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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28

5)
Vas

where x, is the savings ratio in the year preceding the first
(which is taken as given from the past). Note that all R-elements
 above the diagonal should necessarily vanish, because
they represent the effect of controlled variables (x,) on earlier
noncontrolled variables (y, with #<#). The diagonal elements
specify the effectiveness of controlled variables on noncontrolled
 variables in the same year, and the elements below
the diagonal represent lagged effects.
It was stated above that we are interested in minimizing
the sum of squares of the discrepancy between actual and
desired rates of increase of the logarithm of per capita consumption.
 This amounts to minimizing y’y. But this will be
amended to the effect that we shall also be interested in moderate
 changes of the savings ratio, the argument being that
a savings ratio of 209%, last year followed by one of 15%, this
year and then of 259, next year is difficult to realize. To
handle this, we introduce the sum of squares of the successive
differences of the savings ratio:

4
Uh

J

-

+,

D
0
D
I

x — 200% + X2 —

— mn _ ' 2
— x Ar 2x ex + x;

7] Theil - pag. 8