st: st. Simultaneous Equations Model & GMM Estimation

[Bond Tiger <bond0910@ymail.com>]

Hello All,

It would be extremely helpful if you could guide me on the following matter:

I am using a simultaneous equations model and IV-GMM estimation technique 
(2-step GMM or continuously updated GMM) to estimate the following equations:

(1) Y1=a0+a1*Y2+a2*K+E1,
(2) Y2=b0+b1*Y1+b2*L+E2,

L & K are other exogenous variables and E1 & E2 are independent errors. Y2 
is the regressor in (1) & Y1 is the regressor in (2). (I am using a 
cross-section data.)

I will estimate my model using both the equations simultaneously (NOT single 
equation estimation).

However, in order to test the instruments for each of my regressor (Y1 and Y2), 
I am using single equation setup (one equation at a time).The set of IVs for Y1 
and Y2 are different (containing different instruments) and both the sets are 
passing the orthogonality conditions, overidentifying restriction test and weak 
identification tests in the single equation setup, implying that my IVs are 
relevant and can very well identify the equations. In the single equation 
setup, I have also tested for endogeneity of my regressors (Y1 & Y2) and 
found neither of the regressor to be endogenous in the single equation setup. 


Now, my actual model is a SIMULTANEOUS EQUATION model where I am trying to 
estimate both the equations jointly. In the simultaneous equation model my 
regressors are endogenous by model specification, therefore, I am using IV-GMM 
estimation (i.e. instrumental variable GMM technique). Also in my model, I could 

detect the presence of heteroskedasticity and therefore GMM is more efficient 
than 2SLS. So my questions are:

(A) Can I test the IVs in a single equation setup (where neither of the 
regressor is endogenous) and then use those instruments in jointly estimating 
the 2 equations in the simultaneous equations framework?

(B) Is there any way I can test the IVs in a simultaneous equations setup (using 

both the equations)? If yes, could you advice me some references or codes in 
STATA or SAS or MATLAB.

(C) Can I use instrumental variable GMM to estimate the simultaneous equations 
model in which the regressors are endogenous by model specification?

It would be really helpful if anybody can provide some advice & references. I 
will greatly appreciate your help.

Regards,

Bond


      


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