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RE: st: RE: Multicollinerity test in IV regression

From   "Nick Cox" <[email protected]>
To   <[email protected]>
Subject   RE: st: RE: Multicollinerity test in IV regression
Date   Thu, 14 Oct 2004 16:06:25 +0100

Feel free to contradict me, or anybody else,
on any point on which there is an error on confusion. 

Getting things as near right as is humanly possible 
really matters for discerning Stata users. 

I had an interesting little example of multicollinearity
myself yesterday. As geographers, my colleague and I 
regress stuff around the compass 

z = b_0 + b_1 sin(compass direction) + b_2 cos(compass direction) 

sine and cosine as _functions_ are naturally uncorrelated 
on the circle and a good basis (pun?) for looking at 
North-South and East-West contrasts, which as everyone knows
are different in flavour. But in one case some puzzling 
results were traceable to the fact that the data for sin()
and cos() only covered about 90 degrees and were thus 
highly negatively correlated. In this case the diagnosis was 
that the model remained sensible, but that the particular 
dataset necessarily gave wobbly results. 

[email protected] 

Nichols, Austin
> I think the issue of multicollinear X's (or Z's) 
> is more complicated in IV, though I hate to 
> contradict Nick on any point, since if you have 
> two instrumental variables for two endogenous 
> regressors, the problem is not merely high-
> variance coefficient estimates but is a matter 
> of weak instruments as well.  This applies a 
> fortiori to conceptually collinear X's if you 
> will, such as two measures of school quality, or 
> what have you, that may appear by various measures 
> not to be collinear, but are both measuring the 
> same underlying variable with error (from other
> components for which the theoretical justification
> for IV may no longer apply).  The Dufour and
> Taamouti reference provides a way to deal with 
> X1-aX2(approx)=0 _and_ the Z1-bZ2(approx)=0 
> problems, though it is somewhat less satisfying
> than just dropping a regressor...

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