Testing parallel trends for continuous treatment

[Myat Thida Win]

Hello, I am trying to understand how I could show the parallel trends for continuous treatment. I have a standard DiD with treatment intensity instead of a binary treatment. As treatment intensity is zero in the pre-period, I was not clear how to show the parallel trend. Really appreciate your help in advance.

[Stephen Jenkins]

May I suggest some reading of relevant literature and then posting a more refined question? A quick web search yields relevant material such as https://bcallaway11.github.io/posts/...uous-treatment

[Carlo Lazzaro]

Myat:
see also the recent https://www.aeaweb.org/articles?id=10.1257/jel.20251650