182 PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA -
7 =
of the first two elements of the second column. This is the
natural consequence of the necessity to start the development
by reducing consumption at the beginning. It is of course not
the Law of the Medes and the Persians that the period of suc-
cessive decreases should last two years, since the process is
subject to random fluctuations. Table 2 gives a survey of
results and reveals that 2 years is about the average period
during which consumption decreases. When there is little
random variability (0.=0.005) the individual periods of decline
are concentrated closely around this average; but for larger
standard deviations there is also more variability of the decline
periods, as could be expected. The category « other cases »
refers to those in which the period of decline is interrupted
by one or more years during which per capita consumption
increases rather than decreases; e. g., decreases in the first two
years followed by an increase in the third and a decrease in
the fourth year. The signs of changes in the fifth year and later
have been disregarded; they are negative in some isolated
cases for o.=o0.02.
Table 1 shows further that in the first decade the total log-
arithmic increase of per capita consumption is 0.1611, which
corresponds to a percentage increase of about 17. In the second
decade it is much larger: 0.6757 corresponding to a percentage
increase of almost 100. These increases, too, are subject to
random variability. A survey of the quartiles of decade growth
rates is presented in Table 3. The results show a gradual
increase of these quartiles over time. Of course, the increase
is not so regular in every individual case! This is illustrated
by Table I, which indicates that in that case the decade growth
rate decreases in the third and fourth decade. For the set of
all data generated it appears that different values of o, do not
lead to much difference as far as the median growth rates are
concerned, but they do lead to important differences in dis-
persion.
“21 Theil - pag. 18
