System with simultaneous linear and probit equations

[Marco Ercolani]

Dear Statalisters,

What Stata command can I use to estimate a system of equations that contains one linear equation (y is continuous) and two probit (or logit) equations (z1 and z2 are binary)? To clarify things:

I know that if I assumed a linear approximation to the two probits I could estimate:
reg3 (y = x1 x2 x3) (z1 = x1 x2 x4) (z2 = x1 x2 x5)

I also know that if converted y into a binary variable yb I could estimate a trivariate probit:
mvprobit (yb = x1 x2 x3) (z1 = x1 x2 x4) (z2 = x1 x2 x5)

(Finally, I also know that I can include endogenous variables among the regressors and that this is the whole point of system estimation. Otherwise I would just estimate a SURE, but SURE is not what I need on this occasion.)

best wishes,
Marco

[Marco Ercolani]

Dear Statalisters,

At the risk of answering my own question, the (user-written) command I am looking for might be:
cmp

Any further comments welcome.
Marco

[Joseph Coveney]

You can also look into the official gsem. The trick would be to model the correlation between the latent residuals from the probit equation and the residuals of the linear equations, but you probably could adapt the implementation of the bivariate probit model in gsem to do that. The sqrt(2) comment there in that post is handled on p. 144 of Skrondal, A. and Rabe-Hesketh, S. (2004) Generalized Latent Variable Modeling. Multilevel, Longitudinal, and Structural Equation Models. Boca Raton, Fla: Chapman & Hall/CRC.

[Marco Ercolani]

Dear Joseph, thank you very much for suggesting I look at gsem. and for the page reference to Skrondal and Rabe-Hesketh (2004). I will attempt this. Best wishes, Marco.