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st: RE: Suest and Sureg


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Suest and Sureg
Date   Tue, 7 Aug 2007 21:06:40 +0100

Alvaro,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] 
> Sent: 07 August 2007 18:18
> To: statalist@hsphsun2.harvard.edu
> Subject: st: Suest and Sureg
> 
> Dear Stata list,
> 
> maybe this a very basic question. I`m trying to estimate a 
> model using SUR, this technique is new for me. My problem is 
> that command sureg maybe is not taking into account posible 
> heteroskedasticity. Then I have tried suest after regress 
> (someone told me that with this command is possible to run a 
> sur under heterosk on each equation). I notice that the 
> standard errors have change and are very similar to my 
> independent equations regression once adjusted using robust option.
> However, i dont know if this command is really doing a sur 
> regression allowing for correlations among unobservables. I 
> have read some applications that say that is the "correct" 
> way to run that kind of regression (sur model corrected by 
> white). However in other applications i have read that this 
> command is not properly a sur regression. A previous post I 
> have read the following
> 
> "Just to add a bit to Maarten's suggestion: -suest- will let 
> you combine two or more "seemingly unrelated" equations so 
> that you can test cross-equation restrictions and the like.  
> But it won't do "seemingly-unrelated estimation" a la Zellner 
> and -sureg-, i.e., you won't get the efficiency gains 
> possible from estimating the equations as a system. The 
> coefficients reported by -suest- are just the original ones"
> 
> So, my doubt now is bigger. I only want to obtain the correct 
> variance covariance matrix in order to test corss equation 
> hypothesis under to kind of models. The first one uses the 
> same covariates for all the equations and the second one 
> different covariates. Both are OLS-type.

The comment above was by me.

The way to understand what is going on is to think in terms of
efficiency vs. robustness. You get efficiency by modelling the
heteroskedasticity, cross-equation correlations, etc. correctly, and
incorporating these into GLS-type estimates of your coefficients.  You
get robustness by using a covariance estimator that is robust to
heteroskedasticity etc.

-sureg- does traditional SUR.  This is GLS-type estimation that takes
account of cross-equation correlations to get more efficiency.  Since
the cross-equation correlations are modelled, you can test cross-eqn
restrictions and the like.  But -sureg- assumes homoskedasticity, and if
the errors are heteroskedastic, then the SEs reported by -sureg- will be
wrong.

-suest- applies an Eicker-Huber-White-sandwich covariance estimator to a
set of equations estimated by, in your case, OLS.  You don't get the
efficiency that you would get if you modelled the cross-eqn correlations
(like SUR), or for that matter, the efficiency that you would get if you
modelled the heteroskedasticity and did GLS.  But your SEs will be valid
whatever the cross-equation correlations or heteroskedasticity that you
face.

Maybe you want to combine these, or perhaps do SUR with with modelled
heteroskedasticity.  I suppose this is possible, but not with the canned
estimators available in official Stata.  You would have to program them
yourself or find someone else that has already programmed them.

Your options in brief: if you are worried about heteroskedasticity, then
-suest- is your only choice; if you aren't worried about
heteroskedasticity, then both -suest- and -sureg- generate valid SEs,
but -sureg- is more efficient.

Cheers,
Mark

> hope someone can answear me more and if you need more 
> information I can explain the details of my model.
> 
> Thanks a lot
> 
> Alvaro
> 
> 
> 
> 
> 
> 
> 
> 
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