The Regrettable Loss of Mathematical Molding in Econometrics - Mechanism and Causality in Biology and Economics - page 68

the reduced form equation influenced the possible movements of the system in two
ways:

(i) The period and degree of damping of the cyclical movement are to some extent
affected by the presence of such terms.
(ii) Besides that, the cumulants introduce an additional root into the characteristic
equation, which is real and positive, giving rise to a one-sided movement. This
movement is explosive (away from the equilibrium situation) if the algebraic
sum of all coefficients of cumulation terms in the final equation [reduced form
equation] is positive; the movement is damped (gradual approach of the
equilibrium situation) if that sum is negative. (Tinbergen 1939b , p. 147)

However, the cumulants appearing in the reduced form equation were “not all,
and perhaps not even the most important of the cumulants to which the economic
mechanism gives rise in reality” (p. 149). In many other cases, cumulations could
not be distinguished from trends and so remained “hidden.” A rough estimate of the
possible effects of cumulants (including the hidden ones) showed that they would
change the dampening factor at 0.05. Because of the hidden

cumulants, the sign of the sum of the coefficients for the cumulants could not be
determined, but Tinbergen assumed that the positive real root lay somewhere
between 0.75 and 1.25, which leaves the possibility of either a dampened or an
explosive one-sided movement. The latter possibility had to be rejected for not
being in accordance with movements observed in reality. The influence of the
former on the cyclical movement would only be moderate. “To sum up, on the
ground of their small influence under (i) and our ignorance of their effect under (ii),
it seemed both advisable and justified to keep all terms containing cumulants out of
the elimination process” (p. 149). So they will not show up in the reduced form
equation. So, the result was consistent with his earlier result in his 1935 survey
paper that the sum of the coefficients of the integrals should be small (Eq. 4.10 )to
satisfy the wave conditions.
Like the integrals, nor did the two macro-econometric models contain
differentials, but for another reason. Tinbergen had changed his view on the
meaning and role of lags in the mathematical relations. In his earlier business-
cycle schemes, lags meant production lags and referred to time intervals of about
1-2 years. One of the main reasons for introducing differentials was that they
represented more immediate reactions. But in the later macro-econometric models,
lags did not have this specific economic meaning anymore; they came to indicate
time units of, for example, 1 month. If time lags are time units,

the most by

t ¼ 1, differentials

Δ

can be approximated by differences, cf. Eq. ( 4.8 ): y _ y ð t Þ y ð t 1 Þ .

3 Frisch's Memorandum

Although both volumes of Tinbergen's Statistical Testing of Business Cycle Theories
were officially published by the League of Nations in 1939, copies of Tinbergen's
research were circulated in advance in 1938. Ragnar Frisch wrote a memorandum,