Hello,

I am using the ivprobit command and want to calculate predicted probabilities with the margins command afterwards. However, it seems to me that I either do not correctly understand how it's working or the predicted probabilities are incorrectly computed. In short, I think Stata is somewhere using values for the instrument to compute the probabilities when it should not, in my opinion.
The following should work at least in both Stata 15 and 16.

When I use the example from the documentation, I can compute predicted probabilities, e.g. at the means with the "atmeans" option:

Code:
webuse laborsup
ivprobit fem_work fem_educ kids (other_inc = male_educ)
margins, predict(pr) atmeans
Now, Stata gives a predicted probability of .44.
Suspiciously, it shows the instrument male_educ in the "at" section with its mean of 11.966. In my opinion, no value can be assigned to the instrument because the predicted probability should only depend on the given value of the endogenous variable because by assumption(!) of the IV approach the predicted probability is only affected by the instrument via its effect on the endogenous variable.
However, when I use a different value for the instrument, I also get a vastly different predicted probability of .55!

Code:
margins, predict(pr) atmeans at(male_educ = 8)
In my opinion, this cannot be correct, because the value of the instrument should not affect my predictions whenever I specify a value for the endogenous variable (here at mean). This problem also affects the predict command after ivprobit, which will deliver different predictions for two identical observations that only differ in the values of the instrument variable, which should also not be the case.*

Can anybody help me out? Is there any logic I am missing why computing the probabilities in this way is indeed correct and helpful?
Thank you very very much in advance!!


* The documentation says "predict, pr" after ivprobit is "accounting for endogeneity", which I don't really get. When we take the estimated coefficient of the instrumented endogenous variable, we are already taking the endogeneity into account, I don't see any reason why the value of the instrument variable should affect the prediction when we use the estimation results of the IV model.