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Re: st: RE: constraints in reg3
On Wed, 29 Sep 2004 11:33:08 +0100, Neumayer,E <firstname.lastname@example.org> wrote:
> Hi, this takes up a thread from about 4 weeks ago. Kit Baum clarified that if you do
> 1. reg y x1 x2
> 2. reg y1 x1 x2
> 3. reg y2 x1 x2
> and y = y1 + y2, then the coefficient vector of model 1 is the sum of the coefficient vectors on models 2 and 3.
> I did this with xtpcse for data that have both cross-sectional and time-series dimension and find this to be true, of course. However, if I specify xtpcse, corr(ar1) then the coefficient vectors of models 2 and 3 no longer add up to the coefficient vector of model 1. I presume this is because xtpcse, corr(ar1) uses Prais-Winsten, whereas xtpcse without the corr(ar1) option uses OLS. I have two questions:
> a. Can anyone explain why the coefficient vectors of models 2 and 3 no longer add up to the coefficient vector of model 1 if xtpcse, corr(ar1) is used?
I would suspect that -xtpcse- comes up with different estimates of the
AR(1) correlation coefficient, and that's where the models stop being
comparable (and additive): think about GLS with different matrices
inside; they won't add up, although there might be a way to combine
the results with messy and ugly matrix algebra. If it were possible to
restrict the rho to be the same across the two models, then they
should give you the additive answers again.
-xtpcse- does not provide for fixing the rho; -xtregar- does with
-rhof()- option, so that may be something you might want to try out.
> b. Should I accept that the coefficient vectors no longer add up or should I artificially restrict them to be the same?
No good answer from me. You should have a better feel for your
particular substantive problem.
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