Is "no anticipation effect" a must in testing Difference-in-Difference?

[Phuc Nguyen]

I am wondering if we "must" test the "no anticipation effect" if the parallel trend assumption is satisfied? From my understanding, for testing the "no anticipation effect", we normally conduct a placebo effect by shifting the treatment year( for yearly data) to a couple of years before the event year. However, I am wondering if the parallel trend assumption is satisfied, is it a need to test the "no anticipation effect"?

[Maxence Morlet]

The parallel trends assumption ensures that without the treatment, the difference between treated and control groups would have remained identical throughout time. The no anticipation effects assumption is different, and you could argue the test you describe is quite convincing. For the no-anticipation assumption to be satisfied, there must not be bunching of observations or displacement effect right before policy implementation.

I reckon you should carry out the test and argue all DiD assumptions are satisfied. Especially that tests exist for the parallel trends assumption, but literature has not deemed them completely irrevocable.