The Regrettable Loss of Mathematical Molding in Econometrics - Mechanism and Causality in Biology and Economics - page 59

view of the role of mathematics is the Cowles Commission econometric approach.
The Cowles Commission view (see, e.g., Christ 1994 ) was that to understand a
particular aspect of economic behavior, it is necessary to have a system of descrip-
tive equations. These equations should contain relevant observable variables, be
of known form (preferably linear), and have estimatable coefficients. However,
“little attention was given to how to choose the variables and the form of the
equations; it was thought that economic theory would provide this information in
each case” (Christ 1994 , p. 33). This position was explicitly expressed by Tjalling
Koopmans, director of the Cowles Commission, in a paper jointly written with
Herman Rubin and Roy B. Leipnik, “Measuring the Equation System of Dynamic
Economics.”
The analysis and explanation of economic fluctuations has been greatly advanced by the
study of systems of equations connecting economic variables. The construction of such a
system is a task in which economic theory and statistical method combine. Broadly
speaking, considerations both of economic theory and of statistical availability determine
the choice of the variables. (Koopmans et al. 1950 , p. 54)
However, before what is called the Probabilistic Revolution in econometrics,
identification of causal relations was not a matter of economic-theoretical and
statistical significance alone. Mathematical molding was considered as an essential
tool in finding significant causal factors. According to Ragnar Frisch's ( 1933a )
original econometric ideal, all three “viewpoints,” economic theory, statistics, and
mathematics, were necessary, but not by themselves sufficient: “It is the unification
of all three that is powerful. And it is this unification that constitutes econometrics”
(Frisch 1933a , p. 2).
This founding ideal of the Econometric Society, that is, the union of mathemat-
ics, economics, and statistics, however, was lost in later econometric-modeling
practices. In the 1940s, mathematical molding disappeared from the econometric
scene, as Mary Morgan describes in her History of Econometric Ideas ( 1990 ,p.264):
Between the 1920s and the 1940s, the tools of mathematics and statistics were indeed used
in a productive and complementary union to forge the essential ideas of the econometric
approach. But the changing nature of the econometric enterprise in the 1940s caused a
return to the division of labour favoured in the late nineteenth century, with mathematical
economists working on theory building and econometricians concerned with statistical
work.
Mathematical molding disappeared in the changeover from methods to specify
causal mechanisms of business cycles to methods to identify economic structures,
that is, invariant relationships underlying the workings of an economy. Mathemati-
cal molding could fulfill its role in modeling business-cycle mechanisms because of
the assumed close connection between mathematical representations of the busi-
ness-cycle phenomenon and those of the explanatory mechanism. When the econo-
metric program shifted its focus from mechanisms explaining phenomena to
uncovering structural relationships, direct feedback from the phenomenon to the
mechanism was lost, and the role of mathematical molding ceased to exist.