Discussion on "Instrumented difference-in-differences" by Ting Ye, Ashkan Ertefaie, James Flory, Sean Hennessy & Dylan S. Small.

We reinterpret the instrumented difference-in-differences (iDID) under a linear instrumental variables (IV) model. Under the linear IV model, we show why iDID is a clear improvement over two existing methods, difference-in-differences (DID) and a cross-sectional, IV analysis. We also re-express some of the assumptions of iDID using familiar, regression-based identification assumptions. We conclude with a method inspired by the linear IV model that can potentially remedy the weak identification problem in iDID.