I have a question with the non traditional diff in diff with multiple periods. I currently have a balanced panel data with simple diff in diff in multiple periods treatment which could be written as:
$Y_{ist}=α+γs(\text{Treatments})+λ(\text{year dummy}_t)+δD_{st}+ϵ_{ist}$
The above equation allows me to measure the policy after treatment time ($D_{st}$) effect on $Y$.
Now, I would like to measure the effect of another variable (say $Z$) at the post-treatment period from treated group on $Y$ controlling the nature difference of the effect from $Z$ on $Y$ on other dimensions (treat and control, pre and post).
I wonder if this is a triple difference, or a diff-in-diff but with one more interaction of the variable $Z$ on everything.