Re: Re: st: RE: FGLS vs. OLS

[Jordan Silberman <silberman.stata@gmail.com>]

Thanks very much, your explanation makes sense. So FGLS and OLS yield
different coefficients IF FGLS is used with the SUR approach. My
understanding is that it is also possible to use FGLS to estimate
single models, in a "non-SUR" manner. This is described, for example,
in the following article: Achen C. Two-step hierarchical estimation:
Beyond regression analysis. Polit Anal. 2005;13(4):447-456.

Suppose that you just want to use FGLS to compute a single model--say,
a linear regression of y on x. In this case, if you use the command
"sureg (y x)" in Stata, will sureg estimate the model using FGLS? If
so, is it correct that this single model estimated with FGLS should
yield the same point estimate (though different standard errors) as
what you'd get from a simple OLS regression?

Thanks so much,
Jordan

On Wed, Jul 17, 2013 at 7:02 AM, Christopher Baum <kit.baum@bc.edu> wrote:
> <>
> On Jul 17, 2013, at 2:33 AM, Jonathan wrote:
>
>> This makes sense. But my question is--if sureg uses FGLS, and if FGLS
>> yields coefficient estimates that differ from those of OLS, then why
>> do the sureg and regress commands (which should be using FGLS and OLS,
>> respectively) yield the exact same regression coefficients? Is sureg
>> perhaps not really using FGLS?
>
> sureg does use FGLS, but the name of the command refers to seemingly unrelated regressionS, plural.
> You do not have regressionS, but rather a single regression. The FGLS aspect of SUR relates to taking
> advantage of the cross-equation correlations of OLS residuals. As you have only one residual series, there are
> no such correlations. If you do something like
>
> sureg (y1 x1) (y2 x2)
>
> you will see that FGLS does not give you the same point estimates unless (a) the residuals are numerically orthogonal or
> (b) x1 = x2, as mentioned elsewhere. Otherwise estimating these equations as a system will matter.
>
> Cheers
> 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
>                                                                                                    | http://www.crup.com.cn/Item/111779.aspx
>
>
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