current adjustment, where the seasonal adjustment procedure.
is run with all available data each month and factors cannot
be published ahead of time, generally produces initial
seasonally adjusted estimates requiring smaller revisions
than those produced by adjustment using projected factors.
The BLS is continuing to evaluate concurrent adjustment for
the labor force series, and concurrently adjusted alternative
estimates for major labor force series are available to in-
terested users upon request.

Aggregation procedures

BLS maintains and publishes several hundred seasonally
adjusted labor force series in addition to the 192 directly ad-
justed series discussed above. These additional series are pro-
duced by arithmetically combining or aggregating the directly
adjusted series with each other or, in some cases, with series
on population or resident Armed Forces levels, which are
not seasonally adjusted because they are not considered to
have any significant seasonal variation. For example, the
seasonally adjusted levels of total unemployment, civilian
employment, and civilian labor force, and the seasonally ad-
justed unemployment rate for all civilian workers, are all
produced by aggregation of some or all of the seasonally ad-
justed results for the 12 major civilian labor force com-
ponents. The seasonally adjusted level of total unemploy-
ment is the sum of the seasonally adjusted levels of unemploy-
ment for the four age-sex groups—men and women 16 to
19, and men and women 20 years and over. Seasonally ad-
justed civilian employment is the sum of the seasonally ad-
justed levels of employment for the eight employment
components—the same four age-sex groups as noted above
employed in nonagricultural and agricultural industries. The
seasonally adjusted civilian labor force is the sum of all 12
components. The seasonally adjusted civilian unemployment
rate is calculated by taking the total seasonally adjusted
unemployment level as a percent of the total seasonally ad-
justed civilian labor force. For the overall labor force, the
resident Armed Forces level is added to the seasonally ad-
justed civilian labor force, and the seasonally adjusted overall
unemployment rate is, of course, calculated by taking total
seasonally adjusted unemployment as a percent of that labor
force figure.

The principal reason for producing many of the major
seasonally adjusted estimates for the labor force by aggrega-
tion rather than by direct adjustment is that this approach
ensures that the major seasonally adjusted totals will be

arithmetically consistent with at least one major set of com-
ponents. If the totals were directly adjusted along with the
components, such consistency would not, in all likelihood,
occur, since the X-11 is not a sum-preserving procedure;
that is, the sum of the result for two or more directly ad-
justed series will not generally be the same as the result of
directly adjusting the sum of the unadjusted versions of the
same series. Another factor is that it would generally be in-
appropriate to apply seasonal factors computed for an ag-
gregate series to the components of the aggregate. The
various labor force components tend to have significantly
different patterns of seasonal variation; for example, teenage
unemployment tends to peak in June, while unemployment
of adult men tends to peak in the winter months of January
and February. In order to properly estimate these varying
seasonal patterns, it is necessary to directly adjust the com-
ponents. Of course, one of the implications of producing
seasonally adjusted estimates for many major series by ag-
gregation is that exact factors cannot be projected for those
series. However, implicit seasonal adjustment factors can be
calculated after the fact by taking the ratio of the unadjusted
aggregate to the seasonally adjusted aggregate, or, for ad-
ditive implicit factors, the difference between those two
aggregates.

Availability of revised series

This issue of Employment and Earnings contains revised
data for the last 13 months and quarters for many seasonally
adjusted labor force series. Next month’s issue will provide
the 1985-89 revisions for a few hundred of the seasonally
adjusted monthly labor force series most in demand. These
revisions replace the data published in the February 1989
issue for 1985-88 and the seasonally adjusted estimates for
1989 published during the past year. Other than for those
few persons-at-work series revised back to 1978, seasonal-
ly adjusted data for 1984 and earlier years were not revised.

Additional data for any of the several hundred seasonally
adjusted labor force series, as well as the January-June 1990
factors for any of the directly adjusted series beyond the 12
major components, can be obtained from BLS upon request.
Requests for data or inquiries concerning seasonal adjust-
ment methodology or the availability of machine-readable
files of labor force data should be addressed to the Data
Development Staff, Office of Employment and Unemploy-
ment Statistics, Bureau of Labor Statistics, Washington, DC
20212.

13


Possibility of such effects occurring in such reference-period-
based series (focusing instead on series which are
accumulations over all days of each month, such as series
on sales). The at-work series on voluntary part-time and full-
time schedules are affected, however, because significant
numbers of employed persons shift from being at work to
being “‘with a job but not at work”’ in the observed data when
the CPs reference week is the week immediately before or
after Easter. This shift stems primarily from vacations and
can show up only in the data for April, the only month in
which the CPs reference week—the week containing the 12th
of the month—can be the week before or after Easter. In years
in which one of these intersections between Easter and the
CPs reference week occurs, the number of persons at work
in these categories in April tends to decrease substantially.
In other years, when the CPs reference week is further
removed from Easter, the number of persons at work in April
tends to increase, reflecting the pattern for employment in
general. The standard X-11 method averages these two very
different sets of behavior together and produces April
seasonal factors that usually do not adjust very well for either
type of behavior. The new BLS moving-holiday extension
provides a means of averaging the different types of behavior
separately and allowing the differences to be reflected in the
final seasonal factors.

The moving-holiday procedure works as follows for each
series to which it is applied. First, an initial decomposition
into trend-cycle, seasonal, and irregular components is done
with X-11 ARIMA (without ARIMA extrapolation). The
resulting initial seasonal component reflects the standard
X-11 averaging process. The deviations from this average
April seasonal component that are due to the timing of Easter
are reflected in the April values of the resulting initial
irregular component, which tend to be low for the years when
the Easter/cps-reference-week intersection occurred and high
in the years when it didn’t. The second stage of the procedure
computes averages of those April irregular values (including
acorrection for any extremes) within sets of years grouped
in ranges of Easter dates. The most appropriate ranges of
Easter dates for any given series are selected based upon
empirical analysis of the initial irregular component and upon
expert knowledge of how the economic phenomenon as
measured in the series is affected by the proximity or timing
of Easter. The average of the April irregulars within each
set becomes the estimate of the holiday effect (more precisely
the holiday effect net of the average seasonal) in April for
each of the years participating in that set. These holiday
effects then become ‘‘holiday prior-adjustment factors,”
used to prior adjust the April observations for the third stage
of the procedure, which is a second run of the series through
X-11 ARIMA (this time with ARIMA extrapolation if a model
is specified or requested). Finally, combined seasonal factors,
including the projected factors, are computed as the product
of the seasonal factors produced by the second X-11 ARIMA
run, which essentially are the average seasonals reestimated
with the net moving-holiday effect removed, and the holiday
prior-adjustment factors derived in the first two stages.
One benefit of this approach is that seasonal factors

12

for months other than those with moving-holiday effects are
only minimally affected.

Because this procedure involves creating subsets of the
irregular values for the months affected by moving holidays,
it is usually necessary to use more years for the estimation
of the holiday effect in the first two stages than typically need
to be used for the final scasonal adjustment in the third and
final stages. The extra years help to ensure that a reasonable
number of years are available for each subset. For the
estimation of the holiday effect in the three at-work series,
data back to 1967 were used for the two part-time series and
data back to 1970 were used for the series on full-time
schedules. Three subsets were used for estimating the
moving-holiday effects for these series, based on the
following ranges of Easter dates: (1) April 13-19, defining
years in which the CPs reference week for April is the week
immediately before Easter, the timing when this holiday
effect is usually strongest; (2) April 6-12, defining years in
which the cps reference week for April is the week after (and
containing) Easter, when the average effect is similar to but
not as strong as the effect for the week before; and (3) all
other dates of Easter, defining years in which the unadjusted
data are not affected by Easter.

For this year’s final seasonal adjustment of these three at-
work series, data back to 1975 were used in the third stage
of the procedure because of the need to‘revise the historically
seasonally adjusted data back to 1978, a year in which the
confounding effect of the moving holiday had been fairly
substantial in the existing seasonally adjusted data. (The more
usual practice will be to use the regular 10-year period of
data for the final seasonal adjustment of these series and
revise only the most recent 5 years:) In addition to revising
the three directly adjusted series back to 1978, the aggregated
seasonally adjusted series on the total at work in non-
agricultural industries was recomputed back to 1978 to be
consistent with the revised directly adjusted components.

Six-month updates. With respect to the seasonal adjustment
schedule for the labor force series, the current official prac-
tice involves the running of all 192 directly adjusted series
through X-11 ARIMA twice each year, after receipt of June
and December data, with 6 months of projected factors drawn
from each run and historical revisions drawn from the end-
of-year run. This practice allows, among other things, the
prior publication of seasonal factors, which historically has
been regarded by the Bureau of Labor Statistics and other
statistical agencies as an important way of ensuring the open-
ness of their seasonal adjustment procedures, especially
where very sensitive indicators such as the unemployment
rate have been involved. In recent years, a number of
research studies, including a 1987 paper on the labor force
series,? have indicated that the alternative practice of con-

2 G.R. Methé and R.J. McIntire, “‘An Evaluation of Concurrent Seasonal
Adjustment for the Major Labor Force Series," in the 1987 Proceedings
of the Business and Economic Statistics Section, American Statistical
Association; copies of a more complete version of the paper can be
obtained directly from the authors at the Bureau of Labor Statistics.



Revision of Seasonally Adjusted

Labor Force Series

* Robert J. McIntire

The purpose of seasonal adjustment is to eliminate from
economic time series the influence of weather, holidays, the
opening and closing of schools, and other such seasonal
events in order to make it easier to observe and analyze the
cyclical and other nonseasonal movements in the series. The
seasonality which the adjustment process endeavors to
eliminate is represented by seasonal factors. The seasonal
factors used for current adjustment are estimates of how much
the original unadjusted values can be expected to deviate from
underlying trend-cycle levels due to annually recurring
behavior as projected from average seasonal patterns in the
recent past. Even though seasonality involves regularly
recurring patterns, it does tend to change over time, creating
a need for periodic reestimation of factors and revision of
recently adjusted estimates. By including more recent data
in the estimation process, the revision process can provide
better estimates of how much the original, unadjusted
estimates actually deviated from underlying trend-cycle levels
during the recent period, thereby improving the historical
seasonally adjusted data for that period. In addition, the new
information is incorporated to produce the new projected
factors to be used for current seasonal adjustment.

Therefore, at the end of each calendar year, the Bureau
of Labor Statistics reestimates the ‘seasonality of the
unemployment, employment, and other labor force series
derived from the Current Population Survey by including
another full year of data in the estimation process. Based on
this annual reestimation, BLS issues the projected factors for
the first 6 months of the new year as well as revised estimates
of historical seasonally adjusted data for the last 5 years. Each
year’s data are generally subject to five revision cycles before
the values are considered final. The fifth and final revisions
in the earliest of the 5 years are usually quite small, while
the first-time revisions in the most recent year are generally
much more substantial, although even these rarely alter the
essential trends observed in the initial major estimates. This
year’s revisions incorporate data through December 1989 and
provide revised estimates for January 1985 through
December 1989 for all seasonally adjusted labor force series.
In addition, seasonally adjusted data for a few persons-at-
work series were revised back through January 1978 because
of the first-time application of a special new extension of

* Robert J. Mclntire is an economist and Chief of the Data Develop-
ment Staff in the Office of Employment and Unemployment Statistics, Bureau
of Labor Statistics.

the seasonal adjustment procedure that provides a correction
for the moving-holiday effects of Easter in such series. This
extension is discussed in more detail later in this article.

Table 1 contains the new projected seasonal factors to be
applied during the first 6 months of 1990 to the 12 component
series used in the computation of the seasonally adjusted
civilian labor force and unemployment rate. (See the section
on aggregation procedures later in the article.) Projected
factors for the last 6 months of 1990 will be estimated in
early July, based on data through June 1990, and published
in the July issue of this publication.

Effect of revisions

One of the criteria used to evaluate alternative methods
of seasonal adjustment is how close initial estimates are to
later revisions. Policymakers and analysts must make
determinations based on current information, and so it is
important that the initial estimates of current factors for the
seasonal adjustment of major economic series produce
estimates of level and change that are as close as possible
to the improved estimates that will be made after more data
have become available. Even though the revisions currently
being released for the 1989 seasonally adjusted data are not
final, the first revisions are, as mentioned above, usually the
most substantial of the five that will be made and often
indicate the direction any subsequent revisions will take.
Therefore, it is appropriate to compare these first revisions
with the initial estimates. Table 2 shows the overall and
civilian unemployment rates for 1989 as first computed and
as revised, as well as the change due to revision. Both of
the rates, rounded to one decimal place as published, changed
in only 4 or 5 months of the year, with the absolute effect
of the changes never exceeding 0.1 percentage point in any
of those months. Compared to the initial estimates, the
revised rates suggest slightly smoother behavior for the rates
during the year.

Adjustment methods and procedures

The official seasonal adjustment procedure for the labor
force series is the X-11 ARIMA program, which was |
developed ‘at Statistics Canada during the 1970’s as an ex-

9

a


¢

Table 1. Current seasonal adjustment factors for the 12 major civilian labor force components, January-June 1990

Procedure and series January | February March April May June
Multiplicative Adjustment
(Divide factor into original value)
Agricultural employment:
‘Mon. 90 yoare and over... 099 994 937 1.002 1.039, 1.068
Women, 20 years and over. 863 900 923 943 1.049 1.095
Men, 16 to 19 years 612 817 714 1.022 1.130 1.569
Women, 16 to 19 years “651 735 962 978 973 1.486
Nonagricuttural employment:
Men, 20 years and over . 988 989 992 995 4.001 1.008
Women, 20 years and over . 997 998 1.001 4.001 1,000 993
Unemployment:
Men, 20 years and over . 1211 1.186 1.125 1.006 239 937
Women, 20 years and over... 1.049 1.013, 969 “929 969 998
Additive Adjustment
(Subtract factor from original value)
Nonagricultural employment:
Men, 16 to 19 years . -317 344 293 264 -137 426
Women, 16 to 19 years. . 241 -250 -263 -216 143 303
Unemployment:
Men, 16 to 19 years 16 12 -22 87 -19 184
Women, 16 to 19 years .. 44 -50 -64 -64 -9 266

Table 2. Seasonally adjusted unemployment rates in 1989 and

change due to revision

As first computed As revised Change due to revision
Month :
Overall Civilian Overall Civilian Overall Civilian

January 54 54 $3 54 -0.1 0
February 51 5. 51 5.2 0 04
March . 49 5.0 5.0 5.0 a 0
April 5.2 5.3 5.2 53 ° °
May... 5.1 5.2 5.4 52 0 °
June 5.2. 53 5.2 53 0 0
duly .. 5.2 5.2 5.2 5.3 0 a
August ..... 5.4 52 52 5.3 a a
September . . 52 53 53 53 a 0
October... +52 53 5.2 53 0 0
November . 5.3 5.4 53 5.3 0 =A
December... ee eee ee eee eed 63 15.4 53 53 ° “1

1 These rates reflect the use of seasonal factors projected for December 1989
and published in the July 1989 issue of Employment and Earnings and were

tension of and improvement to the widely used X-11 method
developed at the U.S. Bureau of the Census in the 1960’s.?
The X-11 ARIMA method improves current estimates for

most series by allowing recent observations, especially the

last 6 months, to weigh more heavily in the estimates of cur-
rent and recent seasonal factors than did the X-11 alone. The
method provides this improvement through the use of
ARIMA models to extend the data series by 12 months. The
X-11 algorithm for seasonal adjustment is then applied to

1 The primary documentation for the X-11 ARIMA procedure is in The
X-L1 ARIMA Seasonal Adjustment Method, by Estela Bee Dagum (Statis-
tics Canada Catalogue No. 12-564 E, January 1983). (ARIMA is an acro-
nym for Auto-Regressive Integrated Moving Average.) The X-11 method
is described in The X-11 Variant of the Census Method IT Seasonal Adjust-
rmient Program, by Julius Shiskin, Alan Yougg, and John Musgrave (Tech-
nical Paper No. 15, Bureau of the Census, 1967).

10

subject to revision before regular publication of December data.

the extended series.

ARIMA models. ARIMA projections are based only on the past
experience observed in a series itself. ARIMA models have
proved to have good properties for short-term projection or
extrapolation of a large class of time series, especially in a
seasonal adjustment context, since the extrapolations tend to
track intra-year movements quite well. The ARIMA models
in the X-11 ARIMA program used to seasonally adjust the
labor force series are of the Box-Jenkins type.? They can

2 For a more detailed discussion of ARIMA models, refer to previously
cited Dagum (1983) and to G.E.P. Box and G.M. Jenkins, Time Series Anal-
ysis, Forecasting and Control (San Francisco, Holden Day, 1970); and
C.W.I. Granger and P. Newbold, Forecasting Economic Time Series (New
York, Academic Press, 1977).



generally be described with the notation: -
(p,d,q)(P,D,Q) TRANSFORMATION,

Where:

(1) p is the number of regular (nonseasonal)
autoregressive parameters

(2) d is the number of regular differences

(3) q is the number of regular moving average
parameters

(4) P is the number of seasonal autoregressive
tab parameters

(5) D is the number of seasonal differences

(6) Q is the number of seasonal moving average

rs

(7) TRANSFORMATION may be NONE, LOG,

or POWER(n).

While the lettered elements within the parentheses of the
model specifications can theoretically take on many values,
in practice only small values are useful.

For each labor force series which has been extended based
on an ARIMA model, the model has been specifically chosen
as well suited to the particular series, based on a set of
established criteria. The criteria essentially require a model
to: (1) fit the series well, (2) have low average forecasting
errors in the last 3 years prior to the projected year, and (3)
produce residuals (the differences between the observed
values and the values forecast by the model for the observed
period) which follow a random pattern. Acceptable ARIMA
models have been identified and were used for 166 of the
192 labor force series which were directly adjusted at the
end of 1989, including all 12 major civilian labor force
components, whose ARIMA models are shown in table 3. The
models for two of those major components—agricultural
employment for women 16 to 19 years and unemployment
for women 20 years and over—are different from those used
last year. The 26 remaining series for which acceptable
models have not been identified were simply run through the
X-11 part of the program without any ARIMA extrapolations.

X-11] procedures. The procedures used for adjusting the labor
force series within the X-11 part of the process were the same
as those followed last year. A 10-year time period, including
data from January 1980 through December 1989, was used for
the adjustment of all the labor force series except those being
fun through the new moving-holiday extension for the first time.

The X-11 method of seasonal adjustment contained in the
X-11 ARIMA procedure assumes that the original series,
including the 12 extrapolated observations if an ARIMA model
has been applied, is either the product or the sum of three
components—trend-cycle, seasonal, and irregular. The
method uses either a ratio-to- or difference-from-moving-
average approach to estimate the components, depending on
whether the multiplicative or additive model is used. The
seasonally adjusted series values are computed by dividing

Table 3. ARIMA models used in end-of-1989 seasonal adjustment
for the 12 major civilian labor force components

Series Model Transformation

Agricultural employment:

Men,.20 years and over .........] (1.0.0) 0,1,1) Log

Women, 20 years and over....... (1.0.0) 0.2.2) tog

Men, 16 to. 19 years 0.1.2) O.4.1) NONE

Women, 16 to 19 years: 21.2) @.1.1) NONE
Nonagricutural employment:

Men, 20 years and over . (01,2) (01,1) Log

Women, 20 years and over. . (0.1.1) 0.1.1) Loc.

Men, 16 to 19 years ....... 2,1,0) (01,1) NONE

Women, 16 to 19 years. (0.4.1) (11,1) NONE
Unemployment:

Men, 20 years and over 2.1.2) 1.1) NONE

Women, 20 years and over 0.1 ) Log

Men, 16 to 19 years ...... 0.1.2) @.1.1) NONE

Women, 16 to 19 years (0.1.2) (0.1.1) NONE

each month’s original value by the corresponding seasonal
factor if the multiplicative model is used, or by subtracting
the factor if the additive model is used. Of the 12 major
civilian labor force components, the 4 teenage unemployment
and nonagricultural employment series were adjusted using
the additive model, and the other 8 series with the
multiplicative model. Of all the 192 directly adjusted series,
37 were adjusted with the additive model, primarily those
involving teenage employment and unemployment, for which
the seasonal component seems to be fairly independent of
the trend-cycle.

Moving-holiday adjustment. Three of the series directly
adjusted with multiplicative models were seasonally adjusted
using the new moving-holiday extension of X-11 ARIMA which
has been developed at BLS. These three series, all relating to
persons at work, had tested as having significant and well-
defined effects in their April data related to the timing of Easter.
‘The series are: (1 and 2) at work on part-time schedules for
noneconomic reasons, usually work part time, all industries
and nonagricultural industries, both of which are published
monthly in seasonally adjusted form; and (3) at work on full-
time schedules, nonagricultural industries, a seasonally adjusted
series formerly published and still maintained.

The standard X-11 seasonal-factor moving averages in
X-11 ARIMA assume that seasonal behavior in any given
month is relatively consistent from year to year, even though
it may evolve over a number of years. Holidays are one
source of seasonality, and most affect economic data in a
way sufficiently consistent from year to year to allow the
standard X-11 assumption to work reasonably well. Easter,
however, can occur anywhere from March 22 to April 25
and is the principal example of a potential source of the
seasonal or calendar effects generally called “‘moving-holiday
effects’’ in economic series. When these effects are present
and not controlled for, they tend to confound seasonal
component estimation for the affected month or months.

Most of the seasonally adjusted labor force series are not
significantly affected by Easter, and previous work on
moving-holiday effects has generally disregarded the

i