confounding assumption, which states that the generalized odds ratio function relating treatment and treatment-free potential outcome is stable across time periods, a form of distributional parallel trends assumption. Under this assumption, we establish nonparametric identification of virtually any standard treatment effect on the treated, including quantile treatment effects on the treated. We also develop corresponding consistent, asymptotically linear, and semiparametric efficient estimators that leverage modern statistical learning theory. We illustrate our framework through simulation studies and two real-world applications using Zika virus outbreak data and traffic safety data.