Revision of Seasonally Adjusted

Labor Force Series

Robert J. Mcintire

The original data values for many economic time series

are. often substantially influenced by seasonality. This

reflects 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. These 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 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. Usually, the data for the

last 5 years are revised. This time, however, because of the

changes introduced at the beginning of 1994 in the survey

and the processing procedures on which the labor force

series estimates are based,' only the historical seasonal

adjusted data for 1994 forward are being revised, based upon

data through December 1997.

Robert J. McIntire is an economist and Chief of the Division of Data

Development and Publications, Office of Employment and Unemployment

Statistics, Bureau of Labor Statistics.

The new projected seasonal factors to be applied to the 12

component series used in the computation of the seasonally

adjusted civilian labor force and unemployment rate during

the first 6 months of 1998, appear in table 1. (See the section on aggregation procedures later in the article.) Projected

factors for the last 6 months of 1998 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. It is important, therefore, 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 1997 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. The civilian unemployment.rates for 1997 as first computed and as revised, as well

as the changes due to revision, appear in table 2. Rounded

to one decimal place as published, the rate changed in 4 of

the 12 months, and the absolute effect of the changes never

exceeded 0.1 percentage point in any of those months. The

trend observed in the initial estimates was sustained in the

revisions.

Adjustment methods and procedures

The official seasonal adjustment procedure for the labor

force series is the X-ll ARIMA program, which was developed at Statistics Canada during the 1970s as an extension

of and improvement to the widely used X-II method developed at the U.S. Bureau of the Census in the 1960s.2 The

X-II ARIMA method improves current estimates for most

I The changes were described in "Revisions in the Current Population

Survey Effective January 1994" in the February 1994 issue of this publication.

2 The primary documentation for the X-II ARIMA procedure is The

X-II ARIMA Seasonal Adjustment Method, by Estela Bee Dagum (Statistics

Canada Catalogue No. 12-564E, January 1983). (ARIMA is an acronym

for AutoRegressive Integrated Moving Average.) The X-II method is described in The X-II 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 1998 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 ......................•.... (1) .901 .899 .953 .994 1.068 1.083

Women, 20 years and over .........•.....•••••.• .776 .896 .901 .944 1.000 1.025 1.069

Men, 16 to 19 years ....•••••...•.................... .860 .674 .620 .753 .959 1.247 1.502

Women, 16 to 19 years ...................•........ .853 .735 .584 .794 .760 .977 1.485

Nonagricultural employment:

Men, 20 years and over ..•••••••.•.•••••••.••..... 2.996 .985 .989 .994 .996 1.001 1.006

Women, 20 years and over .•..••••••••••••••..•• (1) .995 .999 1.003 1.001 .999 .993

Unemployment:

Men, 20 years and over ......................•.... .938 1.211 1.170 1.146 1.024 .961 .939

Women, 20 years and over ...........••......... .976 1.053 1.008 .988 .918 .956 1.009

Additive adjustment

(Subtract factor from original value)

Nonagricultural employment:

Men, 16 to 19 years ................................. -68 -330 -248 -255 -202 -93 366

Women, 16 to 19 years ................•......••... -96 -238 -252 -170 -207 -109 321

Unemployment:

Men, 16 to 19 years .•..............•....•.•.•.••.... -47 -9 -31 -14 -38 -6 236

Women, 16to 19 years ..•............••...•.•.•... (1) -28 -23 -61 -37 57 197

1 No prior adjustment was done.

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-II alone.

The method provides this improvement through the use of

AAIMA models to extend the data series by 12 months. The

X-ll algorithm for seasonal adjustment is then applied to

the extended series.

ARIMA models. ARIMA projections are based only on the

past experience observed in a series itself. ARIMA models

have proved to have good properties for short-term projectionor 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 AAIMA models in the X-II AAIMA program used

t<), seasonally adjust the labor force series are of the Boxl~qkins type. 3 They ~an generally be described with the

notation:

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

3 Fora more detailed discussion of ARIMA models, refer to previously

cited Dagum (1983) and toG.B.P. Box and G.M. Jenkins, Time SeriesAnalysis, Forecasting and Control (San Francisco, Holden Day, 1970); and C.WJ.

Granger and P. Newbold,Forecasting Economic Tune Series (New Yorlt,

Academic Press, 1977).

2 For this series, the prior adjusted period was pre-1997 rather than pre-1994.

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).

Although the lettered elements within the parentheses of

the model specifications can theoretically take on many values, in practice, only small values are useful.

For each labor force series which has been extended based

on an ARJMA model, the model has been specifically chosen as well suited to the particular series, based on a set of

established criteria. The criteria essentially require a model

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

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

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

4
Table 2. Seasonally adjusted unemployment rates In 1997

and change due to revision

Month As'first As

computed revised Change

January 5.4

February 5.3

March 5.2

April.................................................. 4.9

May 4.8

June 5.0

July ................................•.................. 4.8

August·.............................................. 4.9

September 4.9

October 4.7

November 4.6

Decernber......................................... 14.7

5.3

5.3

52

5.0

4.8

5.0

4.9

4.9

4.9

4.8

4.6

4.7

-0.1

o

o

.1

o

o

.1

o

o

.1

o

o

1 This rate reflects the use of seasonal factors projected for December 1997 as published in the July 1997 issue of Employment and

Earnings and was subject to revision before regular publication of

December data.

period) which follow a random pattern. Acceptable ARIMA

models have been identified and were used for 175 of the

181 labor force series which were directly adjusted at the

end of 1997, including all 12 major civilian labor force components, whose ARIMA models are unchanged since last

year and are shown in table 3. 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-J1 procedures. The procedures used for this year's adjustment of the labor force series within the X-II part of the

process were different from the standard procedures of most

previous years in two respects.

First, prior adjustment factors identical to those used the

last 2 years were used again in these X-ll ARIMA runs to

link the pre-1994 data with the subsequent data for purposes

of seasonal adjustment 4. Additionally, pre-1997 prior

adjustment factors were introduced this year for seven series

that had sufficiently large effects from the population control revisions introduced in January 1997 data ' to potentially distort seasonal estimation without prior adjustment.

The most notable series among the seven are the employment and unemployment levels for Hispanics, the demographic group most affected by the revisions, and one of the

major components, nonagricultural employment for men 20

years and over. The prior adjustment factors used for all 12

major components are shown in table 1 alongside the seasonal factors.

Second, instead of a 10 year span, an 8-year time period,

including data from January 1990 through December 1997,

4 For further discussion of those prior adjustment factors, see "Revisions

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

issue of this publication.

S See "Revisions in the Current Population Survey Effective January

1997" in the February 1997 issue of this publication.

was used for the adjustment of all the labor force series

except for the first-time adjustment of eight educational

attainment series (which begin in 1992). This was done primarily for the sake of keeping the seasonal adjustment process no more complicated than it has to be to serve its principal objectives. Because the population-related revisions to

the unadjusted data discussed in the March 1996 version of

this article could be done only back to 1990, inclusion of

pre-1990 data in these runs would have required the computation and use of additional prior adjustment factors for many

series that would have had little or no effect on the seasonal

adjustment of current data.

The X-II method of seasonal adjustment contained in the

X-ll ARIMA procedure assumes that the original series,

including the 12 extrapolated observations if an ARIMA

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

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

method uses either a ratio-to- or difference-from-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 12 major

civilian labor force components, the 4 teenage unemployment and nonagricultural employment series were adjusted

using the additive model, and the other 8 series with the

multiplicative model. Of all the 181 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-at work

Table·3. ARIMA models used In end-of·1997 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, t,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 .................... (2,1,0)(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) N()NE

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

5
on part-time schedules for noneconomic reasons, usually

work part time, all industries and nonagricultural industries-s-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 control 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, after receipt of June and December data,

with 6 months of projected factors drawn from each run and

historical revisions drawn from the end-of-year run. This

practice allows, among other things, the prior publication of

seasonal factors, which historically has been regarded by

the Bureau of Labor Statistics and other statistical agencies

as an important way of ensuring the 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 re-

-quiring smaller revisions than those produced by adjustment

using projected factors. 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 181 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

groups-men 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

6 OR Methee and RJ. McIntire, "An Evaluation of Concurrent Seasonal

Adjustment for the Major Labor Force Series," in the 1987 Proceedings ofthe

Business and Economic Statistics Section, American Statistical Association.

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.

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.

Availability of revised series

This issue of Employment and Earnings contains revised

monthly and quarterly data for the most recent 13 months

and 12 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 (stats.bls.gov), including ftp access (ftp://stats.bls.gov/pub/special.requests/lf) to

all the revised data. The seasonally adjusted data last published for 1993 and earlier years were not further revised.

The January-June 1998 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 or inquiries concerning the seasonal adjustment methodology 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.

6