SEMAINE D'ÉTUDE SUR LE ROLE DE L ANALYSE ECONOMETRIQUE ETC. 
44.3 
As for instruments which are indirectly causally related tc 
the endogenous variable involved but which fail to add signific- 
antly to the correlation of the regression in question, these can- 
not be significantly correlated with the sample residual from 
that regression. One can therefore argue that the evidence is 
against their being significantly correlated with that residual in 
the probability limit. 
Such an argument can clearly be pushed too far, however. 
[f there are strong a priori reasons to believe that the excluded 
instruments should be included in view of the causal structure 
of the model, one may not want to reject correlation in the 
probability limit because multicollinearity (for the long con- 
tinuance of which there may be no structural reason) leads to 
insignificant correlation in the sample. A modified course of 
action, then, is to include in the regression for any replaced 
variable any instrument which one believes a priori to be im- 
portant in that regression and which appears either in the equa- 
tion to be estimated or in the regression for any other replaced 
variable as computed by the procedures described above (%). 
Clearly, not much is lost by doing this since the added variables 
will not contribute much to the equation in the sample. 
Alternatively, one may go the whole way towards guarding 
against inconsistency from the source under discussion and 
include in the regression for any replaced variable all instru- 
ments which appear in the equation to be estimated or in the 
regression for any other replaced variable as computed by the 
described procedures whether or not such instrument is thought 
a priori to be important in explaining the replaced variable. 
This alternative clearly eliminates the danger under discussion. 
It may, however, reintroduce multicollinearity and may in- 
volve a serious departure from the causal criterion if a prior: 
non-causal instruments are thus included. Nevertheless. it does 
f%) Omitting instruments which do mot so appear does not cause in 
~onsistencv 
> 
Fisher - pag. sc