The Regrettable Loss of Mathematical Molding in Econometrics - Mechanism and Causality in Biology and Economics - page 67

The requirement was that the parameters satisfy the “wave condition” and the
“long wave condition.” The “wave condition” required that the solution to the
above reduced form equation is a sine function, p ( t )

t sin (

t ), so that the time
shape of p ( t ) is cyclic. The “long wave condition” prescribed that the cycle period
should be long compared with the “time units” and that the cycle should not differ
“too much from an undamped [ sic ] one” (p. 280). According to Tinbergen, “these
conditions will be a guide in a statistical test of the different schemes as to their
accord with reality” (p. 280). As a first approximation to these conditions,
Tinbergen put λ ¼ 1 and ω ¼ 0. Then the period of the cycle, 2 π

¼ C λ ω

/ ω , goes to infinity.

Both conditions taken together implied that:

X

n

c i ¼ 0 (4.10)

1

In other words, mechanisms “only then lead to long, not too much damped
waves when the integral terms are of small importance” (p. 281).
Tinbergen considered several mechanisms for their ability to explain the busi-
ness cycle. The wave conditions defined the restrictions on the parameter values.
But to find out whether these possible mechanisms “can explain real business cycles
and which of them resembles reality” (p. 281), statistical verification, however, was
the necessary next step in the analysis.
Tinbergen's research program in the first half of the 1930s can be briefly
characterized as a combination of two methods, mathematical molding and
statistical verification. Mathematical molding generated potential business-cycle
mechanisms, which had to be identified empirically. But also in his subsequent
work in the 1930s, when he built the two very first macro-econometric models,
mathematical molding was part of the modeling process, although less prominent.
The first macro-econometric model was his 1936 model of the Dutch economy. The
second was developed when he was commissioned by the League of Nations to
undertake statistical tests of the business-cycle theories, published in a two-volume
work, Statistical Testing of Business-Cycle Theories ( 1939a , b ). The first volume
contained an explanation of a method of econometric testing and a demonstration,
using three case studies, of what could be achieved. The second volume contained a
model of the United States economy.
The procedure he employed to test existing business-cycle theories consisted of
two stages. Firstly, the variables that a given theory provides must be tested by
multiple regression analysis, and, secondly, the system of numerical values found
for the causal relations must be tested to see whether it really yields a cyclic
movement when used in the reduced form equation.
Mathematical arguments played a crucial role in the assessment of whether
integrals should be built into the model or omitted. This assessment was rather
similar to his 1935 discussion of whether integrals should be part of a business-
cycle mechanism or not. It appeared that the integrals, now called “cumulants,” in