Eliminating Systematic Bias from Difference-in-Differences Design: A Permutational Detrending Strategy

Abstract: Since the initial work by Ashenfelter and Card in 1985, the use of difference-in-differences (DID) study design has become widespread. However, as pointed out in the literature, this popular quasi-experimental design also suffers estimation bias and inference bias, which could be very serious in some circumstances. In this study, we start by investigating potential sources of systemic bias from the DID design. Via analyzing their impact on statistical estimation and inference, we propose a remedy -- a permutational detrending (PD) strategy -- to overcome the challenges in both the estimation bias and the inference bias. We prove that the proposed PD DID method provides unbiased point estimates, confidence interval estimates, and significance tests. We illustrate its statistical proprieties using simulation experiments. We demonstrate its practical utility by applying it to the clinical data EASE (Elder-Friendly Approaches to the Surgical Environment) and the social-economical data CPS (Current Population Survey). We discuss the strengths and limitations of the proposed approach.