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Re: st: st. Simultaneous Equations Model & GMM Estimation

From   Bond Tiger <>
Subject   Re: st: st. Simultaneous Equations Model & GMM Estimation
Date   Sun, 18 Jul 2010 08:48:39 -0700 (PDT)

Thank you very much Dr. Baum for your response. This is what I have understood 
from your response, please correct me if I am wrong......

(1) It would not matter if I use system estimation technique but test my 
instruments in a single equation setup.

(2) I may not have to test for endogeneity of the regressors (Y1 and Y2) in the 
single equation setup as by model specification itself I have considered the 
regressors to be endogenous.

I may consider estimating the equations simultaneously, otherwise if single 
equation estimation is considered efficiency may be lost. Also I may have the 
following situations:

(A) I may consider Seemingly Unrelated Regression (SUR) equations, in which case 
I may have different sets of explanatory variables in both the equations but the 
disturbance terms in both the equations may be correlated (may be some 
unconsidered factors influence the disturbance terms in both the equations) and 
then estimating all the equations simultaneously taking the covariance structure 
of the residuals into account would lead to efficient estimates of parameters. 
Otherwise, single equation estimation would lead to inefficient estimates.

(B) If I consider cross-equation parameter restrictions (in case both the 
equations have common explanatory variables), then also the only way to test or 
impose these restrictions is in a simultaneous equations setup.

Therefore, not ruling out (A) and (B), I may finally estimate both the equations 

(3) So is there any code in STATA for SYSTEM ESTIMATION?

Thank you once again for you response.




----- Original Message ----
From: Christopher Baum <>
To: "" <>
Sent: Sun, July 18, 2010 6:05:27 AM
Subject: Re:  st: st. Simultaneous Equations Model & GMM Estimation

On Jul 18, 2010, at 2:33 AM, Bond wrote:

> 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 
> I am using single equation setup (one equation at a time).The set of IVs for 
> and Y2 are different (containing different instruments) and both the sets are
> passing the orthogonality conditions, overidentifying restriction test and 
> 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 
> 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 
> both the equations)? If yes, could you advice me some references or codes in
> (C) Can I use instrumental variable GMM to estimate the simultaneous equations
> model in which the regressors are endogenous by model specification?

Just  because these are simultaneous equations, there is no need to apply 
systems estimation techniques to estimate them. You can use single-equation 
techniques (such as SSC's -ivreg2-) to estimate them via IV-GMM. The only reason 
you would need a systems estimator is if you had cross-equation constraints on 
the parameters.

Re (A), I don't understand what you mean by 'neither of the regressor is 
endogenous'. If you have set up the model properly, you are specifying that Y2 
is endogenous in the Y1 equation, and vice versa. 

Re (B), as stated above, there is no need to do so.

Re (C), as stated above: yes, you can estimate each equation with IV-GMM.

Kit Baum   |   Boston College Economics & DIW Berlin   |
                              An Introduction to Stata Programming  |
   An Introduction to Modern Econometrics Using Stata  |

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