st: MNL Selection Model

[Mazhar Islam <mazhar13@gmail.com>]

Dear Listers,
I posted the folllowng a couple of days ago. No one reply so far :(
Giving another shot!

I am interested in estimating a two-stage selection model. In the
first stage I have a polychotomous choice (three mutually exclusive
choices)
as a dependent variable while in the second stage I have a binary
dependent variable (success =1, otherwise =0).
I’m estimating the model as follows:I estimate a multinomial logit
model.Then, I calculate three inverse Mills Ratios(IMR) following
Lee(1983) based on the predicted probabilities from the above MNL
model
Finally, I plug in the three IMRs into three separate probit models
for each choice. As in switching regressions, I multiply estimated
coefficients of each model with two counterfactual samples to compare
between result of actual choices and counterfactual choices.
My question is whether this is a right approach. I am aware that I can
use Dubin and McFaddens’ (1984) or Bourguignon, Fournier and Gurgand’s
(2004) approach instead of Lee’s(1983). But as I understand,  all
three approaches are for a continuous second stage dependent variable
(ie. Wage). That is, to use OLS not probit as I have been using.  Is
it okay to use Probit in the second stage?

One of the earlier posters suggested that for a non-linear model like
Probit one should use ML methods to estimate the system of equations.
I searched Statalist, web but couldn’t find a way to implement such an
approach.  It seems Deb’s (2009) Stata module “mtreatreg” may be one
way of doing - but I am not sure.
I would appreciate any help.
Mazhar Islam
Assistant Professor
LeBow College of Business
Drexel University

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