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U n em p lo ym en t Seasonals
The economic data we use general­
ly are seasonally adjusted, thus al­
lowing us to make a direct compar­
ison of, say, a July figure with one
from last February. Adjustment is
especially important for series with
large seasonal movements, such as
the closely-watched unemploy­
ment rate—the total number of
unemployed as a percentage of the
civilian labor force. The series be­
came even more closely watched
last week, when the Bureau of La­
bor Statistics reported that it had
turned upward after a prolonged
year-long decline.
Actually, the seasonally adjusted
unemployment series has moved
through three distinct phases over
the past year—a high plateau close
to the recession peak of 8.9 percent
from May through November of
1975, a steep drop last winter to 7.5
percent in March 1976, and finally
an increase from 7.3 to 7.5 percent
this June. Some observers have at­
tributed most of the puzzling
movement in this series to difficul­
ties with seasonal factors—rightly
so, it would seem, in regard to the
accelerated decline reported early
this year. (An alternate approach
shows the drop taking place at a
steadier pace and over a longer
period, from November 1975
through May 1976, rather than the
reported steep drop from Novem­
ber through March.) In contrast,
the lengthy period of stability after
the recession peak probably did
occur just as reported. As for the
June increase reported last week, it
seems to reflect an essentially un­
solvable problem in setting the
month's seasonals.
1



Unadjusted unemployment

Seasonal movement in unemploy­
ment is dominated by three factors:
the weather, Christmas, and the
school schedule. The highest un­
employment rates occur in January
and February; the lowest are in
September and October. Thus, for
the entire 1948-75 period, the over­
all jobless rate averaged 4.94 per­
cent, but the monthly rates on an
unadjusted basis ranged between
5.69 percent (February) and 4.26
percent (October). This difference
reflects basically the influence of
the weather on outdoor activities,
although the low numbers in the
fall also indicate the return of tem­
porary labor-force members to
school.
Superimposed on this cycle are two
very sharp seasonal swings. From
December to January, the unadjust­
ed unemployment rate increases by
an average of .88 percentage point,
from 4.69 to 5.57 percent, as a result
of post-Christmas layoffs of tem­
porary workers. From May to June,
the rate increases by an average of
.78 percentage point, from 4.59 to
5.37 percent, as a result of increased
jobseeking at the end of the school
year. (These are the average swings
of the 1948-75 period, which of
course are not repeated in every
single year.) In both cases, the addi­
tion to the rate is absorbed over
roughly a four-month span by a
combination of added seasonal em­
ployment and decreased jobseek­
ing by temporary workers. The
months which present difficult ad­
justment problems—primarily Jan­
uary, February and June—are the
( c o n t in u e d o n p a g e 2 )

Opinions expressed in this newsletter do not
necessarily reflect the views of the management of the
Federal Reserve Bank of San Francisco, nor of the Board
of Governors of the Federal Reserve System.

ones most strongly affected by large
seasonal swings or by shifts in un­
derlying factors such as weather.
Constructing seasonals

To handle these problems, seasonal
adjustments may be made in either
of two ways—additive or multipli­
cative. In the additive approach, the
unadjusted unemployment rate is
adjusted each month by the differ­
ence between the average monthly
figure and the average annual
figure—in February's case, by add­
ing -.75 percent, or the difference
between the 5.69-percent historical
February average and the 4.94percent annual average for 1948-75.
In the multiplicative approach, the
unadjusted rate is adjusted each
month by the ratio of the monthly
seasonal and the monthly long­
term average—in February's case,
by using a blow-up factor of -13.2
percent, or -.75 percent divided by
5.69 percent.
The standard seasonal adjustment
program—the Census X-11
program— is basically a complex
multiplicative mechanism which al­
lows for continuously shifting sea­
sonals. Yet despite the sophistica­
tion of this and other approaches,
seasonal adjustment remains more
of an art than a science. Choices
must be made among the various
alternative approaches that are

2




available, and arbitrary decisions
must be made regarding the stabili­
ty of actually observed seasonal
movements—so that different stat­
isticians can reach strikingly differ­
ent conclusions about any single
month's adjustment.
The two basic approaches, additive
and multiplicative, will yield similar
results in those months which ex­
hibit little seasonal movement—or
in those months where a series
fluctuates around its mean, with
little deviation from its trend line.
Differences occur in the more ex­
treme cases, however. With an ad­
ditive adjustment, the amount of
adjustment is assumed to be con­
stant; with a multiplicative adjust­
ment, the amount of adjustment is
assumed to be proportional to the
distance of the series from the
mean. For example, multiplicative
seasonals imply that in a recession,
when unemployment is high, larger
than normal swings occur in sea­
sonal unemployment—a somewhat
questionable assumption. This ap­
proach says, quite reasonably, that
unemployment will be abnormally
high in a recession January or Feb­
ruary, but it also says that the ab­
sorption of that unemployment will
be abnormally rapid in the follow­
ing March and April. While we
might expect a limited amount of
behavior of this type, the major
share of any seasonality in the
unemployment rate would normal­
ly be additive.

Considerations of this kind thus
should influence the selection of an
adjustment method. As a rule of
thumb, variables that grow over
time (such as GNP) usually require
seasonals that also grow—that is,
multiplicative adjustment. But vari­
ables that do not grow (such as the
unemployment rate) usually re­
quire additive seasonals because of
the peculiar cyclical implications of
multiplicative adjustment.
Additive adjustments

Some new light is thrown on the
nation’s jobless data when we com­
pare an additive approach with the
standard multiplicative approach
(the Census X-11 program) that is
utilized in the monthly series pub­
lished by the Bureau of Labor Statis­
tics. Actually, the two series have
moved closely together through
most of the 1974-76 period. Still,
several differences have occurred
which might help explain some of
the puzzling movements in the data
over the past year. In this exercise,
three-month moving averages were
used to smooth the series and
thus limit the effect of statistical
“ noise.”
Most of the monthly figures were
largely impervious to method of
adjustment, showing once again
that some months have far more
reliable seasonal patterns than oth­
ers. But the February figure, when
additively adjusted, was 0.4
percentage point higher than the

3




published figure in each of the last
two years—8.5 percent in 1975 and
8.0 percent in 1976. The difference
resulted from the tendency of mul­
tiplicative methods to produce very
large (downward) adjustments to
extreme months containing very
high unemployment. The effect was
highlighted in the moving average
series, since the February moving
average contains the two months
(January and February) with the
largest seasonals. The standard mul­
tiplicative adjustment thus pro­
duced a slower rise to the recession
peak than the additive adjustment
method, and compressed most of
the recent decline in the rate within
a relatively brief period.
Another major anomaly was the
change occurring in the May-toJune seasonal pattern over the past
several decades. The swing in the
unadjusted data from May to June
rose from an average 0.4 percent in
1948-56 to 0.8 percent in 1957-63
and then to 1.2 percent in 1964-75.
As a result, any adjustment method
is forced to incorporate both the
large size of the annual May-June
swing and the (hard to measure)
shift in that swing over time. We
should thus take the unexpected
June 1976 increase in published
unemployment with a grain of salt
until the more trustworthy July and
August data arrive.
Larry Butler

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BANKING DATA—TWELFTH FEDERAL RESERVE DISTRICT

(Dollar amounts in millions)

Selected Assets and Liabilities
Large Commercial Banks

.

Loans (gross, adjusted) and investments*
Loans (gross, adjusted)—total
Security loans

Commercial and industrial
Real estate
Consumer instalment
U.S. Treasury securities
Other securities
Deposits (less cash items)—total*
Demand deposits (adjusted)
U.S. Government deposits
Time deposits—total*
States and political subdivisions
Savings deposits
Other time deposits!
Large negotiable CD's

Weekly Averages
of Daily Figures
Member Bank Reserve Position
Excess Reserves
Borrowings
Net free(+)/Net borrowed (-)

Amount
Change
Change from
Outstanding
from
year ago
Dollar
Percent
6/30/76
6/23/76
+ 3,204
89,120
+ 391
+ 3.73
+ 471
67,459
+ 2,579
+ 3.98
1,538
34
+ 431
+ 38.93
22,482
+
90
- 639
- 2.76
20,123
+
62
+ 453
+ 2.30
+ 12.34
11,214
+ 1,232
+
50
+ 12.47
9,651
73
+ 1,070
- 445
- 3.57
12,010
7
90,438
+ 2,270
+ 4,206
+ 4.88
+ 1,047
+ 4.37
25,030
+ 1,095
+
84
+ 93.09
531
+ 256
+ 4.48
63,119
+ 699
+ 2,705
- 7.63
6,170
- 510
65
26,172
+ 5,563
+ 26.99
+ 331
+ 267
- 3.25
- 949
28,235
- 18.04
- 2,880
13,081
+ 369
Week ended
Week ended
Comparable
year-ago period
6/23/76
6/30/76

-

1
10
9

-

8
20
12

-

82
258
176

+

859

+

355

Federal Funds—Seven Large Banks
Interbank Federal fund transactions
+ 370
- 548
Net purchases (+)/Net sales (-)
Transactions of U.S. security dealers
+ 176
+
62
Net loans (+)/Net borrowings (-)
“"Includes items not shown separately, individuals, partnerships and corporations.

Editorial comments may be addressed to the editor (William Burke) or to the author . . .
Information on this and other publications can be obtained by calling or writing the Public
Information Section, Federal Reserve Bank of San Francisco, P.O. Box 7702, San Francisco 94120.
Phone (415) 544-2184.