136 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA -
=
longing to less than p different causal orders have infinity in
the unused places. Thus, for example, if p=35, a predetermined
variable of first, second and eighth causal order will be assigned
the vector: (1, 2, 8, 00, 00). The vectors are now ordered lexico-
graphically. That is, any vector, say f, is assigned a number,
3(f), such that, for any two vectors, say f and kh:
(6.1) B(f)>B(k) if and only if either f,>h, or for some
j(I<7<P)
fi=h; G=1, …, j-I) and f.>h,.
The predetermined variables are then ordered in ascending
order of their corresponding B-numbers. This will be called the
3-ordering.
Thus predetermined variables of first causal order are assig-
ned lower numbers than predetermined variables of only higher
causal orders; predetermined variables of first and second
causal order are assigned lower numbers than predetermined
variables of first and only causal orders higher than second
(or of no higher causal order), and so forth (2).
The procedure just described gives an a priori preference
ordering on the set of instrumental variables relative to a
given zero causal order endogenous variable. This ordering
ts in terms of closeness of causal relation. Alternatively, one
may wish to modify that ordering to take further account of
the danger of inconsistency. This may be done by deciding
that current and lagged exogenous variables of a given causal
order are always to be preferred to lagged endogenous variables
of no lower causal order and that lagged endogenous variables
from sectors with lower numbers than that of the equation to
(#2) This is only one way of constructing such an ordering. If there is
specific a priori reason to believe that a given instrument is important in
influencing the variable to be replaced (for example, if it is known to
enter in several different ways with big coefficients) then it should be given
a low number. In the absence of such specific information, the ordering
given in the text seems a natural wav of organizing the structural in-
formation.
6] Fisher - pag. 52
