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# Re: st: Multicollinearity and Time Trends

 From "Justina Fischer" To statalist@hsphsun2.harvard.edu, statalist@hsphsun2.harvard.edu Subject Re: st: Multicollinearity and Time Trends Date Wed, 11 Apr 2012 14:47:45 +0200

```Hi Marten,

I thought similarly....

So the best way of indeitfying these three different trends in the same model would be to start the time trend with a minus sign, letting it cross the zero-line.

I'll keep this in kind for my own research....

Thanks
Justina

-------- Original-Nachricht --------
> Datum: Wed, 11 Apr 2012 14:35:44 +0200
> Von: Maarten Buis <maartenlbuis@gmail.com>
> An: statalist@hsphsun2.harvard.edu
> Betreff: Re: st: Multicollinearity and Time Trends

> On Wed, Apr 11, 2012 at 1:31 PM, Stefan Pichler  wrote:
> > I want to detrend time series data and allow not only for linear trends,
> but also for quadratic and cubic trends. Here is a minimalistic example of
> the data:
> >
> > Y...outcome variable (some randomly typed numbers)
> > year....the year of the observation
> > gen year2=year^2
> > gen year3=year^3
> >
> > gen year1=year-1950 (so that year starts from 1)
> > gen year12=year1^2
> > gen year13=year1^3
>
> > If I tell Stata: "reg Y    year    year2    year3", Stata omits
> year because of collinearity, however if I regress  "Y    year1
> year12    year13" no variable is omitted.
>
> Think of this this way: Stata can distinguish between year12 and year1
> because they are non-linearly related. This non-linearity is greatest
> near 0 (the minimum of the parabola). However, if you get further and
> further away from 0, it becomes almost linear.
>
> Consider these three graphs:
>
> twoway function y = x^2, range(1951 1960)
> twoway function y = x^2, range(1 10)
> twoway function y = x^2, range(-4.5 4.5)
>
> In the last graph it is easiest to distinguish x from its square. This
> is true for us when we look at the graph, but also for computers.
>
> Hope this helps,
> Maarten
>
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
>
> http://www.maartenbuis.nl
> --------------------------
>
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--
Justina AV Fischer, PhD
COFIT Fellow
University of Bern

homepage: http://www.justinaavfischer.de/
e-mail: javfischer@gmx.de. justina.fischer@wti.org
papers: http://ideas.repec.org/e/pfi55.html

*
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```