132 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA -
DS
therefore, the prime reason for avoiding multicollinearity is
that the addition of an instrument which is collinear with the
included ones adds little causal information while using up a
degree of freedom. The elimination of such multicollinearity
ought thus to proceed in such a way as to conserve causal
information. The KLOEK-MENNES proposals may result in
orthogonal combinations of instruments which are not par-
ticularly closely causally related to the included endogenous
variables. Thus such proposals may well be inferior to a
procedure which eliminates multicollinearity by eliminating
instruments which contribute relatively little to the causal
explanation of the endogenous variable to be replaced (2).
Clearly, this may involve using different sets of instruments in
the replacement of different endogenous variables. Proposals
along these lines are given below.
It may be objected, however, that such a procedure may
eliminate multicollinearity in the regression of the included
endogenous variables (other than the left-hand one of the equa-
tion) on the chosen instruments only to encounter it again when
the dependent variable is regressed on the replaced variables
and the instruments appearing in the equation. This is clearly
true (*'); it is unavoidable, however. The fact that the variables
to be replaced by combinations of instruments are all part of
the system to be estimated guarantees that they themselves
must be reasonably highly collinear and related to the included
instruments. It is impossible to reduce that kind of multicol-
linearity without introducing as instruments noise elements
which are unrelated to the included variables, and such intro-
duction clearly gains nothing. If we can secure instrumental
variables which are closely causally related to the included
variables but relativelv uncorrelated with the disturbance of a
(**) This seems to have been one of the outcomes of experimentation
with different forms of principal component analysis in practice. See Tav-
LOR [30a].
(7) It is also true of the KILOEK-MENNES Drocedures.
6] Fisher - pag. 48
