Difference-in-differences estimation under non-parallel trends

Abstract

Classic difference-in-differences estimation relies on the validity of the "parallel trends assumption" (PTA), which ensures that the evolution of the variable of interest in the control group can be used to determine its counterfactual development in the treatment group in the absence of treatment. The plausibility of the PTA is usually assessed by a test of the null hypothesis that the difference between the means of both groups is constant over time before the treatment. However, this procedure is problematic as failure to reject the null hypothesis does not imply the absence of differences in time trends between both groups due to low power to detect economically relevant differences. We provide three tests of equivalence leading to a "common range" (CR) condition that replaces the PTA and which naturally reflects differences between treatment and control. We combine the CR with standard confidence intervals to capture both design and sampling uncertainty in the data and show that the combined confidence intervals yield more reliable inference when the PTA is violated.