1

Richard B. Tiller and Thomas D. Evans

Revision of Seasonally Adjusted

Labor Force Series in 2004

S

hort-run movements in labor force time series are

strongly influenced by seasonality, which refers to

periodic fluctuations that are associated with recurring

calendar-related events such as weather, holidays, and the

opening and closing of schools. Seasonal adjustment is the

process of estimating and removing these fluctuations to yield

a seasonally adjusted series. The reason for doing so is to

make it easier for data users to observe fundamental changes

in the level of the series, particularly those associated with

general economic expansions and contractions.

While seasonal adjustment is feasible only if the seasonal

effects are reasonably stable with respect to timing, direction,

and magnitude, these effects are not necessarily fixed, but

often evolve over time. These evolving patterns are estimated

by the Bureau of Labor Statistics (BLS) using X-12, a

procedure based on moving averages, or “filters,” that

successively average a shifting timespan of data, thereby

providing estimates of seasonal factors that change in a

smooth fashion from one year to the next.

For observations in the middle of the series, a set of

symmetric moving averages with fixed weights produces final

seasonally adjusted estimates. A filter is referred to as being

symmetric if it is centered around the time point being

adjusted with an equal amount of data preceding and

following that point. Standard seasonal adjustment options

imply a symmetric filter using from 6 to 10 years of original

data to produce a final seasonally adjusted estimate.

Obviously, this final adjustment can be made only where there

is enough data beyond the time point in question to adjust

with the symmetric filter.

To seasonally adjust recent data, shorter, asymmetric filters

with less desirable properties must be used. These filters are

referred to as asymmetric because they use fewer observations

after the reference point than preceding it. The weights for

these filters vary depending on how many observations are

available beyond the time point for which estimates are to be

adjusted.

Revisions to a seasonally adjusted estimate for a given

time point continue until enough future observations become

available to use the symmetric weights. This effectively means

waiting up to 5 years for a final adjustment when using

standard options.

Beginning with the release of estimates for December 2003

in January 2004, BLS has adopted the practice of concurrent

adjustment for seasonally adjusting current year labor force

data from the Current Population Survey (CPS) data as it

becomes available each month. Under this practice, the

current month’s seasonally adjusted estimate is computed

using all relevant original data up to and including those for

the current month. Revisions to estimates for previous

months, however, are postponed until the end of the year.

Previously, seasonal factors for the CPS labor force data were

projected twice a year. With the introduction of concurrent

seasonal adjustment, BLS will no longer publish projected

seasonal factors for CPS data. This procedure is discussed

in more detail later in this article.

At the end of each calendar year, BLS reestimates the

seasonal factors for the CPS series by including another full

year of data in the estimation process. Based on this annual

reestimation, BLS revises the historical seasonally adjusted

data for the last 5 years. As a result, each year’s data are

generally subject to five revisions before the values are

considered final.

The fifth and final revisions to data for the earliest of the

5 years are usually quite small, while the first-time revisions

to data for the most recent year are usually much larger. For

the major aggregate labor force series, however, the firsttime revisions rarely alter the essential trends observed in

the initial estimates.

Changes in 2004

Adoption of concurrent seasonal adjustment

As indicated above, the new seasonal adjustment

methodology replaces the projected factor method, which

updated seasonal factors only twice a year. Under the latter

procedure, the seasonal adjustment program was run at the

end of the year to update past estimates using all available

data and produced a set of projected seasonal factors for the

first 6 months of the upcoming year. These projected factors

were subsequently used to seasonally adjust the new original

data as they were collected. At midyear, the historical series

were updated with data for January through June and the

seasonal adjustment program was rerun to produce projected

seasonal factors for July through December of the current

year.

Richard B. Tiller and Thomas D. Evans are mathematical statisticians

on the Statistical Methods Staff, Office of Employment and

Unemployment Statistics, Bureau of Labor Statistics. Telephone: (202)

691-6370 (Tiller) and 691-6354 (Evans); e-mail: Tiller.Richard@bls.gov;

Evans.Thomas@bls.gov.

From: Employment and Earnings, January 2004
2

With concurrent seasonal adjustment, the seasonal

adjustment program is rerun each month as the latest CPS

data become available. The seasonal factors for the most

recent month are produced by applying a set of moving

averages to the entire data set, including data for the current

month. While all previous-month seasonally adjusted

estimates are revised in this process, BLS policy is not to

revise previous months’ official seasonally adjusted estimates

as new data become available during the year. Revisions

will continue to be introduced for the most recent 5 years of

data at the end of each year.

Numerous studies, including that discussed in a 1987 paper

on the CPS labor force series,1 have indicated that the practice

of concurrent adjustment generally produces initial seasonally

adjusted estimates requiring smaller revisions than do those

produced using projected factors. Revisions to data for

previous months also may produce gains in accuracy,

especially when the original data are themselves regularly

revised on a monthly basis. Numerous revisions during the

year, however, should be avoided, because they tend to

confuse data users and substantially increase publication

costs.

The case for revisions to previous-month seasonally

adjusted estimates is less compelling for CPS series, because

the original sample data are normally not revised. Moreover,

an empirical investigation indicated that there were no

substantial gains in estimating month-to-month change by

introducing revisions to the data for the previous month. For

example, it was found that if previous-month revisions were

made to the labor force series, the overall unemployment

rate would be different in only 2 months between January

2001 and November 2002, in each case by only one-tenth of

a percentage point. (More detailed information about this

study is available from the authors upon request.)

Extension of seasonal adjustment to additional

series

Beginning in January 2004, seasonal adjustment has been

extended to three series not previously adjusted. These are

the U-4, U-5, and U-6 alternative measures of labor

underutilization.2 These measures were substantially revised

after the redesign of the CPS in 1994 and were published on

a not seasonally adjusted basis because there was not a time

series sufficiently long to permit evaluation of the quality of

the seasonal adjustment for key components of these

measures. After careful study, BLS determined that the three

labor underutilization measures could be adequately

seasonally adjusted, even though some of their components

could not.

The U-4 measure is computed from the original CPS data

as the total unemployed plus discouraged workers as a percent

of the civilian labor force plus discouraged workers.

Diagnostic testing indicated that the discouraged workers

series is nonseasonal and therefore does not need to be

seasonally adjusted. Thus, the seasonally adjusted U-4 is

derived using the official adjustments for total employment

and unemployment with the original (not seasonally adjusted)

discouraged worker series added.

The U-5 measure adds all other marginally attached

workers to both the numerator and denominator of the U-4

measure. Testing indicated that the all other marginally

attached worker series has seasonality that is weak and

hard to estimate. Therefore, BLS did not seasonally adjust

this series, even though it is added to the seasonally

adjusted components of U-4 to derive an adjusted U-5.

Analysis of the seasonally adjusted U-5 series indicated that

this approach was acceptable because no residual seasonality

was present.

Finally, the U-6 measure extends the U-5 measure to

include workers employed part time for economic reasons

in the numerator. Because this latter series is already

seasonally adjusted, the seasonally adjusted U-6 measure is

easily derived.

Revisions to 2003 estimates

This year’s revisions incorporate data through December

2003 and provide revised estimates for January 1999 through

December 2003 for all previously seasonally adjusted labor

force series. A total of 116 series are directly seasonally

adjusted and many more are indirectly adjusted. (See the

section below on aggregation.)

An important criterion for evaluating alternative methods

of seasonal adjustment is how close initial estimates are to

the results of subsequent revisions. Users of seasonally

adjusted data are often most interested in current information.

Thus, it is desirable that the initial seasonally adjusted

estimates be as close as possible to the improved estimates

made after more data become available. Even though the

revisions currently being released for the 2003 seasonally

adjusted data are not final, the first revisions are usually the

largest, and often indicate the direction of subsequent

revisions.

Table 1 shows the civilian unemployment rates for 2003

as first computed and as revised. Rounded to one decimal

place as published, the rates were unchanged in 9 of the 12

months, and changed by one-tenth of a percentage point in

the remaining 3 months.

Adjustment Methods and Procedures

Beginning in 2003, BLS adopted the use of X-12-ARIMA

as the official seasonal adjustment procedure for CPS labor

force series, replacing the X-11-ARIMA program that had

been used since 1980. Both X-12- and X-11-ARIMA are

based on earlier versions of the widely used X-11 method

1 George R. Methee and Robert 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.

2 For a detailed discussion of these measures, see John E. Bregger and

Steven E. Haugen, “BLS introduces new range of alternative

unemployment measures,” Monthly Labor Review, October 1995, pp.

19-26.
3

developed at the U.S. Census Bureau in the 1960s.3 X-11-

ARIMA added to X-11 the ability to extend the time series

with forward and backward extrapolations from AutoRegressive Integrated Moving Average (ARIMA) models,

prior to seasonal adjustment. The X-11 algorithm for seasonal

adjustment is then applied to the extended series. The use of

forward and backward extensions results in initial seasonal

adjustments that are subject to smaller revisions, on average,

when they are revised after future data become available.

Also developed at the U.S. Census Bureau, the X-12-

ARIMA program includes all of the capabilities of the X-11-

ARIMA program while also introducing major enhancements.

These enhancements fall into three basic categories: (1)

Enhanced ARIMA model selection and estimation, (2)

detection and estimation of outlier, trading day, and holiday

effects, and (3) new postadjustment diagnostics.

For the majority of labor force series that are seasonally

adjusted by BLS, the main steps of the seasonal adjustment

process proceed in the following order:

• Times series modeling—a REGARIMA model (a

combined regression and ARIMA model) is developed

to account for the normal evolutionary behavior of the

time series and to control for outliers and other special

external effects that may exist in the series;

• Prior adjustments—given an adequate REGARIMA

model, the series is modified by prior adjustments for

external effects estimated from the regression part of

the model and extrapolated forward 12 months by the

ARIMA part of the model;

• X-11 decomposition—the modified and extrapolated

series is decomposed into trend, seasonal, and irregular

components using a series of moving averages,

developed in the X-11 part of the program, to produce

seasonal factors for implementing seasonal adjustment;

and

• Evaluation—a battery of diagnostic tests is produced

to evaluate the quality of the final seasonal adjustment.

For two series, the seasonal adjustment process begins

with special user-defined prior adjustments for Easter effects.

(See section below on calendar adjustments.)

Time series modeling

Time series models play an important role in seasonal

adjustment. They are used to identify and correct the series

for aberrant observations and other external effects, as well

as to extend the original series with backcasts and forecasts

so that less asymmetric filters can be used at the beginning

and end of the series.

ARIMA models 4 are designed to make forecasts of a time

series based on only its past values. While these models can

represent a wide class of evolving time series patterns, they

do not account for the presence of occasional outliers and

other special external effects. An outlier represents a sudden

break in the normal evolutionary behavior of a time series.

Ignoring the existence of outliers may lead to serious

distortions in the seasonally adjusted series.

A common form of outlier that presents a special problem

for seasonal adjustment is an abrupt shift in level that may

be either transitory or permanent. Three types are usually

distinguished: (1) An additive change that affects only a single

observation, (2) a temporary change having an effect that

diminishes to zero over several periods, and (3) a level shift

or break in trend, which is a permanent increase or decrease

in the underlying level of the series.

These three main types of outliers, as well as other types

of external effects, may be handled by the time series

modeling component of X-12. This is done by adding to

the ARIMA model appropriately defined regression variables, based on intervention analysis originally proposed by

George E.P. Box and George C. Tiao.5

The combined regression and ARIMA model is referred

to as a REGARIMA model, and is represented by

Yt = + b X Z t t

where Yt is the original series or a log transformation of it, Xt

is a set of fixed regression variables, r represents the

Table 1. Seasonally adjusted unemployment rates in 2003

and change due to revision

As first As

computed revised

January ................................ 5.7 5.8 0.1

February .............................. 5.8 5.9 .1

March .................................. 5.8 5.8 .0

April .................................... 6.0 6.0 .0

May .................................... 6.1 6.1 .0

June ................................... 6.4 6.3 -.1

July .................................... 6.2 6.2 .0

August ................................. 6.1 6.1 .0

September ............................ 6.1 6.1 .0

October................................ 6.0 6.0 .0

November ............................. 5.9 5.9 .0

December .............................

15.7 5.7 .0

1 This rate reflects the use of seasonal factors projected for

December 2003 as published in the July 2003 issue of Employment

and Earnings and was subject to revision before regular publication

of December data.

Month Change

3 For a detailed discussion of X-12-ARIMA, see David F. Findley, Brian

C. Monsell, William R. Bell, Mark C. Otto, and Bor-Chung Chen, “New

Capabilities and Methods of the X-12-ARIMA Seasonal Adjustment

Program,” Journal of Business and Economic Statistics, April 1998, pp.

127-52. For documentation on X-11-ARIMA, see Estela Bee Dagum, The

X-11 ARIMA Seasonal Adjustment Method, catalogue no. 12-564E

(Ottawa, Statistics Canada, January 1983). The X-11 method is described

in Julius Shiskin, Alan Young, and John Musgrave, “The X-11 Variant of

the Census Method II Seasonal Adjustment Program,” Technical Paper

no. 15 (Bureau of the Census, 1967).

4 For a more detailed discussion of ARIMA models, refer to George

E.P. Box and Gwilym M. Jenkins, Time Series Analysis, Forecasting and

Control (San Francisco, Holden Day, 1970); and Sir Maurice Kendall

and J. Keith Ord, Time Series (New York, University Press, 1990).

5 George E.P. Box and George C. Tiao, “Intervention Analysis with

Applications to Economic and Environmental Problems,” Journal of the

American Statistical Association, 1975, pp. 71-79.

Yt = + b X Z t t
4

regression coefficients, and Zt is a standard seasonal ARIMA

model described by the notation (p,d,q)(P,D,Q), where p is

the number of regular (nonseasonal) autoregressive

parameters; d is the number of regular differences; q is the

number of regular moving average parameters; P is the

number of seasonal autoregressive parameters; D is the

number of seasonal differences; and Q is the number of

seasonal moving average parameters.

While the ARIMA model can theoretically be very

complicated, in practice it takes a parsimonious form

involving only a few estimated parameters. (See table 2.)

There are well-developed methods for determining the

number and types of parameters and the degree of

differencing appropriate for a given series.

With respect to specifying the regression component to

control for outliers, X-12 offers two approaches. Major

external events, such as breaks in trend, are usually associated

with known events. In such cases, the user has sufficient

prior information to specify special regression variables to

estimate and control for these effects.

It is rare that there is sufficient prior information to locate

and identify all of the aberrant observations that may exist in

a time series. As a second approach to specifying the

regression component, REGARIMA offers automatic outlier

detection based on work by I. Chang, G.C. Tiao, and C. Chen.6

This is especially useful when a large number of series must

be processed. Of course, both of these approaches may be

combined so that readily available prior information can be

used directly while unknown substantial outliers may still be

discovered.

Model adequacy and length of series. The preference is to

use relatively long series in fitting time series models, but

with some qualifications. Sometimes, the relevance of data

in the distant past for seasonal adjustment is questionable.

The implied X-11 moving average does not use much more

than 5 years of data before and after the central observation

being adjusted. Using a sliding span of 10 years in length,

never revising back more than 5 years at any point, is

sufficient to produce final revised seasonal factors.

Even though the X-12 filters have limited memory, there

are reasons for using longer series. First, for homogenous

time series, the more data used to identify and estimate a

model, the more likely that the model will represent the

structure of the data well and the more accurate the parameter

estimates will be. The exact amount of data needed for timeseries modeling depends on the properties of the series

involved. Arbitrarily truncating the series, however, may lead

to more frequent changes in model identification and to large

changes in estimated parameters, which in turn may lead to

larger-than-necessary revisions in forecasts.

Second, although level shifts and other types of outliers

tend to occur more often in longer series, X-12 has the

capability of automatically controlling for these effects.

Third, some very useful diagnostics available in X-12

typically require a minimum of 11 years of data, and, in some

cases, as much as 14 years of data.

Fourth, attempting to fit longer series often provides useful

insights into the properties of the series, including its overall

quality and the effects of major changes in survey design.

Based on the above considerations, REGARIMA models

are initially estimated for series beginning in 1976 where

data series of this length are available. Extensive use is made

of intervention analysis to estimate the magnitude of known

breaks in CPS series and of automatic outlier detection to

identify and correct for the presence of additional aberrant

observations.

Once a model is estimated, it is evaluated in terms of its

adequacy for seasonal adjustment purposes. The criteria

essentially require a model to fit the series well (no systematic

patterns in the residuals) and to have low average forecasting

errors for the last 3 years of observed data. When there is a

tradeoff between the length of the series and the adequacy of

the model, a shorter series is selected. If a shorter series is

selected, the identification of the model is not changed with

the addition of new data unless the model fails diagnostic

testing.

Acceptable REGARIMA models have been developed for

all of the 116 labor force series that were directly adjusted at

the end of 2003. For each of the eight major civilian labor

force components, table 2 presents the form of the ARIMA

part of the model, the transformation selected, and the starting

date of the series used to fit the model.

Prior adjustments

Prior adjustments refer to adjustments made to the original

data prior to seasonal adjustment. Their purpose is to correct

the original series for atypical observations and other external

effects that otherwise would seriously distort the estimates

of the seasonal factors. These corrections, or prior adjustment

factors, are subtracted from or used as divisors for the original

series, depending on whether the seasonal adjustment is

additive or multiplicative.

Table 2. REGARIMA models used for the eight major civilian

labor force components

Series Model Trans- Series

formation start date

Total employment:

Men, 20 y ears and over ... (0,1,2)(0,1,1) LOG 1976

Women, 20 years and

over ......................... (0,1,0)(0,1,1) LOG 1976

Men, 16 to 19 years ........ (3,1,0)(0,1,1) LOG 1976

Women, 16 to 19 y ears .... (0,1,1)(0,1,1) LOG 1976

Total unemployment:

Men, 20 y ears and over ... (0,1,3)(0,1,1) LOG 1990

Women, 20 years and

over ......................... (1,1,0)(0,1,1) LOG 1990

Men, 16 to 19 years ........ (0,1,1)(0,1,1) LOG 1976

Women, 16 to 19 y ears .... (0,1,1)(0,1,1) LOG 1976

6

I. Chang, G.C. Tiao, and C. Chen, “Estimation of Time Series Parameters

in the Presence of Outliers,” Technometrics, 1988, pp. 193-204.
5

Prior adjustment factors for CPS series may be based on

special user-defined adjustments or handled more formally

with REGARIMA modeling. Most of the prior adjustment

factors for the labor force series are estimated directly from

REGARIMA.

Level shifts. The most common type of outlier that occurs in

CPS series is the permanent level shift. Most of these shifts

have been due to noneconomic methodological changes

related to revisions in population controls and major

modifications to the CPS design.7 One notable economic

level shift was due to the 2001 terrorist attacks. These level

shifts are discussed briefly below.

Population estimates extrapolated from the latest decennial

census are used in the second-stage estimation procedure to

control CPS sample estimates to more accurate levels. These

intercensal population estimates are regularly revised every

10 years to reflect the latest census data and, less frequently,

on other occasions.

During the 1990s, three breaks occurred in the intercensal

population estimates. Population controls based on the 1990

census, adjusted for the estimated undercount, were

introduced into the CPS series in 1994, and, in 1996, were

extended back to 1990. In January 1997 and again in January

1999, the population controls were revised to reflect updated

information on international migration.

The most recent population revisions, which reflect the

results of the 2000 census, were introduced with the release

of data for January 2003 and were extended back to data

beginning in January 2000. Specifically, there was a net

increase in the total population, in large part due to growth

in the numbers of Hispanics.

In 1994, major changes to the CPS were introduced, which

included a redesigned and automated questionnaire and

revisions to some of the labor force concepts and definitions.

For data beginning in 2000, new industry and occupational

classifications were introduced into the CPS.

To test for the possibility that revisions to the population

controls had important effects on those CPS series with large

numerical revisions in 1990, 1997, 1999, or 2000, as well as

to test for effects due to the 1994 redesign, each REGARIMA

model was modified to include intervention variables for

those years. The coefficients for these variables provide

estimates of the direction and magnitude of the intervention

effects.

Intervention effects for 2000 were necessary for selected

employment series primarily related to Hispanic, adult, and

agricultural categories. These effects mainly reflect increases

in adult and Hispanic employment due to the introduction of

Census 2000-based population controls and the decline in

agricultural employment caused by the change in the industry

classification system. (See the article, “Revisions to the

Current Population Survey Effective in January 2003” in the

February 2003 issue of this publication.)

For those series with significant intervention effects, the

estimated level shifts were removed prior to seasonal

adjustment, thereby providing a smooth link to the pre-1990,

pre-1994, pre-1997, pre-1999, and pre-2000 data. The

resulting “prior adjusted” series were then used to estimate

the seasonal factors. These factors were applied to the

original series, without prior adjustment, to obtain the

seasonally adjusted series.

The prior adjustment factors used for all of the eight major

civilian labor force component series are shown in

table 3. Because all eight series are seasonally adjusted with

the multiplicative mode, the prior adjustments also are

multiplicative. That is, the original series is modified prior

to seasonal adjustment by dividing it by its prior adjustment

factor.

September 2001 effect. At the end of 2001, unemployed job

losers were identified as having had substantial upward level

shifts 1 month after the September 11, 2001, terrorist attacks

on the World Trade Center in New York City. (See the

seasonal adjustment article in the January 2002 issue of this

publication for more details.) Also, four additional series,

related to workers employed part time for economic reasons,

were identified as having substantial upward shifts at the time

of the terrorist attacks in September 2001.

Calendar effects. Calendar effects refer to transitory level

shifts in a series resulting from calendar events such as

7 For further discussion of these changes, see the following articles in

previous issues of this publication: “Revisions in the Current Population

Survey Effective January 1994” in the February 1994 issue; “Revisions

in Household Survey Data Effective February 1996” in the March 1996

issue; “Revisions in the Current Population Survey Effective January 1997”

in the February 1997 issue; “Revision of Seasonally Adjusted Labor Force

Series” in the January 1998 issue; “Revisions in the Current Population

Survey Effective January 1999" in the February 1999 issue; “New Seasonal

Adjustment Factors for Household Data Series” in the July 1999 issue;

and “Revisions to the Current Population Survey Effective in January

2003” in the February 2003 issue, available on the Internet at http://

www.bls.gov/cps/rvcps03.pdf.

Mode of

Series adjustment

Pre- Pre- Pre1990 1994 2000

Total employment:

Men, 20 years and

over ....................... Multiplicative .992 .983

Women, 20 years and

over ....................... Multiplicative .988

Men, 16 to 19 years ..... Multiplicative .940 .957

Women, 16 to 19 years . Multiplicative

Total unemployment:

Men, 20 years and

over ....................... Multiplicative

Women, 20 years and

over ....................... Multiplicative

Men, 16 to 19 years ..... Multiplicative

Women, 16 to 19 years . Multiplicative

Prior adjustment

factors

Table 3. Prior adjustment factors for the eight major civilian

labor force components
6

moving holidays or the differing composition of weekdays

in a month between years. These effects have different

influences on the same month across years, thereby distorting

the normal seasonal patterns for the given month.

Two CPS series related to persons at work have significant

effects in their April data due to the timing of Easter. These

series are persons at work on part-time schedules for

noneconomic reasons who usually work part time in all

industries and in nonagricultural industries. These series were

seasonally adjusted with multiplicative models using a

moving-holiday correction. A detailed discussion of the

nature of the Easter effect in these series and of the procedure

used to control for it was included in the January 1990 version

of this article.

X-11 decomposition

The X-11 method of seasonal adjustment contained within

the X-12-ARIMA procedure assumes that the original series

is composed of three components—trend-cycle, seasonal, and

irregular. Depending on the relationship between the original

series and each of the components, the mode of seasonal

adjustment may be additive or multiplicative. Formal tests

are conducted to determine the appropriate mode of

adjustment.

The multiplicative mode assumes that the absolute

magnitudes of the components of the series are dependent

on each other, which implies that the size of the seasonal

component increases and decreases with the level of the

series. With this mode, the monthly seasonal factors are

ratios, with all positive values centered around 1. The

seasonally adjusted series values are computed by dividing

each month’s original value by the corresponding seasonal

factor.

In contrast, the additive mode assumes that the absolute

magnitudes of the components of the series are independent

of each other, which implies that the size of the seasonal

component is independent of the level of the series. In this

case, the seasonal factors represent positive or negative

deviations from the original series and are centered around

zero. The seasonally adjusted series values are computed by

subtracting from each month’s original value the

corresponding seasonal factor.

Given an appropriate choice for the mode of adjustment,

the prior-adjusted and forecasted series is seasonally adjusted

by the X-11 component of X-12. X-11 applies a sequence of

moving average and smoothing calculations to estimate the

trend, seasonal, and irregular components. The method takes

either a ratio-to- or difference-from-moving-average

approach, depending on whether the multiplicative or additive

model is used. For observations in the middle of the series,

a set of fixed symmetric moving averages (filters) is used to

produce final estimates. The implied length of the final filter

under standard options is 72 time points for the 3-by-5

seasonal moving average or 120 time points for the 3-by-9

moving average. That is, to obtain a final seasonally adjusted

estimate for a single time point requires up to 5 years of

monthly data preceding and following that time point. For

recent data, asymmetric filters, with less desirable properties

than symmetric filters, must be used.

All of the civilian labor force component series were

adjusted using the multiplicative mode. In previous years,

unemployed teenagers, nonagricultural employment, and

some other series were additively adjusted. Formal testing

for the mode of seasonal adjustment with REGARIMA

resulted in the rejection of all additive adjustments in favor

of multiplicative adjustments.

Evaluation

A series should be seasonally adjusted if three conditions

are satisfied: The series is seasonal, the seasonal effects can

be estimated reliably, and no residual seasonality is left in

the adjusted series. A variety of diagnostic tools is available

in X-12 to test for these conditions. These include the F

test from the original X-11, the more extensive M and Q

tests from X-11-ARIMA, and a set of tests first available in

X-12. These X-12 tests include sliding-span diagnostics,

frequency-spectrum estimates, and revision-history statistics.

If diagnostic testing shows that any of the three conditions

fails to hold, a series is deemed not suitable for seasonal

adjustment.

Aggregation procedures

BLS directly seasonally adjusts 116 series based on age, sex,

industry, occupation, education, and other characteristics.

BLS also provides seasonally adjusted totals, subtotals, and

ratios of selected series. It is possible to seasonally adjust

an aggregate series either directly or indirectly by seasonally

adjusting its components and adding the results, or dividing,

in the case of ratios. Indirect and direct adjustments usually

will not give identical results. This is so because seasonal

patterns vary across series, there are inherent nonlinearities

in X-12, many series are multiplicatively adjusted, and some

series are ratios.

BLS uses indirect seasonal adjustment for most of the

major labor force aggregates. Besides retaining, so far as

possible, the essential accounting relationships, the indirect

approach is needed because many of the aggregates include

components having different seasonal and trend

characteristics that sometimes require different modes of

adjustment.

Examples of indirectly seasonally adjusted series are the

levels of total unemployment, employment, and the civilian

labor force, and the unemployment rate for all civilian

workers. These are produced by the aggregation of some or

all of the seasonally adjusted series for the eight major civilian

labor force components. The seasonally adjusted level of

total unemployment is the sum of the seasonally adjusted

levels of unemployment for four age-sex groups—men and

women 16 to 19, and men and women 20 years and over.

Likewise, seasonally adjusted civilian employment is the sum

of employment in all industries for the same four age-sex

groups. The seasonally adjusted civilian labor force is the
7

sum of all eight components. The seasonally adjusted civilian

unemployment rate is computed as the ratio of the total

seasonally adjusted unemployment level to the total

seasonally adjusted civilian labor force (expressed in

percentage form).

A problem with producing seasonally adjusted estimates

for a series by aggregation is that seasonal adjustment factors

cannot be directly computed for that series. Implicit seasonal

adjustment factors, however, can be calculated after the fact

by taking the ratio of the unadjusted aggregate to the

seasonally adjusted aggregate, or, for additive implicit factors,

the difference between those two aggregates.

Availability of revised series

This issue of Employment and Earnings contains revised

monthly and quarterly data for the most recent months and

quarters for many seasonally adjusted labor force

series. These revisions replace the seasonally adjusted

estimates previously published. Revised historical seasonally adjusted labor force data also are available in various

forms on the BLS Internet site (www.bls.gov), including

ftp access (ftp://ftp.bls.gov/pub/special.requests/lf/) to all

of the revised data. The seasonally adjusted data

last published for 1998 and earlier years were not further

revised.