Hello statalist users,

I was trying to find some advice on addressing the correlations of error terms across simultaneous equations. There are three equations in my study, which are jointly determined. And the dependent variables of each of these equations are binary. I used the multivariate probit model as the empirical method, but the results revealed that the correlation coefficients of the error terms across these equations are significant. Can I possibly get some suggestions on how to address such correlations? Thanks a lot in advance!

Simultaneous equations in my study are similar to the following ones:

y1=a1*x1+a2*x2+a3*x3+u1
y2=b1*x1+b2*x2+b3*x3+b2*x4+b5*x5+b6*x6+u2
y3=c1*x1+c2*x2+c3*x3+c4*x4+c5*x5+c6*x6+c7*x7+c8*x8 +u3

y1, y2, and y3 are binary, and none of them are included in any equation. In that case, It seems implausible to use the instrumental variables to address the endogeneity issue caused by the correlations of the error terms across these equations.

The coefficients of the error terms are as follows :
Array

All suggestions and insights are welcome. Thanks a lot!!!