SEMAINE D’ ETUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC, 403
observations generally available relative to the number of predetermined
variables, if all lagged endogenous variables are
treated as predetermined.
In addition, if lagged endogenous variables are so treated,
then we have already seen that such treatment raises considerable
difficulties in the likely presence of serial correlation of
the disturbances. On the other hand, economy-wide models
are generally sufficiently closed to make their equations unidentifiable
if only truly exogenous variables are treated as instruments.
We shall discuss the problems raised by serial correlation
in the next section which will be concerned with the question
of how instrumental variables should be chosen in practice to
avoid inconsistency. In the present section, we shall discuss
the properties of the limited-information estimators ignoring
these problems. Such a discussion is not rendered irrelevant
by the practical difficulty of using all variables that are not
current endogenous ones as instruments when the number of
observations is relatively limited. This is so because given the
variables which are to be treated as predetermined, treatment
of all remaining variables as endogenous results in a situation
in which every known limited-information estimator has its precise
counterpart (#2). Thus, for example, if only certain lagged
endogenous and exogenous variables are to be used, replacing
every other (save the normalized one) in a given equation by
its value as computed from a multiple regression on the instruments
and then regressing the normalized variable on the resulting
variables provides the exact analogue of two-stage least
squares.
Of course. in such a situation, and especially where serial
(3) It must be admitted, however, that if different predetermined variables
are used in replacing each included endogenous variable (as suggested
below), them it is not clear how limited-information maximum likelihood
carries over to such cases. Fortunately, this will not matter for our
purposes
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