SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 163
the two-stage method of least squares sets the trap of overfitting
in a new disguise. The transformation (22a) tends to carry
all parameters of the entire primary form into each relation
of the reduced form (*7). Thus if there are some 3 or 4 para-
meters in each behaviour relation of the primary form, and the
primary form involves some 50 behaviour relations, each rela-
tion of the reduced form will involve some 150 parameters, far
more than the number of observations usually available. Well
to note, I am not saying that the model builders walk straight
into the pitfall of overfitting. On the contrary, from the begin-
nings of the theory of ID-systems it has been a rule to specify
each relation of the reduced form as involving all predeter-
mined variables of the entire system, and the ensuing dangers
of collinearities in the empirical parameter estimation have
been recognized for a long time (*). The specific point I wish
to make is that the risk of overfitting is tangible already with
a modest number of variables in the reduced form, owing to
autocorrelation and inertia effects in most or all variables of
the system. Such overfitting will blur the distinction between
an ID-system and the corresponding BEID-system, with risk
that the resulting parameter estimates will be biased. To assess
and evaluate the bias by an aprioristic analysis is extremely dif-
ficult or — at least in practice — impossible, because it leads
into overwhelming complexities even for forecasting systems
of moderate size. The approach of a predictive test will how-
ever reveal the overfitting, and thereby the test will also reveal
the difference between the ID- and BEID-systems and the
ensuing bias in the parameter estimation.
(7) Explicit illustrations are given in Ref. 13, p. 484, and with mors
detail in Ref. 27.
(*) The difficulties at issue were amply emphasized by Professor D W
JORGENSON in the oral presentation of his report. Ref. 48. to the Copenhagen
meeting of Feonometric Society. Tulv 1062
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