Dear all,
I have a binary DV with an endogenous X which I instrument with an interaction variable i.treat##i.post.

When using ivprobit and cmp strategy I get different results and that's because of different sample sizes for the first step.
I wanted to know if there is a problem if we use different sample sizes for the 2 steps in an IV startegy (with cmp)?

I also want to argue that cmp is better because error terms may be correlated and therefore cmp will give more efficient results. But I found out that it is written in ivprobit Stata file that using vce(cluster ...) can be used to control for lack of independence between error terms. Does that mean I cannot prefer cmp because it allows for collinearity between error terms since ivprobit can also allow for this when using the cluster option?

Many thanks.