134 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 
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genous variables sufficiently far in the past that the effects of 
serial correlation are judged to be negligible over the time 
period involved. As shown in the preceding section, that time 
period will generally be shorter for endogenous variables in 
sectors lower-numbered than that in which the equation to be 
estimated appears than for endogenous variables in the same 
or higher-numbered sectors (¥). Clearly, other things being 
equal, the use of current and lagged exogenous variables is 
preferable to the use of lagged endogenous variables and the 
use of lagged endogenous variables from lower-numbered sec- 
tors is preferable to the use of endogenous variables with the 
same (or possibly even a slightly greater) lag from the same 
or higher-numbered sectors than that in which the equation 
to be estimated occurs. We shall suggest ways of modifying 
the use of the causal criterion to take account of this. For con- 
venience, we shall refer to all the eligible instrumental variables 
as predetermined and to all other variables as endogenous. 
Consider any particular endogenous variable in the equation 
to be estimated, other than the one explained by that equa- 
tion. That right-hand endogenous variable will be termed of 
zero causal order. Consider the structural equation (either in 
its original form or with all variables lagged) that explains that 
variable (). The variables other than the explained one 
appearing therein will be called of first causal order. Next, 
consider the structural equations explaining the first causal 
order endogenous variables (). All variables appearing in 
those equations will be called of second causal order with the 
(*) It will not have escaped the reader’s notice that very little guidance 
has been given as to the determination of the absolute magnitude of that 
time period. 
(°°) There must exist such an equation if the variable in question is 
normalized. As stated above, lack of such normalization is a form of in- 
complete specification. 
(*) Observe that endogenous variables appearing in the equation to be 
estimated other than the particular one with which we begin may be of 
positive causal order. This includes the endogenous variable to be explained 
by the equation to be estimated. 
‘61 Fisher - pag. 50