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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