Econometric Questions

[nil11]

Hello,

I need your help on the following econometric issues:

I am doing a simultaneous 2-step estimation (analyzed in Maddala 1983, Model 3) as following:

I have the following set of equations:

Model 1:
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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.

Regards,

Nil