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

[Christopher Baum <kit.baum@bc.edu>]

<>
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 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?

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   |   http://ideas.repec.org/e/pba1.html
                              An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
   An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html


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