I have to perform a semi-parametric first stage based on pscore with a binary treatment and instrument and I'm not sure if I do it right.
My approach was:
firststage.out <- glm(d ~ z + pscore, data=data)
with d = binary treatment and z = binary instrument.
Where I estimated my pscore with:
pscore.model <- glm(z ~ x, family = binomial(link = "probit"))
where x is a vector of covariates and z the binary instrument.
With this approach I got quiet similar results as in the parametric one. But I am not fully convinced that this approach is the right way.
What's your opinion?
sending love <3