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st: Constrained regression in reg3
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:
constraint define 1 [y]x1 = [y1]x1 + [y2]x1
constraint define 2 [y]x2 = [y1]x2 + [y2]x2
reg3 (y x1 x2) (y1 x1 x2) (y2 x1 x2), constr(1) constr(2)
Now my question: If y1 is the much bigger component of y than y2, are the constraints still alright or do I need to "weight" the coefficients from the regression on y1 more than the coefficients from the regression on y2 (hope this makes sense)? I presume no weighting is needed, but I need to be sure about this.
Thanks in advance for your help.
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