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Re: st: Effects of Restrictions on R2


From   "Erasmo Giambona" <e.giambona@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Effects of Restrictions on R2
Date   Mon, 13 Aug 2007 18:02:33 +0200

Dear Olga and Richard,
Thanks for your help. One is is still unclear to me. I get
unrestricted coefficients which are statistically different and also
much different in size (from the restricted ones) but with very
similar R2. Would that mean that although the coefficients appear
different for the two models, they are statistically
indistringuishable from each other?
Thanks,
Erasmo

On 8/13/07, Richard Williams <Richard.A.Williams.5@nd.edu> wrote:
> 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.
>
>
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
> OFFICE: (574)631-6668, (574)631-6463
> HOME:   (574)289-5227
> EMAIL:  Richard.A.Williams.5@ND.Edu
> WWW:    http://www.nd.edu/~rwilliam
>
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