cmp-random effects

[Dayla Spassio]

Good day,
I am trying to estimate the impact of health status expectations (Exp_h) on consumption expectations. I performed a conditional mixed process -CMP-, because the model is non linear, and I have a way of thinking that the regressor (Exp_h (that is binary) is endogenous.
Then, I tried to estimate the model by considering random effects.

cmp(cons= Exp_h x2 x3 ||id:) (Exp_h=z1 z2 x2 x3|| id:) , ind ($cmp_oprobit $cmp_probit) cl(id) cov(indep unstruct)

cons=ordinal dependent variable
Exp_h=endogenous dummy variable
z1 z2 =dummies IV variables

I get the results of the first and second stage equation and finally this last table, which I have difficulty interpreting.
Any suggestions would be welcome. Thank you very much.

Random effects parameters    Estimate    Std. Err.    [95% Conf.    Interval]
                
Level: id             
Cons       
Standard deviations              
_cons    .6071207    .0526769    .5121775    .7196637
Exp_h           
Standard deviations              
_cons    .8759736    .0612121    .7638533    1.004551
                
Level: Observations             
Standard deviations              
Cons    1    (constrained)
Exp_h    1    (constrained)
Cross-eq correlation              
Cons       Exp_h   .4120378    .0875992    .2272259    .5682024

[David Roodman]

The random effect at the id level in the cons equation is estimated to have standard deviation 0.6071207 and that for the Exp_h equation 0.8759736. The observation-level error terms are normalized to have standard deviation 1 because (ordered) probit models have no intrinsic scale. Their cross correlation estimated at 0.4120378.

[Dayla Spassio]

Thanks Professor!