st: Econometric Questions

[Econ Stat <econstat@ymail.com>]

Hello Statalist users,

I need your help on the following econometric issue:
 
I am doing a simultaneous 2-step estimation (analyzed in Maddala 1983, Model 3, using CDSIMEQ program in STATA) as following:
 
I have the following set of equations:
 
Model 1:
--------------
y1= β1’x1 + δ1y2* +  ε1, …………….....eqn(1)
y2*= β2’x2 + δ2y1 +  ε2,  y2=1(y2*>0)….eqn(2)
 
where y1 observed and y2 dichotomous.
(1) I would like to know, can I use the estimates of y2* (i.e., y2*hat) from the 2nd stage regression of the above model (Model 1) and use it as an explanatory variable in a simple probit or ordered probit regression model?
 Like for example in the following probit model,
y3*= φ3’x3 +  γ3y2*hat +  η3,  y3=1(y3*>0).…eqn(3)
 I have a valid theoretical justification for using the predicted value y2*hat (predicted from the 2nd stage of Model 1 i.e. simultaneous equations model) in the y3* equation but I am unsure about the empirical justification. 

(2) Also using the 2nd stage estimates of y2* (i.e., y2*hat from Model 1) as an explanatory variable, can I do a 2-step GMM estimation? 

Please help.

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