Logit model with instrumental variable

[Julie Li]

Dear Statalist,

Hello! I have a question regarding the logit model with instrumental variables. I know we can use '-ivprobit-' command in STATA. However, I wonder if it is ok first to regress y x1 z(z is the instrumental variable), then predict x1hat, and run the logit model again: y x1hat x2, which is similar to 2SLS but the second stage is using MLE. I am asking because I found a big difference in the moderating (interaction) effect between '-ivprobit-' and the latter method, though the main effect seems similar. I don't know what is the reason behind this difference. Thank you very much!

[Julie Li]

Another question is, I don't know whether my code for interaction effect is right (in Stata: 'ivprobit'). I haven't found any manual for this on the internet.
My code is:
gen a = x1* m1
gen a_hat= z*m1
gen b = x1*m2
gen b_hat = z*m2

ivprobit y m1 m2 x2 x3 x4(x1 a b = z a_hat b_hat), twostep

*where x1 is the endogenous variable, z is the instrumental variable, m1 is the first moderator, m2 is the second moderator.

Thank you very much! Really appreciate your help!

[Joro Kolev]

No, you cannot do what you are suggesting in your original post. This is known as a "forbidden regression," and for this to work the expectation operator has to pass through nonlinear functions, which it does not.

I did not understand your question in #2. If you feel like, elaborate.

[Memoona Khan]

Hi Statalist,
I have a question about the difference in difference method and how I run it on Stata and I also have a question about how i set the data according to the treatment group and control group and how I identify the treatment group and control group in a penal dataset.