Revision of Seasonally Adjusted

Labor Force Series

Robert J. McIntire, Richard B. Tiller, and Thomas D. Evans

T

he original data values for many economic time series

are often substantially influenced by seasonality,

reflecting recurring calendar-related effects caused by

weather, holidays, the opening and closing of schools, and

other such seasonal events. Seasonal adjustment is a process

used to estimate and remove that seasonality. The reason for

doing so is to make it easier to observe and analyze the

nonseasonal movements in the series, particularly short-term

movements associated with business cycles.

The seasonal adjustment process produces estimates of

seasonality, called seasonal factors, for the period of observations used in the process and for some projected observations immediately following that period. For the labor force

series, initial seasonal adjustment of current data is done using the projected seasonal factors, which are estimates of how

much the original unadjusted values can be expected to deviate from underlying trend-cycle levels due to recurring behavior as projected from average seasonal patterns in the recent past.

Even though seasonality involves regularly recurring

patterns, it does tend to change or at least evolve over time,

creating a need for periodic reestimation of factors and

revision of recently adjusted estimates. By including more

recent data in the estimation process, the revision process

can provide better estimates of how much the original,

unadjusted estimates actually deviated from underlying trendcycle levels during the recent period, thereby improving the

historical seasonally adjusted data for that period. In addition,

the new information is incorporated to produce the new

projected factors to be used for current seasonal adjustment.

Therefore, at the end of each calendar year, the Bureau of

Labor Statistics (BLS) reestimates the seasonality of the unemployment, employment, and other labor force series derived

from the Current Population Survey (CPS) by including another full year of data in the estimation process. Based on this

annual reestimation, BLS issues the projected factors for the

first 6 months of the new year as well as revised estimates of

historical seasonally adjusted data for the last 5 years. Each

year's data are generally subject to five revision cycles

before the values are considered final. The fifth and final

revisions in the earliest of the 5 years are usually quite small,

Robert J. McIntire is the former Chief of the Division of Data Development

and Publications and 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 -

while the ftrst-time revisions in the most recent year can be

much more substantial, although even these rarely alter the essential trends observed in the initial major estimates. This year's

revisions incorporate data through December 2001 and provide revised estimates forJanuary 1997 through December 200 1

for all previously seasonally adjusted labor force series.

Table 1 contains the new projected seasonal factors to be

applied during the first 6 months of 2002 to the 12 component series usedin the computation of the seasonally adjusted

civilian labor force and unemployment rate. (See the section

on aggregation procedures later in the article.) Projected factors for the last 6 months of 2002 will be published in the

July issue of this publication.

Effect of revisions

One of the criteria used to evaluate alternative methods of

seasonal adjustment is how close initial estimates are to subsequent revisions. Policymakers and analysts must make determinations based on current information, and so it is important that the initial estimates of current factors for the seasonal adjustment of major-economic series produce estimates

of level and change that are as close as possible to the improved estimates that will be made after more data have become available. Even though the revisions currently being

released for the 2001 seasonally adjusted data are not final,

the first revisions are usually more substantial than, and often indicate the direction of, any subsequent revisions. Therefore, it is appropriate to compare these first revisions with

the initial estimates. Table 2 shows the civilian unemployment rates for 2001 as first computed and as revised, as well

as the changes due to revision. Rounded to one decimal place

as published, the rates were unchanged in 7 of the 12 months,

and changed by ± 0.1 percentage point in the remaining 5

months. The effects of the revisions would be more evident

if the rates were computed to more decimal places.

Adjustment methods and procedures

The official seasonal adjustment procedure for the labor force

series is the X-II ARIMA program, which was developed at

Statistics Canada during the 1970s as an extension of and

improvement to the widely used X-ll method developed at

I The primary documentation for the X-ll ARIMA procedure is The

X-Il ARIMA Seasonal Adjustment Method, by Estela Bee Dagum (Statistics Canada Catalogue No. 12-564E, January 1983). (ARIMA is an acronym for Auto-Regressive Integrated Moving Average.) The X-II method is

described in The X-if Variant of the Census Method II Seasonal Adjustment

Program, by Julius Shiskin, Alan Young, and John Musgrave (Technical

Paper No. IS, Bureau of the Census, 1967).

3
Table 1. Pre-1994 prior adjustment and January-June 2002 seasonal adjustment factors for the 12 major

civilian labor force components

Prior Seasonal adjustment factors

Procedure and series adjustment

factors January February March April May June

Multiplicative adjustment

(Divide factor into original value)

Agricultural employment:

Men, 20 years and over .......................... C) .895 .885 .924 1.005 1.052 1.076

Women, 20 years and over ..................... .776 .935 .969 .979 1.026 1.057 1.046

Men, 16 to 19 years .............•.................. .860 .607 .590 .695 .856 1.121 1.393

Women, 16 to 19 years ........................... .853 .650 .653 .754 .787 1.229 1.627

Nonagricultural employment

Men, 20 years and over .......................... 2.996, 1.00~ .993 .994 .996 .999 .999 1.003

Women, 20 years and over ..................... 3.996 1.000 1.003 1.007 1.003 1.001 .994

Unemployment:

Men, 20 years and over .......................... .938 1.202 1.201 1.147 .982 .936 .937

Women, 20 years and over ..................... .976 1.093 1.030 1.018 .929 .957 1.036

Additive adjustment

(Subtract factor from original value)

Nonagricultural employment:

Men, 16 to 19 years ................................ -68 -302 -218 -162 -179 -94 432

Women, 16 to 19 years ........................... -96 -190 -164 -200 -163 -135 365

Unemployment:

Men, 16 to 19 years ................................ -47 49 34 -35 -70 -72 208

Women, 16 to 19 years ........................... (') -61 -27 -18 -67 -9 177

1 No prior adjustment was done.

2 For this series, the factors are pre-1997 and pre-1999. The first

factor shows the adjustment of pre-1997 data relative to subsequent

data, the second factor shows the adjustment of pre-1999 data relative to subsequent data. The actual net adjustment to pre-1997 data

is the product of the two factors.

3For this series, the prior adjusted period was pre-1999 rather than

pre-1994.

the U.S. Census Bureau in the 1960s.1 The X-ll ARIMA

method improves current estimates for most series by allowing recent observations, especially those of the last 6 months,

to weigh more heavily in the estimates of current and recent

seasonal factors than did the X-ll alone. The method provides this improvement through the use of ARIMA models

to extend the data series by 12 months. The X-ll algorithm

for seasonal adjustment is then applied to the extended

series.

(p,d,q)(P,D,Q) TRANSFORMATION,

Where:

(1) P is the number of regular (nonseasonal)

autoregressive parameters

(2) d is the number of regular differences

(3) q is the number of regular moving average

parameters

(4) P is the number of seasonal autoregressive

parameters

(5) D is the number of seasonal differences

(6) Q is the number of seasonal moving average

parameters

(7) TRANSFORMATION may be NONE, LOG,

or POWER(n).

ARIMA models. ARIMA projections are based only on the

past experience observed in a series itself. ARIMA models

have proved to have good properties for short-term projection or extrapolation of a large class of time series, especially

in a seasonal adjustment context, since the extrapolations tend

to track intra-year movements quite well. The ARIMA models in the X-ll ARIMA program used to seasonally adjust

the labor force series are of the Box-Jenkins type.' They can

generally be described with the notation:

2 For a more detailed discussion of ARIMA models, refer to previously

cited Dagum (I983) and to G.B.P. Box and G.M. Jenkins, TIme Series AMlysis, Forecasting and Control (San Francisco, Holden Day, 1970); and C.W.J.

Granger and P. Newbold, Forecasting Economic Time Series (New York,

Academic Press, 1977).

While the lettered elements within the parentheses of the

model specifications can theoretically take on many values,

in practice, only small values are useful. (See table 3.)

For each labor force series which has been extended based

on an ARIMA model, the model has been specifically

4

f

1,
Table 2. Seasonally adjusted unemployment rates In 2001

and change due to revision

Month As first As Change

computed revised

January 4.2 4.2 a

February 4.2 4.2 a

March 4.3 4.3 a

April 1.. 4.5 4.5 a

May ..............................•................... 4.4 4.4 a

June 4.5 4.6 0.1

July ,........................... 4.5 4.6 .1

August 4.9 4.9 a

September 4.9 5.0 .1

October 5.4 5.4 a

November 5.7 5.6 -.1

December 15.9 5.8 -.1

1 This rate reflects the use of seasonal factors projected for December 2001 as published in the July 2001 issue of Employment and

Earnings and was subject to revision before regular publication of

December data.

chosen as well suited to the particular series, based on a set

of established criteria. The criteria essentially require a model

to: (1) Fit the series well, (2) have low average forecasting

errors in the last 3 years prior to the projected year, and (3)

produce residuals (the differences between the observed values and the values forecast by the model for the observed

period) which follow a random pattern. Acceptable ARIMA

models have been identified and were used for 176 of the

182 labor force series which were directly adjusted at the

end of 200 1, including all 12 major civilian labor force components, whose ARIMA models are shown in table 3 and are

unchanged from last year. The six remaining series for which

acceptable models have not been identified were simply run

through the X-II part of the program without any ARIMA

extrapolations.

X-II procedures. The procedures used for this year's adjustment of the labor force series within the X-ll part of the

process were different from the standard procedures of most

previous years in one respect. Because of the changes introduced at the beginning of 1994, 1997, and 1999 in the

survey and processing procedures on which the labor force

series estimates are based, prior adjustment factors were used

in these X-II ARIMA runs to link the pre-1994, pre-1997,

and/or pre-1999 data with the subsequent data for purposes

of seasonal adjustment. 3 Without prior adjustment, those

changes could have caused distortion in the seasonal decomposition. The prior adjustment factors used for all 12 major

3 For further discussion of these prior adjustment factors and the changes

that they control for, 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.

components are shown in table 1 alongside the seasonal

factors. A 12-year time period, including data from January

1990 through December 2001, was used for the

adjustment of all the labor force series except for the eight

educational attainment series (which begin in 1992), and the

one series for persons not in the labor force who currently

want a job (which begins in 1994).

The X-II method of seasonal adjustment contained in the

X-ll AR.MA procedure assumes that the original series,

including the 12 extrapolated observations if an ARIMA

model has been applied, is either the product or the sum of

three components-trend-cycle, seasonal, and irregular. The

method uses either a ratio-to- or difference-from-movingaverage approach to estimate the components, depending on

whether the multiplicative or additive model is used. The

seasonally adjusted series values are computed by dividing

each month's original value by the corresponding seasonal

factor if the multiplicative model is used, or by subtracting

the factor if the additive model is used. Of the 12major civilian

labor force components, the 4 teenage unemployment and

nonagricultural employment series were adjusted using the

additive model, and the other 8 series with the multiplicative

model. Of all the 182 directly adjusted series, 48 were adjusted

with the additive model, including most teenage employment

and unemployment series, for which the seasonal components

were found to be fairly independent of the trend-cycle.

Moving-holiday adjustment. Two of the series directly adjusted with multiplicative models were seasonally adjusted

using the moving-holiday extension of X-II ARIMA which

was developed at BLS. Both holiday-adjusted series-persons at work on part-time schedules for noneconomic

reasons who usually work part time in all industries and

nonagricultural industries-had tested as having significant

and well-defined effects in their April data related to the

timing of Easter. A detailed discussion of the nature of the

Easter effect in these series and of the procedure used to conTable 3. ARIMA models used In end-of-2001 seasonal

adjustment for the 12 major civilian labor force components

Series Model Transformation

Agricultural employment:

Men, 20 years and over ............. (1,0,0)(0,1,1) LOG

Women, 20 years and over ........ (0,1 ,1)(0,1 ,1) LOG

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

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

Nonagricultural employment:

Men, 20 years and over ............. (0,1,1 )(0,1,1) LOG

Women, 20 years and over ........ (0,1,4)(0,1,1) LOG

Men, 16 to 19 years ................... (4,1,1 )(0,1,1) NONE

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

Unemployment:

Men, 20 years and over ............. (0,1,3)(0,1,1) LOG

Women, 20 years and over ........ (0,1,1)(0,1,1) LOG

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

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

5
trol for it as part of the seasonal adjustment process was

included in the January 1990 version of this article.

Six-month updates. The current official practice for the seasonal adjustment of the labor force series involves the running of all directly adjusted series through X-II ARIMA

twice each year. This is done after receipt of June and

December data, with 6 months of projected factors drawn

from each run and historical revisions drawn from the endof-year run. This practice allows, among other things, the

prior publication of seasonal factors, which historically has

been regarded by the Bureau of Labor Statistics and other

statistical agencies as an important way of ensuring the openness of their seasonal adjustment procedures, especially where

very sensitive indicators such as the unemployment rate have

been involved. A number of research studies, including a 1987

paper on the labor force series," have indicated that the alternative practice of concurrent adjustment, where the seasonal

adjustment procedure is run with all available data each month

and factors cannot be published ahead of time, generally produces initial seasonally adjusted estimates requiring smaller

revisions than those produced by adjustment using projected

factors. The BLS is continuing to compute and evaluate concurrent adjustment for the labor force series.

Aggregation procedures

BLS maintains and publishes several hundred seasonally

adjusted labor force series in addition to the 182 directly adjusted series discussed above. These additional series are

produced by arithmetically combining or aggregating the

directly adjusted series with each other or, in some cases,

with series on population which are not seasonally adjusted

because they are not considered to have any significant seasonal variation. For example, the seasonally adjusted levels

of total unemployment, civilian employment, and civilian

labor force, and the seasonally adjusted unemployment rate

for all civilian workers, are all produced by aggregation of

some or all of the seasonally adjusted results for the 12 major civilian labor force components. The seasonally adjusted

level of total unemployment is the sum of the seasonally adjusted levels of unemployment for the four age-sex groupsmen and women 16 to 19, and men and women 20 years and

over. Seasonally adjusted civilian employment is the sum of

the seasonally adjusted levels of employment for the eight

employment components-the same four age-sex groups as

noted above employed in nonagricultural and agricultural

industries. The seasonally adjusted civilian labor force is the

sum of all 12 components. The seasonally adjusted civilian

unemployment rate is calculated by taking the total seasonally adjusted unemployment level as a percent of the total

seasonally adjusted civilian labor force.

4 G.R. Methee and RJ. 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.

The principal reason for producing many of the major

seasonally adjusted estimates for the labor force by aggregation rather than by direct adjustment is that this approach

ensures that the major seasonally adjusted totals will be

arithmetically consistent with at least one major set of components. If the totals were directly adjusted along with the

components, such consistency would not, in all likelihood,

occur, since the X-II is not a sum-preserving procedure. That

is, the sum of the result for two or more directly adjusted

series will not generally be the same as the result of directly

adjusting the sum of the unadjusted versions of the same

series. Another factor is that it would generally be inappropriate to apply seasonal factors computed for an aggregate

series to the components of the aggregate. The various labor

force components tend to have significantly different

patterns of seasonal variation; for example, teenage unemployment tends to peak in June, while unemployment of

adult men tends to peak in the winter months of January and

February. In order to estimate properly these varying seasonal patterns, it is necessary to adjust the components

directly. Of course, one of the implications of producing seasonally adjusted estimates for many major series by aggregation is that exact factors cannot be projected for those

series. However, implicit seasonal adjustment factors can be

calculated after the fact by taking the ratio of the unadjusted

aggregate to the seasonally adjusted aggregate, or, for

additive implicit factors, the difference between those two

aggregates.

Effects of September 11 on seasonal adjustment

The seasonally adjusted total unemployment rate jumped

four-tenths of a percentage point in October and continued

to increase through December 2001. This unusually large

increase to a new level raises the issue as to whether there

has been a sudden change in trend for unemployment and

perhaps for other labor force categories. This would seem to

be a real possibility because October is the month in which

the initial impact of the September II, 200 I, terrorist attacks

would be expected to be seen in the CPS data.

A specific event that causes a time series to deviate from

its expected evolutionary pattern is often referred to as

an intervention. Should such an event occur in the CPS and

nothing is done to adjust for it, the projections of seasonal

factors and revisions to the historical factors may be seriously distorted.

To test for the possibility that the terrorist attacks had

important effects on the CPS series, each ARIMA model used

for forecasting was modified to include an intervention variable. This variable is a dummy regressor or indicator variable, which flags October as the timing of the intervention

and assumes the intervention is permanent. The coefficient

for this variable provides an estimate of the direction and

magnitude of the intervention effect.

Out of the 182 series that are directly seasonally adjusted,

2 series, unemployed job losers and unemployed private wage

and salary workers in the transportation and public utilities

6
industry, were identified as having had substantial upward

level shifts that seriously distorted their seasonal patterns.

Before seasonally adjusting these two series, the estimated

level shifts were removed in a process called prior adjustment. Prior adjustment factors that reflect 75 percent of the

estimated intervention coefficients were actually used to guard

against overadjustment. Estimation of the seasonal factors

was then done on the adjusted series. These factors were then

applied to the original series without prior adjustment to obtain the seasonally adjusted series.

While this assessment was made with the limited amount

of data available following September 11, additional data will

be available at midyear to reassess these effects. Moreover,

the projected seasonal factors for the first part of2002 were

not much affected by the events of September 11. The seasonally adjusted total unemployment rate was not affected at

all since none of the 12 series used to derive the rate appear

to need intervention adjustment.

Availability of revised series

This issue of Employment and Earnings contains revised

monthly and quarterly data for the most recent 13 months

and calendar quarters for many seasonally adjusted labor force

series. These revisions replace the seasonally adjusted estimates previously published for those periods. Revised historical seasonally adjusted labor force data also are available

in various forms on the Internet (www.bls.gov), including

ftp access (ftp:llftp.bls.govlpublspecial.requestsllfl) to all

the revised data. The seasonally adjusted data last published

for 1996 and earlier years were not further revised.

The January-June 2002 factors for any of the directly

adjusted series beyond the 12 major 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.

7