Synthetic Control Methods and Difference-In-Differences

There is a fast growing literature in econometrics on estimating causal effects in settings with panel or longitudinal data, building on the recent difference-in-differences and synthetic control literatures. This is driven by an empirical literature with many applications. These range from settings with few cross-sectional units and many or few time periods, to many cross-sectional units. Sometimes there are few, or even only one treated unit, and sometimes many. I will review some of this recent literature including some of the examples, focusing in particular on the synthetic difference in differences estimator, and some of the relations with matrix completion literature. I will also discuss implications for randomized experiments. I will discuss some of the remaining challenges in the literature.