I think the use of a nonlinear estimation process (probit) in order to produce the first stage of your IV is not appropriate. IVs are an instance of a broader class control function approachs. For example, as with typical two-stage IV approaches, your SE will be off unless properly adjusted.

I think the use of a nonlinear estimation process (probit) in order to produce the first stage of your two stage estimate is not appropriate. For example 2sls is an instance of a broader class control function approachs. Even with typical two-stage linear approaches, your SE will be off unless properly adjusted.