Imputation Methods for the Current Employment Statistics Survey 

Kennon R. Copeland1 and Lan Pham2

1NORC at the University of Chicago, 2U.S. Bureau of Labor Statistics 

1

4350 East-West Hwy, Ste 800, Bethesda, MD 20814, (Copeland-Kennon@norc.org) 

2

2 Massachusetts Avenue, N.E. Washington, DC 20212 (Pham.Lan@bls.gov) 

I. Introduction 

The Bureau of Labor Statistics’ (BLS) Current Employment Statistics (CES) survey collects employment, hours, 

and earnings data monthly from a sample of over 300,000 U.S. establishments. To provide timely information, 

initial estimates are generated three to four weeks after the survey reference period. Final estimates, incorporating 

late reports received after production of the preliminary estimates, are released two months later. Benchmark 

estimates, incorporating administrative population data from the BLS’ ES-202 program for March of the prior year, 

are released annually with the data for May. 

Nonresponse potentially introduces bias into survey estimates, if respondents differ from nonrespondents relative to 

the variables of interest, and also reduces the effective sample size of a survey, thereby increasing variances for 

survey estimates. Estimation methods are developed so as to account for nonresponse and lessen its impact on bias 

and variance. These methods, however, assume nonresponse is ignorable within defined estimation cells and, hence, 

do not distinguish among various patterns of nonresponse. Nonresponse is used here to encompass both 

nonreporting and late reporting. Late reporting is temporal nonresponse, as the data become available at a 

subsequent point in time. 

The objective of this research is to identify imputation methods that yield decreased revisions in month-to-month 

change and total employment estimates. Alternative methods are proposed, and findings are presented relative to 

criteria under which the alternative methods should be applied and performance of the resulting employment 

estimates relative to the current method. 

This paper builds upon previous research into CES late reporting and nonresponse imputation reported in Copeland 

(2003a) Copeland (2003b), Copeland (2004a), Copeland (2004b), and Copeland and Valliant, 2007). The CES 

imputation research conducted in this project was divided into two phases – model definition (Phase I) followed by 

model performance assessment (Phase II). Section II presents a brief overview of the CES survey design and 

estimation methodology, Section III defines and profiles the issue associated with CES late reporting and 

nonresponse, Section IV discusses model definition, Section V discusses model refinement and assessment, and 

Section VI provides a summary and next steps. 

II. CES Survey Design and Estimation 

The BLS completed a major redesign of the CES survey in 2003 (Werking, 1997; Bureau of Labor Statistics, 2003), 

moving the survey from its historical quota sample design to a probability sampling basis. The new sample design 

is a stratified, simple random sample of establishments from the BLS’s Longitudinal Data Base, with strata defined 

by state, industry, and employment size. Sampling rates for each stratum are determined through optimum 

allocation to minimize variance of total employment level. 

Data must be reported within a two to three week period for inclusion in the initial published estimates (referred to 

as first closing estimates) for the month. As additional responses are received after this first closing of the collection 

period, the estimates for a given month are revised twice (referred to as second and third closing estimates) to 

incorporate data from late reporters. The first closing estimate of month-to-month change is derived by subtracting 

the prior month’s second closing estimate from the current month’s first closing estimate. 

Estimates are generated through use of a weighted link-relative estimator, which uses a weighted sample trend 

within an estimation cell, based upon common reporters between the prior and current months, to move forward the 

prior month’s estimate for that cell. Units determined to be atypical are treated separately. The current estimator for 

total employment (Bureau of Labor Statistics, 2001) takes the following form for month t and closing k  1,2,3
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 wiYti 

C

  

ˆ isct ,t1|k

, R

Yt|k   Yˆ  Y   Y   wY 

ct 1|(k 1)  t 1i



  ti

c1   i t 1i 

isct ,t1|k

, Atyp 

isct ,t1|k

, Atyp



isct ,t1|k

, R 

C   

  ˆ  LRct,t 1|k



Yct 1|(k 1)  Yt 1i



  Yti

c1 

 

isct ,t1|k

, Atyp 

 isct ,t1|k

, Atyp

where 

c  1,...,C refers to estimation cell (defined by industry and, for selected industries, region) 

s represents the set of sample establishments in estimation cell c that, as of closing k , reported data for ct ,(t1 |) k

both months t and t 1 

Atyp represents the set of sample establishments in s determined to be Atypical ct ,(t1 |) k

R represents the set of reporting sample establishments in sct ,(t1 |) knot classified as Atypical 

wi

is the sampling weight for sample establishment i

Yti is the total employment reported for month t by sample establishment i

Yˆ

ct1|( k 1) represents the prior month, t 1, link-relative estimate for estimation cell c based upon data reported 

as of closing k 1 (with a maximum value of three) for month t 1 (which corresponds to closing k for 

month t ) 

The link-relative, LRct,(t1) , is thus a growth rate estimate for the period t 1 to t . Differences in estimates between 

closings will be due solely to the inclusion of late responses, while differences between estimated and benchmark 

values will be due to the combined effects of sampling, nonresponse, late reporting (if comparing first or second 

closing estimates), and measurement error. An implicit assumption of the estimator is that, within an estimation cell 

and closing, establishments not reporting data (nonsampled, nonreporting, late reporting) for both months t and 

t 1 are assumed to have the same growth rate as for those establishments reporting data, i.e., the sampling, 

response, and reporting timeliness mechanisms are ignorable (Rubin, 1976). 

III. CES Late Reporting/Nonresponse

Survey nonresponse is frequently classified on the basis of reason for nonresponse. Panel surveys add another 

dimension to the response mechanism, that being response status at different points in time. Little and David (1983) 

distinguished three types of panel survey nonresponse – attrition (sample unit stops reporting), late entry (sample 

unit does not report initially), and reentry (sample unit has a gap in reporting). 

Copeland (2003b) developed the following alternative classification, appropriate for the CES survey, reflecting the 

current month’s reporting status, and timing of reporting for current month reporters: 

Reporters 

Early Reporters 

First Closing Reporters – sample establishments reporting data for the month prior to the cutoff date for 

processing first closing estimates 

Late Reporters 

Second Closing Reporters – sample establishments reporting data for the month after the cutoff date for 

processing first closing estimates, but prior to the cutoff date for processing second closing estimates 

Third Closing Reporters – sample establishments reporting data for the month after the cutoff date for 

processing second closing estimates, but prior to the cutoff date for processing third closing estimates 

Nonreporters – sample establishments not reporting data for the month 

Complete Nonreporters – sample establishments not reporting for any month 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Attritors – sample establishments reporting data for at least one month, but which no longer report data 

Episodic Nonreporters – sample establishments not reporting data for the month, but which do report for a 

subsequent month 

All three nonreporter types impact the overall accuracy of the CES estimates, regardless of closing. Late reporters 

(second closing reporters, third closing reporters) affect the accuracy of preliminary estimates only. The extent of 

the impact late reporters have on the preliminary estimates can be assessed by examining the direction and 

magnitude of revisions between first and third closing estimates. 

IV. Imputation Research Phase I: Model Definition

Phase I of the research was intended to identify characteristics for consideration in imputation and to develop 

alternative imputation models for broader assessment in Phase II. 

A. Consideration of Alternative Models

Consideration of alternatives was restricted to several simple models that would be operationally efficient to 

implement. All assumed prior history for a particular establishment provided useful ancillary information for 

estimating current month employment. The following models were considered: 

Model 1: Year-lagged-establishment: Establishment growth rate for current month is consistent with that seen for 

the same month in the prior year 

Yt12i

LRti  LRt12i Yˆ 

ti  Yt1i 

Yt13i

Model 2: Month-lagged establishment: Establishment growth rate for the current month is consistent with that seen 

for the immediately prior month 

Yt1i

LRti  LRt1i Yˆ 

ti  Yt1i 

Yt2i

Model 3: Year-lagged deviation: Deviation of establishment growth rate for the establishment from the 

corresponding cell growth rate for the current month is consistent with that seen for the same month in the prior year 

 Y 

t12ci LR  LR  LR  LR Yˆ  Y  LR    LR 

tci tc t12ci t12c tci t1ci tc t12c 

    Y

  t13ci 

B. Model Performance Assessment

The performance of each of these models was compared to the performance of the current model (the Link Relative, 

or Model 0) 

LRtci  LRtc Yˆ 

tci  Yt1ci  LRtc

First, a subset of the CES sample establishments was identified for use in assessing model performance. This subset 

(referred to here as “Influencers”) consisted of establishments with a weighted employment greater than or equal to 

0.1% (or >[5/{# of reporting establishments}], if this latter value is greater than 0.1%) of the total weighted 

employment for the supersector in at least one month between Jan ’04 and May ’081

. All data reported for the 

Influencer establishments was used in the analysis, resulting in 42,596 establishment-months, distributed by 

supersector and size as indicated in Table 4. 

1 This definition provided for not only designation of large establishments (e.g., most establishments with 500+ 

reported employment in at least one month), but also relatively larger establishments in smaller cells. Use of a 

criteria taking into account number of reporting establishments was used to avoid automatically designating 

Influencer establishments in cases where there were a small number of reporting establishments, in which case it 

would be expected that at least one establishment would account for >0.1% of the total weighted employment for a 

supersector. 
 

 

 

 

 

 

 

 

 

 

Table 4

CES Sample Influencers

Supersector

# of Establishment-Months

Total

Size (Based on prior month employement)

5,000- 2,500- 1,000-

10,000+ 9,999 4,999 2,499 500-999 250-499 100-249 <100

Total 42,596 7,086 4,882 5,412 7,642 4,970 4,102 4,011 4,491

Business 1,832 292 353 130 226 215 99 243 274

Construction 701 1 8 63 112 134 202 181

Education 1,849 1,068 333 124 83 82 79 26 54

Finance 3,805 195 733 1,036 374 401 400 357 309

Government 3,791 3,642 102 10 27 10

Information 7,715 62 178 724 2,786 1,024 909 1,039 993

Leisure 1,301 69 550 198 210 112 28 77 57

Durable Goods Mfg 2,820 504 1,226 694 88 179 47 28 54

Mining 1,870 9 25 68 579 272 185 313 419

Non-durable Goods Mfg 2,957 97 290 731 254 474 557 401 153

Other Services 2,375 3 242 395 556 341 300 538

Retail Trade 1,559 625 444 18 153 91 109 32 87

Transportation 5,074 444 497 1,058 1,025 785 465 280 520

Utilities 2,418 67 72 258 1,270 254 194 163 140

Wholesale Trade 2,529 9 78 113 109 413 545 550 712

Next, performance of the current and three alternative models was determined using both an establishment level 

assessment and an employment estimate level assessment. 

The establishment level assessment was derived by measuring the error in the predicted value for the establishment 

determined by the model: 

ˆ M M ErrYti   Yˆ 

ti ti  Y

where 

M

Yˆ 

ti  predicted value for establishment i in month t, as determined by model M

Yti  reported value for establishment i in month t

Several summary statistics were examined at the supersector, size, and supersector x size level: 

Median Absolute Error 

ˆ M MedAbsErr  M  median ErrYti 

t,i

Error IQR 

M M

   75  ˆ ErrIQR M   25thPercentileErr Yˆ thPercentile Err Y    ti ti

t,i t,i

Error 90/10 

ˆ M ˆ M Err90 /10  M  90 thPercentileErrY 10 thPercentileErrY  ti ti

t ,i t,i

The employment estimate level assessment was derived by measuring the error in the 1st closing employment 

estimate at the supersector level determined by the model, relative to the 3rd closing employment estimate: 

M M   1   3 ErrYˆ   Yˆ  Yˆ 

SS ,t SS ,t SS ,t

where 

ˆ M   1 YSS ,t  1st closing estimate for supersector SS in month t, using imputed employment as determined by model 

M for late reporting Influencer establishments (note, current model uses only 1st closing reporters, not 

imputed values for late reporting Influencer establishments) 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ˆ   3 YSS ,t  3rd closing estimate for supersector SS in month t

C. Results

Results were examined from both an establishment level and an establishment estimation level perspective. NOTE: 

All referenced tables in the Establishment Level Assessment section are provided at the end of this document, rather 

than with the text, due to the size of the tables. 

Establishment Level Assessment. Looking at the summary statistics at the supersector level (Table 5), it can be 

seen that the current model yields the best performance measures (highlighted in yellow in the table) for all three 

summary statistics for twelve of the fifteen supersectors. For Education and Government, however, both Models 1 

and 3 yield better performance measures for all three summary statistics than does the current model. For Retail 

Trade, Model 1 yields better Median Absolute Error and Error IQR performance measures than does the current 

model, while the current model yields the best Error 90/10 performance measure. 

Looking at the summary statistics at the size level (Table 6), it can be seen that the current model yields the best 

performance measures (highlighted in yellow in the table) for all three summary statistics for all but the largest size 

category. For the 10,000+ size category, however, both Models 1 and 3 yield better performance measures for all 

three summary statistics than does the current model. 

It is by examining summary statistics at the size x supersector level that the relationship between size and 

supersector can be seen. Detailed information analogous to that provided in Tables 5 and 6 were prepared in a Table 

7 not presented her due to size, and frequencies of the best performance measure were tallied separately by size and 

supersector and are provided in Tables 8, 8a, 9, and 9a. Tables 8 and 9 provide frequencies based on all Models, 

whereas Tables 8a and 9a provide frequencies based solely on Model 1, which is the model which has the best 

performance. 

As can be seen in Tables 8 and 8a, Model 1 yields better performance measures than the current model in roughly 

half the supersectors for establishments of size 5,000+. For establishments of size less than 2,500, the current model 

tends to yield best performance across supersectors, with the exception of Construction (where Model 2 yields better 

performance measures for establishments of size 500-2,499) and Retail Trade (where both Models 1 and 3 yield 

better performance measures for establishments of size 500-2,499. This latter finding can be ascertained by 

examining the detailed information (not presented here). 

As can be seen in Tables 9 and 9a, Model 1 yields better performance measures than the current model for 

Government (which only has sufficient sample for establishments of size 5,000+) and yields better performance 

measures than the current model in roughly half the size categories for Education and Retail Trade. For the 

remaining supersectors, the current model tends to yield the best performance measures across size categories. 

Further examination as provided in Tables 10 and 10a shows that Model 1 offers performance improvement 

opportunities for establishments of size 5,000+ for many supersectors (with the exception of Finance, Durable 

Goods Mfg, and Wholesale Trade), while performance improvement opportunities for establishments of size 500-

4,999 appears limited to Retail Trade. 

Establishment Estimate Level Assessment. Based upon findings from the establishment level assessments, 

employment level assessment was carried out for Model 1. In addition, the set of Influencer establishments used in 

the employment estimate level assessment was restricted to large (5,000+) establishments, as this is the set for which 

Model 1 appears to offer opportunities for improvement across most supersectors. Note that not all months were 

included in the employment estimate level for all supersectors, as there could be some months in which no large 

Influencer establishments were late reporters. 

Model 1 yielded the lower absolute error for just over 60% of the cases. When looking at extreme errors, both the 

current model and Model 1 yielded roughly the same number of errors greater than 0.5 percentage points; however, 

when looking at errors greater than 0.2 percentage points, Model 1 did yield fewer errors, primarily in Government, 

Education, and Transportation. While positive results for the first two supersectors were expected given the findings 

from the establishment level assessment, the finding for Transportation was unexpected. Comparing errors of 

smaller sizes show virtually no difference between the current model and Model 1 (results not shown). 
 

 

 

 

 

 

 

 

 

 

 

X 

- I 

,, 

-

"":. 

'Sc'-

'I;. 

{. 

~ . 

Table 11

Model Performance for Employment Estimates

Jan '04 to May '08

# Lower Abs(Err) # Abs(Err) >0.5% # Abs(Err) >0.2%

Model Model Model

(1) (1) (1) (0) (0) (0) Year-lagged Year-lagged Year-lagged Current Current Current Establishment Establishment Establishment Supersector

Business 25 40 0 0 6 5

Construction 0 1 0 0 0 0

Education 27 41 1 0 11 8

Finance 21 39 0 0 2 2

Government 25 41 6 5 18 11

Information 10 17 1 2 2 4

Leisure 19 41 0 0 6 5

Durable Goods Mfg 22 41 0 1 5 6

Mining 1 2 0 0 1 1

Non-durable Goods Mfg 20 38 0 0 5 5

Other Services 2 2 0 0 0 0

Retail Trade 17 39 1 1 12 11

Transportation 27 41 2 4 19 15

Utilities 15 24 0 0 9 8

Wholesale Trade 11 15 0 0 1 1

Total 242 422 11 13 97 82

To show the impact of Model 1 on errors greater than 0.2 percentage points, the distribution of the absolute errors 

were graphed (Figure 2). The graph shows that between roughly the ninth and twenty-fifth percentile of the 

distribution (which correspond to absolute errors for the current model from 0.18 to 0.32 percentage points), Model 

1 yields smaller absolute errors than does the current model (generally on the order of 0.03 to 0.04 percentage points 

smaller). For the remainder of the distribution, the two models yield essentially the same absolute errors. 

Figure 2

Distribution of Absolute Errors in 1st Closing Estimates

Current Model, Alternative Model (1)

Imputing for Late Reporting Establishments with Size of 5,000+

2.5%

Current

Alternative Model (1)

Absolute Error (Relative to 3rd Closing Estimate)

2.0%

Points1.5% Percentage 1.0%

0.5%

0.0%

0 0.1 0.2 0.3 0.4 0.5 0.6

Cumulative Distribution

0.7 0.8 0.9 1
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

D. Conclusions

Results suggest use Model 1 in imputing current month employment for selected late reporters offers opportunity for 

improvement in first closing employment estimates. Further analysis is required to refine criteria in terms of size 

and supersector for application. 

In addition, there are other characteristics which should be considered, which were not part of this analysis. Work 

by Butani, et al (2005), suggested employment growth may differ by single vs. multi-establishments employers. 

While this work utilized reported employment size, further analysis should make use of design size for 

establishments to provide more stability in the definition criteria. Consideration of performance by month and 

relative to overall employment trends (e.g., use of prior year employment growth may not be a good predictor when 

employment trends have reversed – in these situations, Model 3 may be useful) should also be part of the analysis. 

V. Phase II: Model Refinement and Assessment 

During Phase I several alternative methods were explored, and one method (Model 1) recommended for assessment 

during Phase II. The work in Phase II is intended to refine the criteria under which Model 1 should be applied, and 

to assess the performance of the resulting employment estimates relative to the current model. 

A. Criteria Refinement

Results from Phase I of this research suggested the Model 1 may offer improved performance when applied to large 

establishments and in selected sectors. The first activity in the Phase II research was to conduct further analysis to 

identify criteria defining the set of establishments for which improved performance under Model 1 can be expected. 

Accuracy by Establishment Characteristics: The first analysis entailed assessing the accuracy of imputed 

employment at the establishment level by selected characteristics: establishment size; establishment type; state; 

calendar month; difference in monthly change between current month and same month prior year; direction of 

monthly change for current month and same month prior year. 

Change and direction characteristics were determined as follows: 

For each estimation cell, the difference between the current month 1st closing link relative and the 1st closing link 

relative from 12 months prior was calculated 

For each estimation cell, the direction of monthly change was defined as 

0 if link relatives were either both greater than 1.0 or both less than 1.0 

1 if current month link relative was greater than 1.0 and 12 months prior link relative was less than 1.0 

1 if current month link relative was less than 1.0 and 12 months prior link relative was greater than 1.0 

Within each supersector, sort in decreasing order the observed differences across all months and estimation cells 

and segment into quintiles to create a “growth change” variable (valued as 1, 2, 3, 4, or 5, based on the 

quintile) 

The accuracy of imputation based on the current method and Model 1 was calculated for each month/establishment 

in employment size class 7 (500-999 employees) or 8 (1,000+ employees), based upon establishments reporting 

employment by 3rd closing in a month. The relative error for imputation was defined as 

M Yti Yti ErrYˆ  

ˆ M

ti Yti

where 

M

Y repr ˆ 

ti esents the imputed employment for establishment in month 

Yti represents the actual reported employment for establishment in month 

The summary statistic examined was the median absolute error for month/establishments within a given 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

characteristic set. 

M MedAbsErr  M  median ErrYˆ 

ti 

t,iA

Table 12 provides summary information from the imputation assessment. As can be seen Method 1 yields lower 

median absolute errors for many characteristics, for Government, Information, and Utilities. It can also be seen that 

for establishments in Quintile 1 and Quintile 5 relative to growth change, Method 1 yields lower median absolute 

errors for one-third or more of the supersectors. 

Table 12

Characteristics for Which Imputation Model 1 Yields Lower Median Absolute Error than Current Method

Jan '05 - Jun '08

Supersector

Establishment

Size

Establishment

Type Growth Change Direction Change Month State

Size Size

Class 7 Class 8

Single Multi Quintile Quintile Quintile Quintile Quintile

1 2 3 4 5

-1 0 1 # #

Business 0 0

Construction X X 0 6

Durable Goods Mfg 0 3

Education 0 1

Finance 0 0

Government X X X X X X X X 6 43

Information X X X X X X X X 12 25

Leisure X X X 0 5

Mining X X 7 18

Non-durable Goods Mfg X X 0 9

Other Services 0 6

Retail Trade 1 0

Transportation X 0 3

Utilities X X X X X X X X X X X 11 20

Wholesale Trade 0 13

Impact on Estimates: The second analysis entailed comparing monthly levels and month-over-month growth rates 

under the current model and Model 1 to actual growth rates at the establishment level, summarized by various 

establishment characteristics. The time period for the criteria refinement analysis was January 2005 1st closing 

through June 2008 3rd closing. 

Three methods applying Model 1 were included in this analysis. These methods represent different forms in which 

imputed employment could be applied for implementation. At the estimation cell level, these models are: 

Method 1.1: Imputed values are used in deriving the Link-Relative, with the form of the estimator being the same as 

that currently used. 

ˆ

  1.1   ˆ 1.1   1.1 Y  

ct|k  LRct,  t 1 |k





Y   k 1  Y  t 1 i





c t 1 |  Yti



Atyp  t1 | isct ,  t1 |k, i sct ,  k, Atyp

where 

wY  wYˆ 

i ti i ti

  isct ,  k

,R is 1.1 t1 | c   t1 | k

LRct,  t 1 |  k 

wiY  t 1 i  wiY  t 1 i

i R s  t 1 | sct , 1 | k

, i

t c    k

s represents the set of sample establishments in estimation cell c that, as of closing k , reported data c(t 1)|k

for both month t 1 , but not for month t

Method 1.2: Imputed values are not use in deriving the Link-Relative; rather the weighted sums of values for the 
 

 

 

 

 

 

 

 

 

 

 

establishments with imputed values are handled separately as are those for unweighted sums for Atypical 

establishments. 

ˆ

1.2   0  ˆ1.2 Y  LR  ˆ 

Y  Y  wY 



ct k | ct , t 1 |  k  Y  wY 



ct 1  t  1 i

isct , t1 |  k

, Atyp

i

isc t1 |  k

t  1 i



ti

isct , t1 |  k

, Atyp

i

isc t  k 1 | 

ti

where 

  0 LRct, t 1 |  k  current link-relative 

Method 1.3: This is analogous to Method 1.2, the difference being unweighted sums of values for the establishments 

with imputed values are handled separately as are those for Atypical establishments. 

 

ˆ

1.2   0 ˆ1.2 Y ˆ 

ct|k  LRct ,t 1|k

Yct 1  Yt 1i  Yt 1i



  Yti  Yti 



isct ,t1|k, Atyp isc t1|k isct ,t1|k, Atyp isc t1|k

Performance was assessed on the basis of relative mean square error to the current 3rd closing estimates, and was 

assessed by calendar month within supersector, s : 

2 

s L  ˆ

  ˆ  3 

C M

  M 1 Ycs

,l,m  Ycs,l,m

RelMSEs 

LC 

 Yˆ

  3 





s cs   1 l 1  c , s

l,m 

where 

M refers to an imputation method (Current, 1.1, 1.2, 1.3) 

s refers to a calendar month (January, February, etc.) 

l refers to a calendar year (2005, 2006, 2007, 2008) 

c refers to an estimation cell within supersector s s

Table 13 provides a summary of the comparison of RelMSE to that for the current method for the three alternative 

methods. First, Methods 1.2 and 1.3 generally yield lower RelMSE for more months than Method 1. Second, the 

Method 3 yields lower RelMSE than the current method in at least eight months for Education, Government, 

Leisure, Other Services, and Retail Trade. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 13

Number of Calendar Months for Which Alternative Method has Lower

RelMSE than Current Method

Jan '05 - Jun '08

Supersector Method 1.1 Method 1.2 Method 1.3

Business 6 7 6

Construction 4 5 6

Durable Goods Mfg 4 3 3

Education 6 7 9

Finance 4 7 7

Government 9 9 8

Information 4 6 5

Leisure 9 9 9

Mining 5 5 5

Non-durable Goods Mfg 4 4 7

Other Services 5 8 9

Retail Trade 7 8 8

Transportation 6 6 6

Utilities 7 7 6

Wholesale Trade 5 5 6

VI. Summary and Next Steps 

In summary, it appears that use of a simple model making use of the prior year’s month-over-month growth for first 

closing nonreporters meeting some minimum size criteria within selected supersectors could offer improvements to 

the stability of employment revisions. This approach would derive imputed employment for designated first closing 

nonreporters as 

Yt12i

Yˆ

ti  Yt1i 

Yt13i

The set of first closing nonreporters for which imputation would be carried out would be restricted on the basis of 

size (larger establishments) and possibly supersector. An advantage of the proposed imputation model is that 

imputed employment can be pre-processed once the prior month reporting is complete, with imputations used based 

upon the results of current month reporting outcomes. 

Further refinement of imputation criteria is desirable. In addition, further analysis of performance when employment 

trends are changing is needed to determine thresholds which identify when the imputation model will not yield 

accurate results. 

References

Bureau of Labor Statistics. (2001), Chapter 7, “Estimation,” Current Employment Statistics Manual: U.S. Bureau 

of Labor Statistics, Washington, D.C. 

Bureau of Labor Statistics. (2003), “BLS Establishment Estimates Revised to Incorporate March 2002 

Benchmarks,” Employment and Earnings: U.S. Bureau of Labor Statistics, Washington, D.C. 

Butani, S., Werking, G., and Kapani, V. (2005), “Alternative Imputation Methods for Employment Data,” 

Monthly Labor Review: U.S. Bureau of Labor Statistics, Washington, D.C., 3-15 

Copeland, K.R. and Valliant, R. 2007. "Imputing for Late Reporting in the Current Employment Statistics 

Survey." Journal of Official Statistics, 23:69-90. 

Copeland, K.R. 2004a. “An Approach to Late Reporting and Nonresponse Imputation for the Current 

Employment Statistics Survey,” Proceedings of the Section on Survey Research Methods, American 

Statistical Association. 
 

 

 

 

 

 

 

 

 

Copeland, K.R. 2004b. “Panel Survey Estimation in the Presence of Late Reporting and Nonresponse,” PhD 

Thesis, University of Maryland, College Park, Maryland. 

Copeland, K.R. 2003a. “Nonresponse Adjustment in the Current Employment Statistics Survey.” Proceedings 

of the Federal Committee on Statistical Methodology Conference. 

Copeland, K.R. 2003b. “Reporting Patterns in the Current Employment Statistics Survey,” Proceedings of the

Section on Survey Research Methods, American Statistical Association. 

Little, R.J.A. and David, M.H. (1983), “Weighting Adjustments for Non-response in Panel Surveys,” Working 

paper: U.S. Bureau of the Census, Washington, D.C. 

Rubin, D.B. (1976), “Inference and Missing Data,” Biometrika, 63, 581-592. 

Werking, G.S. (1997), “Overview of the CES Redesign,” Proceedings of the Section on Survey Research

Methods, American Statistical Association, pp. 512-516. 
 

 

 

 

Table 5

Establishment Level Performance Measures

by Supersector

Model

Supersector (0)

Current

(1)

Year-lagged 

Establishment

(2)

Month-lagged

Establishment

(3)

Year-lagged 

Deviation

Median Absolute Error

Business 1.52% 2.05% 2.15% 2.02%

Construction 4.13% 6.70% 5.68% 8.13%

Education 1.18% 0.74% 1.21% 0.77%

Finance 0.81% 1.17% 1.07% 1.31%

Government 1.49% 0.63% 1.34% 0.70%

Information 1.16% 1.60% 1.59% 1.84%

Leisure 2.21% 2.48% 2.86% 2.51%

Durable Goods Mfg 0.75% 0.91% 0.87% 1.08%

Mining 1.60% 2.11% 2.17% 2.36%

Non-durable Goods Mfg 1.08% 1.49% 1.44% 1.75%

Other Services 2.33% 3.13% 3.98% 3.16%

Retail Trade 1.54% 1.54% 1.85% 1.57%

Transportation 1.42% 1.89% 1.96% 1.98%

Utilities 0.65% 0.78% 0.82% 1.00%

Wholesale Trade 1.30% 2.24% 2.13% 2.76%

Error IQR

Business 3.05% 3.96% 4.34% 4.09%

Construction 8.31% 13.49% 11.58% 17.01%

Education 2.35% 1.48% 2.48% 1.57%

Finance 1.61% 2.34% 2.12% 2.63%

Government 3.01% 1.26% 2.69% 1.39%

Information 2.32% 3.20% 3.18% 3.71%

Leisure 4.43% 4.96% 5.62% 5.06%

Durable Goods Mfg 1.48% 1.83% 1.74% 2.21%

Mining 3.27% 4.20% 4.31% 4.85%

Non-durable Goods Mfg 2.12% 3.00% 2.86% 3.52%

Other Services 4.59% 6.35% 8.04% 6.39%

Retail Trade 3.16% 3.06% 3.81% 3.14%

Transportation 2.84% 3.81% 3.90% 3.95%

Utilities 1.30% 1.54% 1.64% 2.01%

Wholesale Trade 2.62% 4.46% 4.25% 5.54%

Error 90/10

Business 10.53% 14.80% 15.91% 14.86%

Construction 25.81% 44.51% 34.74% 62.38%

Education 6.74% 5.86% 12.56% 5.95%

Finance 4.60% 6.79% 6.96% 7.81%

Government 8.06% 4.31% 11.64% 4.24%

Information 7.22% 11.19% 11.25% 11.23%

Leisure 10.93% 15.48% 17.34% 15.34%

Durable Goods Mfg 4.01% 5.83% 5.98% 9.14%

Mining 8.57% 13.80% 13.27% 21.59%

Non-durable Goods Mfg 6.50% 9.72% 9.57% 11.48%

Other Services 15.13% 19.44% 28.50% 19.50%

Retail Trade 7.84% 7.96% 11.03% 7.96%

Transportation 8.61% 12.13% 13.35% 12.08%

Utilities 3.16% 4.20% 4.76% 4.81%

Wholesale Trade 8.68% 14.28% 13.39% 20.76%
 

Table 6

Establishment Level Performance Measures

by Size

Model

(1) (2) (3) (0) Size Year-lagged Month-lagged Year-lagged Current Establishment Establishment Deviation

10,000+

5,000-9,999

2,500-4,999

1,000-2,499

500-999

250-499

100-249

<100

10,000+

5,000-9,999

2,500-4,999

1,000-2,499

500-999

250-499

100-249

<100

10,000+

5,000-9,999

2,500-4,999

1,000-2,499

500-999

250-499

100-249

<100

Median Absolute Error

1.13% 0.68% 1.11% 0.76%

0.91% 0.92% 0.97% 1.07%

0.85% 1.09% 1.03% 1.24%

1.03% 1.27% 1.30% 1.47%

1.42% 1.87% 1.95% 2.09%

1.56% 2.26% 2.23% 2.46%

2.01% 3.04% 3.13% 3.20%

2.77% 5.22% 5.09% 5.50%

Error IQR

2.27% 1.37% 2.26% 1.50%

1.82% 1.87% 1.94% 2.13%

1.70% 2.19% 2.06% 2.50%

2.05% 2.53% 2.61% 2.93%

2.80% 3.77% 3.92% 4.22%

3.10% 4.50% 4.47% 4.94%

4.02% 6.09% 6.27% 6.37%

5.71% 10.42% 10.22% 10.98%

Error 90/10

6.45% 4.36% 9.56% 4.54%

5.03% 5.87% 6.67% 6.53%

4.68% 6.30% 7.01% 7.23%

5.56% 7.38% 8.04% 7.97%

7.45% 10.58% 11.20% 11.73%

8.70% 13.52% 13.63% 14.73%

11.25% 17.44% 16.98% 19.01%

20.88% 35.20% 35.96% 37.08%
 

 

Table 8

Frequency with which Model has Best Performance Measure

by Size (within Supersector)

Size (0)

Current

Model

(1) (2)

Year-lagged Month-lagged

Establishment Establishment

(3)

Year-lagged 

Deviation

Median Absolute Error

10,000+ 4 5 2 0

5,000-9,999 5 4 2 1

2,500-4,999 10 2 1 0

1,000-2,499 12 0 1 1

500-999 12 1 1 0

250-499 11 0 1 0

100-249 11 0 0 0

<100 13 0 1 0

Error IQR

10,000+ 4 4 2 1

5,000-9,999 6 4 2 0

2,500-4,999 12 1 0 0

1,000-2,499 12 1 1 0

500-999 13 0 0 1

250-499 11 1 0 0

100-249 11 0 0 0

<100 14 0 0 0

Error 90/10

10,000+ 4 5 0 2

5,000-9,999 9 2 0 1

2,500-4,999 13 0 0 0

1,000-2,499 13 0 0 1

500-999 13 1 0 0

250-499 11 0 0 1

100-249 11 0 0 0

<100 13 0 0 1
 

 

 

 

 

Table 9

Frequency with which Model has Best Performance Measure

by Supersector (within Size)

Supersector (0)

Current

Model

(1) (2)

Year-lagged Month-lagged

Establishment Establishment

(3)

Year-lagged 

Deviation

Business

Construction

Education

Finance

Government

Information

Leisure

Durable Goods Mfg

Mining

Non-durable Goods Mfg

Other Services

Retail Trade

Transportation

Utilities

Wholesale Trade

7

3

3

8

0

6

5

5

5

7

6

2

7

7

7

Median Absolute Error

1 0

1 2

3 1

0 0

1 0

1 1

1 1

0 1

0 1

1 0

0 0

2 1

1 0

0 1

0 0

0

0

0

0

1

0

0

0

0

0

0

1

0

0

0

Business

Construction

Education

Finance

Government

Information

Leisure

Durable Goods Mfg

Mining

Non-durable Goods Mfg

Other Services

Retail Trade

Transportation

Utilities

Wholesale Trade

7

5

4

8

0

7

5

5

6

7

6

2

7

7

7

Error IQR

1 0

0 1

3 0

0 0

2 0

0 1

1 1

0 1

0 0

1 0

0 0

2 0

1 0

0 1

0 0

0

0

0

0

0

0

0

0

0

0

0

2

0

0

0

Error 90/10

Business 7 0 0 1

Construction 6 0 0 0

Education 5 2 0 0

Finance 8 0 0 0

Government 1 1 0 0

Information 6 2 0 0

Leisure 5 0 0 2

Durable Goods Mfg 6 0 0 0

Mining 6 0 0 0

Non-durable Goods Mfg 7 1 0 0

Other Services 6 0 0 0

Retail Trade 2 1 0 3

Transportation 7 1 0 0

Utilities 8 0 0 0

Wholesale Trade 7 0 0 0
 

 

Table 8a

Frequency with which Model has Best Performance Measure

by Size (within Supersector)

Size

Model

(1)

(0) Year-lagged

Current Establishment

Median Absolute Error

10,000+ 5 6

5,000-9,999 6 6

2,500-4,999 10 3

1,000-2,499 13 1

500-999 13 1

250-499 12 0

100-249 11 0

<100 14 0

Error IQR

10,000+ 5 6

5,000-9,999 6 6

2,500-4,999 12 1

1,000-2,499 12 2

500-999 13 1

250-499 11 1

100-249 11 0

<100 14 0

Error 90/10

10,000+ 4 7

5,000-9,999 9 3

2,500-4,999 13 0

1,000-2,499 13 1

500-999 13 1

250-499 12 0

100-249 11 0

<100 13 1
 

 

 

Table 9a

Frequency with which Model has Best Performance Measure

by Supersector (within Size)

Supersector

Model

(1)

(0) Year-lagged

Current Establishment

Business

Construction

Education

Finance

Government

Information

Leisure

Durable Goods Mfg

Mining

Non-durable Goods Mfg

Other Services

Retail Trade

Transportation

Utilities

Wholesale Trade

Median Absolute Error

7 1

5 1

4 3

8 0

0 2

6 2

6 1

6 0

5 1

7 1

6 0

3 3

7 1

7 1

7 0

Business

Construction

Education

Finance

Government

Information

Leisure

Durable Goods Mfg

Mining

Non-durable Goods Mfg

Other Services

Retail Trade

Transportation

Utilities

Wholesale Trade

Error IQR

7 1

5 1

4 3

8 0

0 2

7 1

5 2

6 0

6 0

7 1

6 0

2 4

7 1

7 1

7 0

Business

Construction

Education

Finance

Government

Information

Leisure

Durable Goods Mfg

Mining

Non-durable Goods Mfg

Other Services

Retail Trade

Transportation

Utilities

Wholesale Trade

Error 90/10

7 1

6 0

5 2

8 0

1 1

6 2

5 2

6 0

6 0

7 1

6 0

3 3

7 1

8 0

7 0
 

 

 

Table 10

Frequency with which Model has Best Performance Measure

by Supersector (within Size 5,000+)

Supersector

Model

(1)

(0) Year-lagged

Current Establishment

Business

Construction

Education

Finance

Government

Information

Leisure

Durable Goods Mfg

Mining

Non-durable Goods Mfg

Other Services

Retail Trade

Transportation

Utilities

Wholesale Trade

Median Absolute Error

1 1

0 0

0 2

2 0

0 2

0 2

1 1

2 0

0 0

1 1

0 0

1 1

1 1

1 1

1 0

Business

Construction

Education

Finance

Government

Information

Leisure

Durable Goods Mfg

Mining

Non-durable Goods Mfg

Other Services

Retail Trade

Transportation

Utilities

Wholesale Trade

Error IQR

1 1

0 0

0 2

2 0

0 2

1 1

0 2

2 0

0 0

1 1

0 0

1 1

1 1

1 1

1 0

Business

Construction

Education

Finance

Government

Information

Leisure

Durable Goods Mfg

Mining

Non-durable Goods Mfg

Other Services

Retail Trade

Transportation

Utilities

Wholesale Trade

Error 90/10

1 1

0 0

0 2

2 0

1 1

0 2

1 1

2 0

0 0

1 1

0 0

1 1

1 1

2 0

1 0
 

 

 

Table 10a

Frequency with which Model has Best Performance Measure

by Supersector (within Size 500 - 4,999)

Supersector

Model

(1)

(0) Year-lagged

Current Establishment

Business

Construction

Education

Finance

Government

Information

Leisure

Durable Goods Mfg

Mining

Non-durable Goods Mfg

Other Services

Retail Trade

Transportation

Utilities

Wholesale Trade

Median Absolute Error

3 0

2 1

2 1

3 0

0 0

3 0

3 0

3 0

2 1

3 0

3 0

0 2

3 0

3 0

3 0

Business

Construction

Education

Finance

Government

Information

Leisure

Durable Goods Mfg

Mining

Non-durable Goods Mfg

Other Services

Retail Trade

Transportation

Utilities

Wholesale Trade

Error IQR

3 0

2 1

2 1

3 0

0 0

3 0

3 0

3 0

3 0

3 0

3 0

0 2

3 0

3 0

3 0

Business

Construction

Education

Finance

Government

Information

Leisure

Durable Goods Mfg

Mining

Non-durable Goods Mfg

Other Services

Retail Trade

Transportation

Utilities

Wholesale Trade

Error 90/10

3 0

3 0

3 0

3 0

0 0

3 0

3 0

3 0

3 0

3 0

3 0

0 2

3 0

3 0

3 0