I am using a CF/2SRI method to estimate the effect of an endogenous discrete explanatory variable, with a non-linear first stage. It appears to be common practice (in economics at least) to argue and show correlation between the instrument and instrumented variable for the first stage.
I am getting used to showing marginal effects when I am using non-linear models. However I am wondering if in this scenario there is any sense in displaying marginal effects, as the residual is not based on the marginal effects but on the (residual from the) main regression.
This feeling is exacerbated by the fact that the first stage does not really have any practical application, as it is not an estimation of the instrumented variable. It just a (linear) projection and the parameters there are defined in a way that make the errors uncorrelated with the regressors.
I guess I almost answered my own question, but I am nevertheless interested to hear someone else's opinion on this.
Question: Showing the marginal effects of a first stage regression, is there any point?