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

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

On Jul 19, 2010, at 2:33 AM, Bond wrote:

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

Re point (1) above: not quite so, but if your instruments reject the overidentifying restrictions in single-equation estimation, stop there.

Re point (2): in specifying (in any estimator) which variables you consider endogenous, you invoke the appropriate estimator.

Re point (A): the discussion of SUR is irrelevant. SUR does not handle equations with endogenous regressors. It is OLS applied to each equation, taking account of the error correlations across equations. If any of the regressors are endogenous, SUR is inconsistent.

Re point (B): just because the equations contain the same regressors, there is no implication that there are cross-equation restrictions unless theory suggests such.

Re point (3): the only 'canned' code is that of reg3, which is a very old and severely limited implementation of three-stage least squares (it does not, for instance, allow for anything beyond iid errors: no robust, cluster, HAC, IV-GMM, etc.)  Unless you can conclusively argue that your errors are iid, I would not use it. I would use single equation estimation with IV-GMM.

Kit




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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