I would like to test if the "gap" in a discrete variable,Y, changes between two groups from year to year.
In the setting of a Linear Probability Model I would estimate the following equation:
Array
And then test the 𝛿𝑗 coefficients. I want to replicate the same exercise but in a Probit/logit setting but I am unsure about how to proceed.
I cannot find the right code to get the marginal effects analogous to 𝛿𝑗 and I am not sure that this is even the right approach.
Summarizing, my goal is to quantify how the probit marginal effect of Treat, ß1, changes year by year and to test whether those differences are statistically significant.
Any ideas?

Note: My data is a repeated cross section. I do not have a panel data set.