This question is not strictly related to Stata, I will remove if it is inappropriate.

In a diff-in-diff framework, I have discovered that a control variable (say variable x) differently affects the outcome variable, depending on the treatment status. Variable x is time-varying but constant across treated and controls. Therefore, if I insert x as a regressor I will not capture the different impact fro treated and untreated, of x on y.

One way I have in mind is: generating interaction terms between x and dummy variables for treatment/control and include them in the regression as regressors in place of x.
I mean:x_treat=x* DummyTreatment and x_control=x*(1-DummyTreatment)

Probably the fact that a control variable differently affects the outcome variables can be problematic for the parallel trend assumption. However, I am wondering whether we can solve this problem with this approach.

Thank you!

Cross-posted here: https://www.econjobrumors.com/topic/...1#post-5011971