Running a Roy model in Stata (by hand?)

Dear Statalist members,

I am having an issue that I could not solve by scrolling various fora, manuals and papers...

I have a Roy model type of problem: I would like to assess the effect of a binary treatment d on a dependent variable y (list of ordered outcomes). I would like to compare y when d = 1 with y when d = 0. From what I could gather, the Roy model handles this where d = y1 is treatment indicator, and I observe either y = y2 if d = 1 or y = y3 when d = 0. So, the Roy model should allow for both selection on observables (via regressors x) and selection on unobservables (ε).

How can I model this via Stata, given that I have an ordered list of outcome? Can I include the treatment variable, which is the dependent variable of my selection equation, in the outcome equation in combination wih the Inverse Mill's Ratio that I would compute from the selection equation? Will it create collinearity between my variables? Do I need exclusion restriction? Based on my dataset, I could not find any...

I was thinking of doing something like:

probit d x1 x2 x3

predict Zgamma, xb

gen Invmills=normden(Zgamma)/norm(Zgamma)

ologit (or mlogit) y d x1 x2 x3 Invmills

Do I need to bother about heteroscedasticity?

What if I use in the outcome equation an alternative measure of the treatment d, dependent variable of the selection equation?

I have seen in some papers a selection hazard variable being computed after the IMR, such as:

gen Selhazard = normden(Zgamma)/(1-norm(Zgamma))

How could I make use of this?

Thank you for your help and your insight! I am receiving somewhat confusing advice...

Clotilde