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AW: st: RE: Goodness of fit measure akin to R-squared for 0-constant or noconstant


From   "Martin Weiss" <martin.weiss1@gmx.de>
To   <statalist@hsphsun2.harvard.edu>
Subject   AW: st: RE: Goodness of fit measure akin to R-squared for 0-constant or noconstant
Date   Fri, 24 Apr 2009 15:45:30 +0200

>> 

"0 growth of GDP should be on pure economic grounds equal 0 growth in
jewellery demand"


Just out of curiosity, and somewhat unrelated to Stata: Why is that, and
what kind of "pure economic ground" are you referring to (who inhabits this
ground)? Why could a country not stand still overall, and its rich
inhabitants still demand more jewellery? Maybe I am missing somthing very
fundamental, but Germany certainly stood almost still in the 1990s, and yet
you would not have been able to tell from the number of newly opened
jewellery shops. 

I do understand that a (closed) economy can only consume what it produces,
but why can the share of jewellery in the consumption mix not increase while
the overall sum of consumable output does not grow? Maybe this economy
invested a little less, and instead chose to live it up with jewellery?


HTH
Martin


-----Ursprüngliche Nachricht-----
Von: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Bas de Goei
Gesendet: Freitag, 24. April 2009 15:34
An: statalist@hsphsun2.harvard.edu
Betreff: Re: st: RE: Goodness of fit measure akin to R-squared for
0-constant or noconstant

oops...well, I should have been clearer indeed. You're right that it
is supposed to be growth of GDP predicting growth of Jewellery demand.

0 growth of GDP should be on pure economic grounds equal 0 growth in
jewellery demand, or at least never positive - the forecast resulting
from this corresponds very well with our expectations on where it
would sit amongst other countries.

Durbin Watson has been defined without intercept (as far as I
understand), but you'd have to use a different table for the upper and
lower bound. Please see here for a reference:

http://www.nd.edu/~wevans1/econ30331/Durbin_Watson_tables.pdf

I re-calculated R-squared with Kvalseth's preferred method (see
reference below: thanks Nick), which works fine for normal OLS without
a constant.

I am now trying to make it work with the AR(1) regression that results
from the Prais command in Stata. I have some problems with how to
treat the Rho in Kvalseths formula. Any ideas?



On Fri, Apr 24, 2009 at 1:10 PM, Nick Cox <n.j.cox@durham.ac.uk> wrote:
> I don't understand the substantive reasoning here, as regressing GDP on
> demand for jewellery seems a backward way to predict the latter. Perhaps
> "on" has a differing meaning here. Or perhaps you mean GDP growth and
> jewellery demand growth: your posting appears contradictoru on this and
> in any case is not very clear to me.
>
> On general grounds the origin of zero GDP and zero jewellery demand
> would seem likely to be a long way away from the bulk of the data!
>
> On one very specific and one very general technical point:
>
> My recollection is that the Durbin-Watson test is only defined for a
> model with intercept, but I can't find chapter and verse for that
> possibly garbled memory.
>
> Although its title is not your exact question, the material in
>
> FAQ     . . . . . . . . . . . . . . . . . . . . . . . Do-it-yourself
> R-squared
>        . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .  N.
> J. Cox
>        9/03    How can I get an R-squared value when a Stata command
>                does not supply one?
>                http://www.stata.com/support/faqs/stat/rsquared.html
>
> has much bearing on your situation.
>
> It pushes various simple ideas. Here's one: in many models, and yours
> seems to be among them, it is simple and natural to think of
>
> correlation between observed and predicted
>
> or its square as one measure of model merit. Naturally, _no_ single
> measure can ever tell the complete story.
>
> Nick
> n.j.cox@durham.ac.uk
>
> P.S. later contributions to this thread mentioned a paper without ever
> giving a proper full reference. Here it is:
>
> Kv{\aa}lseth, T.O. 1985. Cautionary note about $R^2$. American
> Statistician 39: 279-285.
>
> Bas de Goei
> ===========
>
> I am currently creating forecasts for jewellery demand in India by
> regressing GDP on demand for jewellery.
>
> Let me first give the required background:
> I have data going back to 1980. In a regression based on GDP over
> time, you obviously run into the problem of serial autocorrelation,
> though this is neccesarily a problem for a forecast, my boss wants
> "only regressions that pass Durbin Watson test".
>
> I really have two problems:
>
> The first is that the normal OLS regression result indicated a
> positive intercept. However, economically this would mean that even
> when there is no growth in GDP, there would still be growth in the
> demand for jewellery. Of course, there was the problem that the model
> did not pass the Durbin Watson test. Fitting the model with the GLS
> approach (the prais command in Stata), did improve the model, but it
> kept (as expected) the intercept positive.
>
> I decided to inspect the data more closely, and to drop two outliers
> from the data. The intercept under the Prais command is now still
> positive, but it has become insignificant. I decided that there is
> justification to re-run the regression with a 0 intercept. However,
> this balloons the F statistic and the R-squared. I now understand why
> that is, given the mathematics behind the R squared calculation.
>
> My question is, how would you calculate in Stata a "correct" or
> "alternative" R-squared, or a goodness of fit measure, which you can
> use to compare it to the model with a constant??
>
>
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