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Seasonal Adjustment

Over the course of a year, the size of the Nation’s labor force,

the levels of employment and unemployment, and other measures of labor market activity undergo sharp fluctuations due

to such seasonal events as changes in weather, reduced or

expanded production, harvests, major holidays, and the opening and closing of schools. Because these seasonal events

follow a more or less regular pattern each year, their influence

on statistical trends can be eliminated by adjusting the statistics from month to month. These adjustments make it easier

to observe the cyclical and other nonseasonal movements in

the series. Seasonally adjusted series for selected labor force

and establishment-based data are published monthly in

Employment and Earnings.

Household data

Beginning in January 2003, BLS started using the X-12-

ARIMA (Auto-Regressive Integrated Moving Average)

seasonal adjustment program to seasonally adjust national

labor force data from the Current Population Survey (CPS),

or household survey. This program replaced the X-11 ARIMA

program which had been used since January 1980. For a

detailed description of the X-12-ARIMA program and its

features, 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. See “Revision of Seasonally Adjusted Labor Force Series

in 2003,” in the February 2003 issue of this publication for a

discussion of the introduction of the use of X-12 ARIMA for

seasonal adjustment of the labor force data and the effects

that it had on the data.

Beginning in January 2004, BLS converted to the use of

concurrent seasonal adjustment to produce seasonally

adjusted labor force estimates from the household survey.

Concurrent seasonal adjustment uses all available monthly

estimates, including those for the current month, in

developing seasonal factors. Previously, seasonal factors

for the CPS data had been projected twice a year. As a result

of this change in methodology, BLS no longer publishes

seasonal factors for the labor force data. For more information

on the adoption of concurrent seasonal adjustment for the

labor force data, see “Revision of Seasonally Adjusted Labor

Force Series in 2004,” in the January 2004 issue of this

publication available on the Internet at http://www.bls.gov/

cps/cpsrs2004.pdf.

Revisions of historical data, usually for the most recent 5

years, are made only at the beginning of each calendar year.

However, as a result of the revisions to the estimates for 1970-

81 based on 1980 census population counts, revisions to

seasonally adjusted series in early 1982 were carried back to

1970. In 1994, data were revised only for that year because of

the major survey redesign and the introduction of 1990

census-based population controls, adjusted for the estimated

undercount, into the Current Population Survey. In 1996, 1990-

93 data also were revised to incorporate these 1990 censusbased population controls and seasonally adjusted series

were revised back to 1990. Subsequent revisions were carried

back only to 1994 through 1998, when the standard 5-year

revision period was reinstated.

All labor force and unemployment rate statistics, as well

as the major employment and unemployment estimates, are

computed by aggregating independently adjusted series. For

example, for each of the major labor force components— employment, and unemployment—data for four sex-age groups

(men and women under and over 20 years of age) are separately adjusted for seasonal variation and are then added to

derive seasonally adjusted total figures. The seasonally adjusted figure for the labor force is a sum of four seasonally

adjusted civilian employment components and four seasonally adjusted unemployment components. The total for

unemployment is the sum of the four unemployment components, and the unemployment rate is derived by dividing the

resulting estimate of total unemployment by the estimate of

the labor force. Because of the independent seasonal adjustment of various series, components will not necessarily add

to totals.

Each January issue (March issue in 1996 and February

issue in 2003) of Employment and Earnings contains revised

seasonally adjusted data for selected labor force series based

on the experience through December and a description of the

current seasonal adjustment procedure.

National establishment data

BLS also uses the X-12-ARIMA seasonal adjustment program

to seasonally adjust national establishment-based

employment, hours, and earnings series derived from the

Current Employment Statistics (CES) program. (Use of X-12

ARIMA to seasonally adjust the CES data began in June

1996, with the release of the March 1995 benchmark revisions.)

Individual series are seasonally adjusted using either a

multiplicative or an additive model. For employment, seasonal

adjustment factors are directly applied to the component

levels. Individual 3-digit NAICS levels are seasonally adjusted,

and higher-level aggregates are formed by the summation of

these components. Seasonally adjusted totals for hours and

earnings are obtained by taking weighted averages of the

seasonally adjusted data for the component series.

Revised seasonally adjusted national establishmentbased series based on the experience through January 2004

and a detailed description of the current seasonal adjustment

From: Employment and Earnings, February 2004
222

procedure appear in the February 2004 issue of Employment

and Earnings.

Concurrent seasonal adjustment. Beginning in June 2003

with the May 2003 first preliminary estimates, BLS began

computing seasonal factors concurrently with the monthly

estimate production. Previously, the factors were forecasted

twice a year. Concurrent seasonal adjustment is expected to

provide a more accurate seasonal adjustment, and smaller

revisions from the first preliminary estimates to the final

benchmarked estimates, than the semiannual updates. As a

result of the adoption of concurrent seasonal adjustment,

the CES program has discontinued the publication of

projected seasonal factors.

Additive and multiplicative models. Prior to the March 2002

benchmark release in June 2003, all CES series were adjusted

using multiplicative seasonal adjustment models. Although

the X-12-ARIMA seasonal adjustment program provides for

either an additive or a multiplicative adjustment depending

on which model best fits the individual series, the previous

CES processing system was unable to utilize additive

seasonal adjustments. A new processing system, introduced

simultaneously with the conversion to NAICS in June 2003,

is able to utilize both additive and multiplicative adjustments.

The article, “Revisions to the Current Employment Statistics

National Estimates Effective May 2003,” published in the

June 2003 issue of this publication contains a list of which

series are adjusted with additive seasonal adjustment models

and which series are adjusted with multiplicative models.

The article also lists which series are subject to the calendareffects modeling described below.

Variable survey intervals. Beginning with the release of the

1995 benchmark, BLS refined the seasonal adjustment

procedures to control for survey interval variations,

sometimes referred to as the 4- versus 5-week effect.

Although the CES survey is referenced to a consistent

concept—the pay period including the 12th of each month—

inconsistencies arise because there are sometimes 4 and

sometimes 5 weeks between the week including the 12th

in a given pair of months. In highly seasonal industries,

these variations can be an important determinant of the

magnitude of seasonal hires or layoffs that have occurred at

the time the survey is taken, thereby complicating seasonal

adjustment.

Standard seasonal adjustment methodology relies heavily

on the experience of the most recent 3 years to determine the

expected seasonal change in employment for each month of

the current year. Prior to the implementation of the adjustment,

the procedure did not distinguish between 4- and 5-week

survey intervals and the accuracy of the seasonal expectation

depended in large measure on how well the current year’s

survey interval corresponded with those from the previous

3 years. All else being the same, the greatest potential for

distortion occurred when the current month being estimated

had a 5-week interval but the 3 years preceding it were all

4-week intervals, or conversely, when the current month

had a 4-week interval but the 3 years preceding it were all

5-week intervals.

BLS uses REGARIMA (regression with autocorrelated

errors) modeling to identify the estimated size and

significance of the calendar effect for each published series.

REGARIMA combines standard regression analysis, which

measures correlation among two or more variables, with

ARIMA modeling, which describes and predicts the behavior

of data series based on its own past history. For many

economic time series, including nonfarm payroll employment,

observations are autocorrelated over time. That is, each

month’s value is significantly dependent on the observations

that precede it; these series, thus, usually can be successfully

fit using ARIMA models. If autocorrelated time series are

modeled through regression analysis alone, the measured

relationships among other variables of interest may be

distorted due to the influence of the autocorrelation. Thus,

the REGARIMA technique is appropriate to measuring relationships among variables of interest in series

that exhibit autocorrelation, such as nonfarm payroll

employment.

In this application, the correlations of interest are those

between employment levels in individual calendar months

and the lengths of the survey intervals for those months.

The REGARIMA models evaluate the variation in

employment levels attributable to 11 separate survey interval

variables, one specified for each month, except March. March

is excluded because there is almost always 4 weeks between

the February and March surveys. Models for individual

basic series are fitted with the most recent 10 years of data

available, the standard time span used for CES seasonal

adjustment.

The REGARIMA procedure yields regression coefficients

for each of the 11 months specified in the model. These

coefficients provide estimates of the strength of the

relationship between employment levels and the number of

weeks between surveys for the 11 modeled months. The

X-12-ARIMA software also produces diagnostic statistics

that permit the assessment of the statistical significance of

the regression coefficients, and all series are reviewed for

model adequacy.

Because the 11 coefficients derived from the REGARIMA

models provide an estimate of the magnitude of variation in

employment levels associated with the length of the survey

interval, these coefficients are used to adjust the CES data to

remove the calendar effect. These “filtered” series then are

seasonally adjusted using the standard X-12-ARIMA

software previously used.

For a few series, REGARIMA models did not fit well; these

series are seasonally adjusted with the X-12 software but

without the interval-effect adjustment. There are several

additional special effects modeled through the REGARIMA

process which are described below.
223

Construction series. BLS continues its special treatment in

seasonally adjusting the construction industry series, which

began with the 1996 benchmark revision. In the application

of the interval-effect modeling process to the construction

series, there initially was difficulty in accurately identifying

and measuring the effect because of the strong influence of

variable weather patterns on employment movements in the

industry. Further research allowed BLS to incorporate

interval-effect modeling for the construction industry by

disaggregating the construction series into its finer industry

and geographic estimating cells and tightening outlier

designation parameters. This allowed a more precise

identification of weather-related outliers that had masked the

interval effect and clouded the seasonal adjustment patterns

in general. With these outliers removed, interval-effect

modeling became feasible. The result is a seasonally adjusted

series for construction that is improved because it is

controlled for two potential distortions, unusual weather

events and the 4- versus 5-week effect.

Floating holidays. BLS also makes special adjustments for

average weekly hours and average weekly overtime series to

account for the presence or absence of religious holidays in

the April survey reference period and the occurrence of Labor

Day in the September reference period.

Local government series. A special adjustment also is made

in the local government, excluding education series in

November each year to account for variations in employment

due to the presence or absence of poll workers.

Refinements in hours and earnings seasonal adjustment.

With the release of the 1997 benchmark, BLS implemented

refinements to the seasonal adjustment process for the hours

and earnings series to correct for distortions related to the

method of accounting for the varying length of payroll

periods across months. There is a significant correlation

between over-the-month changes in both the average weekly

hour (AWH) and the average hourly earnings (AHE) series

and the number of weekdays in a month, resulting in

noneconomic fluctuations in these two series. Both AWH

and AHE show more growth in “short” months (20 or 21

weekdays) than in “long” months (22 or 23 weekdays). The

effect is stronger for the AWH than for the AHE series.

The calendar effect is traceable to response and

processing errors associated with converting payroll and

hours information from sample respondents with semimonthly

or monthly pay periods to a weekly equivalent. The response

error comes from sample respondents reporting a fixed

number of total hours for workers regardless of the length

of the reference month, while the CES conversion

process assumes that the hours reporting will be variable.

A constant level of hours reporting most likely occurs when

employees are salaried rather than paid by the hour,

as employers are less likely to keep actual detailed hours

records for such employees. This causes artificial peaks in

the AWH series in shorter months that are reversed in longer

months.

The processing error occurs when respondents with

salaried workers report hours correctly (vary them according

to the length of the month), which dictates that different

conversion factors be applied to payroll and hours. The CES

processing system uses the hours conversion factor for both

fields, resulting in peaks in the AHE series in short months

and reversals in long months. Currently, the CES processing

system can accommodate only one conversion factor per

reporter.

The series to which the length-of-pay-period adjustment

is applied are not subject to the 4- versus 5-week adjustment,

because the modeling cannot support the number of variables

that would be required in the regression equation to make

both adjustments.

State establishment data

Seasonally adjusted nonfarm payroll employment data by

selected industry supersectors for all States and the District

of Columbia are presented in table B-7 of this publication.

As with the national establishment data, the State

establishment data are seasonally adjusted with the X-12-

ARIMA seasonal adjustment program. Seasonal adjustment

factors are applied directly to the employment estimates at

the supersector level and then aggregated to the State totals

for most States. For a few States that do not have many

publishable seasonally adjusted supersectors, however, total

nonfarm data are seasonally adjusted directly at the

aggregate level. The recomputation of seasonal factors and

historical revisions are made coincident with the annual

benchmark adjustments.

Region and State labor force data

Beginning in 1992, BLS introduced publication of seasonally

adjusted labor force data for the census regions and divisions, the 50 States, and the District of Columbia (tables C-1

and C-2). Beginning in 1998, regional aggregations are derived

by summing the State estimates.

Seasonal adjustment of the State labor force data is done

in two steps. First, a signal plus noise model is fit to the data

series to filter out the effects of sampling errors that result

from the small sample size of the State estimates. In the

second step, the error-corrected labor force series is then

seasonally adjusted with the X-12-ARIMA seasonal

adjustment program.

Seasonal adjustment factors are computed and applied

independently to the component employment and

unemployment levels and then aggregated to regional or State

totals. Current seasonal adjustment factors are produced for

6-month periods twice a year. Historical revisions usually are

made at the beginning of each calendar year. Because of the

separate processing procedures, totals for the Nation, as a

whole, differ from the results obtained by aggregating regional

or State data.