Identification with sharp difference-in-discontinuities and discontinuity-in-differences

This note revisits identification for difference-in-discontinuities (DIDISC) and discontinuity-indifferences (DISCID) when treatment assignment is sharp. I show that both estimands equal the average treatment effect at the cutoff (ATC) under two assumptions. The first assumption is the continuous trends assumption. The second assumption is no anticipation at the cutoff.