3

Richard B. Tiller and Thomas D. Evans

Revision of Seasonally Adjusted

Labor Force Series in 2007

Short-run movements in labor force time series are

strongly influenced by seasonality—periodic

fluctuations 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 users to observe fundamental changes in

the level of the series, particularly changes 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. The evolving patterns are estimated

by X-12-ARIMA, 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 1 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 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 that

uses 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 are 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 such filters vary with the number of observations

that are available beyond the time point for which estimates

are to be adjusted. Seasonally adjusted data for the current

year are produced with a technique known as concurrent

adjustment. Under this practice, the current month’s seasonally

adjusted estimate is computed with the use of all relevant

original data up to and including data for the current month.

Revisions to estimates for previous months, however, are

postponed until the end of the year. 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 standard options are used.

At the end of each calendar year, BLS reestimates the

seasonal factors for the Current Population Survey (CPS)

series by including another full year of data in the estimation

process. On the basis of this annual reestimation, BLS revises

the historical seasonally adjusted data for the previous 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 generally much larger. For

the major aggregate labor force series, however, the first-time

revisions rarely alter the essential trends observed in the initial

estimates.

Changes in 2007

Revisions to 2006 estimates

This year’s revisions incorporate data through December 2006

and provide revised estimates for January 2002 through

December 2006 for all previous seasonally adjusted labor force

series. There are 129 series that are directly seasonally

adjusted and many more that are derived from these series.

(See the subsequent section titled “Aggregation procedures.”)

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 2006 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 January

to November 2006, as first computed and as revised. The

seasonally adjusted unemployment rate did not change for

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. Telephones: (202)

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

Evans.Thomas@bls.gov.
4

Table 1. Seasonally adjusted unemployment rates in 2006

and change due to revision

As first As

computed revised

January ........................................... 4.7 4.7 0.0

February .......................................... 4.8 4.8 .0

March .............................................. 4.7 4.7 .0

April .................................................. 4.7 4.7 .0

May .................................................. 4.6 4.6 .0

June ................................................. 4.6 4.6 .0

July .................................................. 4.8 4.8 .0

August ............................................. 4.7 4.7 .0

September ....................................... 4.6 4.6 .0

October ........................................... 4.4 4.4 .0

November........................................ 4.5 4.5 .0

Month Change

any month in 2006. Note that the rate for December 2006 was

the final month of the series and has no revision.

Extension of seasonal adjustment to additional

series

Beginning with the release of data for January 2006, seasonal

adjustment was extended to 13 series not previously

adjusted. These were total multiple jobholders, employed

nonagricultural wage and salary workers by gender, and five

industry employment series by gender. Only the series on

total multiple jobholders was published. The industry series

included agriculture, forestry, fishing, and hunting; arts,

entertainment, and recreation; construction; educational

services; and retail trade. More information about these

industry series is available on the BLS Web site at http://

www.bls.gov/cps/constio198399.htm. No new series will be

added with the release of January 2007 data.

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 developed

at the U.S. Census Bureau in the 1960s.1 Statistics Canada

added to X-11 the ability to extend the time series with forward

and backward extrapolations from Auto-Regressive

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 the adjusted data are revised after future data become

available.

Developed at the U.S. Census Bureau, the X-12-ARIMA

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

program, while introducing new, 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-cycle, seasonal, and

irregular components by means of 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 subsequent section titled “Prior

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 models2

 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

1

 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).
5

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 the level of the

data that may be either transitory or permanent. Three types

of outliers 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 a break in the trend of the data, which

represents 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 times 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.3

The combined regression and ARIMA model is referred

to as a REGARIMA model and is represented by

 ,

where, Yt is the original series or a logarithmic transformation

of it, Xt is a set of fixed regression variables, represents the

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. First, 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.

Second, because 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.4

 This approach is

especially useful when a large number of series must be

processed. Of course, both 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 times series models, but

with some qualifications. Sometimes, the relevance of data in

the distant past to 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 it is 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 time

series 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 their overall

2 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). 3

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

Applications to Economic and Environmental Problems,” Journal

of the American Statistical Association, vol. 70, no. 353, 1975, pp.

71–79.

Table 2. REGARIMA models used for the eight major civilian

labor force components

Series Model Trans- Series

formation start date

Total employment:

Men, 20 years 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 years ..... (0,1,1)(0,1,1) LOG 1976

Total unemployment:

Men, 20 years 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 years ..... (0,1,1)(0,1,1) LOG 1976

Y XZ t tt = + β

β

4

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

Parameters in the Presence of Outliers,” Technometrics, 1988, pp.

193–204.
6

quality and the effects of major changes in survey design.

On the basis of the foregoing considerations, REGARIMA

models are initially estimated for series beginning in 1976,

where data series of that 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 (there should

be 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. In this case, 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 labor force series that are directly adjusted. 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.

Concurrent seasonal adjustment

Concurrent seasonal adjustment began at BLS with the

release of estimates for December 2003 in January 2004. This

practice replaced the projected-factor method, which updated

seasonal factors only twice a year. Under the latter procedure,

projected seasonal factors were 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.

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, extended by extrapolations,

including data for the current month. While all previousmonth 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. Instead, revisions are 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,5

 have indicated that concurrent

adjustment generally produces initial seasonally adjusted

estimates requiring smaller revisions than do estimates

produced with the projected-factor method. 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 to increase publication costs

substantially.

The case for revisions to previous-month seasonally

adjusted estimates is less compelling for CPS series, because

the original sample data normally are not revised. Moreover,

an empirical investigation indicated that there were no

substantial gains in estimating month-to-month changes 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.)

Prior adjustments

Prior adjustments are 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. Prior adjustment factors are

subtracted from or used as divisors for the original series,

depending on whether the seasonal adjustment is additive

or multiplicative.

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 such shifts

have been due to noneconomic methodological changes

related to revisions in population controls and to major

modifications to the CPS design.6

 One notable economic

level shift was due to the 2001 terrorist attacks.

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.

5

 George R. Methee and Robert J. McIntire, “An Evaluation of

Concurrent Seasonal Adjustment for the Major Labor Force Series,”

in Proceedings of the Business and Economic Statistics Section

(Alexandria, VA, American Statistical Association, 1987).

6

 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.
7

Mode of Series adjustment Pre- Pre- Pre1990 1994 2000

Total employment:

Men, 20 years and

over .............................. Multiplicative .993 .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

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 major 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.

Population revisions, which reflected the results of Census

2000, were introduced with the release of data for January

2003 and were extended back to data beginning in January

2000. Since 2003, population controls also are updated in

January to reflect new estimates of international migration in

the postcensus period.

In 1994, major changes to the CPS were introduced,

including 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 also were introduced.

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 related primarily 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 a decline in

agricultural employment caused by the change in the industry

classification system. (See “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, which, in turn, 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.

Due to an unusual revision in the population controls in

January 2000, the unadjusted employment level of black males

20 years or over had a strong upward shift in the first quarter

of 2000. This temporary effect is permanently removed from

the seasonally adjusted series with the use of the REGARIMA

model.

Effect of September 2001. 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.

Calendar effects. Calendar effects are transitory level shifts

in a series that result from calendar events such as 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 exhibit

significant effects in their April data due to the timing of

Easter: “Persons at work on part-time schedules for

noneconomic reasons who usually work part time in all

industries” and “persons at work on part-time schedules for

noneconomic reasons who usually work part time in

nonagricultural industries.” These series were seasonally

adjusted with multiplicative models with a moving-holiday

correction. A detailed discussion of the nature of the

Easter effect in those 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
8

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 unity. 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 the corresponding seasonal factor from each

month’s original value.

Given an appropriate choice for the mode of adjustment,

the prior-adjusted, 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-cycle, 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 with 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. Among these tools are

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. The latter include sliding-span diagnostics, frequencyspectrum estimates, and revision-history statistics. If

diagnostic testing shows that any of the three conditions

listed fails to hold for a given series, that series is deemed not

suitable for seasonal adjustment.

Aggregation procedures

BLS directly seasonally adjusts series on the basis of 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, because (1) seasonal patterns

vary across series, (2) there are inherent nonlinearities in X12, (3) many series are multiplicatively adjusted, and (4) 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, as well as the unemployment rate for all civilian

workers. These series 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 16 to 19 years, women 16 to 19 years, men 20

years and over, 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 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 as a

percentage).

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
9

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 2001 and

earlier years were not further revised.