st: endogenous regressor in bioprobit and cmp

["Elena Pirani" <pirani@disia.unifi.it>]

Dear Statalist users,
I am trying to run a bivariate ordinal probit model, i.e.:
y_1=x1 x2 x3 x4
y_2=x1 x2 x3 y_1
that is a bivariate probit with an endogenous regressor (y_1) and where x4 is my
instrumental variable for y_1.
Following bioprobit paper and routine of Sajaia (2008) it seems that the correct
sintax is:

bioprobit (y_1 = x1 x2 x3 x4 )  (y_2 = x1 x2 x3) , end
that enables to obtain the parameter gamma.

However if I add the endogenous variable y_1 in the second equation, i.e.
bioprobit (y_1 = x1 x2 x3 x4 )  (y_2 = x1 x2 x3 y_1)
without the option "end"  I get estimates that are different from the first model
specification.
I obtain an estimation for the parameter y_1 in the second equation that is different
from gamma in the previous formulation (and in this case I don't have gamma!)

Could someone help me? Which is the difference? Which is the more correct approach?
Moreover, does someone knows why the option "end" described in the paper of Sajaia
is not present in the current version of online help of Stata?

Please note that when using cmp sintax
cmp (y_1 = x1 x2 x3 x4 )  (y_2 = x1 x2 x3 y_1) ...
I obtain estimation coefficient similar to the bioprobit without "end" option.

I would greatly appreciate any assistance which you might be able to provide.
Thanks
Elena
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