128 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA -

2

causal connection must therefore exist, the question naturally
arises of why it must be one in which the instrumental variables.
cause the included ones. If correlation is all that matters,
surely the causal link might be reversed or both variables influnced
 by a common third one.
This is not the case. Consider first the situation in which
the proposed instrumental variable is caused in part by variables
 included in the model. To the extent that this is the
case, no advantage is obtained by using the proposed instrumental
 variable over using the included variables themselves.
Obviously, the included variables are more highly correlated
with themselves than with the proposed instrument. Further,
correlation with the disturbances will be maintained if the proposed
 instrument is used. To the extent that the proposed
instrument is caused by variables unrelated to the included
variables, correlation with the disturbances will go down, but
so also will correlation with the included variables.
The situation is similar if the proposed instrumental variable
and one or more of the included ones are caused in part by
a third variable. In this case, it is obviously more efficient to
use that third variable itself as an instrument, and, if this is
done, no further advantage attaches to the use of the proposed
instrumental variable in addition. (The only exception to this
occurs if data on the jointly causing variable are not available.
In such a case, the proposed instrument could be used to
advantage.)
In general, then, an instrumental variable should be known
to cause the included variables in the equation, at least indirectly.
 The closer is such a causal connection the better. As
can easily be seen from our discussion of block-recursive
systems, however, in many cases the closer is that connection
the greater the danger of inconsistency through high correlations
 with the relevant disturbances. In such systems, for
example, current endogenous variables in low-numbered sectors
directlv cause current endogenous variables in high-numbered

‘61 Fisher - pag. 44