Background............................................................1

Concepts.................................................................1

Sample Design .......................................................4

Data Sources and Collection Methods...................4

Estimating Methods...............................................5

Technical References...........................................17

Chapter 2. 

Employment, Hours, and Earnings 

from the Establishment Survey

T IN THIS CHAPTER

he Bureau of Labor Statistics (BLS) conducts the Current Employment Statistics (CES) survey, collecting 

data each month on employment, hours, and earnings 

from a sample of nonagricultural establishments. The sample 

includes about 140,000 businesses and government agencies, 

which cover approximately 440,000 individual worksites 

drawn from a sampling frame of roughly 9.0 million Unemployment Insurance tax accounts. The active CES sample 

includes approximately one-third of all nonfarm payroll employees. From these data, BLS, along with State labor market 

information agency partners, prepares and publishes a large 

number of employment, hours, and earnings series in considerable industry and geographic detail. CES data are available 

at http://www.bls.gov/ces/home.htm. 

Background

The first monthly studies of employment and payrolls by 

BLS began in 1915 and covered four manufacturing industries. With increasing interest in employment data during 

the Great Depression, BLS increased its output; and by 

1933, employment, average hourly earnings, and average 

weekly hours were published for total manufacturing, 90 

manufacturing industries, and 14 nonmanufacturing categories. Early estimates of hours and earnings were made 

for production and nonsupervisory employees, who represented about 80 percent of all employees in the private sector. In 2010, BLS published official hours and earnings for 

all private-sector employees for the first time.

Interest in employment statistics for States and areas 

also grew. Even before BLS entered the field, in 1915, three 

States—Massachusetts, New York, and New Jersey—were 

preparing employment statistics. In 1915, New York and 

Wisconsin entered into cooperative agreements with BLS, 

whereby sample data collected from employers by a State 

agency would be used jointly with BLS to prepare State 

and national series. By 1940, estimates of total nonfarm 

employment for all 48 States and the District of Columbia 

were available. Since 1949, the CES program has been a 

Federal-State program that provides employment, hours, 

and earnings information by industry on a national, State, 

and metropolitan area basis. By 1980, cooperative arrangements were in effect with all 50 States, the District of Columbia, Puerto Rico, and the U.S. Virgin Islands. (National 

estimates exclude data for Puerto Rico and the U.S. Virgin 

Islands.)

Concepts

Establishment

An establishment is an economic unit, such as a factory, 

mine, store, or office that produces goods or services. It 

generally is at a single location and is engaged predominantly in one type of economic activity. Where a single 

location encompasses two or more distinct activities, these 

are treated as separate establishments, if separate payroll 

records are available, and the various activities are classified under different industry codes.

Employment

Employment data refer to persons on establishment payrolls who received pay for any part of the pay period that 

includes the 12th day of the month. 

Data exclude proprietors, the unincorporated self-employed, unpaid volunteer or family workers, farm workers, 

and domestic workers. Salaried officers of corporations are 

included. Government employment covers only civilian 

employees; military personnel are excluded. Employees 

of the Central Intelligence Agency, the National Security 

Agency, the National Imagery and Mapping Agency, and 

the Defense Intelligence Agency also are excluded.

1
Persons on establishment payrolls who are on paid sick 

leave (for cases in which pay is received directly from the 

firm), on paid holiday, or on paid vacation, or who work 

during a part of the pay period—even though they are unemployed or on strike during the rest of the period—are 

counted as employed. Not counted as employed are persons 

who are on layoff, on leave without pay, or on strike for the 

entire period, or who were hired but have not yet reported 

during the period.

In addition to employment data for all employees, the 

total number of women employees is collected. In private 

industries, CES collects data on production and related 

employees in manufacturing and mining and logging, construction employees in construction, and nonsupervisory 

employees in private service-providing industries; collectively, all these workers are often referred to as production 

employees. 

Production and related employees include working supervisors and all nonsupervisory employees (including 

group leaders and trainees) engaged in fabricating, processing, assembling, inspecting, receiving, storing, handling, packing, warehousing, shipping, trucking, hauling, 

maintenance, repair, janitorial, guard services, product 

development, auxiliary production for plant’s own use (for 

example, power plant), recordkeeping, and other services 

closely associated with the above production operations.

Construction employees in the construction sector include: Working supervisors, qualified craft workers, 

mechanics, apprentices, helpers, laborers, and so forth, 

engaged in new work, alterations, demolition, repair, 

maintenance, and the like, whether working at the site of 

construction or in shops or yards at jobs (such as precutting and preassembling) ordinarily performed by members of the construction trades.

Nonsupervisory employees include those individuals in 

private, service-providing industries who are not above the 

working-supervisor level. This group includes individuals such as office and clerical workers, repairers, salespersons, operators, drivers, physicians, lawyers, accountants, 

nurses, social workers, research aides, teachers, drafters, 

photographers, beauticians, musicians, restaurant workers, 

custodial workers, attendants, line installers and repairers, 

laborers, janitors, guards, and other employees at similar 

occupational levels whose services are closely associated 

with those of the employees listed. 

An employment benchmark is a complete count of employment used to adjust estimates derived from a sample. CES 

sample-based estimates are benchmarked annually. The 

basic source of benchmark data for the CES survey is the 

Quarterly Census of Employment and Wages (QCEW) 

program, which collects employment and wage data from 

States’ unemployment insurance (UI) tax records. The 

QCEW represents a virtual census of employment in the 

United States, covering about 97 percent of all jobs on civilian payrolls. (The benchmark process is explained in detail in later sections of this chapter.) 

Indexes of diffusion of employment change measure the 

dispersion of employment change in industries over a specified time span. The overall indexes are calculated from 

seasonally adjusted employment series for 4-digit NAICS 

industries and cover all nonfarm payroll employment in 

the private sector. Diffusion indexes are also calculated for 

manufacturing using employment in 4-digit NAICS industries.

To derive the indexes, each component industry is assigned a value of 0, 50, or 100 percent, depending on 

whether its employment showed a decrease, no change, or 

an increase, respectively, over the time span. The average 

value (mean) is then calculated, and this percent is the diffusion index number.

The reference point for diffusion analysis is 50 percent, 

the value indicating that the same number of component 

industries had increased as had decreased. Index numbers above 50 show that more industries had increasing 

employment and values below 50 indicate that more had 

decreasing employment. The margin between the percent 

that increased and the percent that decreased is equal to the 

difference between the index and its complement—that is, 

100 minus the index. For example, an index of 65 percent 

means that 30 percent more industries had increasing employment than had decreasing employment [65-(100-65) = 

30]. However, for dispersion analysis, the distance of the 

index number from the 50-percent reference point is the 

most significant observation.

Although diffusion indexes commonly are interpreted 

as showing the percent of components that increased over 

the time span, the index reflects half of the unchanged components, as well. (This is the effect of assigning a value of 

50 percent to the unchanged components when computing 

the index.)

Hours and earnings

The CES hours and earnings series are derived from reports of payrolls and the corresponding paid hours for all 

employees and also for the various types of production employees. Hours and earnings are for private-sector employees.

Payroll refers to the payroll for full- and part-time workers who received pay for any part of the pay period that 

includes the 12th day of the month. The payroll is reported 

before deductions of any kind, such as those for old-age and 

unemployment insurance, group insurance, withholding 

tax, bonds, or union dues; also included is pay for overtime, 

2
holidays and vacation, sick leave paid directly by the firm, 

and commissions paid at least monthly. Bonuses (unless 

earned and paid regularly each pay period); other pay not 

earned in the pay period reported (such as retroactive pay); 

and the value of free rent, fuel, meals, or other payment in 

kind are excluded. Employee benefits (such as health and 

other types of insurance, contributions to retirement, and 

so forth, paid by the employer) also are excluded.

Total hours during the pay period include all hours worked 

(including overtime hours), hours paid for standby or reporting time, and equivalent hours for which employees 

received pay directly from the employer for sick leave, holidays, vacations, and other leave. Overtime and other premium pay hours are not converted to straight-time equivalent hours. The concept of total hours differs from those of 

scheduled hours and hours worked. 

Average weekly hours relate to the average hours per worker for which pay was received and is different from standard or scheduled hours. Factors such as unpaid absenteeism, labor turnover, part-time work, and stoppages cause 

average weekly hours to be lower than scheduled hours of 

work for an establishment. Group averages further reflect 

changes in the workweek of component industries. Average weekly hours are the total weekly hours divided by the 

employees paid for those hours.

Overtime hours represent that portion of average weekly 

hours that exceeded regular hours and for which overtime 

premiums were paid. If an employee were to work on a 

paid holiday at regular rates, receiving as total compensation his holiday pay plus straight-time pay for hours 

worked that day, no overtime hours would be reported. 

Overtime hours data are collected only from manufacturing establishments. 

Because overtime hours are premium hours by definition, weekly hours and overtime hours do not necessarily 

move in the same direction from month to month. Such 

factors as work stoppages, absenteeism, and labor turnover 

may not have the same influence on overtime hours as on 

average hours. Diverse trends at the industry group level 

also may be caused by a marked change in hours for a component industry in which little or no overtime was worked 

in both the previous and current months.

Average hourly earnings are on a “gross” basis. They reflect not only changes in basic hourly and incentive wage 

rates, but also such variable factors as premium pay for 

overtime and late-shift work and changes in output of 

workers paid on an incentive plan. They also reflect shifts 

in the number of employees between relatively high-paid 

and low-paid work and changes in workers’ earnings in individual establishments. Averages for groups and divisions 

further reflect changes in average hourly earnings for individual industries. 

Averages of hourly earnings differ from wage rates. 

Earnings are the actual return to the worker for a stated 

period; rates are the amount stipulated for a given unit of 

work or time. The earnings series do not measure the level 

of total labor costs on the part of the employer because the 

following are excluded: benefits, irregular bonuses, retroactive items, payroll taxes paid by employers.

Average hourly earnings, excluding overtime-premium 

pay, are computed by dividing the total worker payroll for 

the industry group by the sum of total worker hours and 

one-half of total overtime hours. No adjustments are made 

for other premium payment provisions, such as holiday pay, 

late-shift premiums, and overtime rates other than time and 

one-half. Average hourly earnings excluding overtime are 

calculated only for manufacturing industries.

Average weekly earnings are derived by multiplying average weekly hours estimates by average hourly earnings estimates. Therefore, weekly earnings are affected not only 

by changes in average hourly earnings but also by changes 

in the length of the workweek. Monthly variations in such 

factors as the proportion of part-time workers, stoppages 

for varying reasons, labor turnover during the survey period, and absenteeism for which employees are not paid may 

cause the average workweek to fluctuate.

Long-term trends of average weekly earnings can be affected by structural changes in the makeup of the workforce. For example, persistent long-term increases in the 

proportion of part-time workers in retail trade and many 

of the services industries have reduced average workweeks 

in these industries and have affected the average weekly 

earnings series.

Real earnings data (those expressed in constant 1982-84 

dollars) result from the adjustment of average hourly and 

weekly earnings by the BLS Consumer Price Indexes. Real 

earnings for production and nonsupervisory employees 

are deflated by the Consumer Price Index for Urban Wage 

Earners and Clerical Workers (CPI-W), while real earnings 

for all employees are deflated by the Consumer Price Index 

for All Urban Consumers (CPI-U). Real earnings indicate 

the purchasing power of money earnings after adjustment 

for changes over time in the prices of consumer goods and 

services. These data cannot be used to measure changes 

in living standards as a whole, which are affected by other 

factors such as total family income, the extension and incidence of various social services and benefits, and the duration and extent of employment and unemployment. The 

long-term trends of these earnings data also are affected by 

changing mixes of full-time and part-time workers, highpaid and low-paid workers, and so on. 

3
Indexes of aggregate weekly hours and payrolls. Indexes 

of aggregate weekly hours are calculated by dividing the 

current month’s aggregate hours by the average of the 12 

monthly figures, for the base year. Indexes are based on 

2007 averages for all employees and on 2002 averages for 

production and nonsupervisory employees. For basic industries, the hours aggregates are the product of average 

weekly hours and employment of workers to which the 

hours apply (all employees or production and nonsupervisory employees). At all higher levels of industry aggregation, hours aggregates are the sum of the component aggregates.

Indexes of aggregate weekly payrolls are calculated by 

dividing the current month’s aggregate by the average of 

the 12 monthly figures for the base year. Indexes are averages for production and nonsupervisory employees. For 

basic industries, the payroll aggregates are the product of 

average hourly earnings and aggregate weekly hours. At all 

higher levels of industry aggregation, payroll aggregates 

are the sum of the component aggregates.

Industrial classification

All data on employment, hours, and earnings for the Nation 

and for States and areas are classified in accordance with 

the 2007 North American Industry Classification System 

(NAICS), specified by the U.S. Office of Management and 

Budget. The United States, Canada, and Mexico share this 

classification system, and, thus, it allows a direct comparison of economic data across the three countries. 

Establishments are classified into industries on the basis 

of their primary activity. Those that use comparable capital equipment, labor, and raw material inputs are classified 

together. This information is collected on a supplement to 

the quarterly unemployment insurance tax reports filed by 

employers. For an establishment engaging in more than 

one activity, the entire employment of the establishment 

is included under the industry indicated by the principal 

activity.

Sample Design

The CES sample design is a stratified, simple random 

sample of worksites, clustered by UI account number. The 

sample strata, or subpopulations, are defined by State, 

industry, and employment size, yielding a State-based 

design. Sampling rates for each stratum are determined 

through optimum allocation, which distributes a fixed 

number of sample units across a set of strata to minimize 

the overall variance or sampling error on the primary estimate of interest, the statewide total nonfarm employment 

level.

The sampling frame, and the CES sample itself, are 

updated twice a year with new quarters of UI-based universe data. This helps keep the sample up-to-date by adding firm births and deleting business deaths. In addition, 

the design specifies an annual update process, which includes sample frame maintenance and the redrawing of 

the entire sample for the first quarter of each year. Frame 

maintenance provides for the updating of industry, employment size class, and metropolitan area designations 

and for the merging of semiannual birth samples into the 

overall frame.

Data Sources and Collection Methods

Sample data

Each month, BLS collects data on employment, payroll, 

and paid hours from a sample of establishments. To encourage participation in this voluntary survey, BLS uses 

a variety of collection techniques, tailored to individual 

firm preferences. Data collection centers (DCCs) perform 

initial enrollment of each firm via telephone, collect the 

data for several months via Computer Assisted Telephone 

Interviewing (CATI) and where possible transfer respondents to a self-reporting mode such as touch-tone data entry (TDE), FAX or Internet collection. Very large, multiestablishment firms are often enrolled via personal visit, 

and ongoing reporting is established via electronic data 

interchange (EDI). These firms provide electronic files to 

BLS that include data from all their worksites.

For the few establishments that do not use the above 

methods, data are collected using mail, and transcript.

Sample enrollment. BLS has a comprehensive program of 

new sample unit solicitation in the DCCs. Approximately 

55,000 new sample units are enrolled in the CES survey 

each year to account for the births of new firms, to realign 

the sample distribution with the universe distribution, and 

to rotate a portion of the sample. All firms with 1,000 or 

more employees are asked to participate in the survey, as 

is a sample of firms across all employment sizes. When 

firms are rotated into the sample, they are retained for 2 

years or more. When a respondent is rotated out of the 

sample, BLS will not ask the firm to participate for at least 

3 years.

Data reporting. Each month, respondents extract the employment, hours, and earnings data from their payroll records and submit it to BLS. Data are collected for the pay 

period that includes the 12th of each month. 

A CES reporting form (BLS form 790 series) is provided to all CES respondents except those that report via 

electronic file. The form provides a convenient means to 

record payroll data each month. Six variations of the basic CES form are used, and each variation is tailored for 

the data items, concepts, and definitions of major industry sectors. Separate forms are used for mining and logging, construction, manufacturing, service-providing industries, public administration, and educational services. 

4
The wedge is linear; eleven-twelfths of the March difference is added to the February estimate, ten-twelfths to the 

January estimate, and so on, back to the previous April 

estimate, which receives one-twelfth of the March difference. This assumes that the total estimation error since 

the last benchmark accumulated at a steady rate throughout the current benchmark year.

Estimates for the 7 months following the March benchmark also are recalculated each year. These post-benchmark estimates reflect the application of sample-based 

monthly changes to new benchmark levels for March and 

the computation of new business birth/death factors for 

each month. 

Following the revision of basic employment estimates, 

estimates for women employees and production and nonsupervisory employees are recomputed using the revised 

all-employee estimates and the previously computed sample ratios of these workers to all employees. All basic series 

of employment, hours, and earnings are re-aggregated to 

obtain estimates for each sector and higher level of detail. 

Other derivative series (such as real earnings and payroll 

indexes) also are recalculated. New seasonal adjustment 

factors are calculated and all data series for the previous 5 

years are re-seasonally adjusted before full publication of 

all revised data in February of each year.

Monthly Estimation

Stratification. The CES sample is stratified into basic 

estimation cells for purposes of computing national employment, hours, and earnings estimates. Basic cells are 

defined primarily by detailed industry at the 3-, 4-, 5-, or 

6-digit NAICS level. Aggregation results in additional 

summary cells.

In addition to the basic and summary estimation cells, 

a small number of independently estimated cells exist and 

do not aggregate to the summary cell levels.

The Current Employment Statistics (CES) or establishment survey estimates of employment are generated 

through an annual benchmark and monthly sample link 

procedure. Annual universe counts or benchmark levels 

are generated primarily from administrative records on 

employees covered by unemployment insurance (UI) tax 

laws. These annual benchmarks, established for March 

of each year, are projected forward for each subsequent 

month based on the trend of the sample employment and 

an adjustment for the net of business births and deaths employment. Benchmarks and monthly estimates are computed for each basic estimating cell and summed to create 

aggregate-level employment estimates.

Matched sample. CES uses a matched sample concept to 

produce estimates. A matched sample is defined to be all 

sample members that have reported data for the reference 

month and the month prior. Excluded from the matched 

CES data collection forms are available on the BLS Web 

site at http://www.bls.gov/ces/idcfcesforms.htm.

The design of the CES form is important for maintaining continuity and consistency in reporting from month 

to month. The use of a single form for a 6-month period 

allows the respondent to compare the latest data with data 

submitted in prior months. 

All reported data, regardless of method of collection, 

are edited by BLS to ensure the information is correctly 

reported and is consistent with the data reported by the 

establishment in earlier months. The data are further edited to detect processing and reporting errors that might 

have been missed during collection. When questionable 

reports are discovered at any stage of the editing process, 

BLS contacts the respondents for clarification or correction. The staff of the BLS Washington office prepares national estimates of employment, hours, and earnings using the edited data. The State agencies also cooperate with 

BLS to develop State and metropolitan area estimates. 

Estimating Methods

Benchmark data

For the establishment survey, annual benchmarks are 

constructed to realign the sample-based employment totals for March of each year with the UI-based population 

counts for March. These population counts are less timely 

than sample-based estimates and are used to provide an 

annual point-in-time census for employment. For National series, only the March sample-based estimates are 

replaced with UI counts. For State and metropolitan area 

series, all available months of UI data are used to replace 

sample-based estimates. State and area series are based 

on smaller samples and are, therefore, more vulnerable 

to both sampling and non-sampling errors than National 

estimates.

Population counts are derived from the administrative 

file of employees covered by UI. All employers covered 

by UI laws are required to report employment and wage 

information to the appropriate State workforce agency 

four times a year. Approximately 97 percent of total nonfarm employment within the scope of the establishment 

survey is covered by UI. A benchmark for the remaining 

3 percent is constructed from alternate sources, primarily 

records from the Railroad Retirement Board and County Business Patterns. The full benchmark developed for 

March replaces the March sample-based estimate for each 

basic cell. The monthly sample-based estimates for the 

year preceding and the year following the benchmark are 

also then subject to revision.

Monthly estimates for the year preceding the March 

benchmark are readjusted using a “wedge back” procedure. The difference between the final benchmark level 

and the previously published March sample estimate is 

calculated and spread back across the previous 11 months. 

5
sample is any sample unit that reports that it is out-of-business. This aspect of the estimation methodology is more 

fully described in the section on estimation of business 

births and deaths employment below. 

Estimates of all employees require that only the number 

of total employees be reported for the current estimated 

month and the prior month. The matched sample for estimates of production/nonsupervisory employees includes 

reporting units that reported both all employees and production/nonsupervisory employees for both the previous 

and current months. The matched sample for estimates of 

women employees includes reporting units that reported 

both all employees and women employees for both the previous and current months. 

The matched sample for average weekly hours and 

average hourly earnings of all employees includes responding units that have reported all employees and the 

corresponding worker hours and payrolls for both the 

previous and current months. The matched sample for 

average weekly hours and average hourly earnings of 

production/nonsupervisory employees, includes reporting units that have reported production/nonsupervisory 

employees and their corresponding worker hours and 

payrolls, as well as all employees, for both the previous 

and current months. 

For average weekly overtime estimates of all employees, which are calculated for manufacturing industries 

only, the matched sample includes reporting units that 

have reported all employees and the corresponding work 

hours, payrolls, and overtime hours for both the previous and current months. The matched sample for average 

weekly overtime hours of production/nonsupervisory employees includes production/nonsupervisory employees 

and their corresponding worker hours, payrolls, and overtime hours, as well as all employees, for both the previous 

and current months. 

Variables for national estimates. The weighted-link-relative formula is used to calculate estimates of all employees, while the difference-link-and-taper formula is used 

to calculate all other data types. Both formulas use data 

reported that meets the matched sample criteria. The difference-link-and-taper formula also uses estimates for the 

month prior to the reference month or derivatives of estimates, such as ratios. See the table of variable definitions 

for the link-relative and difference-link-and-taper formulas on page 7. 

National employment. The weighted link-relative estimator for the all employee series uses the sample trend in 

the cell to move the previous level to the current-month 

estimated level. A model-based component is applied to 

account for the net employment resulting from business 

births and deaths not captured by the sample.

The weighted link-relative technique is efficient in that 

it takes advantage of a reliable, complete count of employment and of the high correlation between levels of employment in successive months in identical establishments. 

Current-month estimate of all employees is 

defined as

Business birth and death estimation. In a dynamic economy, firms are continually opening and closing. These 

two occurrences offset each other to some extent. That is, 

firms that are born replace firms that die. CES uses this 

fact to account for a large proportion of the employment 

associated with business births. This is accomplished by 

excluding business death units from the matched sample 

definition. Effectively, business deaths are not included in 

the sample-based link portion of the estimate, and the implicit imputation of their previous month’s employment is 

assumed to offset a portion of the employment associated 

with births.

There is an operational advantage associated with this 

approach, as well. Most firms will not report that they have 

gone out of business; rather, they simply cease reporting 

and are excluded from the link, as are all other nonrespondents. As a result, extensive follow-up with monthly nonrespondents to determine whether a company is out-of-business or simply did not respond is not required.

Employment associated with business births will not 

exactly equal that associated with business deaths. The 

amount by which it differs varies by month and by industry. As a result, the residual component of the birth/death 

offset must be accounted for by using a model-based approach.

Birth-death residual = Population - Sample-based 

estimate + Error

During the net birth/death modeling process, simulated 

monthly probability estimates over a 5-year period are 

created and compared with population employment levels. 

Moving from a simulated benchmark, differences between 

the series across time represent a cumulative birth/death 

component. Those residuals are converted to month-tomonth differences and used as input series to the modeling 

process.

Models are fit using X-12 autoregressive integrated 

moving average (ARIMA). Outliers, level shifts, and temporary ramps are automatically identified. 

AE� c = �AE� p - Σ

j

 aep,j

* � ×

Σ

i

�wi × aec,i� - Σ

j

�wj × aec,j

* �

Σ

i

�wi × aep,i� - Σ

j

�wj × aep,j

* � + Σ

j aec,j

* + bc

for all i � I and j � J

6
7

• All estimated values are shown in upper case. 

• All sample measures (shown in lower case) are based on a matched sample. 

• The estimator for women employees takes the same form as the estimator for production/nonsupervisory employees, where PE and PER are the estimates for women employees and women-to-all employee ratio, respectively, and matched sample totals pe are the matched sample totals for women. 

• The estimator for average weekly hours for production/nonsupervisory employees takes the same form as 

average weekly hours for all employees, where AE and AWH represent estimates of production/nonsupervisory employees and average weekly hours of production/nonsupervisory employees, respectively, and the matched sample 

totals ae and wh represent matched sample totals for production employees and wh for production/nonsupervisory 

employees, respectively. 

• The estimator for average hourly earnings for production/nonsupervisory employees takes the same form as average 

hourly earnings for all employees, where AHE and WH represent estimates of production/nonsupervisory employees and their work hours, and the matched sample totals pr and wh represent matched sample totals of payroll and 

work hours for production/nonsupervisory employees 

• The estimators for average weekly overtime take the same form as average weekly hours, where AWH represents 

the estimates of average weekly overtime hours and wh represents the matched sample for total overtime hours reported. Overtime estimates are calculated for manufacturing industries only. 

Variable definitions

Variable Description All 

employees 

Production/ 

nonsupervisory (or 

women employees) 

Average weekly hours 

(or average weekly 

overtime hours) 

Average 

hourly 

earnings 

* Atypical sample data. X X X X 

α 0.9 X X X 

β 0.1 X X X 

c Current month. X X X X 

p Previous month. X X X X 

ܣܧ෢

Estimated employment for all 

employees (or for production/ 

nonsupervisory employees when 

estimating their respective hours). 

X X X 

ae 

Reported all employees (or production/ 

nonsupervisory employees when 

estimating their respective hours). 

X X X 

AHE ෣

Estimated average hourly earnings for 

all employees (or for production/ 

nonsupervisory employees when 

estimating their respective earnings). 

X 

AWH ෣

Estimated average weekly hours for all 

employees (or for production/ 

nonsupervisory employees when 

estimating their respective hours). 

X 
Variable Description All 

employees 

Production/ 

nonsupervisory (or 

women employees) 

Average weekly hours 

(or average weekly 

overtime hours) 

Average 

hourly 

earnings 

pr 

Reported weekly payroll for all 

employees (or for production/ 

nonsupervisory employees when 

estimating their respective earnings). 

X 

ݓ Weight associated with a CES report. X X X X 

wh 

Reported weekly hours for all 

employees (or for production/ 

nonsupervisory employees when 

estimating their respective hours and 

earnings). 

X X 

WH෢

Estimated weekly hours for all 

employees (or production/ 

nonsupervisory employees), derived 

from estimates of average weekly 

hours and employment. 

X 

8

Variable Description All 

employees 

Production/ 

nonsupervisory (or 

women employees) 

Average weekly hours 

(or average weekly 

overtime hours) 

Average 

hourly 

earnings 

* Atypical sample data. X X X X 

α 0.9 X X X 

β 0.1 X X X 

c Current month. X X X X 

p Previous month. X X X X 

ܣܧ෢

Estimated employment for all 

employees (or for production/ 

nonsupervisory employees when 

estimating their respective hours). 

X X X 

ae 

Reported all employees (or production/ 

nonsupervisory employees when 

estimating their respective hours). 

X X X 

AHE ෣

Estimated average hourly earnings for 

all employees (or for production/ 

nonsupervisory employees when 

estimating their respective earnings). 

X 

AWH ෣

Estimated average weekly hours for all 

employees (or for production/ 

nonsupervisory employees when 

estimating their respective hours). 

X 

b net birth/death factor. X 

i a matched CES report for sample data 

variables shown in lower case. X X X X 

j a matched CES report where the 

current month is atypical. X X X X 

PE෢ Estimated production/nonsupervisory 

(or women) employees. X 

pe Reported production/nonsupervisory 

(or women) employees. X 

PER ෣

Estimated ratio of production/ 

nonsupervisory (or women) employees 

to all employees. 

X 

ae 

Reported all employees (or production/ 

nonsupervisory employees when 

estimating their respective hours). 

X X X 

AHE ෣

Estimated average hourly earnings for 

all employees (or for production/ 

nonsupervisory employees when 

estimating their respective earnings). 

X 

AWH ෣

Estimated average weekly hours for all 

employees (or for production/ 

nonsupervisory employees when 

estimating their respective hours). 

X 

b net birth/death factor. X 

i a matched CES report for sample data 

variables shown in lower case. X X X X 

j a matched CES report where the 

current month is atypical. X X X X 

PE෢ Estimated production/nonsupervisory 

(or women) employees. X 

pe Reported production/nonsupervisory 

(or women) employees. X 

PER ෣

Estimated ratio of production/ 

nonsupervisory (or women) employees 

to all employees. 

X 
The net birth/death model component figures are unique 

to each month and exhibit seasonal patterns that can result 

in negative adjustments in some months. 

Weighted-link-and-taper estimator is used for all data 

types except for “all employees.” The estimator accounts 

for the over-the-month change in the sampled units, but 

also includes a tapering feature used to keep the estimates close to the overall sample average over time. The 

taper is considered to be a level correction. This estimator 

uses matched sample data; it tapers the estimate toward 

the sample average for the previous month of the current matched sample before applying the current month’s 

change; and it promotes continuity by heavily favoring 

the estimate for the previous month when applying the 

numerical factors.

Production and nonsupervisory employees. To obtain estimates of production (or construction or nonsupervisory) 

worker employment, the ratio of weighted production employees to the weighted all employees in the sample is 

assumed to equal the same ratio in the universe. The current month’s production worker ratio, thus, is estimated 

and then multiplied by the all-employee estimate. The 

weighted-difference-link-and-taper formula, described 

in the section on hours and earnings, is used to estimate 

the current month’s production worker ratio. This formula adds the change in the matched sample’s production 

worker ratio (the weighted-difference link) to the prior 

month’s estimate, which has been slightly modified to reflect changes in the sample composition (the taper). (See 

page 10.) An analogous method is used to estimate the 

number of women employees. 

Women employees. Estimation of the series for women 

employees is identical to that described for production 

employees, with the appropriate substitution of women 

employees values for the production worker values in the 

previous formulas.

Estimates for each type of series (all employees, production employees, and women employees) for individual 

basic estimating cells are summed to obtain corresponding 

totals for broader industry sectors. 

Hours and earnings

Average weekly hours and average hourly earnings. Independent benchmarks are not available for the hours 

and earnings series; consequently, the levels are derived 

directly from the CES weighted-sample averages. (See 

pages 10 and 11.) Before hours and earnings sample averages or estimates are calculated, all employees, production employees and aggregate hours and payrolls must be 

multiplied by sample weights both for the month for which 

estimates are being made and for the prior month. To establish average weekly hours for a basic estimating cell, 

the sum of reported worker hours for the establishments 

classified in the cell is divided by the total number of all 

employees or production employees reported for the same 

establishments. To establish average hourly earnings, the 

reported payroll is divided by the reported worker hours 

for the same establishments. 

Average weekly hours and average hourly earnings for 

industries and groups above the basic estimating cell level 

are weighted averages of the figures for component cells. 

Average weekly hours for each basic estimating cell are 

multiplied by the corresponding estimate of the number of 

all employees to derive aggregate worker hours. Payroll 

aggregates are the product of the aggregate worker hours 

and average hourly earnings. Payroll and worker-hour aggregates for industry groups and divisions are the sums of 

the aggregates for the component industries. 

Average weekly hours for industry groups are obtained 

by dividing the worker-hour aggregates by the corresponding all-employee estimates. Average hourly earnings for 

industry groups are computed by dividing payroll aggregates by worker-hour aggregates. This method is equivalent to weighting average weekly hours by the estimated 

number of all employees in the universe and weighting 

average hourly earnings by the estimated worker hours for 

the universe. 

For all levels, from basic estimating cells to sector level 

and higher aggregates, average weekly earnings are computed by multiplying average hourly earnings by average 

weekly hours. 

Current month estimate of overtime hours

Estimation of overtime hours is identical to that described 

for average weekly hours, with the appropriate substitution of overtime hours values for the weekly hours values 

in the previous formula.

Estimation formulas for hours and earnings for production employees are essentially the same as hours and earnings for all employee series, whereby all ‘AE’ estimates 

and ‘ae’ sample terms are replaced by ‘PE’ estimates and 

‘pe’ sample, respectively.

9
10

Current-month estimate of production or nonsupervisory employees is defined as

PE�c=��AE� c- Σ

j

aec,j

* � × PER �c�+Σ

j pec,j

*

, where 

PER �c= �α × PER �p�+�β × 

Σ

i �wi × pep,i� - Σj �wj × pep,j

* �

Σ

i

�wi × aep,i� - Σ

j �wj × aep,j

* �

�+ 

Σ

i �wi × pec,i� - Σj �wj × pec,j

* �

Σ

i

�wi × aec,i� - Σ

j

�wj × aec,j

* � �

Σ

i �wi × pep,i� - Σj

�wj × pep,j

* �

Σ

i

�wi × aep,i� - Σ

j

�wj × aep,j

* �

for all i � I and j � J

AWH �c= α × AWH �p + β ×

�

�

�

�

��

Σ

i

�wi × whp,i� - Σ

j

�wj × whp,j

* �

Σ

i

�wi × aep,i� - Σ

j

�wj × aep,j

* � �× �AE� p- Σ

j

aep,j

* � + Σ

j

whp,j

*

AE� p

�

�

�

�

�

 +

�

�

�

�

��

Σ

i

�wi × whc,i� - Σ

j

�wj × whc,j

* �

Σ

i

�wi × aec,i� - Σ

j

�wj × aec,j

* � �× �AE� c - Σ

j

aec,j

* � +Σ

j

whc,j

*

AE� c

�

�

�

�

�

 -

�

�

�

�

��

Σ

i

�wi × whp,i� - Σ

j

�wj × whp,j

* �

Σ

i

�wi × aep,i� - Σ

j

�wj × aep,j

* � �× �AE� p - Σ

j

aep,j

* � + Σ

j

whp,j

*

AE� p

�

�

�

�

�

for all i � I and j � J

Current-month estimate of average weekly hours for all employees
11

Current month estimate of average hourly earnings for all employees

AHE �c= α × AHE �p + β ×

�

�

�

�

��

Σ

i �wi × prp,i� - Σj �wj × prp,j

* �

Σ

i

�wi × whp,i�- Σ

j

�wj × whp,j

* �

�× ���� p - Σ

j

whp,j

* � + Σ

j

prp,j

*

WH� p

�

�

�

�

�

 +

�

�

�

�

��

Σ

i �wi × prc,i� - Σj �wj × prc,j

* �

Σ

i

�wi × whc,i� - Σ

j

�wj × whc,j

* �

�× �WH� c - Σ

j

whc,j

* � + Σ

j

prc,j

*

WH� c

�

�

�

�

�

 -

�

�

�

�

��

Σ

i �wi × prp,i� - Σj �wj × prp,j

* �

Σ

i

�wi × whp,i�- Σ

j

�wj × whp,j

* �

�× �WH� p - Σ

j

whp,j

* � + Σ

j

prp,j

*

WH� p

�

�

�

�

�

for all i � I and j � J

AHE �c= α × AHE �p + β ×

�

�

�

�

��

Σ

i �wi × prp,i� - Σj �wj × prp,j

* �

Σ

i

�wi × whp,i�- Σ

j

�wj × whp,j

* �

�× ���� p - Σ

j

whp,j

* � + Σ

j

prp,j

*

WH� p

�

�

�

�

�

 +

�

�

�

�

��

Σ

i �wi × prc,i� - Σj �wj × prc,j

* �

Σ

i

�wi × whc,i� - Σ

j

�wj × whc,j

* �

�× �WH� c - Σ

j

whc,j

* � + Σ

j

prc,j

*

WH� c

�

�

�

�

�

 -

�

�

�

�

��

Σ

i �wi × prp,i� - Σj �wj × prp,j

* �

Σ

i

�wi × whp,i�- Σ

j

�wj × whp,j

* �

�× �WH� p - Σ

j

whp,j

* � + Σ

j

prp,j

*

WH� p

�

�

�

�

�

for all i � I and j � J

AHE �c= α × AHE �p + β ×

�

�

�

�

��

Σ

i �wi × prp,i� - Σj �wj × prp,j

* �

Σ

i

�wi × whp,i�- Σ

j

�wj × whp,j

* �

�× ���� p - Σ

j

whp,j

* � + Σ

j

prp,j

*

WH� p

�

�

�

�

�

 +

�

�

�

�

��

Σ

i �wi × prc,i� - Σj �wj × prc,j

* �

Σ

i

�wi × whc,i� - Σ

j

�wj × whc,j

* �

�× �WH� c - Σ

j

whc,j

* � + Σ

j

prc,j

*

WH� c

�

�

�

�

�

 -

�

�

�

�

��

Σ

i �wi × prp,i� - Σj �wj × prp,j

* �

Σ

i

�wi × whp,i�- Σ

j

�wj × whp,j

* �

�× �WH� p - Σ

j

whp,j

* � + Σ

j

prp,j

*

WH� p

�

�

�

�

�

for all i � I and j � J
12

Robust Estimation Procedure 

The matched sample sometimes contains a small number of 

observations that may have a large and adverse effect on the 

estimate of the relative change. The influence of such 

observations may be due to large survey weights, an 

unusual level or change in reported employment, or the 

combined effect of these factors. If left untreated, influential 

observations may cause unreasonable jumps in the monthly 

estimates, especially at detailed publication levels. 

The Robust Estimation procedure is designed to reduce 

the effect of the influential observations on the estimate of 

the relative over-the-month change. At the same time, it is 

recognized that the unusual and influential sample 

movements may represent similar behavior in the target 

population and a heavy intervention to the regular 

estimation procedure may lead to biased estimates. This is 

especially true if the sample is large. Therefore, the 

estimator is designed to reduce the volatility of the estimates 

due to extreme outlying reports while controlling the 

intervention to protect against the incurred bias. 

Definition of influential reports. The CES weighted link 

relative estimate is based on the ratio of the two survey 

weighted sums. A scatterplot of the weighted employment 

reported in two consecutive months provides an insight on 

what units influence the estimate. Two examples are shown 

in Figure 1: the survey weighted employment reported for 

the month (t) is plotted against the weighted employment 

reported for the previous month (t-1). The line shows the 

survey weighted link relative trend of matched sample data.

An influential report would have a relatively large 

survey weight and/or a large change in its reported 

employment. Numerically, the influence of a report on the 

sample link relative estimate can be expressed in the form 

of weighted residuals: 

di,t = wi �yi,t

– Rt yi,t-1� (1)

where, 

yi,t and yi,t-1 denote, respectively, a unit’s current and 

previous months reported employment; wi is the selection 

weight; Rt is the sample link relative estimate in a given 

basic estimation cell. The formula identified by (1). 

The influential reports are those having large positive or 

negative values of the weighted residuals compared to the 

other sample units. The extreme residuals are reduced to 

specific cut-off values. The cut-off values depend on the 

distribution of the weighted residuals in a given series and 

are determined independently for each month and industry 

series. Pushing the extreme residuals to the cut-off values is 

accomplished by using an appropriate weight adjustment 

factor. 

The procedure used for the CES robust estimation is a 

particular variation of a general method of weight reduction 

known as “winsorization.” See Kokic and Bell (1994). 

The actual cut-off values are determined by examining 

the relative distances of units with extreme weighted 

residuals to the nearest but less extreme values in the same 

cell and month. 

Determining Weight Adjustment Factors. The first step 

consists of calculating the weighted residuals using formula 

(1). The weighted residuals from individual establishments 

are aggregated to the UI account level within each 

estimation cell. This is done because reports within a UI 

account may have similar reported change in employment. 

Since they are similar, it is possible that none of the 

individual reports will be identified as an outlying unit. At 

the same time, the UI level residual aggregated from all the 

responding establishments may be extreme and very 

different from other responding UI accounts in the cell. 

Figure 1

basic estimation cell. The formula is identified by (1).
The residuals may legitimately have very different values 

depending on the employment size class of the sampled UI 

accounts. To remove the effect of the size class, the residuals 

are “centered” within each size class, i.e., the average of the 

residuals within size classes is subtracted from each original 

residual. 

The cut-off values are determined separately for the extreme positive and extreme negative residuals. The procedures are similar for the positive and negative residuals and 

are described here only for the positive residuals. 

First, sort the residuals in each cell in descending order. 

Let di denote the i-th largest centered positive residual: 

d1 ≥ d2 ≥ ... ≥ dn. 

Set the value F1 = d1 and F2 = 2d2 – d1. 

The general formula for Fk is: 

Fk = (k + 1) dk – (d1 + d2 + ... +dk). (2) 

Proceed with the computations of the sequence of F1,...,Fk 

until, at some step k, Fk ≤ 0. Typically, this point is reached 

after only a few steps. Next, compute the cut-off value as the 

point between residuals dk and dk-1 using the formula: 

L = a . dk + (1 – a) . dk-1 , (3) 

where 

a =0.8Fk-1 ⁄(0.8Fk-1– 0.2Fk ). 

The initial adjustments for units whose residuals are greater 

than L are: 

init.adji = L/di. 

The cut-off values defined using the described procedure 

are always placed between some neighboring ordered residuals, so that all the residuals on the right from a cut-off value 

are greater than the cut-off value, although they may be very 

close to it. Based on the historical CES estimates, it has been 

found that the following rules for determining the final adjustments work the best. 

For certainty units, if the initial adjustment is less than 

0.5, then a unit is declared to be atypical, representing only 

itself. The atypical data is removed from the matched sample 

set and is not used in the estimation of the sample link relative. If the initial adjustment for a certainty unit is greater or 

equal to 0.5, no intervention is required and the adjustment 

is reset to 1. 

For non-certainty units, if the initial adjustment is less 

than or equal to 0.3, then a unit is declared atypical and it is 

not used in the sample link relative estimation. If the initial 

adjustment is greater than 0.4, then the final adjustment is 

reset to 1. Adjustments between 0.3 and 0.4 are applied to 

the sample weight. The final adjusted weight is required to be 

equal or greater than 1. For example, if the resulting adjusted 

weight falls below 1, the final weight is reset to 1. 

An intervention, such as a weight adjustment, into the 

regular estimation procedure would reduce the variance of 

the estimate but it may introduce a bias. Therefore, the intervention, especially in samples of moderate to large sizes, 

should be done with caution. For example, it is possible that 

there exist units in the non-sampled part of the population 

that are similar to the influential observations in the sample. 

Moderating the effect of the sample’s influential units may 

lead to a reduction in the representativeness of the sample. 

Since the non-sampled part of the population is not available, 

it is difficult to judge the amount and the need of intervention based only on the observed sample. One way to protect 

against unwarranted intervention is to verify its necessity using historical CES estimates. If the estimate falls within the 

historically observed bounds, then the intervention is deemed 

unnecessary and the weight adjustments are discarded. 

At the very first step of the procedure, the sample link 

relative estimate is used when defining the residuals. This 

estimate may itself be affected by the extreme influential 

observations. Therefore, the whole procedure is performed a 

second time. The atypical units determined during the initial 

run are not used in calculating the adjustment factors during 

the second run. 

The reports identified by the robust estimation techniques 

are treated as atypical in the link-relative technique, while all 

other matched sample responses are treated as typical in the 

link-relative technique. 

Special Estimation Situations

Small domain model. Relatively small sample sizes in some 

industries limit the reliability of the weighted-link-relative 

estimates of all employees. For a few industries (identified in 

the annual benchmark article, http://www.bls.gov/web/ces 

bmart.htm), BLS uses the CES small domain model (SDM). 

In addition, BLS and some cooperating State partners use the 

CES SDM for those State and metropolitan area employment 

series that have small samples. Estimation of nonsupervisory 

employees, average weekly hours, and average weekly and 

hourly earnings uses the standard weighted link-and-taper 

methodology. 

The CES SDM is a weighted least squares (WLS) model 

with two employment inputs: (1) an estimate based on available CES sample for that series, and (2) an ARIMA projection based on trend from 10 years of historical QCEW data.

Estimator Based on Fay-Herriot Model. To estimate employment for State supersector cells with smaller sample sizes, 

the CES program uses an estimator based on the Fay-Herriot 

model. See Fay and Harriot (1979). In the smaller cells, a 

direct sample-based estimate of the over-the-month change 

in employment is often unreliable due to the large variance, 

although the direct estimator is assumed to be approximately 

unbiased. 

13
In order to make more stable estimates, additional information is used. The model is formulated for a set of States in 

a given supersector b and at a given month t. (Since the indexes b and t in the following description are the same for all 

States involved in the model, they are suppressed to simplify 

the notation.) 

Let Ra denote a true value of the relative over-the-month 

employment change in State a, Ra

(1) is a direct sample-based 

estimate, and Ra

(2) is an ARIMA forecast of the relative 

change. The model used in CES is formulated as follows: 

Ra

(1) = Ra

 + ea (1) 

and

Ra = β Ra

(2) + ua

, (2)

for a set of States a = 1,...,K (within a supersector b at time 

t). The error terms ea and ua are assumed to be independent 

and normally distributed, with mean zero. The variance of 

the direct sample estimate Ra

(1) (and thus the variance of ea

) 

is Va

(1). It is estimated based on the sample and is smoothed 

using several years of data, to add stability. The values for 

the variance of the random effects of ua, denoted A, and the 

parameter β are estimated from the model using the method 

described in the Fay and Herriot (1979) paper.

The resulting model estimator Ra

(FH) can be presented as 

a weighted average of the sample-based estimate and an adjusted ARIMA forecast, as follows: 

Ra

(FH) = γa

(1) Ra(1) + γa(2) (2) β Ra(2) (3)

The weights γa

(1) and γa(2) are:

γa 

(1) = A + Va (1) and γa

(2)= 1– γa(1)

The β Ra

(2) component of the weighted average a described 

in equation (3) is called a synthetic part of the estimator. The 

variance, A, depends on the strength of the relationship between Ra

 and the forecasts Ra

(2), across the States in a given 

supersector, as specified by equation (2). The relative magnitudes of A and Va

(1) indicate how much weight should be given to the synthetic part relative to how much weight should 

be given to the sample-based estimate. If the linear relationship described in (2) holds without error, A = 0, all weight 

would go to the synthetic part β Ra

 (2) however, if Ra(2) is a poor 

predictor, then A is large and more weight would be given to 

the direct sample estimate. The strength is “borrowed” across 

States within a supersector to estimate β, thus “correcting” 

the time series forecast using the “adjusted” β Ra

(2) value, and 

to obtain A, the estimated “strength” of the prediction. 

The model estimate of the employment level is obtained 

by applying the model-based estimate of the relative change 

to the preceding month’s level of employment. For a month 

t, the estimator of the employment level is a State a supersector b is:

Education and Religious Organizations. Due to the small 

sample in religious organizations (NAICS 8131), and definitional exclusions in the collection of data for educational 

services (NAICS 611), certain ratios for these series are recalculated with each benchmark to allow for the creation 

of aggregate totals. Production worker and women worker 

ratios, average hourly earnings, and average weekly hours 

for these series are calculated based on the weighted average of the previous year’s professional and technical 

services, education and health services, leisure and hospitality, and other services’ annual averages. BLS sets 

the March benchmark values based on the prior calendar 

year’s annual averages.

The education services series uses the nonsupervisory employee ratio, average hourly earnings, and average weekly 

hours calculated from the weighted average. The religious 

organizations series uses the production employee ratio, 

women employee ratio, average hourly earnings, and average weekly hours calculated from the weighted average. In 

both cases, the ratios, average hourly earnings, and average 

weekly hours are held constant through the next benchmark.

Railroad estimates. BLS obtains monthly employment counts 

for class 1 railroads, which are not included in the QCEW 

universe. The Department of Transportation Surface Transportation Board (STB) publishes a mid-month employment 

count for the survey week of the previous month. (http://

www.stb.dot.gov/econdata.nsf/) BLS uses this data to estimate employment for railroads. The data from STB are also 

used to set the benchmark employment levels and hours and 

earnings.

Residential and Nonresidential Specialty Trade Contractors estimates. Residential and nonresidential employment 

estimates in Specialty Trade Contractors (NAICS 238) are 

produced as breakouts under the standard NAICS coding 

structure. Benchmarks for these series are developed from 

the QCEW data and independent estimates for these series 

are made on a monthly basis and raked to the estimates produced under the standard structure to ensure that the sum of 

the residential specialty trade contractors and nonresidential 

specialty trade contractors series is consistent with the published total for specialty trade contractors at the 3-digit NAICS level.

The raking adjustment follows the following methodology: 

Estimates are derived independently for the residential 

and nonresidential groups at the 4-digit NAICS level for 

each region. Regional estimates are rounded and summed to 

the 4-digit NAICS level for both the residential and nonresidential groups. Within each 4-digit NAICS series, ratios of 

residential-to-total employment and nonresidential-to-total 

employment are calculated.

At the 4-digit NAICS level, the sum of the residential/

nonresidential series is subtracted from the official industryregion cell structure total to determine the amount that must 

14

A 

γab, t = γab, t-1 Rab,t (4) (FH) (FH)
be raked. The total amount that must be raked is multiplied by 

the ratios to determine what percentage of the raked amount 

should be applied to the residential group and what percentage should be applied to the nonresidential group. 

Once the residential and nonresidential groups receive their 

proportional amount of raked employment, the two groups are 

aggregated again to the 4-digit NAICS level. At this point, employment is equal to the 4-digit NAICS total derived from the 

official industry-region cell structure. This raking process also 

forces additivity at the 3-digit NAICS level. 

No estimates of women employees, construction employees, or hours and earnings are made for the residential and 

nonresidential series. 

Real earnings data are expressed in constant 1982–84 dollars. Real earnings are computed by dividing average hourly 

earnings and average weekly earnings by the BLS Consumer 

Price Indexes. Real earnings for all employees are deflated 

by the Consumer Price Index for All Urban Consumers (CPIU), while real earnings for production and nonsupervisory 

employees are deflated by the Consumer Price Index for Urban Wage Earners and Clerical Workers (CPI-W). 

Average hourly earnings, excluding overtime-premium pay, 

are computed by dividing the total worker payroll for the industry group by the sum of total worker hours and one-half 

of total overtime hours. No adjustments are made for other 

premium payment provisions, such as holiday pay, late-shift 

premiums, and overtime rates other than time and one-half. 

Average hourly earnings excluding overtime are calculated 

only for manufacturing industries.

Seasonally adjusted series

Many economic statistics reflect a regularly recurring seasonal movement that can be measured from past experience. By 

eliminating that part of the change attributable to the normal 

seasonal variation, it is possible to observe the cyclical and 

other non-seasonal movements in a series. Seasonally adjusted series are published regularly for selected employment, 

hours, and earnings series. 

X-12 ARIMA software, developed by the U.S. Census 

Bureau, is used to seasonally adjust CES data on a concurrent basis, meaning the software incorporates estimates up 

through and including the current month’s data to achieve 

the best possible series. Using special features of X-12 

ARIMA, adjustments are made to remove the effect of the 

variable number of weeks between surveys from month to 

month (about 1 month in 3 has a 5-week instead of a 4-week 

interval) and to remove the effect of the variable number of 

work days in the reference month, to adjust for moving holidays, and to adjust for the variations in the number of election 

poll workers in November from year to year. CES processes 

concurrent seasonal adjustment on a monthly basis using the 

latest estimates of employment, hours, and earnings. Seasonally adjusted employment series for broader industry groups 

are obtained by summing the seasonally adjusted data for the 

component industries. Seasonally adjusted hours and earnings averages for broader level industry groups are weighted 

averages of the seasonally adjusted component series. For 

more information on seasonal adjustment of CES series, see 

http://www.bls.gov/ces/cesseasadj.htm.

Data Presentation

The national series on employment, hours, and earnings are 

available on the Internet and appear in several BLS publications. The summary data are first published each month in 

The Employment Situation news release (http://www.bls.

gov/ces/#news), which contains preliminary national estimates of nonfarm employment, average weekly hours, and 

average hourly and weekly earnings in the preceding month 

for industry sectors. Preliminary estimates are based on tabulations of data for less than the full sample to permit early 

release of these widely used economic indicators. This release is normally issued on Friday, 3 weeks after the reference week. The news release also includes a brief analysis 

of current trends in employment, hours, and earnings. The 

Real Earnings news release is published concurrent with the 

Consumer Price Index news release.

Detailed employment, hours, and earnings data also are 

available on the Internet on the morning of The Employment 

Situation news release. Data can be accessed through the 

CES database section on the CES homepage (http://www.

bls.gov/ces/#data). Where sample adequacy and response 

rates allow, estimates at the NAICS 4-, 5-, and 6-digit detail 

are published on the Internet on a 1-month lag. Final (prebenchmark) figures are issued 1 month later. In addition, special articles describe technical developments in the program. 

The Monthly Labor Review also presents CES data in articles 

analyzing industry employment, hours, and earnings trends. 

National data also are disseminated in the publications or 

online databases of other Federal agencies, such as the U.S. 

Department of Commerce, the Board of Governors of the 

Federal Reserve System, and the Council of Economic Advisers. Data also are regularly republished in summary form 

or for specific industries in many trade association journals, 

the labor press, and in general reference works. 

In addition to national estimates, monthly employment 

estimates for all 50 States, the District of Columbia, Puerto 

Rico, the U.S. Virgin Islands, and selected metropolitan areas 

are published in the online Employment and Earnings.

1

Detailed State and metropolitan area industry data also are 

available monthly in releases published by the State employment security agencies that cooperate with BLS in producing the State and area estimates. State and area data also are 

available from the State and area current employment statistics homepage http://www.bls.gov/sae/, which contains 

extensive information related to the CES State and area program, including contacts, news releases, and data. 

15

1

 Employment, hours, and earnings for the Nation as a whole exclude 

Puerto Rico and the U.S. Virgin Islands.
Comparison with the Current Population Survey

The Bureau of Labor Statistics (BLS) has two monthly surveys that measure employment levels and trends: the Current 

Employment Statistics (CES) survey, also known as the payroll or establishment survey, and the Current Population Survey (CPS), also known as the household survey. Employment 

estimates from both surveys are published in The Employment Situation news release each month. The estimates differ 

because the surveys have distinct definitions of employment 

and distinct survey and estimation methods. 

The Current Employment Statistics survey, also known as 

the payroll survey, excludes unpaid family workers, domestic 

workers in private homes, agricultural workers, proprietors, 

and other self-employed persons, all of whom are covered by 

the CPS. Moreover, the payroll survey counts a person who 

is employed by two or more establishments at each place of 

employment, but the household survey counts a person only 

once, and classifies the individual according to the major activity. Certain persons on unpaid leave for the entire reference period are counted as employed under the household 

survey but are not included in the employment count derived 

from the payroll survey. 

The household survey emphasizes the employment status 

of individuals and provides information on the demographic 

characteristics (sex, age, and race) of the labor force. The 

survey is not well suited to furnishing detailed information 

on the industrial and geographic distribution of employment. 

The establishment survey provides limited information on 

personal characteristics of workers; however, it is an excellent source for detailed industrial and geographic data. In addition, it provides hours and earnings information that relates 

directly to the employment figures. The payroll and household surveys thus complement each other. 

To better understand differences in the surveys’ employment measures, as well as divergences that sometimes occur 

in their trends, see http://www.bls.gov/web/ces_cps_trends.

pdf. Additional information on the methodologies of the two 

surveys can be found in the Quick Guide to Methods and 

Measurement Issues on the BLS Web site at http://www.bls.

gov/bls/empsitquickguide.htm. 

Uses

Data from the CES program, along with CPS data, are the 

first major economic indicators released each month. As such, 

they are used in the formulation of fiscal and economic policy. 

CES employment estimates are a primary component of the 

Index of Coincident Economic Indicators and have proved to 

be an extremely reliable measure of current economic activity. The manufacturing average weekly hours series is used 

in the Index of Leading Economic Indicators (LEI), which 

forecasts changes in the business cycle.

Aggregate earnings data are the major component of the 

preliminary personal income estimates in the National Income and Product Accounts. Productivity measures (chapters 

10 and 11) and the Industrial Production Index are based on 

the aggregate hours data. Employment series are a basic input 

for employment projections by BLS (chapter 13) and State 

labor market information agencies.

The series also are used in the private sector by business 

firms, labor unions, universities, trade associations, and private research organizations to study economic conditions and 

to develop plans for the future. Business firms, for example, 

use the employment, hours, and earnings data for guidance in 

plant location, sales, and purchases. 

Reliability of Estimates

The establishment survey, like other sample surveys, is subject 

to two types of error, sampling and non sampling error. The 

magnitude of sampling error, or variance, is directly related to 

the size of the sample and the percentage of universe coverage achieved by the sample. The establishment survey sample 

covers over one-third of total universe employment; this yields 

a very small variance on the total nonfarm estimates. 

Most sample surveys publish sampling error as their only 

measure of error; however, the CES can derive an annual 

approximation of total error, on a lagged basis, because of 

the availability of the independently derived universe data. 

While the benchmark error is used as a measure of total error 

for the CES survey estimate, it actually represents the difference between two independent estimates derived from separate survey processes (specifically, the CES sample process 

and the UI administrative process) and thus reflects the errors 

present in each program. Historically, benchmark revisions 

have been very small for total nonfarm employment, ranging 

from -0.7 to +0.6 percent. 

The estimation of sample variance for the CES survey is 

accomplished through use of the method of Balanced Half 

Samples (BHS). This replication technique uses half samples 

of the original sample and calculates estimates using those 

subsamples. The CES survey uses a modification to the basic BHS method known as Fay’s method. Rather than using 

only half of the sample in deriving each replicate estimate, 

this method uses adjustments to the original sample weights 

applied to both halves of the sample, thus allowing use of 

all sample units for each replicate estimate. The sample variance is calculated by measuring the variability of the replicate estimates. The sample units in each sampling strata are 

divided into two random groups. Columns of the Hadamard 

matrix (which is a special 0-1 matrix) of appropriate order 

are mapped to the strata. Each row of the Hadamard matrix 

defines a replicate subsample: the random group indicators 

are matched to the 0-1 entries of each row of the Hadamard 

matrix thus defining a set of units for each replicate. Weights 

for units that belong to a replicate half-sample are multiplied 

by a factor of 1+y, where weights for units in the other half 

of the sample are multiplied by a factor of 1–y. Replicate 

estimates are calculated using the same estimation formula 

as used for the full-sample estimate.

16
Variances statistics are useful for comparison purposes, but they do have some limitations. Variances reflect 

the error component of the estimates that is due to surveying only a subset of the population, rather than conducting 

a complete count of the entire population. However, they 

do not reflect the non-sampling error, such as response 

errors and bias due to non response. The overall performance of the CES employment estimates is best measured 

in terms of the benchmark revisions. The variances of the 

over-the-month change estimates are very useful in determining when changes are significant at some level of 

confidence.

The formula used to calculate CES variances

 

where

 is the α th replicate estimate,

 

k is the number of replicates, and, is the original full–

sample estimates.

17

present measures of the reliability of the data and the magnitude of revisions due to benchmark adjustments. (See 

http://www.bls.gov/ces/#technical.)

Technical Information: Estimation Methods for Business Births 

and Deaths. (See http://www.bls.gov/ces/cesbdtech.htm.)

Mueller, Kirk, “Impact of business births and death in the 

payroll survey,” May 2006, Monthly Labor Review.

Kokic, P. N., and Bell, P. A. (1994), “Optimal Winsorizing 

Cutoffs for a Stratified Finite Population Estimator,” Journal of Official Statistics, 10, 419-435. 

Fay, R.E. and Herriot, (1979). Estimates of Income for Small 

Places: an Application of James-Stein Procedure to Census Data, Journal of the American Statistical Association, 

74, 269-277. 

Technical References

Employment from the BLS household and payroll surveys: 

summary of recent trends. Describes differences in the 

employment measures from the CES and CPS surveys, as 

well as divergences that sometimes occur in their trends. 

(See http://www.bls.gov/web/ces_cps_trends.pdf.) 

Seasonal Adjustment in the Current Employment Statistics Program. Describes in detail the seasonal adjustment methodology and software employed by the Current Employment Statistics Program. It is important to note that this describes seasonal 

adjustment only as it relates to the CES program’s implementation. (See http://www.bls.gov/ces/cessa_oview.pdf.) 

Technical Notes To Establishment Data Published in Employment and Earnings. An up-to-date, concise description 

of concepts and methods used to develop establishmentbased employment, hours, and earnings data from the Current Employment Statistics program. Provides tables that 

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