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re: st: xtivreg2 gmm2 : robust vs cluster(id) vs bw(#) dkraay(#)


From   Christopher Baum <kit.baum@bc.edu>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   re: st: xtivreg2 gmm2 : robust vs cluster(id) vs bw(#) dkraay(#)
Date   Fri, 16 Mar 2012 13:34:36 -0400

<>
Paulo said

> I have a question regarding the command -xtivreg2. Usually, when
> working with  robust standard errors,this affects the standard error
> of the coefficients but not the coefficients themselves. This is true
> in -regress or -xtreg, for example. This is also true in 2SLS (see
> example 1 below using xtivreg2 and comparing robust to heterosk and
> Clustered SE).
> 
> However, I got into trouble when applying the GMM version of
> -xtivreg2. In example 2 below, the use of alternative robust standard
> errors actually have an impact on the coefficients. In fact, when
> using the different roust standard  errors white 1980 (robust),
> Clusters (clusters(id)) Newey and West 1987 (bt(#)), Driscoll and
> Kraay 1998 (dkraay(#)) available with "xtivreg2   , gmm2", you will
> always get not only different standard errors but also different
> coefficients.
> 
> I woudl appreciate if anyone of this list could give me a hint on why
> this is the case for GMM. Also, I would be more tahn appy if you can
> point at some references to look at this a bit in more detail. For
> example, I have looked at the documentation related to the command
> -ivreg2 but I could not find any explanation of this.


I answer this for simple IV-GMM estimation, i.e. ivreg2 (Baum-Schaffer-Stillman, SSC) or -ivregress gmm-. 
The logic extends to IV-GMM on a panel, e.g., xtivreg2 (Schaffer, SSC).

When you apply a different VCE estimator (robust/"White", cluster-robust, HAC/"Newey-West") to OLS or IV (2SLS),
the point estimates are unchanged, but the VCE and standard errors change. If you apply GMM while
assuming i.i.d. errors, or when allowing for robust SEs in an exactly identified equation, the coefficients and
standard errors will be identical to those of IV/2SLS because GMM in those circumstances is the special
case defined by IV/2SLS.

But if you apply GMM to an overidentified equation, with non-i.i.d. errors, both the coefficients and the VCE
will be altered. You are no longer solving a least squares problem; you are solving a GMM problem of minimizing
Hansen's J, and that in fact will lead to coefficients that do not represent the 'least squares' in terms of their
associated residuals. However, they will unambiguously be more efficient than IV/2SLS counterparts 
computed with the same VCE assumptions. But this also implies that, since the VCE plays a role in the 
optimal weighting matrix, the coefficients themselves are functions of the estimated VCE. The iterated
GMM technique known as GMM-CUE illustrates that nicely. 

For more details, please see the two Baum-Schaffer-Stillman Stata Journal papers (2003, 2007) referenced in
ivreg2 or xtivreg2 help. They are freely downloadable from IDEAS or stata-journal.com.

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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