SERIES CORRELATED WITH EXPENSES 249 
on borrowed money and this series are of the inverse or negative 
type. Similar inverse relations are present when the positions of 
the correlated series are reversed—that is, when salaries and 
wages are made the dependent and ratios of interest and discounts 
on borrowed money the independent variable. The explanation 
of the relation in the first case holds for that in the second. 
Moreover, in the discussion of the nature and degree of corre- 
lation obtaining between interest on deposits and interest and 
discounts on borrowed money—the first being the independent 
and the second being the dependent variable—it was found that 
the relations are negative or inverse. When the positions of the 
series are reversed as to the type of variable, the same relations 
hold. The explanation found for the type of association in the 
first case also applies in the second case. It will be recalled that 
the causal order extends through investments and time deposits. 
Accordingly, it is instructive to observe the type of correlation 
found between ratios in each of these series—district differences 
being paired—and ratios of interest and discounts on borrowed 
money. It is apparent from Table 147 that the correlation is 
negative for both series. 
It is difficult briefly to summarize the findings of this chapter, 
and only those relating to series correlated with the total expense 
seem to require restatement. 
For the collective member banks by districts, it tends to be true, 
as shown in Table 148, that whenever and wherever® ratios of 
total expense to earning assets are relatively high or are increas- 
ing from year to year, both time deposits and gross earnings, as 
percentages of earning assets, are high or are increasing. Con- 
versely, if the former are low or tend to decrease, the latter are 
also low and tend to decrease. On the other hand, if ratios of 
total expense, expressed in this form, are high, ratios of invest- 
ments to earning assets tend to be low, and vice versa. Moreover, 
if ratios of total expense to earning assets are high, they also tend 
to be high in relation to gross earnings. In a word, high or low 
ratios of total expense are associated with high or low ratios of 
lime deposits and of gross earnings, and with low or high ratios 
of investments. 
8 “Whenever” refers to ratios in any one of the years 1919 to 1925, or to the 
percentage changes in the respective ratios from year to year. “Wherever” refers 
to the respective Federal Reserve districts.