SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 
42’ 
Now, it may be thought that this result is a rather poor 
return for all the effort we have put into securing it. While 
one can certainly conceive of stronger results, the usefulness 
of the present one should not be underestimated. We remarked 
at the beginning of this section that one important desideratum 
of an instrumental variable was a close causal connection with 
the variables appearing in the equation to be estimated. In 
general, economy-wide (and most other) econometric models 
have the property that variables with low lags are often (but 
not always) more closely related to variables to be explained 
than are variables with high ones. There may therefore be 
a considerable gain in efficiency in the use of recent rather than 
relatively remote endogenous variables as instruments, and it is 
important to know that in certain reasonable contexts this may 
be done without increasing the likely level of resulting incon- 
sistency. To the discussion of the causal criterion for instru- 
mental variables we now turn. 
6. CAUSALITY AND RULES FOR THE USE OF ELIGIBLE INoTX. 
MENTAL VARIABLES 
6.1. The Causal Criterion for Instrumental Variables 
We stated above that a good instrumental variable should 
directly or indirectly causally influence the variables in the 
equation to be estimated in a way independent of the other 
instrumental variables and that the more direct is such in- 
fluence, the better. This statement requires some discussion. 
So far as the limiting example of an instrument completely 
unrelated to the variables of the model is concerned, the lesson 
to be drawn might equally well be that instrumental variables 
must be correlated in the probability limit with at least one 
of the included variables. While it is easy to see that some 
o] Fisher - pag. 43