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

I discuss the assumptions needed for identification of average treatment effects and local average treatment effects in instrumented difference-in-differences (IDID), and the possible trade-offs between assumptions of standard IV and those needed for the new proposal IDID, in one- and two-sample settings. I also discuss the interpretation of the estimands identified under monotonicity. I conclude by suggesting possible extensions to the estimation method, by outlining a strategy to use data-adaptive estimation of the nuisance parameters, based on recent developments.