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., Université de Montréal, 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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