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st: re: reg3 option -robust-

From   Christopher Baum <[email protected]>
To   <[email protected]>
Subject   st: re: reg3 option -robust-
Date   Tue, 19 Oct 2010 10:40:54 -0400

Brian said

One option would be to use the -gmm- command.  There is a discussion of
systems estimators in the corresponding manual entry.

Presumably you want to use the -robust- option because you think the errors
are heteroskedastic.  By using -gmm- you can select a weight matrix that
specifically allows for heteroskedasticity, implementing what Wooldridge
calls the GMM 3SLS estimator in his graduate textbook.

If you were to use -reg3- knowing that you have heteroskedastic errors, it's
not clear to me that there would be any advantage over using
equation-by-equation 2SLS.  The weight matrix used in standard 3SLS assumes
homoskedasticity.  Unless the errors really are homoskedastic I don't think
you can make any claims about 3SLS being more efficient than 2SLS since
you're using the "wrong" weight matrix.

Good point, but I don't think the fact that one could cook up a -gmm- solution obviates the need for bringing canned -sureg- and -reg3- into the 21st century (no longer your concern, understood!)  When I teach SUR I point out that there is no value in using SUR on a set of equations with identical regressors, BUT you may still want to do it to consider cross-equations restrictions and tests of same. I can now do robustified tests on -sureg- by pretending that I have a nonlinear system, but why should I need to do that? Smells like TSP as of 1970s, in which the only system estimator was an iterative one.

By the same token, although you are quite correct that the improved efficiency of 3SLS is limited to the homoskedastic case, and using Wooldridge's estimator would be a better idea with non i.i.d. errors, one might want to perform a robustified test of cross-equation restrictions using -reg3-. I don't see why one cannot do that with -reg3-, even if a better estimator (Wooldridge's GMM-3SLS) is available.


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

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