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...
-----Original Message-----
From: Marcello Pagano [mailto:[email protected]]
Sent: Wednesday, October 13, 2004 10:55 PM
To: [email protected]
Subject: Re: st: RE: Multicollinerity test in IV regression
Oops. My apologies. That should read if X1-X2=0 , then drop both
and introduce X1+X2. Of course, what Austin says is correct.
What the argument here is, and I heard this from John Tukey, is if
basically both X1 and X2 seem to be measuring the same thing based
on this sample region, why be forced into a choice where you might
choose the wrong one (as judged by future experimentation).
m.p.
Nichols, Austin wrote:
>Um... if X1+X2=0 then the coefficient on (X1+X2)
>must be indeterminate, no?
>
>See
>_______________________________
>Dufour, J.-M. and M. Taamouti (2003),
>"Projection-Based Statistical Inference in Linear
>Structural Models with Possibly Weak Instruments",
>Discussion Paper, C.R.D.E., Universit� de Montr�al, 42 pages
>_______________________________
>for another approach to possibly collinear X's
>
>-----Original Message-----
>A better solution might be to replace all offending predictors
>by (a) linear combination(s) that make sense. For example if
>X1+X2=0, then drop both X1 and X2 and replace them with the
>new variable X1+X2. You can extend this to the more general
>situation.
>
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