138 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 
J) ™ 
if not, omit it and proceed to the next lower-numbered instru- 
ment. 
Continue in this way. At every step, a given instrument is 
tested to see whether it contributes significantly to multiple 
correlation in the presence of all instruments which are a priori 
preferred to it and all other instruments which have already 
passed the test. When all instruments have been so tested, 
the ones remaining are the ones to be used. 
6.4. Discussion of the Rules 
The point of this procedure (or the variants described be- 
low) is to replace the right-hand endogenous variables in the 
equation to be estimated by their regression-calculated values 
using instruments which satisfy the causal criterion as well 
as possible while keeping inconsistency at a tolerable level. 
Certain features require discussion. 
In the first place, multicollinearity at this stage of the pro- 
ceedings is automatically taken care of in a way consistent 
with the causal criterion. If some set of instruments is highly 
collinear, then that member of the set which is least preferred 
on a priori grounds will fail to reduce correlation significantly 
when it is tested as just described. It will then be omitted 
and the procedure guarantees that it will be the least preferred 
member of the set which is so treated. If the B-ordering is used, 
this will be the one most distantly structurally related to the 
endogenous variable which is to be replaced. Multicollinearity 
will be tolerated where it should be, namely, where despite its 
presence each instrument in the collinear set adds significant 
causal information. 
Second, it is evident that the procedure described has the 
property that no variable will be omitted simply because it is 
highly correlated with other variables already dropped. If two 
variables add significantly to correlation when both are present 
61 Fisher - pag. 54