SEMAINE D'ÉTUDE SUR LE ROLE DE L'ANALYSE ECONOMETRIQUE ETC.
an
criteria given and that it may be better to accept some incon-
sistency by using endogenous variables with lower lags. Fi
nally, after going only a few periods back, the chances are
high in practice that adding an exogenous variable with a still
higher lag adds a variable which is very highly correlated with
the instruments already included and therefore adds little inde-
pendent causal information (*). While the use of lagged
exogenous variables is therefore highly desirable, it may not
be of sufficient practical help to allow the search for instru
mental variables to end.
Whatever collection of current exogenous, lagged exogenous
and (none, some, or all) lagged endogenous variables are used
however, the multicollinearity difficulty just encountered tends
to arise. Some method must be found for dealing with it.
One set of interesting suggestions in this area has been
provided by KLOEK and MENNES (°°). Essentially, they pro-
pose using principal component analysis in various ways on
the set of eligible instruments in order to secure orthogonal
linear combinations. The endogenous variables are then
replaced by their regressions on these linear combinations
(possibly together with the eligible instruments actually ap-
pearing in the equation to be estimated), and the dependent
variable regressed on these surrogates and the instruments
appearing in the equation. Variants of this proposal are alsc
examined.
This suggestion has the clear merit of avoiding multicol-
linearity, as it is designed to do. However, it may eliminate
such multicollinearity in an undesirable way. If multicollinear-
ity is present in a regression equation, at least one of the
variables therein is adding little causal information to that
already contained in the other variables. In replacing a given
endogenous variable with its regression on a set of instruments,
Fa.
(*) This is especially likely if the exogenous variables are principally
ones such as population which are mainly trends.
(*) Kroek and MEexNEs [17]
6] Fisher - pag. 47
