SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIOUE ETC. 400 
the circumstances under which such choices are likely to be 
appropriate. Most of our discussion will be in terms of the 
assumptions that must be approximately satisfied if a given 
variable is to be eligible for inclusion as an instrument. We 
thus postpone to the next section the important question of 
how the eligible candidates ought in fact to be used. Until 
further notice, then, we discuss only whether and under what 
circumstances a given single variable ought to be treated as 
predetermined. 
In general, we desire two things of a variable which is to 
be treated as predetermined in the estimation of a given equa- 
tion. First, it should be uncorrelated in the probability limit 
with the disturbance from that equation; second, it should clo- 
sely causally influence the variables which appear in that 
equation and should do so independently of the other prede- 
termined variables (®¥). If the first criterion is not satisfied, 
treating the variable as predetermined results in inconsistency; 
if the second fails, such treatment does not aid much in estim- 
ation — it does not reduce variances. In practice, these requi- 
rements may frequently not be consistent and one has to com- 
promise between them. The closer the causal connection the 
higher may be the forbidden correlation. Thus, in one limit, 
the use of ordinary least squares which treats all variables on 
the right-hand side of the equation as predetermined perfectly 
satisfies the second but not the first criterion. In the other limit, 
the use of instrumental variables which do not directly or in- 
directly causally influence any variable in the model perfectly 
meets the first requirement but not the second (3%). In general, 
one is frequently faced with the necessity of weakening the first 
requirement to one of low rather than of zero correlation and 
{(*) It should therefore be relatively uncorrelated with the other va- 
riables used as instruments so that lack of collinearity is not really a separate 
criterion. We shall return to this in the next section. 
(*) If only such variables are available for use (or if an insufficient 
number of more interesting ones are) then the equation in question is 
underidentified and even asymptotic variances are infinite. 
Fisher - pag. 25