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Re: st: Effects of Restrictions on R2


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Effects of Restrictions on R2
Date   Mon, 13 Aug 2007 10:08:22 -0500

At 06:58 AM 8/13/2007, Erasmo Giambona wrote:
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).
The simplest approach is to run the unrestricted model and then give the command

test X2 = X3, coef


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.
With 10,000 cases, it doesn't take much for a difference in coefficients to be statistically significant.


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Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
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EMAIL: Richard.A.Williams.5@ND.Edu
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