SERIES CORRELATED WITH DEPOSITS 199 
total deposits, are invariably opposite. This condition, however, 
does not necessarily hold when the deviations by type are clas- 
sified into percentage groups, and when the net deviations or 
year-to-year changes are calculated,” although it is required for 
the averages of all plus and minus deviations.? 
Moreover, since for any district, if the ratio of demand deposits 
to total deposits is above, the corresponding ratio of time deposits 
to total deposits is below the district average, it follows that the 
average net deviation in any series paired with demand deposits 
above the district level is the same as the net deviation in that 
series paired with the time deposits below the district level.? 
Similar relations hold for net year-to-year changes and net devia- 
tions from yearly averages. Accordingly, having determined 
the net deviations and year-to-year changes in a number of series 
paired with variable amounts of demand deposits in terms of 
total deposits, it is unnecessary to discuss at length similar rela- 
tions between these same series and variable time deposits. 
Table 121, for each of a number of series of bank data, gives 
the net deviations from the seven-year district levels obtaining 
in districts having ratios of time deposits to total deposits deviat- 
ing by sign and classified percentage amounts from the corre- 
sponding levels. The relations here shown are, in general, and 
as is indicated above, the reverse of those given in Table 111, but 
differ for certain of the dispersion groups. It will be observed 
that total expense is expressed in units of earning assets and of 
gross earnings, and that when time deposits are high or low, such 
expense is high or low, respectively, as thus measured. These 
are the relations for the country as a whole, the correlations 
applying to yearly district ratios relative to the levels obtaining 
for the period 1919-1925. Do such relations hold for groups 
of banks in any one district? Fortunately, an answer to this 
question is available from studies made by the Federal Reserve 
Bank of Boston for member banks in the Boston district. 
Table 122 shows the ratios!® of total expense to gross earnings 
for all member banks in the Boston Federal Reserve District, 
T As witness the detail, for instance, for total expense in Tables 111 and 121. 
8 Compare the respective totals in Tables 111 and 131. 
? See the total sections for ratios of total expense in Tables 111 and 121. 
10 These percentages are not arithmetic averages, but are reported to be those 
which are “most nearly typical of the greatest number of banks.”