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be estimated are always to be preferred to endogenous variables 
with the same lag and causal order from the same or higher 
numbered sectors. One might even go further and decide that 
all current and lagged exogenous variables of finite causal order 
are to be preferred to any lagged endogenous variable. 
However the preference ordering is decided upon, its exist: 
ence allows us to use a posteriori information to choose a sel 
of instruments for the zero causal order endogenous variable 
in the way about to be described. Once that set has been cho- 
sen, that endogenous variable is replaced by its regression on 
the instruments in the set and the equation in question estim- 
ated by least squares regression of the left-hand endogenous 
variable on the resulting right-hand variables (2). 
We use a posteriori information in combination with the 
a prior: preference ordering in the following manner. Suppose 
that there are T observations in the sample. Regress the zero 
causal order endogenous variable on the first T-2 instruments 
in the preference ordering (a regression with one degree of free- 
dom). Now drop the least preferred of these instruments from 
the regression. Observe whether the multiple correlation of 
the regression drops significantly as a result. (The standard 
here may be the significance level of R? or simply its value 
corrected for degrees of freedom.) If correlation does drop 
significantly, then the T-2nd instrument contributes significantly 
to the causation of the zero order endogenous variable even in 
the presence of all instruments which are a priori more closely 
related to that variable than it is. It should therefore be retain- 
ed. If correlation does not drop significantly, then the variable 
in question adds nothing and should be omitted. 
Now proceed to the T-3rd instrument. If the T-2nd instru- 
ment was retained at the previous step, reintroduce it; if not, 
leave it out. Observe whether omitting the T-3rd instrument 
reduces the multiple correlation significantly. If so, retain it, 
(2) An important modification of this procedure is described below 
‘61 Fisher - pag. 53