24

Richard B. Tiller and Thomas D. Evans

Revision of Seasonally Adjusted

Labor Force Series in 2003

S

hort-run movements in labor force time series are

strongly influenced by seasonality, which refers to

nearly periodic fluctuations of about 1 year in duration

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 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 produce 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. Obviously, this final adjustment can

be made only when 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 5 years for a final adjustment when using

standard seasonal adjustment options.

During the current year, limited use is made of new data

to estimate seasonal factors. The seasonal factors are forecast

for the first 6 months of the year based on data ending in

December of the last year. For the second half of the year,

seasonal factor forecasts are prepared based on data through

June of the current year. This limited use of current data

tends to increase the size of the revision to the initial

seasonally adjusted estimates compared with an alternative

procedure, known as concurrent adjustment, which uses all

available data to prepare a seasonally adjusted estimate of

the most recent month’s data.

A number of research studies, including a 1987 paper on

the labor force series1 derived from the Current Population

Survey (CPS), have indicated that the alternative practice of

concurrent adjustment generally produces initial seasonally

adjusted estimates requiring smaller revisions than those

produced using projected factors. BLS is continuing to

compute and evaluate concurrent adjustment for the labor

force series.

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 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 revisions 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 usually much larger, although

even these rarely alter the essential trends observed in

the initial estimates for the major aggregate labor force

series.

Important Changes in 2003

Adoption of X-12 ARIMA, an improved seasonal adjustment

program, and several major changes to the CPS affect how

the seasonal adjustment of the labor force time series is

conducted this year. As discussed below in more detail, these

changes in the CPS will cause breaks in some of the labor

force series, but in many cases they are adequately controlled

for by using special options available in X-12.

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; e-mail:

Tiller_R@bls.gov; Evans_T@bls.gov

1 G.R. Methee 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.

From: Employment and Earnings, February 2003
25

Change in seasonal adjustment program

This year, the program used to seasonally adjust CPS data

has been updated from X-11 ARIMA, used by BLS since

1980, to the X-12-ARIMA program. The adoption of X-12

has led to expanded use of a model-based approach to prior

adjustments and the use of longer time series to develop

ARIMA models and evaluate the quality of seasonal

adjustment. The features and use of the program are

discussed in more detail later in this article.

New industry and occupational classification

systems

The CPS industry and occupational series are based on new

industry and occupational classification systems derived

respectively from the 2002 North American Industry

Classification System and the 2000 Standard Occupational

Classification system. These new classification systems result

in breaks in the time series for industry and occupational

data. As a result, seasonally adjusted detailed industry and

occupational estimates from the household survey will not

be presented until enough data classified under the new

systems become available to make a determination, based

on diagnostic testing, that these estimates meet minimum

quality standards. Selected series for agriculture and

nonagricultural industries will continue to be seasonally

adjusted.

The procedure for seasonally adjusting the total CPS

civilian labor force, employment, and the unemployment rate

will be affected by the change in industrial classification. In

the past, adding up the directly seasonally adjusted estimates

for eight age-sex-industry series yielded the seasonally

adjusted total employment level. (See the section on

aggregation procedures later in this article.) These eight

series consisted of teenagers and adults by sex in agriculture

and nonagricultural industries. Under the new industrial

classification system, there is a major decline in the size of

the agricultural sector due to a less inclusive definition of

that sector. This has a major effect on total agricultural

employment, and an even larger effect when agricultural

employment is disaggregated by age and sex. For this reason,

BLS is dropping the industry, age, and sex detail for deriving

the seasonally adjusted total employment series.

With the loss of industry detail, employment for only four

age-sex groups (teenage men, teenage women, men aged 20

years and over, and women aged 20 years and over) will be

directly seasonally adjusted and the sum of these four groups

will constitute the seasonally adjusted total employment

level. The change in the procedure for adjusting total

employment also affects estimates of the total labor force

and the unemployment rate. Total unemployment, however,

will not be affected because industry detail has not been used

to derive this total.

The change in procedure for deriving total seasonally

adjusted employment, using only the four age-sex groups,

has little effect on the adjusted labor force series. For this

reason, it is not necessary to revise adjusted total

employment, labor force, and the unemployment rate back

beyond the usual revision period of 5 years.

Seventeen employment series based on aggregate industry

levels—that is, agriculture and nonagricultural—will

continue to be seasonally adjusted. These series relate to

class of worker and part-time workers for those industries.

CPS industry data series from January 2000 to December

2002 have been recoded to reflect the new industrial

classification system. This will cause the break in the

agricultural series to appear as a large drop in level between

December 1999 and January 2000.

New race and ethnicity classifications

The CPS questions on race and Hispanic origin have been

modified to comply with the new standards for maintaining,

collecting, and presenting Federal data on race and ethnicity.

A major change is that respondents may select more than

one race when answering the survey. Prior to January 2003,

individuals who belonged to more than one race were forced

to pick a single primary race. The CPS series for whites and

blacks will now refer to persons who report, respectively,

that they are white (and no other race) and black or African

American (and no other race). Nationally, only 1.3 percent

of the civilian noninstitutional population aged 16 years and

older belonged to more than one race in May 2002, so this is

not likely to have a major effect on the white and black series.

Unlike those for race, modifications to the questions for

determining Hispanic status may have an effect on the

Hispanic labor force series. Respondents will continue to

be asked a separate question to determine if they are Hispanic,

but this question has been altered in important ways. Prior

to 2003, respondents were first asked about their race and

then asked to designate their or their ancestors’ country of

origin. Persons were than designated as Hispanic if their, or

their ancestors', origins lay in certain countries. Respondents

are now asked directly if they are Spanish, Hispanic, or Latino

before being asked about their race.

BLS will continue to seasonally adjust Hispanic total

employment and unemployment but will not introduce

seasonally adjusted data for detailed age and sex categories

at this time. The reason is that the new ethnicity question

may change the composition of those who identify

themselves as Hispanic and this may alter the seasonal

patterns, particularly for specific age and sex categories. As

more data become available, BLS will make a determination

as to the feasibility of seasonally adjusting more detailed

Hispanic series.

New population controls

Also beginning in 2003, population controls based on Census

2000 will be used in the current monthly CPS estimation

process. In addition, CPS data series from January 2000

through December 2002 have been revised to reflect the

introduction of the Census 2000-based population controls.

Revisions further back in time were not considered feasible,

primarily because the 1990 census-based intercensal
26

population estimates were adjusted for the estimated

undercount in the 1990 census, whereas the 2000 censusbased estimates have no undercount adjustment. This will

cause a break to occur in some of the historical series between

December 1999 and January 2000. In particular, there is a

net increase in total population, due to increases in the

number of Hispanics, adults, and whites that more than offset

decreases in the number of teenagers and blacks.

Effect of Changes

Normally, the only reason for making yearly revisions to

seasonally adjusted series is to account for new information

in the latest available data. This year, however, revisions

also will be affected by the changes in the CPS and the

adoption of the X-12 ARIMA seasonal adjustment program.

The changes introduced into the CPS this year affect the

number of series that are directly seasonally adjusted. Prior

to 2003, 182 series based on age, sex, industry, occupation,

and other characteristics were directly seasonally adjusted;

beginning in 2003, 116 series are directly seasonally

adjusted. Eighty-one series have been eliminated: most of

these were related to industry and occupation. Fifteen

aggregate series, previously derived from detailed series that

are no longer seasonally adjusted, are now directly seasonally

adjusted at the aggregate level.

In another change, the length of many of the series used

for time series modeling has been extended. Models for six

of the eight major labor force series are estimated using data

beginning in 1976. (See table 1.) The revisions to the

seasonally adjusted estimates, however, do not need to extend

beyond 5 years because of the limited memory of X-12 filters.

The purpose of using a longer time series is to improve the

quality of the time series models used to support the seasonal

adjustment process. (See the section on time series models

below for further discussion.)

Another change concerns the use of prior adjustments to

correct a series for outliers. Previously, prior adjustments

were confined to special events occurring in 1994, 1997,

and 1999. Additional prior adjustments have been added to

account for the changes in the data beginning in 2000, as

well as for special events that occur in the part of the series

that has been extended to earlier years.

This y ear’s revisions incorporate data through December

2002 and provide revised estimates for January 1998 through

December 2002 for all previously seasonally adjusted labor

force series. Table 2 contains the prior adjustment factors

and the new projected seasonal factors to be applied during

the first 6 months of 2003 to the eight component series

used in the computation of the seasonally adjusted civilian

labor force and unemployment rate. (See the section on

aggregation procedures later in this article.) Projected factors

for the last 6 months of 2003 will be published in the July

issue of this publication.

An important criterion for evaluating alternative methods

of seasonal adjustment is how close initial estimates are to

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 2002 seasonally adjusted data are not

final, the first revisions are usually the largest, and often

indicate the direction of subsequent revisions. This year,

however, the revisions reflect both new observations and the

changes in the CPS data discussed earlier.

Table 3 shows the civilian unemployment rates for 2002

as first computed and as revised. Rounded to one decimal

place as published, the rates were unchanged in 4 of the 12

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

the remaining 8 months. Both the initial and revised series

show the same overall rise in the rate from 5.6 percent in

January to 6.0 percent in December.

Adjustment Methods and Procedures

As indicated earlier, the official seasonal adjustment

procedure for the labor force series has been changed this

year to X-12 ARIMA from the X-11 ARIMA program that

had been in use by BLS since 1980.

Both X-12 and X-11 ARIMA are based on the widely

used X-11 method developed at the U.S. Census Bureau in

the 1960s.2 X-11 ARIMA added to X-11 the ability to extend

2 For a detailed discussion of X-12 ARIMA see, D.F. Findley, B.C.

Monsell, W.R. Bell, M.C. Otto, and B.C. Chen, “New Capabilities and

Methods of the X-12-ARIMA Seasonal Adjustment Program,” Journal of

Business and Economic Statistics, April 1998, Vol. 16, No. 2, pp.127-152.

For documentation on X-11 ARIMA, see The X-11 ARIMA Seasonal Adjustment Method, by Estela Bee Dagum (Statistics Canada Catalogue No.

12-564E, January 1983). The X-11 method is described in The X-11 Variant of the Census Method II Seasonal Adjustment Program, by Julius

Shiskin, Alan Young, and John Musgrave (Technical Paper No. 15, Bureau

of the Census, 1967).

Table 1. REGARIMA models used for the eight major civilian

labor force components

Series Model Trans- Length

formation of series

Total employment:

Men, 20 y ears and over ..... (0,1,2)(0,1,1) LOG 1976-2002

Women, 20 years and

over .................................. (0,1,0)(0,1,1) LOG 1976-2002

Men, 16 to 19 y ears ........... (3,1,0)(0,1,1) LOG 1976-2002

Women, 16 to 19 y ears ...... (0,1,1)(0,1,1) LOG 1976-2002

Total unemployment:

Men, 20 y ears and over ..... (0,1,3)(0,1,1) LOG 1990-2002

Women, 20 years and

over .................................. (1,1,0)(0,1,1) LOG 1990-2002

Men, 16 to 19 y ears ........... (0,1,1)(0,1,1) LOG 1976-2002

Women, 16 to 19 y ears ...... (0,1,1)(0,1,1) LOG 1976-2002
27

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 they are recalculated after future data

become available.

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

program includes all 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 post-adjustment diagnostics.

For the majority of labor force series 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;

• 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 models3 are designed to make forecasts of a time

series based only on 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.

3 For a more detailed discussion of ARIMA models, refer to G.E.P. Box

and G.M. Jenkins, Time Series Analysis, Forecasting and Control (San

Francisco, Holden Day, 1970); and M. Kendall and J.K. Ord, Time Series

(New York, University Press, 1990).

Table 2. Prior adjustment and January-June 2003 seasonal adjustment factors for the eight major civilian labor force

components

Mode of

Prior adjustment factors Projected seasonal adjustment factors

Series

adjustment Pre- Pre- Pre- January February March April May June 1990 1994 2000

Total employment:

Men, 20 y ears and over............ Multiplicative .975 .982 .986 .989 .991 .999 1.003 1.006

Women, 20 y ears and over ...... Multiplicative .987 .998 1.003 1.006 1.003 1.001 .993

Men, 16 to 19 years ................. Multiplicative .939 .957 .897 .920 .947 .939 .985 1.133

Women, 16 to 19 years ............ Multiplicative .935 .946 .944 .942 .954 1.115

Total unemployment:

Men, 20 y ears and over............ Multiplicative 1.216 1.183 1.148 1.009 .933 .938

Women, 20 y ears and over ...... Multiplicative 1.082 1.033 1.011 .947 .962 1.026

Men, 16 to 19 years ................. Multiplicative 1.033 1.024 .959 .881 .896 1.337

Women, 16 to 19 years ............ Multiplicative .917 .928 .969 .894 .994 1.354

Table 3. Seasonally adjusted unemployment rates in 2002

and change due to revision

As first As

computed revised

January ........................................... 5.6 5.6 .0

February .......................................... 5.5 5.6 0.1

March .............................................. 5.7 5.7 .0

April ................................................. 6.0 5.9 -.1

May ................................................. 5.8 5.8 .0

June ................................................ 5.9 5.8 -.1

July .................................................. 5.9 5.8 -.1

August ............................................. 5.7 5.8 .1

September....................................... 5.6 5.7 .1

October ........................................... 5.7 5.8 .1

November........................................ 6.0 5.9 -.1

December........................................ 6.0 6.0 .0

Month Change
28

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, which 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 Box

and Tiao4.

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, b 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 1.)

There are well developed methods for determining the

number and type 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 prior information is available 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 Chang, Tiao, and Chen. 5 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

directly used 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

from the distant past for seasonal adjustment is questioned.

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 obtain 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 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 large changes to

estimated parameters, which in turn may lead to larger-thannecessary 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 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 the observed data. When there

is a tradeoff between 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 it 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 2002. For each of the eight major civilian

labor force components, table 1 presents the form of the

ARIMA part of the model, the transformation selected, and

the length of the series used to fit the model.

Prior adjustments

The purpose of prior adjustments is to correct the original

series for atypical observations and other external effects

that otherwise would seriously distort the estimates of the

4 G.E.P. Box and G.C. Tiao,“Intervention Analysis with Applications

to Economic and Environmental Problems,” Journal ofthe American

Statistical Association, vol. 70, 1975, pp. 71-79.

5

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

in the Presence of Outliers,” Technometrics, vol. 30, 1988, pp. 193-204.
29

seasonal factors. These corrections, or prior adjustment

factors, are subtracted from the original series if the seasonal

adjustment is additive. If the seasonal adjustment is

multiplicative, the original series is divided by these values.

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.6 One notable economic

level shift was due to the 2001 terrorist bombings. These 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

2000 census, were introduced with the release of data for

January 2003 and were extended back to data beginning in

January 2000. The nature and effect of these revisions have

been discussed previously.

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, as discussed above, 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 2000-based census population controls and the decline in

agricultural employment caused by the change in the industry

classification system.

A number of intervention effects previously identified in

selected series for 1994, 1997, and 1999 were found to no

longer be significant, and some additional interventions for

1990 and 1980 were added to account for the use of longer

series.

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 eight major

civilian labor force component series are shown in table 2,

together with the seasonal factors. 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 and unemployed private wage and salary workers in

the transportation and public utilities industry were identified

as having had substantial upward level shifts 1 month after

the September 11, 2001, terrorist bombings of the World

Trade Center in New York City. (Because of the introduction

of the new industry classification system, the seasonal

adjustment of the second series was discontinued.) (See 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 bombings.

Calendar effects. Calendar effects refer to transitory level

shifts in a series resulting from calendar events such as

moving holidays or the differing composition of weekdays

in a month between years. These effects have different

influences on data for 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 initially seasonally adjusted with multiplicative models

using the moving-holiday extension of X-11 ARIMA

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; and “New

Seasonal Adjustment Factors for Household Data Series” in the July 1999

issue.
30

developed at BLS. This procedure has been adapted to

X-12 ARIMA. 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

uses 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 about 120 time points.

That is, to obtain a final seasonally adjusted estimate for a

single time point requires 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 tests

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 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 labor force,

and the unemployment rate for all civilian workers. These

are produced by 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 the

same four age-sex groups for employment in all industries.

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 in

percentage form).

A problem with producing seasonally adjusted estimates

for a series by aggregation is that seasonal adjustment factors

can not be directly computed and projected 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
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additive implicit factors, the difference between those two

aggregates.

Availability of revised series

This issue of Employment and Earnings contains revised

data for the most recent 12 months 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 1997 and earlier years were

not further revised.

The January-June 2003 factors for any of the directly

adjusted series beyond the eight major labor force

components can be obtained from BLS upon request.

Requests for the seasonal factors used for the labor force

data should be addressed to the Division of Data

Development and Publications, Office of Employment and

Unemployment Statistics, Bureau of Labor Statistics,

Washington, DC 20212.