Estimation Procedures for the Bureau of Labor Statistics Current Employment Statistics Program 

Shail Butani, Rachel Harter, and Kirk Wolter 

Key Words: Ratio estimator, raked ratio estimator, generalized regression estimator, composite estimation, variance 

estimation, seasonal adjustment 

Any opinions expressed in this paper are those of the authors and do not constitute policy of the Bureau of Labor 

Statistics. 

I. Introduction 

For the first time in decades, the Bureau of Labor 

Statistics (BLS) is planning a major sample redesign of 

the Current Employment Statistics (CES) Survey. An 

overview of the redesign including the transition and 

implementation phase is given in Werking (1997), 

while the goals, sample design parameters, features, 

and characteristics are described in Butani, Stamas, and 

Brick (1997). 

The CES is a Federal/State cooperative program. The 

BLS produces national estimates at detailed industry 

levels, and the states produce industry estimates for 

state totals and major metropolitan statistical areas 

(MSAs); the level of state industry detail varies from 

state to state and by MSAs. The statistics estimated at 

the national level include all employees, production and 

nonsupervisory workers, and women workers. For 

production and nonsupervisory workers, the CES 

program also estimates average weekly hours and 

average hourly earnings. Additionally, BLS produces 

estimated average overtime hours for the manufacturing 

sector. The states publish estimates for all employees 

and some combination of the other statistics. The exact 

combination varies by state. 

The primary advantage of the CES estimates is their 

timeliness. The preliminary estimates, generally 

released on the first Friday of every month for 

employment levels and for trends from the preceding 

month, are among the first economic indicators 

available. Several months later, more complete 

information becomes available from the BLS’ Covered 

Employment and Wages Program, commonly known as 

the ES-202 Program. The ES-202 Program is an 

administrative file based primarily on each states’ 

unemployment insurance programs in which virtually 

all employers participate. Under this program, the 

employers file quarterly contribution reports on 

employment for each month during the quarter and total 

quarterly wages for each of their U.I. accounts; a U.I. 

account may consist of more than one establishment 

(worksite or location). These establishments are known 

collectively as the Business Establishment List (BEL). 

Although there are minor differences between the CES 

and ES-202 in scope, coverage, and reporting 

procedures, the ES-202 data can be, and generally are, 

considered “truth” for employment for most industries. 

Today’s CES employment estimates are benchmarked 

(aligned or ratio adjusted) once per year to the ES-202 

figures for March, and the other statistics are 

recomputed accordingly. In the redesigned CES 

survey, the ES-202 data will play a major role in 

estimation as well as control totals for benchmarking 

employment. 

In this paper, we summarize the research and 

recommendations with respect to the estimation process 

and identify known issues that remain to be researched. 

We begin by giving a brief overview of the steps in 

estimation after the collection of sample data. The new 

estimation procedures include: (1) editing procedures 

for erroneous data, (2) adjustment for misaligned data, 

(3) adjustments for outliers, (4) imputation for missing 

data, (5) simple unbiased estimation, (6) estimation 

incorporating ES-202 employment data as an auxiliary 

variable, (7) estimation for births/deaths, (8)composite 

estimation, (9) seasonal adjustment, (10) variance 

estimation, and (11) benchmarking or realignment to 

ES-202 employment data. Before describing these 

steps, we define selection weights and make 

distinctions between sampling units and establishments 

and between estimation and model cells. 

II. Definitions and Terms 

Selection weights—These are defined as inverse of the 

probability of selection. 

Sampling units and establishments--As discussed by 

Butani, Stamas, and Brick (1997), the sampling unit is 

the unemployment insurance (UI) account. During the 

estimation process, however, all the reported data as 

well as information with respect to industry and MSA 

of each establishment will be utilized. 

Estimation and Modeling Cells--The new sample 

design and estimation process make use of different 

types of cells, or groupings of units. There are 

allocation cells for determining sample sizes, selection 

cells, imputation cells, model cells for estimating 

parameters, and estimation cells. 
 2

For state estimates, model cells are MSA by industry 

groupings, while for national estimates they are by 

industry groupings only; the model cells are used for 

estimating parameters. In terms of industry detail, the 

nation and each state will have its own set of model 

industries since the importance of industries varies 

geographically (e.g., automobile manufacturing in 

Michigan, meat packing in Iowa). Within a state, 

model industries will also vary from major industry 

division (e.g., mining in Iowa) to 4-digit industry (e.g. 

meat packing in Iowa), taking into account benchmark 

employment, the number of establishments, and the 

percentage of employment in the sample; at the national 

level, they will vary from 2 to 4-digit SIC (Standard 

Industrial Classification) level. 

Model industries also play an important role during 

imputation and one type of adjustment for outliers. The 

estimation cells can be at any level specified by the 

users; the estimation level may be at a higher or lower 

level than the model cell or model industry. 

III. Editing and Adjustments for Erroneous Data 

Some of the current edits are logical, while others are 

empirical that can be applied both at micro and macro 

levels. An example of a logical edit is that production 

workers must be equal to or less than all employees. 

An example of an empirical edit is to require a 

reporter’s employment to fall within an expected range 

based on that reporter’s or industry’s past history. At 

the macro level, edits are typically based on 

observations of over-the-month trends in the context of 

historical levels and trends. The current edit 

procedures, however, are not standardized among the 

states. A workgroup is in the process of finalizing a 

standardized set of edits that are to be used by all states 

and by BLS. Additionally, these edits will be 

consistent with the ES-202 edits [ES-202 Manual] 

developed by BLS that have a proven track record over 

a number of years. A brief description of the ES-202 

edits is given below. 

The edit for employment data of continuing units is a 

sequential six step edit; once a record passes one of the 

steps, it proceeds to the total quarterly wage edit. In 

other words, a record must fail all six steps in order to 

be flagged for verification. In the first three steps, the 

comparison of the current month data is made to the 

previous month data; then to account for seasonality, 

the three steps are repeated and the comparison is made 

to the same month a year ago. In the first step, the test 

is on absolute difference; this test is designed to bypass 

reports that have small absolute change in employment, 

especially those that have been reporting constant 

employment in the past (e.g., 3, 3, 3, 3 to 5). It is 

estimated that over 50 percent of the records are 

bypassed with this edit. The second test is designed to 

account for small percentage changes (e.g., 500 to 

540). The parameters for the first two tests are based 

on historical data and vary by employment size but not 

by industry. The third is a t-test that takes into account 

a record’s variability. For new units, the employment 

must be less than some prespecified level, which is also 

based on historical data. 

Wage data are edited in two sequential steps. In the 

first edit, a record is flagged if the absolute difference 

between the current and previous quarter wages 

exceeds some parameter (currently $10,000). Records 

that fails this edit are subject to an interquartile range 

edit based on the Hoaglin, Iglewizc, and Tukey test. 

Their work uses the upper and lower quartiles (FU & 

FL) to define outliers. To begin, the average quarterly 

wages are ranked from smallest to largest, with X(1)

being the smallest value and X(n) being the largest 

value. The quartiles are then determined by the 

formulas X(f) and X(n+1-f) where f = .5[ (n+3)/2]. 

Outliers are then defined as all observations falling: 

below FL - k* (FU - FL) or above FU + k*(FU - FL), 

where k is a parameter. 

A major consideration that was given in developing the 

ES-202 edits is their efficiency in terms of manual 

review (flagging the right records), computer 

processing, and timeliness. With seven million records 

(establishments) to process each quarter, the editing 

must be on a flow basis in order to be efficient. This 

also means the parameters must be based on historical 

data rather than on cell distributions at a current point 

in time which may change as more data are received 

and will certainly be different for state vs. national 

cells. The same thought process is being given to 

processing of CES data because of its vast sample size 

and general two week turn-around time between data 

collection and release of estimates. Editing on a flow 

basis is especially suited for CES because of its 

automated data collection environment (Clayton 1997); 

with online editing, it saves a call back to the 

respondents. The editing of the data will be performed 

at the U.I. account level (sampling unit). For 

employment data, each unit’s history will be brought 

forward from the frame (ES-202). For other data 

series, historical data from the current CES will be used 

to set the parameters (e.g., ratio of production workers 

to all employee, and average weekly hours) until a unit 

establishes its own history. In order to prioritize the 

cases, a score will be assigned to each unit, and to 

improve the editing process over time, an audit trail is 

also being programmed. 
 3

IV. Outliers and Atypical Adjustments 

The new design is being programmed to have atypical 

adjustments for three types of outliers. The 

identification of the first two types of outliers will be 

automated while the third type will be based on analyst 

judgment. To begin the atypical adjustment process, all 

units are assigned atypical weights equal to selection 

weights. 

At the time of estimation, a sampling unit (U.I. 

Account) is considered a Type I outlier if it has grown 

in employment by three or more size classes or by more 

than 500 employees from where it was sampled---

allocation and sampling size classification is 

determined by a unit’s maximum monthly employment 

over the 12 month period on the frame. Type I outliers 

are termed “representative outliers” in that they are 

representative of the population as a whole at the state 

or allocation industry level on a probability basis but 

not of small domains like MSA or 4-digit SIC. A 

sampling unit that is identified as Type I gets an 

atypical weight that is equal to one-half of its selection 

weight, provided the selection weight is greater than or 

equal to 2.000. The atypical weights of the other 

sampling units in the state/allocation industry/size class 

are increased accordingly to account for the excess 

weighted employment of the Type I atypical unit 

[Business Survey Methods, Chapter 26]. 

Type II outliers are identified through comment codes 

that are assigned at the time of data collection; a 

common example of this type of outlier pertains to 

strikes by workers. Type II outliers are termed 

“nonrepresentative outliers” or “self-representative” 

units in that they are not representative of the 

population as a whole. A Type II outlier is given an 

atypical weight of 1.000, and the atypical weights of 

the remaining sampling units in the state/allocation 

industry/size class are increased accordingly to account 

for the excess weight (i.e. selection weight minus 

1.000) of the Type II atypical unit. This way the sum 

of the atypical weights in an allocation cell is equal to 

the number of units in the population [Business Survey 

Methods, Chapter 26]. During the review of the 

estimates, the analysts will have the option to override 

both Type I and II outliers. 

Type III outliers are those establishments that the 

analysts, during their review of the estimates, consider 

to be “self representative”. These establishments are 

treated in the same manner as the Type II units; that is, 

they receive an atypical weight of 1.000. For 

operational reasons, the atypical weights of the 

remaining units in the state/model industry(not 

allocation industry)/size class are increased. 

The reason that weights of the non-atypical units are 

being adjusted is that in CES even a very small 

underestimation bias is a major concern. One of the 

goals of the redesign is to keep the annual benchmark 

revision to within 0.2 percentage point. 

V. Imputation 

Explicit imputation for missing data is a new feature in 

the redesign. Because missing values will be imputed, 

weighting for nonresponse adjustment will not be 

necessary. For the most part, imputation for all 

employees is theoretically comparable to past practice. 

The new design also incorporates several alternative 

options, like the establishment trend of a year ago, and 

the analysts will be able to override an imputed value if 

better information from some independent source is 

available. Imputation is performed at the state/model 

industry/size class level. The four size classes for 

imputation purposes are 1-9, 10-49, 50-249, and 250 or 

more employees. For nonparticipants, the initial month 

employment will be imputed as the latest available ES202 data times the sample trend of the model 

industry/imputation size class. Additionally, the 

imputed values will be replaced each time an updated 

ES-202 data become available. Employment is 

imputed as: 

 ( )

( )

y y

w y

w y

AEit AEi t

jt

sel

AEjt

jt

sel

AEj t

=















 −

−

∑

∑ 1

1

where, wjt

sel is selection weight for unit j, and Σ

indicates the sum across all units j that were nonatypical and that responded for both months t and t-1. 

It is important to note that the selection weight in the 

denominator is for time period t and not t-1 because of 

matched respondents, sample rotation, and updates to 

the sample due to frame maintenance. 

Four different imputation methods for unit nonresponse 

and the most common combinations of item 

nonresponse among production workers, hours, and 

payroll were tested. The methods are: composite 

estimation (λ=0.5, and λ=1.0); proportional-to-cell 

average for month t; and monthly trend (same 

procedure as for employment except different 

characteristics like production workers are substituted). 

The test was performed on current CES respondents for 

March 1994 to March 1995. In this simulation, 

imputation cells were at the 2-digit industry by 4 size 

classes as defined above. 
 4

Composite estimation--The imputed value of 

production workers (PW) is 

( )

( )

( ) ( )

( )

y y

y

y

y

w y

w y

PWit AEit

PWi t

AEi t

PWi t

jt

sel

AEjt

jt

sel

AEj t

= 















+

−











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

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−

−

−

−

∑

∑

λ

λ

1

1

1

1

1

, 

where y AEit , ( ) y AEi t−1 , and ( ) y PWi t−1 may be reported 

or imputed and ∑ is as defined above. In the first 

method tested, λ =.5 . In the second method, λ=1.0. 

The imputed value of hours (H) is 

( )

( ) ( )

( )

y y

y

y

w y

w y

w y

w y

Hit PWit

Hi t

PWi t

jt

sel

Hjt

jt

sel

PWjt

jt

sel

Hj t

jt

sel

PWj t

=









































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























−

− −

−

∑

∑

∑

∑

1

1 1

1

. 

Finally, the imputed value of payroll ($) is 

( )

( ) ( )

( )

y y

y

y

w y

w y

w y

w y

it Hit

i t

Hi t

jt

sel

jt

jt

sel

Hjt

jt

sel

j t

jt

sel

Hj t

$

$

$

$

=



































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

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





−

− −

−

∑

∑

∑

∑

1

1 1

1

. 

Proportional-to-cell average--This is the current 

method. 

y AEit w y

w AE PWit

jt

sel

PWjt

jt

sel

jt

= 















∑

∑

y y

w y

w y Hit PWit

jt

sel

Hjt

jt

sel

PWjt

= 















∑

∑

y y

w y

w y it Hit

jt

sel

jt

jt

sel

Hjt

$

$ = 















∑

∑

In the first three methods, the initial month values were 

set at proportional-to-cell average; while for the fourth 

method, the initial values were set proportional-toemployment (e.g., total hours/total employment). 

The details of the simulations on hours and earnings 

imputation is given in Grden (1997). No method was 

consistently best across major industry divisions and 

characteristics (e.g., average weekly hours, average 

weekly earnings) in terms of level and month-to-month 

change. Overall, the two composite methods 

performed more consistently for all industries, with the 

results differing only slightly between the two methods. 

Statistically, proportional-to-cell-average will yield 

larger variability from month-to-month at the microdata 

level, and monthly trend can yield inconsistent results 

(e.g., production workers greater than all employee). 

Between the two composite methods, the one where 

λ=1.0 consistently yields smaller average absolute 

errors at the microdata level in estimating production 

workers, and so based on this criteria, it is a better 

method. Additionally, this method is simpler than the 

one with λ=0.5. In the new design, therefore, the 

composite estimation method with λ=1.0 will be used. 

Technically, with λ=1.0, it is no longer a composite. 

VI. Estimators 

Employment--To begin the research on estimators, a 

multi-year simulation study was conducted using ES202 data for the period April 1989-September 1994 

from Iowa. In this study, ten random samples, 

according to the sample design, were selected and 

estimates were tabulated for four different estimators 

with some built-in nonresponse pattern. They are: 1) 

current link relative (Butani, Stamas, Brick, 1997), this 

estimator does not use sampling weights; 2) weighted 

link relative; 3) ratio estimator 

$

$

Y

X

X





 



 which is 

equivalent to generalized regression estimator (GRE) 

with no intercept; and 4) GRE with intercept. These 

estimators were evaluated in terms of: mean and 

maximum percentage benchmark revision for March 

1991-94, and relative standard errors on the mean 

revisions; mean and maximum error in estimated 

month-to-month percent change; and mean and 

maximum revisions between preliminary and final 

estimates. While no estimator consistently performed 

the best across industries and time, the current link 

relative estimator produced biased results at certain 

time periods and for certain industries. Overall, the 

ratio estimator was more robust and easiest to 

implement. 

At this point, employment estimator for state estimates 

was established as: ∑ wit

aty* witBMF *yit where, witaty is 

the atypical weight (selection weight adjusted for 

outliers), and wt

BMF calculated at the state/model 
 5

industry level and attached to each unit i within the 

state/model industry. 

wt

BMF X

X w x i

sel i

= = ∑ $

total universe employment of the noncertainty units

 in the model industry at benchmark month (t=0) , 

where, xi is the benchmark employment of the ith in the 

sample ∑ is over all the non-certainty units that are in 

sample for model industry at time t. Since wit

BMF is 

accounting for sampling variability at benchmark 

month (t=0), all certainty units receive a wit

BMF =1.000. 

Note: The use of wit

aty instead of witsel in the 

denominator leads to an underestimation bias. In the 

simulations performed for the 11 states, the mean 

percentage revision based on ten samples for each state 

were tabulated for March 1991, 92, 93, and 94. The 

results indicated a consistent underestimation (see 

table). As mentioned elsewhere, for CES, bias is more 

of a problem than variance because of large sample 

size. 

Since the wit

BMF are calculated without regard to MSA 

data, the use of ratio estimator gave large relative 

standard errors for MSA estimates. In order to produce 

reliable estimates for both industry (statewide) and 

MSA, the GRE without intercept and raked ratio 

estimator were considered. For very small domains, 

borth estimators are problematic. GRE can produce 

negative employment values, while raked ratio 

estimator generates estimates of zero employment for 

subdomains with no sample units. See Harter (1997) 

for estimators for small domains. For operational 

reasons, raked ratio estimator was selected for industry 

and MSA estimates. The raked ratio estimator utilizes 

the benchmark weight concept and adjusts estimates in 

not one, but two directions—MSAs and model 

industries both within a major industry division. These 

factors are calculated by iteratively adjusting 

benchmark weighted employment for MSAs by model 

industries to MSA major industry division total and to 

state model industries total. This iterative adjustment 

process continues until the marginal sample totals are 

within a tolerance limit of the fixed benchmark levels; 

currently, the tolerance level is 100 employees. 

The raked ratio estimator improved the reliability of the 

MSA estimates without sacrificing the reliability of the 

industry estimates at the state level. 

Mean % Benchmark Revisions (March) and Mean Relative RMSEs 

Averaged Over 10 Samples, All CES Industries, and 4 Years 

 Mean % Benchmark Revision Rel Root Mean Squared Error 

 

Raked Ratio 

Ratio 

X wx i

sel Σ i

Ratio 

Xw x i

ATY Σ i Raked Ratio 

Ratio 

X wx i

sel Σ i

Ratio 

Xw x i

ATY Σ i

California -.01 .03 .35 .38 .38 .46 

Connecticut .09 .09 .25 .58 .55 .51 

Florida .03 .07 .56 .74 .67 .77 

Illinois -.02 -.01 .25 .43 .39 .37 

Iowa .04 .00 .13 .66 .67 .58 

Massachusetts -.04 -.05 .11 .53 .52 .48 

Michigan .07 .06 .21 .46 .45 .44 

New Jersey -.06 -.02 .28 .71 .62 .57 

New York .14 .12 .31 .39 .36 .44 

Pennsylvania .09 .10 .46 .55 .52 .61 

Texas -.16 -.08 .53 .57 .52 .71 

The estimator for state estimates, including MSAs and 

MSA by industry, is: ∑ wit

aty* witBMF *yit ; where, wtBMF 

is the raked ratio estimator. For national estimates, it is 

essentially the same estimator. The only difference 

being that wt

BMF is calculated at the national model 

industries level with no geography component; hence, 

the term ratio estimator. Since the sample size is quite 

large at higher levels of aggregation, the sum of the 

state estimates are virtually the same as independently 

produced national estimates. In the empirical study 

conducted on the simulations of the 50 states plus 

District of Columbia, the difference at the total private 

employment level was less than 0.05 percentage point. 

This difference is much smaller than the difference 

arising from performing independent seasonal 

adjustments to national and states data. 

Production Workers, Hours, and Earnings—For these 

characteristics, independent research was conducted by 

West, Kratzke, and Grden (1997), Harter (1997), and 
 6

Grden (1997); they tested numerous estimators. The 

decision is based on Grden (1997) research that tested 

three estimators. They are: ratio estimator, weighted 

link-relative, and the current link and taper estimator. 

The same estimator as the one for employment is being 

adopted for them as well. Estimates of average weekly 

hours are derived by taking the ratio of total hours to 

total production workers; similarly average hourly 

earnings is the ratio of total payroll to the total hours. 

Three Different Estimators--In the new design, three 

sets of estimates will be produced for each 

characteristic at the national, state, and MSA level. 

They are: the simple unbiased , ∑ wit

sel *yit ; raked ratio 

(state) or ratio (national) with selection weights, ∑

wit

sel* witBMF *yit ; and raked ratio or ratio with atypical 

adjusted weights, ∑ wit

aty* witBMF *yit , the official 

estimates. By comparing the first two estimates, the 

effect of the benchmark factors can be gauged. Also, 

by comparing the latter two estimates, the effect of 

atypical adjustments can be gauged. 

VII. Estimation for Births/Deaths 

Direct estimation of births in establishment surveys has 

always been problematic due to lack of a 

comprehensive and timely sampling frame [Stamas, 

Goldenberg, Cantor, 1997]. In theory, direct 

measurement of deaths or out-of-businesses should be 

possible from the sample; in practice, however, it is 

very hard to make a distinction between nonrespondent, 

out-of-business, and ownership changes in CES 

because of its vast sample size and short data collection 

period. Estimation procedures for this major and 

complex topic are described in Butani, Kratzke, and 

Shierholz (1997) and in Getz and Kropf (1997). 

VIII. Summary and Future Issues 

Of the many steps involved in estimation, so far the 

focus has been primarily on edits, adjustments for 

outliers, imputation, estimators, and birth/death issues; 

work has also begun on variance estimation. Work in 

the area of composite estimation, if necessary; seasonal 

adjustment; benchmarking; sample rotation; and further 

improvements will begin once the data from the new 

design become available.