Probit Interaction Marginal Effects

[Bruno Jimenez]

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:

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.

[FernandoRios]

Hi Bruno,
Unfortunately, you cannot estimate the effect of "delta_i" only, because of the nonlinear nature of probit or logit models.
There are couple of options, however that you can use:

margins year, dydx(treat)
margins r.year##r.treat, dydx(treat)
margins , dydx(treat) over(year)

They will give you the marginal change in the probability success if treated across years.
HTH

[Bruno Jimenez]

Thanks, I'll try everything and see which one gives me the results that I want.
UPDATE:
After testing all of these

 
 margins r.year##r.treat, dydx(treat)

Seems to be what I am looking for, however I am not entirely sure of what Stata is doing. Could you tell me what does the r. prefix does please?

[FernandoRios]

As far as I know, this is what the command (as i suggested) works.
If you estimate a probit model with interaction like this:

P(Y|D,T) =F( a0 +a1*D +a2*T+a3*D*T)

where F is our Cumulative normal function.
If you use the syntax:

margins r.D##r.T

Stata estimates different probabilities:
E(P(Y=1|D=1)); E(P(Y=1|D=0)), E(P(Y=1|T=1)) ; E(P(Y=1|T=0))
E(P(Y=1|D=1,T=1)) ; E(P(Y=1|D=1,T=0)) ; E(P(Y=1|D=0,T=1)); E(P(Y=1|D=0,T=0))

and uses them to evaluate how the expected probabilities change for the treated or untreated group (D) before and after treatment T.

[Bruno Jimenez]

I understand, thanks.