The Regrettable Loss of Mathematical Molding in Econometrics - Mechanism and Causality in Biology and Economics - page 72

This practice of mathematical molding was also criticized by Trygve Haavelmo,
a student of Frisch, in his ( 1940 ) paper “The Inadequacy of Testing Dynamic
Theory by Comparing Theoretical Solutions and Observed Cycles.” On the basis
of an example, Haavelmo demonstrated that “'correction' of the form of a priori
theory by pure inspection of the apparent shape of time series is a very dangerous
proceeding and may lead to spurious 'explanations'” (p. 321). The example he gave
showed that when an apparent trend, which was “not strongly justified on a priori
reasons,” is built into the model, things are often assumed to be structural, whereas
they are merely the effect of cumulation of random events and thus, in fact, are
spurious.
Haavelmo's warning against building time shapes of the variables into the model
was one of the arguments for cutting off the empirical feedback from the phenome-
non in question to modeling its causal mechanism. The paper was the basis for his
later paper on autonomy. In it he showed that when apparent shapes of time series,
like temporary trends, are confused with structure, the real explanation for apparent
changes in structure is in fact “the disappearance of spurious elements introduced
in our theory by the trend fitting” (p. 321). It should, however, be noted that
Haavelmo only discussed the danger of building in temporary appearances which
are mistaken as steady characteristics of the phenomena or, in other words, as
stylized facts about the phenomena. It would take 30 years before the strategy of
using facts about a phenomenon to assess parameter values remerged under the new
name “calibration.” This strategy could only flourish once the high-days of the
Cowles Commission approach were over.
4 Haavelmo's Probability Approach
Haavelmo's ( 1944 ) The Probability Approach in Econometrics echoed Frisch's
memorandum in many respects, in particular its terminology, but it is important to
be aware of the change in scope. There was not only a shift from linear to nonlinear
equations, and the concomitant change in mathematical technique from linear
algebra to implicit function theory, but the point of departure also differed (see
for this Aldrich 1994 , pp. 205-206). Haavelmo envisaged a situation in which the
form of the equations is given by the relevant economic theory and the unknowns
are the values of the economic structural parameters, while to Frisch all that is given
is the possibility there are one or more linear relations between the variables.
Nevertheless, Haavelmo also distinguished between the identification problem
and the autonomy problem.
The problem of identification was that “one or more of the parameters to be
estimated might, in fact, be arbitrary with respect to the system of equations”
(p. 84). This problem came down to a study of the properties of the joint probability
distribution of the random (observable) variables in a stochastic equation system.
Within this framework, two “fundamental” problems could be formulated, namely,