172 
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-ele- 
ments 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 noncon- 
trolled 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 con- 
sumption. This amounts to minimizing y’y. But this will be 
amended to the effect that we shall also be interested in mo- 
derate 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