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 equation.
 First, it should be uncorrelated in the probability limit
with the disturbance from that equation; second, it should closely
 causally influence the variables which appear in that
equation and should do so independently of the other predetermined
 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 estimation
 — it does not reduce variances. In practice, these requirements
 may frequently not be consistent and one has to compromise
 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 indirectly
 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 variables
 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