Biology Reference
In-Depth Information
Haavelmo distinguished between two different notions of “influence,” namely,
“potential influence” and “factual influence.” Let
y
be a theoretical variable defined
as a function of
n
independent “causal” variables
x
1
,
x
2
,
...
,
x
n
:
y
¼
Fx
1
; ...;
ð
x
n
Þ
(4.13)
Both notions of influences can be clarified by the following equation:
y
¼
F
1
Δ
x
1
þþ
F
n
Δ
x
n
(4.14)
Δ
, indicate a change in magnitude. The terms
F
i
indicate how much
y
will change due to a change in magnitude of factor
x
i
.
Then “potential influence” of the factor
x
i
upon
y
can be represented by
F
i
. Thus,
“for a given system of displacements
The deltas,
Δ
x
n
, the potential influences
are, clearly, formal properties of the function
F
” (pp. 23-24). The “factual
influence” upon
y
of the variable
x
i
can be represented by
F
i
Δ
x
1
,
x
2
,
...
,
Δ
Δ
Δ
x
i
.
6
According to Haavelmo, this distinction between potential and factual influence
was fundamental.
For, if we are trying to explain a certain observable variable,
y
, by a system of causal
factors, there is, in general, no limit to the number of such factors that might have a
potential
influence upon
y
. But Nature may limit the number of factors that have a
nonnegligible
factual
influence to a relatively small number. (Haavelmo
1944
, p. 24)
,
x
n
) (see Eq.
4.13
) explains the actual
observed values of
y
, provided the factual influence of all the unspecified factors
together were very small as compared with the factual influence of the specified
factors
x
1
,
Thus, the relationship
y
¼
F
(
x
1
,
...
,
x
n
.
This might be the case even if (1) the unspecified factors varied considerably, provided their
potential influence was very small, or if (2) the potential influences of the unspecified
factors were considerable, but at the same time these factors did not change much, or did so
only very seldom as compared with the specified factors. (Haavelmo
1944
, p. 25)
However, “our greatest difficulty in economic research” does not lie in
establishing simple relations, but rather in the fact the empirically found relations,
derived from observation over certain time intervals, are “still simpler than we
expect them to be from theory, so that we are thereby led to
throw away
elements of
a theory that would be sufficient to explain apparent 'breaks in structure' later”
(p. 26). This was the so-called problem of autonomy of economic relations. Some of
these relations have very little autonomy because their existence depends upon the
simultaneous fulfillment of a great many other relations. Highly autonomous
relations were those that “describe the functioning of some parts of the mechanism
irrespective
of what happens in some
other
parts” (p. 28). This was the “principal
...
6
In Boumans (
2005
), it is shown that Haavelmo's definitions of potential and factual influences
can be represented in this way.
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