Universal Difference-in-Differences

Difference-in-differences (DiD) is a popular method to evaluate causal effects of real-world policy interventions. To identify the average treatment effect on the treated, DiD relies on the parallel trends (PT) assumption, which states that the time trends for the average of treatment-free potential outcomes are parallel across the treated and control groups. A well-known limitation of the PT assumption is its lack of generalization to causal effects for discrete outcomes and to nonlinear effect measures. In this paper, we consider Universal Difference-in-Differences (UDiD) based on an alternative assumption to PT for identifying treatment effects for the treated on any scale of potential interest, and outcomes of an arbitrary nature. Specifically, we introduce the odds ratio equi-confounding (OREC) assumption, which states that the generalized odds ratios relating the treatment-free potential outcome and treatment are equivalent across time periods. Under the OREC assumption, we establish nonparametric identification for any potential treatment effect on the treated in view. Moreover, we develop a consistent, asymptotically linear, and semiparametric efficient estimator for any given treatment effect on the treated of interest which leverages recent learning theory. We illustrate UDiD with simulations and two real-world applications in labor economics and traffic safety evaluation.