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st: Effects of Restrictions on R2


From   "Erasmo Giambona" <e.giambona@gmail.com>
To   statalist <statalist@hsphsun2.harvard.edu>
Subject   st: Effects of Restrictions on R2
Date   Mon, 13 Aug 2007 13:58:33 +0200

Dear statalisters,

I am estimating two modes using the same sample (about 10,000 observations):

A: Yi= a1+ a2 Xi2+a2 Xi3 + a3 Xi4 + ei - the estimates on X2 and X3
are restricted to be the same (RESTRICTED MODEL)

B: Yi= a1+ a2 Xi2+a3 Xi3 + a4 Xi4 + ei - the coefficients on X2 and X3
are NOT restricted to be the same (UNRESTRICTED MODEL).

I understand from Jan Kmenta, Elements of Econometrics, Macmillan
(1971), pp: 448-449 that the R2 for the unrestricted model will always
be higher. What I don't understand is whether the R2 can be
significantly higher if the unrestricted coefficients are
significantly different from the restricted coefficients. Indeed, my
unrestricted coefficients are significantly different from the
restricted coefficients and yet the R2's are almost identical. I find
this result puzzling.

Any help is appreciated.

Erasmo
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