  # st: RE: constraints in reg3

 From "Neumayer,E" To Subject st: RE: constraints in reg3 Date Wed, 29 Sep 2004 11:33:08 +0100

```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?
b. Should I accept that the coefficient vectors no longer add up or should I artificially restrict them to be the same?

Any help greatly appreciated.

Eric Neumayer

-----Original Message-----
From: Kit Baum [mailto:kitbaum@mac.com]
Sent: 25 August 2004 21:45
To: statalist@hsphsun2.harvard.edu
Subject: st: constraints in reg3

Eric said
I have a dependent variable y, which is the sum of 2 components, such
that y = y1 + y2.

I want to regress y on x1 and x2. I also want to regress each one of y1
and y2 on the same explanatory variables x1 and x2 to assess their
effect on each sub-component of y. If I typed

1. reg y x1 x2
2. reg y1 x1 x2
3. reg y2 x1 x2

then I would have no guarantee that the estimated coefficients in
regressions 2 and 3 on the individual components of y (i.e. y1 and y2)
are compatible with the estimated coefficient on the aggregate
dependent variable y. As far as I understand I can ensure compatibility
by estimating the model: (with constraints)

When there are linear relations between the dependent variables, one
cannot estimate a full system. That is well-known when, e.g., the dep
vars add up to 1, as in the case of budget or portfolio shares. But it
is true here too, and if you think about it it must be so. This is not
reg3, in the sense of 3SLS, since there are no instruments; it is
really SURE. But you can't do SURE on this problem (which is why I'm
capturing the result; otherwise it would stop). On the other hand, you
don't need to use a systems estimator and constraints (and we know that
SURE with identical regressors is the same as . Check out the degree to
which the coefficient vector on model 1 compares with the sum of the
coefficient vectors on models 2 and 3. That is not by chance.

Kit

webuse klein,clear
capt noi sureg ( wagepriv consump yr) ( wagegovt consump yr) ( wagetot
consump yr)
reg  wagepriv consump yr
mat p = e(b)
reg  wagegovt consump yr
mat g = e(b)
reg  wagetot consump yr
mat t = e(b)
mat check = t - p - g
mat list p
mat list g
mat list t
mat list check

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