Dear all,
I am applying gsem to address the endogeneity using two different commands I found on Stata website as follows:
Model 1. gsem (y1<- y2 x1 x2 L, oprobit)(y2 <-x1 x2 x3 x4 x5 L), var(L@1) latent(L)
(the command can be found here: https://www.stata.com/meeting/german...ukker_gsem.pdf)
-> Result: adaptive quadrature failed to converge, cannot compute an improvement -- discontinuous region encountered

Model 2. gsem (y1<- y2 x1 x2 L@a, oprobit)(y2 <-x1 x2 x3 x4 x5 L@a), var(L@1) latent(L)
(the recommended command can be found here: https://blog.stata.com/2013/11/07/fi...-gsem-command/)
-> Result: good. However, all coefficients and std, p-value are the same as the results of the command that excludes the latent L, like Model 3 below.

Model 3. gsem (y1<- y2 x1 x2, oprobit)(y2 <-x1 x2 x3 x4 x5)
One thing I noticed is that latent L in model 2 above is insignificant in both equations.
I tried to run Model 2 and Model 3 using the data set on the page that recommends Model 2. The models with and without L@a give different results, and the coefficients of L are significant.

I also run the model with only the main equation (without instruments), like this:

Model 4: gsem (y1<-y2 x1 x2, oprobit)
The results of the equation y1 = f(y2, x1, x2) in models 2, 3, 4 are exactly the same.

I would appreciate if someone can help answer some questions:
Which command, in model 1, or model 2 above is more appropriate? Why does Stata recommend such two different commands that give different results?
What conclusions can be drawn upon the exact results of 3 models above? Can I conclude that there is no endogeneity existing in this case?
Thank you.
Best,
Annie.