On Synthetic Difference-in-Differences and Related Estimation Methods in Stata

In this article, we describe a computational implementation of the synthetic difference-in-differences (SDID) estimator of Arkhangelsky et al. (2021, American Economic Review 111: 4088-4118) for Stata. SDID can be used in many circumstances where treatment effects on some particular policy or event are desired and repeated observations on treated and untreated units are available over time. We lay out the theory underlying SDID both when there is a single treatment adoption date and when adoption is staggered over time, and we discuss estimation and inference in each of these cases. We introduce the sdid command, which implements these methods in Stata, and provide several examples of use, discussing estimation, inference, and visualization of results. Along with SDID, the sdid command allows for the implementation of standard synthetic control and difference-in-differences methods in an identical framework, permitting estimation, inference, and the generation of graphical output in a computationally efficient way.