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exception of the zero causal order variable and those endo-
genous variables of first causal order the equations for which
have already been considered. Note that a given predetermined
variable may be of more than one causal order. Take now
those structural equations explaining endogenous variables of
second causal order. All variables appearing in such equations
will be called of third causal order except for the endogenous
ones of lower causal order, and so forth. (Any predetermined
variables never reached in this procedure are dropped from
the eligible set while dealing with the given zero causal order
variable.)
The result of this procedure is to use the a priori structural
information available to subdivide the set of predetermined
variables according to closeness of causal relation to a given
endogenous variable in the equation to be estimated. Thus,
predetermined variables of first causal order are known to
cause that endogenous variable directly; predetermined va-
riables of second causal order are known directly to cause
other variables which directly cause the given endogenous
variable, and so forth. Note again that a given predetermined
variable can be of more than one causal order, so that the
subdivision need not result in disjunct sets of predetermined
variables.
We now provide a complete ordering of the predetermined
variables relative to the given endogenous variable of zero
causal order (%!). Let p be the largest number of different
causal orders to which any predetermined variable belongs. To
each predetermined variable we assign a p-component vector.
The first component of that vector is the lowest-numbered causal
order to which the given predetermined variable belongs; the
second component is the next lowest causal order to which it
belongs, and so forth. Vectors corresponding to variables be-
(¢) I am indebted to J. C. G. Boor for aid in the construction of the
following formal description.
61 Fisher - pag. 51
