Attachment 2 - Us of Administrative Data to Explore Effect of Establishment Nonresponse Adjustment

USE OF ADMINISTRATIVE DATA TO EXPLORE EFFECT OF ESTABLISHMENT NONRESPONSE
ADJUSTMENT ON THE NATIONAL COMPENSATION SURVEY ESTIMATES December 2006
Chester H. Ponikowski and Erin E. McNulty, Bureau of Labor Statistics
Chester H. Ponikowski, BLS, Postal Square Building Suite 3160, 2 Massachusetts Ave. NE,
Washington, DC 20212
KEY WORDS: Unit nonresponse, bias, weighting cells

our conclusion and propose issues for further research
in Section IV.

I. INTRODUCTION
Unit non-response is a well known but undesirable
problem in sample surveys including the National
Compensation Survey (NCS) Program. In NCS, unit
non-response occurs because of refusal or inability of a
sample establishment to participate in the survey. In
addition non-response may occur because of inability of
an interviewer to make contact with a sample
establishment within a specified survey data collection
cycle. Since non-responding sample establishments’
data on employee earnings may be systematically
different, that is, larger or smaller on average from
responding establishments, there may be bias in the
survey estimates due to non-response. Non-response
also causes an increase in the variance of survey
estimates because the effective sample size is reduced.
However, bias is usually considered to be a bigger
concern because in the presence of a significant bias a
calculated confidence interval will be centered on the
wrong value and thus will be misleading.
The goal of adjusting for non-response is to
reduce bias due to non-response. Over the years, a
number of techniques have been presented in statistical
literature for adjusting for unit and item non-response
(Sverchkov et al, 2005, Kalton and Kasprzyk, 1982;
Rubin, 1978; Platek and Gray, 1978). Sverchkov et al
propose adjusting for non-response via calibration.
Kalton and Kasprzyk describe several methods and their
properties. The most common technique for unit nonresponse is to adjust sampling weights of responding
establishments to account for non-responding
establishments within a specified set of weighting
classes or cells. The weighting cells are defined by
available auxiliary variables. The effectiveness of the
weighting adjustment in reducing the bias depends on
the auxiliary variables’ ability to explain the response
propensity and the main study estimates, and to identify
the most important domains (Sarndol and Lundstrom,
2005).
This paper explores the effect of non-response
adjustment on estimates in the National Compensation
Survey. We describe the NCS in Section II; present
empirical analysis and results in Section III; and state

II.
DESCRIPTION
OF
COMPENSATION SURVEY

THE

NATIONAL

The NCS is an establishment survey of wages and
salaries and employer-provided benefits conducted by
the Bureau of Labor Statistics (BLS). It is the
combination of three previously separate surveys: the
Employer Cost Index (ECI), the Employee Benefits
Survey (EBS), and the locality wage survey. The ECI
publishes national indexes that track quarterly and
annual changes in wages and benefit costs and also
publishes quarterly cost level information on the cost
per hour worked of each component of compensation.
The EBS annually publishes the incidence and detailed
provisions of selected employee benefit plans. The
locality wage survey publishes occupational wages for
a sample of localities, census divisions, and for the
nation as a whole. In addition to the continued
publication of these surveys products, new products
linking benefit costs and provisions will be published as
part of the NCS. All state and local governments and
private sector industries, except for farms and private
households, are covered in the survey. All employees
are covered except the self-employed.
The Longitudinal Database (LDB) serves as the
sampling frame for the NCS survey and was used as the
administrative data for this study. The LDB is created
from State Unemployment Insurance (UI) files of
establishments, which are obtained through the
cooperation of the individual state agencies.
The integrated NCS sample consists of five rotating
replacement sample panels. Each of the five sample
panels will be in sample for five years before being
replaced by a new panel selected annually from the most
current frame. The NCS sample is selected using a
three-stage stratified design with probability
proportionate to employment sampling at each stage.
The first stage of sample selection is a probability
sample of areas; the second stage is a probability
sample of establishments within sampled areas; and the
third stage is a probability sample of occupations within
sampled areas and establishments.
Currently the NCS sample consists of 152 areas
based on the Office of Management and Budget (OMB)

1994 area definitions. In 2003 OMB released a new set
of area definitions. The new area definitions define a set
of Core Based Statistical Areas (CBSA) and designate
the remaining geographical areas as outside CBSA
counties. The outside CBSA areas for NCS sampling
purposes are usually clusters of adjacent counties, not
single counties. The NCS has selected a new sample of
areas using the 2003 OMB definitions which will replace
the current set of primary sampling units (PSUs) over
the next few years. A more detailed description of the
NCS sample design is available from the BLS website:
www.bls.gov/opub/hom/pdf/homch8.pdf.
The NCS locality wage program collects wage data
for a sample of occupations within sampled
establishments. During the initial interview or update
interview some sample establishments refuse to provide
or are unable to provide wage data. This results in
establishment or unit non-response. Ignoring the
establishment non-response could result in substantial
bias in estimates and incorrect variance estimates.
In our study, we used the administrative and NCS
private industry sample data from the Chicago
Consolidated Metropolitan Statistical Area (CMSA) for
2003. The definition of the Chicago CMSA is provided
in the 1997 BLS Handbook of Methods.
The
administrative data provided us with auxiliary variables
as well as data on establishment earnings and
employment. The administrative data are available
approximately nine months after the reference date for
the quarterly data collection. The NCS data provided
the sample size allocated to private industry in the
Chicago area and distribution of NCS non-respondents
among industries and establishment size classes. The
non-respondents in the NCS are establishments that do
not provide any earnings data.
The useable
establishments are establishments with earnings data
for at least one sampled occupation. The in-scope
sample size for private industry in the Chicago survey
area in 2003 was 651 establishments.
III. EMPIRICAL ANALYSIS AND RESULTS
To investigate the effect of establishment nonresponse adjustment on NCS estimates, we calculated
and compared response rates for subgroups of the
sample, as defined by the auxiliary variables that form
the weighting adjustment cells; calculated average
earnings for the entire NCS sample, useable
establishments, and non-responding establishments;
and conducted a simulation study using administrative
data.
To find out whether the NCS has a potential
problem with bias due to non-response, we compared
response rates among subgroups of the sample. If

response rates do not vary among subgroups of the
sample and missing data are missing at random, then the
sample is usually considered not biased as a result of
non-response. The NCS defines non-response cells by
industry and size class, so we examined response rates
in these categories. The response rates were computed
by dividing weighted employment of useable
establishments by the sum of useable and refusals. The
NCS program uses 110 weighting adjustment cells that
are defined by industry-size class cross products of the
categories listed in Table 1.
The response rates shown in Table 1 indicate that
response rates vary widely among industry groups and
to a lesser extent among size classes. For example, food
stores, finance, insurance, and real estate (FIRE),
business
services,
and
education
services
establishments have response rates much lower than
the overall average response rate of 62 percent, while
rates in mining, banking, savings and loans, and nursing
homes are higher. Size class response rates range from
58 percent for establishments within the 1000-2499
employee group to 67 percent for establishments in the
2500+ employee group.
Table 1. Establishment Response Rates by Industry
and Size Class in Chicago
Characteristic
Response Rate
Industry
Mining
75
Construction
54
Manufacturing Durables
73
Manufacturing Non-Durables
66
Transportation
69
Communications
78
Electric, Gas, Sanitary Services
67
Wholesale
58
Retail
57
General Merchandise Stores
61
Food Stores
44
FIRE
41
Banking, Savings, and Loans
76
Insurance
44
Services
66
Business Services
49
Health
60
Nursing Homes
77
Hospitals
71
Education Services
50
Elementary & Secondary Educ.
73
Higher Education
59
Size Class
50 – 99
66
100 – 249
60
250 – 999
60

1000 – 2499
58
2500+
67
Total
62
The results in Table 1 confirm that industry and size
class variables are important auxiliary variables for
forming the weighting adjustment cells in NCS. Also
the uneven response rates indicate that the NCS may
have a potential problem with bias due to non-response.
In our next step of analysis, we assessed how well
NCS adjustments for non-response compensate for data
lost to establishment non-response. We matched the
NCS sample establishments with units on the
administrative data file and extracted their earnings and
employment information from the file. The earnings data
on the administrative file are available at the
establishment level only.
We calculated average
monthly earnings for the respondents, nonrespondents, and total sample. The initial sample
weights were used in the calculations of estimates. The
total sample estimates simulate estimates that might be
produced if NCS had no non-response. The estimates
based on respondents simulate estimates that might be
obtained using initial sample weights that were adjusted
for non-response using a single weighting adjustment
cell. In addition, we calculated average earnings for
respondents using initial sample weights that were
adjusted for non-respondents using current weighting
adjustment cells and procedures. Collapsing of cells
was done using the NCS collapse pattern when
adjustment factor was greater than 4.0 within a cell.
These estimates simulate published estimates. The
results are presented in Table 2, attached at the end of
paper.
The average monthly earnings shown in Table 2
indicate that overall average earnings of nonrespondents are about 9.6 percent higher than the total
sample ($3,934.45 versus $3,588.22). The overall average
earnings of respondents are about 8.3 percent lower
than the average earnings of the total sample ($3,291.21
versus $3,588.22). When initial sample weights of
responding establishments are adjusted for nonresponding establishments using current NCS
weighting adjustment cells, the overall average earnings
of respondents are about 5.6 percent lower ($3,385.88
versus $3,588.22).
The differences in average earnings of
respondents, non-respondents, and the total sample are
more pronounced for some industry and establishment
size class estimates. For example, for services the
average earnings for respondents are 12.4 percent lower
($2,282.65 versus $2,606.35) and for non-respondents
21.4 percent higher ($3,163.69 versus $2,606.35) than the
average earnings of the total sample.
For the
establishment size class of 250-999 workers the average

earnings for respondents are 14.6 percent lower
($3,025.70 versus $3,543.90) and for non-respondents
the average earnings are 18.0 percent higher ($4,183.19
versus $3,543.90) than average earnings of the total
sample. However, the differences in average earnings of
respondents and non-respondents by industry and
employment size class do not always follow this pattern.
Non-respondents in establishments with 2,500 or more
employees, for example, have lower average earnings
than the respondents and the total sample.
In most cases, when initial sample weights of
responding establishments are adjusted for nonresponding establishments, the differences in average
earnings between respondents and the total sample are
smaller; non-response procedures tend to bring the
respondents’ values closer to the actual, full-sample
values. Nevertheless, the adjusted estimates continue
to lean in the direction of the respondents’ data. The
results in Table 2 indicate that the NCS locality wage
estimates that are generated using weights adjusted for
non-response appear to be affected by non-response,
that is, the estimates appear to be biased.
The amount of bias in estimated average earnings
cannot be determined from a single sample. To measure
the amount of bias in the average earnings estimates, we
drew a total of 100 samples of the same size and same
industry composition as the original sample. The
samples were taken from the same frame as the NCS
sample in the study; this frame is also the administrative
source of the wages and employment figures
summarized in Table 2. For each sample a response set
was obtained by using the current NCS sample
response rates within each non-response adjustment
cell. The non-respondents within each non-response
adjustment cell were assigned at random.
We generated two sets of estimates. In the first set
we used the initial sample establishment weight, and in
the second set we used the initial sample establishment
weight adjusted for non-response. The sample weight
adjustment was done using the current NCS weight
adjustment procedures and cells that have five size
classes. In addition, we investigated how estimates and
variances are impacted when the five employment size
classes are collapsed to two employment size classes
and then used in sample weight adjustment for nonresponse. When the adjustment factor exceeded 4.0
within a cell, the collapsing of cells was done using the
NCS collapse pattern
The variances for each sample were computed
using
balanced
repeated
replication
(BRR)
methodology. For a detail description of the BRR
methodology see Wolter (1985).

The formulas used to calculate the amount of bias
in average earnings and ratios of bias to standard
deviation are as follows:

B

r

= E( y ) − E( y ) = Y

d

d

dr

=

B σ
d

d

dr

−Y

d

d

where,
is the bias in average earnings for domain d
d

B

E ( y dr) is the expected value of average earnings
of respondents in domain d over the 100 samples

E ( y d ) is the expected value of average earnings
of the total sample in domain d over the 100
samples

Y

dr

is the average earnings of respondents in

domain d

Y
r

d

d

is the average earnings in domain d
is the ratio of the bias to standard deviation in

domain d
is the standard deviation for the average
d

σ

earnings in domain d
The results in Table 3 (attached at the end of paper)
indicate that the amount of bias in average monthly
earnings is reduced when weights are adjusted to
account for non-response.
In the total monthly
earnings estimate of $4,210.03 there is a negative bias of
$25.33 when no weight adjustment is done to account
for non-response compared to a negative bias of only
$3.22 when weight adjustment is done to account for
non-response. This is true even when a smaller number
of size classes, that is, two size classes, is used in
carrying out the adjustment.
The amount of bias in average monthly earnings
varies widely among industry groups.
Mining,
Construction, Manufacturing, Transportation, Utilities,
Wholesale and Retail Trade and Education Services
show a negative bias ranging from $140.38 to $19.71,
and FIRE, Business Services, and Health Services show
a positive bias in a range of $10.71 to $220.72. Five out
of the eight industry groups have a negative bias.
The number of size classes used in adjustment of
weights for non-response seems to have an impact on
bias and variance. However, the impact on bias seems
to be very minimal. The overall average earnings are
underestimated by $3.22 when five sizes classes are

used to adjust for non-response and overestimated by
$5.44 when two size classes are used in adjustment for
non-response.
The variance on overall average
earnings is $74,474 when two size classes are used
compared to $76,900 when five size classes are used in
adjustment for non-response. The mean square error on
overall average earnings is $74,504 when two size
classes are used compared to $76,919 when five size
classes are used. The slight reduction in mean square
error indicates that the NCS program may benefit from
using fewer than five size classes in the adjustment of
weights for non-response.
To determine the effect of bias on the accuracy of
estimates, we calculated the ratio, d , defined above,

r

for each industry group estimate. Cochran (1953) points
out that the effect of bias on accuracy of an estimate is
negligible if the bias is less than one tenth of the
standard deviation of the estimate. A ratio between 0.1
and 0.2 is considered to have a modest impact on
accuracy of an estimate. The calculated ratios are
presented in Table 4.
The results in Table 4 show that the effect of
bias on the accuracy of selected industry estimates is
usually
negligible.
Mining,
Construction,
Manufacturing, FIRE, Business Services, and Health
Services have ratios that are less than 0.10 when the
current five size classes are used in the adjustment of
weights for non-response.
The ratios for
Transportation, Utilities, Wholesale and Retail Trade
suggest that bias in these estimates has a modest
impact on accuracy. The ratio for Education Services is
0.32 which indicates that the bias in this estimate has
somewhat noticeable impact on accuracy of this
estimate.
Table 4. Ratio of the Bias to the Standard Deviation by
Domain and Number of Size Classes Used in
Adjustment for Non-response
Domain
for 5
for 2

r

Mining/Construction
Manufacturing
Transportation/Utilities
Wholesale/ Retail
FIRE
Business Services
Health Services
Education Services
Total

d

size classes
0.02
0.07
0.14
0.22
0.09
0.08
0.08
0.32
0.01

r

d

size classes
0.002
0.09
0.10
0.13
0.12
0.05
0.01
0.23
0.02

When two size classes are used in weighting
adjustments for non-response, the effect of bias on

precision of estimates is usually smaller. The ratios are
lower for Mining, Construction, Transportation,
Utilities, Wholesale and Retail Trade, Business Services,
Health Services, and Education Services. The ratios for
Manufacturing and FIRE are only slightly higher 0.07
versus 0.09 and 0.09 versus 0.12, respectively. The ratio
for Education Services went down from 0.32 to 0.23.
The ratios indicate that it might be advantageous to use
a different number of size classes for different industry
groups in carrying out weighting adjustments for nonresponse.
IV. CONCLUSION AND ISSUES FOR FURTHER
RESEARCH

wage as an auxiliary variable would lend strength to reweighting procedures. We would like to further explore
what size class definitions result in the lowest mean
square error of NCS estimates. In addition, we would
like to investigate the current criteria used for collapsing
weighting adjustment cells. As part of this work we
would like to determine whether requiring a minimum
number of responding establishments within weighting
adjustment cells has an impact on bias and variance of
estimates. Also, we would like to explore using both the
magnitude of the weight adjustment factor and number
of responding units in the criteria for collapsing
weighting adjustment cells.
REFERENCES

In this study, we have explored the effect of
establishment non-response adjustment procedures on
NCS estimates. Using data from NCS Chicago survey
area, we calculated and compared response rates for the
auxiliary variables that are used in forming the weighting
adjustment cells . We found that response rates vary by
industry group and establishment employment size
class, the auxiliary variables.
To determine whether non-response might be
biasing survey estimates, we used administrative data to
calculate average earnings for responding units, nonresponding units, and the entire NCS sample in the area.
We noted that the NCS weighting adjustment helps
reduce the bias due to non-response; the industry and
employment size class are powerful auxiliary variables in
treating non-response. However, the NCS program
could gain from using fewer size classes in forming
weighting adjustment cells in some industries.
We selected 100 samples from the original frame
and then calculated the ratio of the bias to the standard
deviation to assess the effect of bias on the precision of
average monthly earnings estimates. We noted that the
effect of bias on the precision of estimates is usually
negligible. The industry where bias has a modest
impact on industry estimates could likely benefit from
different number of size class categories.
To extend this study, we would like to examine data
from several other survey areas and time periods. We
plan to include localities of different size and with
different levels of non-response. We plan to compare
the direction and magnitude of the bias across time and
across areas. If it turns out that there are some
consistent trends, then there may be justification for
making a non-response bias adjustment. We would like
to perform some evaluation of coverage of confidence
intervals. We would also like to investigate whether
there are any other auxiliary variables that may be useful
in reducing bias due to non-response. In particular, we
would like to explore whether using average monthly

BLS Handbook of Methods (Bulletin 2490, April 1997),
Washington, D.C.: Bureau of Labor Statistics, 57-67.
Cochran, William G. (1953), Sampling Techniques, New
York: John Wiley & Sons, Inc.
Ernst, L.R., Guciardo, C., Ponikowski, C.H., and
Tehonica, J. (2002), “Sample Allocatio and Selection
for
the
National
Compensation
Survey,”
Proceedings of the Section on Survey Research
Methods, Washington, D.C.: American Statistical
Association.
Kalton, G., and Kasprzyk, D. (1982), "Imputing for
Missing Survey Responses," Proceedings of the
Survey Research Methods Section, Washington,
D.C.: American Statistical Association, 22-31.
Little, R.J.A., (1986), Missing Data Adjustment in Large
Surveys, Journal of Business & Economic Statistics,
6, 287-296.
Oh, H. L. and Scheuren, F. J. (1983), Weighting
Adjustment for Unit Nonresponse, In W.G. Madow,
I. Olkin and D. B. Rubin (editions), Incomplete Data
in Sample Surveys, Vol. 2, New York: Academic
Press.
Platek, R., and Gray, G.B. (1978), "Nonresponse and
Imputation," Survey Methodology, 4, 144-177.
Rubin, D.B. (1978), "Multiple Imputations in Sample
Surveys--A Phenomenological Bayesian Approach
to Nonresponse," Proceedings of the Section on
Survey Research Methods, Washington, D.C.:
American Statistical Association, 20-34.
Rizzo, L., Kalton, G. and Brick, J. M. (1996), A
Comparison of Some Weighting Adjustment
Methods for Panel Nonresponse, Survey
Methodology, 22, 43-53.
Sarndal, C.E. and Lundstrom, S. (2005), Estimation in
Surveys with Nonresponse, London: John Wiley &
Sons, Inc.
Sverchkov, M., Dorfman, A. H., Ernst, L.R., Moehrle,
T.G., Paben, S. P., and Ponikowski, C.H. (2005), “On

Non-response
Adjustment
via
Calibration,”
Proceedings of the Section on Survey Research
Methods, Washington, D.C.: American Statistical
Association.
Wolter, Kirk M. (1985), Introduction to Variance
Estimation, New York: Springer-Verlag, Inc.

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

Table 2. Average Monthly Earnings for NCS Responding, Non-responding, and Total Sample by Selected Industry
and Size Class Domains
Domain

Total Sample

Non-Responding
Sample

$ 5,009.94

Responding Sample
Without Weights
Adjusted for Nonresponse
$ 5,441.59

$ 4,440.27

Responding Sample
with Weights
Adjusted for Nonresponse
$ 5,197.06

Construction/
Mining
Fire
Manufacturing
Services
TPU
Wholesale/Retail
Trade
50-99
100-249
250-999
1000-2499
2500 or more
Total

$ 5,171.23
$ 4,193.16
$ 2,606.35
$ 5,322.25
$ 2,750.03

$ 4,108.36
$ 4,079.40
$ 2,282.65
$ 6,227.09
$ 2,562.55

$ 5,591.18
$ 4,376.33
$ 3,163.69
$ 4,255.47
$ 2,894.30

$ 4,262.07
$ 4,060.77
$ 2,279.32
$ 7,214.92
$ 2,701.75

$ 3,250.27
$ 3,267.87
$ 3,543.90
$ 3,940.40
$ 4,683.79
$ 3,588.22

$ 3,076.22
$ 2,692.19
$ 3,025.70
$ 3,493.42
$ 5,573.08
$ 3,291.21

$ 3,558.65
$ 3,727.78
$ 4,183.19
$ 4,493.30
$ 3,693.30
$ 3,934.45

$ 3,644.35
$ 2,614.15
$ 3,096.14
$ 3,276.69
$ 5,785.78
$ 3,385.88

Table 3. Average Monthly Earnings and Variances for Total Sample and Estimates of Bias Based on 100 Samples
by Industry and Number of Size Classes Used in Weights Adjustment for Non-response
Domain

5 Size Classes
Construction/Mining
Manufacturing
Transportation/Utilities
Wholesale/Retail Trade
FIRE
Business Services
Health Services
Education Services
Total
2 Size Classes
Mining/Construction
Manufacturing
Transportation/Utilities
Wholesale/Retail Trade
FIRE
Business Services
Health Services
Education Services

Total
Sample

Variance of
Total
Sample

Bias of
Responding
Sample
Without
Weights
Adjusted
for Nonresponse

Variance of
Responding
Sample

Bias of
Responding
Sample
With
Weights
Adjusted
for Nonresponse

Variance of
Responding
Sample
With
Weights
Adjusted
for Nonresponse

$5,180.73
$5,167.19
$4,507.31
$2,883.67
$9,499.93
$3,398.98
$3,072.04
$3,294.37
$4,210.03

453,722
105,616
99,327
53,291
2,272,052
151,923
14,402
176,835
31,334

$1.08
-$50.05
$13.22
-$5.08
-$292.62
$68.29
-$18.87
-$114.85
-$25.33

974,610
158,501
179,829
104,979
3,719,494
240,389
18,339
190,276
48,394

-$19.71
-$29.56
-$60.38
-$67.89
$220.72
$41.93
$10.71
-$140.38
-$3.22

908,627
197,810
191,508
92,633
6,603,822
302,329
19,178
188,517
76,909

$5,180.73
$5,167.19
$4,507.31
$2,883.67
$9,499.93
$3,398.98
$3,072.04
$3,294.37

453,722
105,616
99,327
53.291
2,272,052
151,923
14,402
176,835

$1.08
-$50.05
$13.22
-$5.08
-$292.62
$68.29
-$18.87
-$114.85

974,610
158,501
179,829
104,979
3,719,494
240,389
18,339
190,276

-$1.60
-$37.68
-$41.34
-$40.92
$296.85
$23.89
-$1.01
-$99.63

990,795
183,744
184,630
96,839
6,130,439
279,453
20,884
190,076

Total

$4,210.03

31,334

-$25.33

48,394

$5.44

74,474