The Regrettable Loss of Mathematical Molding in Econometrics - Mechanism and Causality in Biology and Economics - page 71

“autonomy.” These were the equations that “maintained unaltered while other
features of the structure were changed” (p. 417).
The higher this degree of autonomy, the more fundamental is the equation, the deeper is the
insight which it gives us into the way in which the system functions, in short, the nearer it
comes to being a real explanation . Such relations form the essence of 'theory'. (Frisch
1995 , p. 417)
Unfortunately, autonomy is “not like the irreducibility a mathematical property
of a closed system but is built on some sort of knowledge outside this system”

(p. 416). Passive observation only lead to coflux equations, and generally spoken
these relations are far from able to give information about the autonomous struc-
tural relations. Therefore, it is necessary to use active observation, namely, experi-
mentation, as Frisch recommended.
In his memorandum of 1938, the concept of autonomy was not further
explicated. Ten years later, Frisch gave a more explicit description of what he
meant by the idea of autonomy:
Take any equation and ask the question: is the technical and institutional setting which
surrounds it and the behaviour of the individuals involved such that this particular equation
will hold good even though other equations involving the same variables are destroyed
through technical, institutional or behaviouristic changes or through the fixation of some
specific variables in the system, for instance through a specific economic measure. This, it
seems, is the only way in which it is possible to define a 'causal' relation as distinguished
from an incidental covariation between economic magnitudes. (Frisch 1948 , pp. 368-369)

...

As we have seen above, Tinbergen used the characteristics of the business cycle
to acquire information about the causal structure: tests of mathematical significance
were used to infer the shape of the equations of the mechanism plus the relevant
causal factors. So, an essential part of the model-building process is mathematical
molding: a mathematical formalism is sought that is able to generate the relevant
characteristics of the phenomena that should be explained or described. Next, the
parameters are quantified in such a way that the model precisely picks out these
characteristics. This latter stage is called tuning. Because, in the model-building
process, mathematical molding and testing for mathematical significance are both
sides of the same coin in the model-building process, justification is built-in. In
Boumans ( 1999 ), where this argument is developed, three examples of models are
discussed of which two were built in the same period as Tinbergen's modeling
work: Kalecki's ( 1935 ) and Frisch's ( 1933b ) business-cycle model. Kalecki tuned
his parameters such that his model generated a maintained cycle with a period of
10 years. Frisch tuned the parameters such that his model generated three damped
cycles of which two had a period in accordance with the observed cycle periods.
Frisch's memorandum, however, showed that this feedback from the shape of a
business cycle to its generating mechanisms was cut off when the mechanism was
represented by difference equations instead of (mixed difference-)differential
equations. The direct and close relationship between cyclical behavior and differ-
ential equations does not exist for difference equations.