Instrumented Multinomial Probit Using cmp

[Andrew Meyer]

I am estimating an instrumented multinomial probit model using Roodman's cmp. As an aside, I have found this package very useful in a variety of contexts.
My model is as follows:
outcome_j=education+epsilon_j
education=instrument+error.

There are 4 alternatives for the outcome variable. Education is modeled as endogenous, so I instrument for education with "instrument."
Using cmp, I enter
cmp (outcome= education, iia) (education=instrument), ind($cmp_mprobit $cmp_cont)

I understand that we need to choose a base alternative outcome and then the model estimates influence of education on other outcomes relative to this base outcome. What I am struggling with, however, is that I get very different results for the education equation depending on which outcome is used as the base outcome in the multinomial probit equation. Shouldn't the impact of instrument on education be the same regardless of which alternative is used for the base outcome in the "2nd stage?" (To use an analogy to 2sls.)

Can anybody help me with what I am missing here? Does the normalization in the probit equation also affect interpretation in the education equation? Or could it be a maximization issue where I am finding a local max or something? For what is is worth, convergence has been elusive with this estimation and I have only had luck using the "difficult" option. The maximized values of the likelihood functions differ based upon which alternative is the base outcome.

Thanks for any ideas!

[David Roodman]

This is an interesting question. I think to check my intuitions, I would test the estimator on a simulated data set in which the fit should be very clean, with a large sample size and relatively small error terms. I would use drawnorm to generate error terms with the assumed structure. The errors in the outcome equations would not be correlated with each other, but would be correlated with the education equation.
--David

[Andrew Meyer]

Thank you for your reply David. Your suggestion is a good one. I simulated some data and estimated the model. The estimated effect of the instrument on education is the same regardless of how I define the "2nd stage" outcome variable. This agrees with intuition, so there must be something else going on with the more complicated model on my real world data. I will continue to investigate. Thanks again for the suggestion.