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Re: st: Multicollinearity and Time Trends

From   Maarten Buis <>
Subject   Re: st: Multicollinearity and Time Trends
Date   Wed, 11 Apr 2012 14:35:44 +0200

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 L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen

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