Re: st: Effects of Restrictions on R2

[Richard Williams <Richard.A.Williams.5@ND.edu>]

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
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