Convergence issues with recursive two equation system in cmp

[John Vinland]

Dear Statalist,

I am trying to estimate a recursive two-equation system using Stata’s cmp command. The dependent variable of the first equation is a binary outcome (y1), while the dependent variable of the second equation is a multinomial outcome (y2, 5 possible outcomes).
My command is roughly of this format:

cmp (y1 = x1 x2 x3 i.x4 i.x5 i.x6 i.x7 i.x8) ///
(y2 = y1 x9 x10 x3 i.x4 i.x5 i.x6 i.x7 i.x8), ///
Indicators ($cmp_probit $cmp_mprobit) technique(bhhh) robust

Problems I’m encountering:

1. Ill-conditioned regressors:
   • I receive warnings about ill-conditioned regressor matrices for all equations before the full model is estimated. For example: Warning: regressor matrix for _mp_cmp_y5 equation appears ill-conditioned. (Condition number = 288.35056.). This might prevent convergence.
   • I have checked the correlation matrix of the variables I’m using and don’t see anything problematic. In fact, I have tried removing some variables from the model (which does not change the errors I get) and running regressions separately (as standard probits, without the cmp command) for each outcome to see if a specific variable is at fault, which does not seem to be the case.
2. Convergence issues:
   • The full model fails to converge unless I manually reduce ghkdraws() and adjust nrtolerance(). With the default draws (252 in my sample) and using the bhhh technique, I get the following error: ghk2: covariance matrix is not positive-definite. Mata run-time error
   • Using the default technique without bhhh, the model fails because it cannot create a concave function in all iterations, eventually giving a time error. Even specifying the difficult option does not help.
   • I am only able to achieve convergence with a very small number of draws (e.g., 20) and bhhh. However, this produces unreasonable coefficients (e.g., 30–40 on some variables, even though the outcomes are binary), and the results are unstable between runs, both I assume due to the limited amount of draws I force.

Finally, I would like to add that my sample contains a considerable number of observations (above 15,000), without any missing data.

I would greatly appreciate any advice on producing stable and reliable estimates for this kind of recursive two-equation system.

Thank you in advance for your guidance!