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st: constraints in reg3


From   Kit Baum <kitbaum@mac.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: constraints in reg3
Date   Wed, 25 Aug 2004 16:45:11 -0400

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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