5/28/98

Selecting the Employment Cost Index Survey Sample as a Subsample of the

National Compensation Survey

Lawrence R. Ernst and Chester H. Ponikowski

Bureau of Labor Statistics

2 Massachusetts Ave. N.E., Room 3160, Washington, DC 20212

1. Introduction

The National Compensation Survey (NCS) is a new statistical program that will both replace

the existing Occupational Compensation Survey (OCS) program and integrate it with the

Employment Cost Index (ECI) and the Employee Benefit Survey (EBS), creating one

comprehensive survey program. The OCS program publishes locality and national

occupational wage data used by the President’s Pay Agent and private sector compensation

specialists, among others. The ECI publishes national indexes which track quarterly and

annual changes in employers’ labor costs and also cost level information annually on the cost

per hour worked of each component of compensation. The EBS publishes annually

incidence and detailed provisions of selected employee benefit plans.

Although the ECI and EBS sampling have been integrated for several years, the OCS and

ECI/EBS have been independent samples, collected separately by regional field staff. These

survey programs are being combined because of a desire to lessen the respondent burden and

to maximize the use of limited resources. Similar to the OCS program, the NCS produces

estimates of occupational wages for Locality Pay and constructs national estimates from a

probability selection of establishments stratified geographically and by industrial activity.

The NCS also will maintain the current products of the EBS and ECI surveys.

One of the primary goals of the integration of these Bureau of Labor Statistics (BLS) surveys

is to select future establishment sample for the Employment Cost Index (ECI) survey as a

subsample of the larger National Compensation Survey (NCS). The current NCS sample of

establishments was selected with probability proportional to size (pps), with total

employment being the measure of size, from a frame covering establishments with 50 or

more employees. The current NCS sample generally consists of two independent samples, as

explained in Section 3, with some establishments selected twice. The conversion of the ECI

to a subsample of the NCS will be accomplished by selecting and initiating five subsamples

of the current NCS sample over three years.

In designing the subsampling plan for the ECI we came across several issues that may be of

interest to survey practitioners who may have a need to select subsamples of a larger

establishment sample. Under our plan the subsampling probabilities are determined with the

goal that all establishments in an industry stratum in the universe with the same frame
2

employment have the same overall chance of being in the ECI sample, regardless of the

geographic PSU in which they are located. Even though the NCS sample is actually two

independent samples with some establishments selected twice, the subsampling plan insures

that no establishment will be selected more than once in ECI. In addition the plan handles

the additional complexities arising from the fact that the current NCS sample consists only of

establishments with frame employment of at least 50, while the ECI has no minimum

employment restrictions, necessitating supplemental ECI samples of the smaller

establishments.

This paper describes the sample design for the NCS (Section 2), our plans for subsampling

the NCS sample (Section 3), alternative approaches to sample allocation and selection

(Section 4), and selection and weighting of subsamples of the ECI samples (Section 5).

2. Sample Design for the NCS

The NCS sample is selected using a 3-stage stratified design with probability proportional 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 of sample selection is a probability sample of occupations within

sampled areas and establishments.

The selection of sample areas is done by first dividing the entire area of the United States,

consisting of counties and independent cities, into primary sampling units (PSUs). In most

States, a PSU consists of a county or a number of contiguous counties. Metropolitan areas,

as defined by Office of Management and Budget (OMB), are used as a basis for forming

PSUs. Outside of metropolitan areas, each county defines a PSU.

The PSUs with similar average wages as measured by Unemployment Insurance reports

wage are grouped into strata within each of the 9 BLS economic regions. Then one PSU is

selected from each stratum with the probability of selection proportional to the employment

of the PSU. There are 33 PSUs that are self-representing, and these include the 18

Consolidated Metropolitan Statistical Areas (CMSAs) and 15 largest Metropolitan Statistical

Areas (MSAs). The remaining strata are formed by combining PSUs that are MSAs and

have similar average annual pay into 45 MSA strata, and PSUs that are non-MSAs and have

similar average annual pay into 73 non-MSA strata. The PSUs selected with probability

proportionate to PSU employment from these strata, are non-self-representing because each

one chosen represents the entire stratum. In addition the NCS design was supplemented with

3 PSUs to meet requirements of Federal Employee Pay Comparability Act of 1990,

commonly known as Locality Pay. Since these 3 additional PSUs were not part of the

original sample design they were not used in selecting the ECI sample.

The sample of establishments is drawn by first stratifying the sampling frame for each PSU

by industry and ownership (private, state government and local government). The number of

sample establishments allocated to each stratum is approximately proportional to the stratum

employment. Each sampled establishment is selected within a stratum with a probability

proportional to its employment. The set of industry strata were chosen because of a desire to
3

produce estimates of major industry divisions as well as selected individual industries that

are traditionally produced for the ECI and locality products.

After the sample of establishments is drawn, occupations are selected in each sampled

establishment. The number of occupations selected in an establishment depends on the total

number of employees in the establishment. Anywhere from 4 to 20 occupations are selected

within sampled establishments. The probability of an occupation being selected is

proportionate to its employment within the establishment. For more detailed description of

the NCS sample design, refer to the BLS Handbook of Methods (Bulletin 2490, April 1997)

and Black et al (1997).

3. Plans for Subsampling the NCS Sample

For both the NCS and the ECI, the sampling frames are partitioned into a set of industry

strata, with the sampling independent from stratum to stratum. Consequently, the ECI

sampling process below actually applies to the separate selection of the sample in each

industry stratum, although generally we will not be specifically stating this in the discussion.

For example, when we speak of “the ECI sample” we really mean the ECI sample in a single

industry stratum.

The ECI selection process roughly proceeds as follows. The ECI sample that will enter

sample over the next three years will consist of five panels. First a single sample, denoted as

the S sample, will be selected. The establishments in this sample with assigned employment

≥ 50 will be selected as a subsample of the NCS sample, which in turn was selected from a

UDB frame denoted as the D0 frame. The remainder of the S sample will be selected

directly from the most recent available UDB frame, denoted as the D1 frame, at the time that

the S sample is selected; that is the D1 frame is more recent than the D0 frame. Then five

subsamples of the S sample, denoted 1 5S ,...,S , will be selected. Those establishments that

are selected into S from the NCS sample with certainty are in each of the 1 5S ,...,S samples.

The remaining units in S are assigned to exactly one of these samples. These samples are not

the final ECI samples, which will be denoted 1 5S′,...,S′ . Now 1 1

S′ = S and for all k, Sk

′ will

include all NCS sample units in Sk. However, the units in Sk for k ≥ 2 selected from D1

will generally not be in Sk

′ . Instead, the units with assigned employment <50 in Sk′ will be

selected from an updated frame, Dk. For each sample PSU j the number of establishments,

n jk , with assigned employment <50 in Sk

′ selected from PSU j is the same as the number of

such units in Sk. Thus, the selection of units from D1

 in Skfor k ≥ 2 is only done for the

purpose of determining the allocation of the <50 establishments among the sample PSUs in

2 5

S′ ,..., S′ , not for actually selecting the sample establishments.

There are several additional frames involved in selecting the ECI sample. Let Gk Lk, ,

k = 0,...,5 , denote the subframes of Dk consisting of establishments with assigned

employment ≥ 50 and <50, respectively. Next let ( ~ ) ( ) Lk = Lk G0 ∪ Gk ∩ L0

′ , and
4

Ck G Lk = ∪ ′

0

, k =1....,5 , that is Lk

′ is a subframe of Dk

 that can be considered a

modification of Lk obtained by removing from Lk those establishments that are also in G0,

and would otherwise be listed twice in Ck, and adding in those establishments in Gk ∩ L0,

that is units that otherwise would not be listed in Ck since they are in neither G0 or Lk. Ck

is the universe for selecting the Sk

′ sample, with the assigned employment in its G0

component taken from the D0 frame and its assigned employment from the Lk

′ component

arising taken from the Dk frame. Finally, abbreviate G = G0, L L1 = ′ , and C = C1.

We proceed to discuss in detail the sampling and weighting for the selection of the S sample

from the C frame, which involves three stages of sampling. The first stage is the selection of

the sample PSUs. Let F denote the set of sample PSUs and for any PSU j, let p j denote the

probability that j ∈ F . Let C′ denote the set of establishments in C in sample PSUs. C′ is

the frame for the second stage of sampling. The weight, wFij , associated with the first stage

of selection is given by wFij = 1/ p j

if ij ∈C′ , wFij = 0 if ij ∈C ~ C′ .

The second stage is the selection of the NCS sample units from establishments in C′ ∩ G .

There is an extra complexity here because for most of the sample PSUs, the set of NCS

establishments was selected as two independent samples for the following reason. The NCS

data collection process for the PSUs for which data collection began early took longer than

originally anticipated. As a result, in order to meet scheduled completion dates, a smaller

sample than originally intended was selected for the remaining sample PSUs. This reduced

size sample, which in most PSUs consisted of 1/2 the original intended number of

establishments is known as the A sample. Later it was decided to restore the original sample

size in those PSUs where it had been cut. This was accomplished by selecting a second

sample, known as the B sample, in each such PSU, with the B sample selected independently

of the A sample. As a result, the same establishment may be selected twice for NCS, once in

the A sample and once in the B sample. For each sample PSU, both the A and the B samples

are systematic pps samples of the G frame, with assigned employment the measure of size.

The NCS sample is then the set of all establishments in A ∪ B . We let C′′ be the subset of

C′ consisting of all establishments in C′ that are either in the NCS sample or the L frame.

C′′ is the frame used in the third stage of sampling.

For each ij ∈C′, where ij denotes establishment i in PSU j, we associate a weight, wNij ,

arising from the selection of the NCS sample from the sample PSUs and hence the selection

of the units that are in C ′ Nij

sampling. Let wNij = 1 ij∈C′ ∩ L , since all these units are in C′′ regardless of the NCS

sample. As for units ij in C′ ∩ G , if ij is in the A sample letwAij denote the reciprocal of the

probability of selecting this unit in the sample A given that j∈ F ; if ij is not in the A sample

let wAij = 0. wBij is defined analogously. Then let wNij =aAwAij +aBwBij , where aA aB,

are factors which satisfy
5

+ = 1 aA aB, (1)

and

B A B A a /a = n / n , (2)

where A Bn , n are the number of sample establishments in samples A and B, respectively.

Requirement (1) is needed to obtain weights that yield unbiased estimates, as will be shown

later, while (2) is used to minimize variances for estimates for the combined A and B samples

under the assumption that the ratio of the variances for estimates obtained from these two

samples are inversely proportional to the ratio of their sample sizes. In some sample PSUs

the A sample was not reduced from the originally intended sample size, in which case there is

no B sample; hence = 0 aB

 andwBij = 0 for all establishments in these PSUs in C′ ∩ G .

Also let wNij = 0 if ij∈C ~ C′, since such units have no chance of selection in C′′. The

assignment to each establishment of a single weight, wNij , arising from the selection of the

NCS sample from sample PSUs, even if the establishment was selected in both the A and B

samples, is the key to insuring that no establishment is selected more than once in ECI.

Let Ω = {wNij : ij ∈C}. To select the S sample establishments fromC′′, that is the final stage

of selection, first sort the establishments in C′′ by PSU and within PSU by ECI pseudo

standard industry code (PSIC), and then assigned employment, denoted Tij . The PSICs

partition each industry stratum into a set of finer industries. Then, using the measure of size

wNijTij p j/ , simply select a systematic pps sample of units in C′′. For ij∈ S , let wΩij be

the reciprocal of the probability that ij∈ S conditioned on Ω , while wΩij = 0 for ij∈C ~ S .

Thus wΩij is the weight associated with the third stage of selection.

The overall weight for each ij in C , denoted wSij , reflecting the three stages of selection just

described is simply the product of the weights for each stage of selection, that is

wSij = wFij wNij wΩij . (3)

We proceed to demonstrate that the weights wSij yield unbiased estimates of totals and are as

close to being inversely proportional to Tij as possible given the constraint that S ∩ G is a

subsample of the NCS sample. In fact it is the desire to have wSij be inversely proportional

to Tij that motivated the use of the measure of size wNijTij p j/ .

We first show that

E(wSij ) = 1, ij ∈C , (4)
6

which, by Ernst(1989), is sufficient to prove that wSij yield unbiased estimates of totals. To

establish (4), we observe that by the definitions of wAij wBij wNij , , ,

E(wAij j∈ F) =1, E(wBij j∈ F) =1 if ≠ 0 Ba ,

which together with (1) establish that

E(wNij j∈ F) =1. (5)

Furthermore by the definitions of wFij ,wΩij ,

E(wFij ) =1, E(wΩij wNij ) =1 if wNij ≠ 0, (6)

We combine (3), (5) and (6) to conclude

E(wSij) = E[wFijE(wNij wFij)E(wΩij wNij)] = 1.

To show that the weights wSij are as close to being inversely proportional to Tij as possible,

we proceed as follows. Let IΩ be the final sampling interval used in selecting the S sample,

where the notation for IΩ is chosen to indicate the dependence of the sampling interval on

Ω . Then for establishment ij in the S sample, /( ) ij j wNijTij wΩ = p IΩ if wNijTij / p j ≤ IΩ ,

and wΩij =1 otherwise. Consequently,

Ω

Ω Ω

= >

= ≤

w p w T p I

w I T w T p I

Nij j Nij ij j

Sij ij Nij ij j

/ if /

/ if /

(7)

Thus, for those units for which wNijTij / p j ≤ IΩ we have that wSij is inversely proportional

to Tij .

If we had selected the entire S sample directly from C′ without the intermediate step of

selecting the NCS sample from C′ ∩ G , then the measure of size for each unit ij in C′ for

this sampling would be Tij p j/ instead of wNijTij p j/ , the measure of size when selecting S

from C′′. The use of Tij p j/ as a measure of size in this situation yield weights that are as

close to being inversely proportional to Tij as possible, using the reasoning above but with

wNij =1 for all units.

In fact, we first developed the measure of size Tij p j/ as an appropriate measure of size for

use when the sampling frame is a universe frame for the sample PSUs and then generalized
7

this measure of size to apply to a situation when the final sample is selected from a frame

like C′′ which involves an intermediate stage of sampling.

4. Alternative Approaches to Sample Allocation and Selection

Before deciding on Tij p j/ as the measure of size to use in the case of a universe frame, two

alternatives to this measure of size were considered and rejected. Both of these alternative

approaches would have allocated the total sample first among the sample PSUs and then

selected the units within each PSU. The first would have allocated the total sample among

the PSUs proportional to total employment in the PSU and then allocated within a PSU to

each industry stratum proportional to the employment in the industry within the PSU. There

are two problems with this approach. First, since a small PSU has a smaller probability of

selection then a larger PSU, allocating a smaller number of establishments to such a PSU

would result in a lower overall probability of selection, and hence a higher weight, for an

establishment in a small PSU than for an establishment with the same assigned employment

in a larger PSU. Secondly, if the set of sample PSUs were underrepresented in a particular

industry, then the sample allocation to that industry would be low, increasing the variance of

estimates for the industry.

The second alternative approach would have allocated among the sample PSUs proportional

to the total employment in the geographic stratum, rather than the employment in the PSU,

and then would have allocated among the industries within the PSU proportional to the

employment in the industry in the geographic stratum, rather than the PSU. This approach

has neither of the problems that the first approach does. However, it has the problem that if a

PSU has a low proportion of its employment in a particular industry relative to the other

PSUs in the geographic stratum, then the probability of selection for an establishment in that

industry in the PSU would tend to be higher than for an establishment of the same size in a

sample PSU in a different stratum that has a high proportion of its employment in that

industry relative to the other PSUs in the geographic stratum. In fact, if there are few enough

establishments in an industry in the PSU, it is possible that the sample allocation to the PSU

for that industry might be more than the number of establishments in the industry universe

for that PSU.

The procedure of assigning a measure of size Tij p j/ to each establishment and then

selecting in each industry a systematic pps sample across PSUs is roughly equivalent to a

third alternative, that is allocating separately in each industry among all PSUs proportional to

the total employment within the industry within the PSU divided by the probability of

selection of the PSU. There is one difference between the third alternative and the approach

of assigning a measure of size Tij p j/ to each establishment. If the sample in each industry

stratum is first allocated among the PSUs and then independently selected in each PSU, as in

the third alternative, then a noncertainty establishment with a given assigned employment

would have a higher selection probability in a PSU for which a large proportion of the

employment in the industry is in certainty establishments than would an establishment of the

same size in a PSU with a small proportion of total employment in the industry in certainty
8

establishments. This is because when the certainty establishments are removed and the

sampling interval recomputed in the sampling process, this is done separately in each PSU in

the third alternative.

5. Selection and Weighting of Subsamples of the ECI Samples

We now turn to the selection of the five subsamples 1 5 S ,...,S discussed earlier and the

selection and the weighting of the five final ECI samples 1 5 S′,...,S′ . For any establishment ij

in Ck, we let wijk denote the weight associated with selection of the units in Sk

′ taking into

account all stages of selection. Then wijk = 0 for ij in k k C ~ S′ . Now if ij is in C′′∩G and,

conditioned on Ω , it a certainty unit in selecting S from C′′ , then, as noted earlier, the

establishment is in each of the Sk Sk

, ′ and hence by (7)

wijk wSij wNji p j = = / . (8)

The remaining units in S, which we denote by S *, are sorted by PSU first and then within

PSU by ECI PSIC and assigned employment. These units are allocated among 1 5S ,...,S as

follows. Let n be the total number of such units and let nk be the number of such units

allocated to S , k = 1,...,5. k Typically, each nk will be within 1 of n / 5, although the

procedure allows for any allocation. A systematic equal probability sample of S *of size 1

n

is selected and designated as 1S . A systematic equal probability sample of ~ 1S* S of size

2

n is next selected and designated as 2S and so forth.

All units ij in Sk ∩ S *∩G are in kS′ , k =1,...,5 and all units in S1 ∩ S *∩L are in 1

S′ , in

accordance with our earlier description of the selection process. Consequently, for those

units, by (7),

/ /( ) ijk Sij k n Tijnk w = w n n = IΩ , (9)

where in (9), wSij is the weight associated with the selection of the S sample from C and

n nk/ is the weight associated with selecting Sk ∩ S * from S *.

For k = 2,3,4,5 , the sampling and weighting is more complicated for selecting the units in

Sk

′ ~ G , since, as mentioned earlier, C′′ is used in obtaining the allocation of these units

among the sample PSUs and PSICs, while the specific units selected are obtained from Lk

′ ,

not L. That is, for each sample PSU j and PSIC c we let n jck be the number of units in

Sk ∩ L in that PSU × PSIC cell and then select a systematic pps sample of size n jck from

among units in Lk

′ that are in PSU j and PSIC c, where the measure of size for unit ij in Lk′ is
9

its assigned employment in Lk

′ , denoted Tijk . The selected units are the establishments in

Sk Lk

′ ∩ ′ .

To obtain wijk for units ij in Lk

′ , we first let wijk′ denote for a unit in Sk′ the reciprocal of the

probability of selecting ij from Lk

′ to be in Sk′ conditioned on n jck , and let wijk′ = 0 if

Lk Skij∈ ′ ~ ′ , where through the remainder of this section it is understood that c is the PSIC to

which establishment ij belongs.

Then

E(wijk′ n jck ) = 1 if n jck ≠ 0 . (10)

Consequently, if we let for ij in Lk

′ ,

j F

w j F

E n

n

p

w ijk

jck

jck

j

ijk

= ∉

′ ∈

Ω

=

0 if

 if

( )

1

, (11)

it follows from (10) and (11) that E wijk p j

( Ω) = 1/ if j∈ F , E(wijk Ω) = 0 if j∉ F , and

hence E(wijk ) = 1 as required to produce unbiased estimates of totals.

Next we compute ( Ω) E n jck for j∈ F to completely evaluate (11). Let Tjc denote the total

employment in PSU × PSIC cell jc on the L frame and n jc + denote the number of units in

S ∩ L from this cell. Let n jc′ denote the number of these units which, conditioned on Ω ,

are certainty unit in selecting S from C′′ and let Tjc′ denote the total employment in the cell

among units on the L frame other than these n jc′ units. Then the total measure of size of all

L frame establishments in cell jc other than the n jc′ conditional certainty units for the

selection of S from C′′ is Tjc p j

′ / and consequently,















 ′

Ω = Ω = ′ +

+ Ω

+

+ p I

T

n

n

n

E n

n

n

E n

j

jc

jc

k

jc

k

jck ( ) ( ) . (12)

Finally we combine (11) and (12) to conclude
10

k k

j

jc

j k jc

jck ijk

ijk ij S L

p I

T

p n n

n n I w

w ∈ ′ ∩ ′















 ′

′ +

′

=

Ω

+ Ω

 if (13)

Thus for ij in Sk

′ , wijk is given by (8), (9), or (13) depending on whether ij is in S ~ S * ,

S *∩G , or Lk

′ .

Note that it may seem surprising that any units in S ∩ L can be conditional certainty units in

selecting S from C′′ , since the assigned employment of each such unit is less than 50.

However, the measure of size for a unit used in selecting S from C′′ is its assigned

employment divided by the probability of selection of its PSU. In some cases the probability

of selection of the PSU is so small that the measure of size is large despite the relatively

small assigned employment.

REFERENCES

Black, S. R., Ernst, L. R., and Tehonica, J. (1997), “Sample Design and Estimation for the

National Compensation Survey,” in Proceedings of the Survey Research Methods Section,

American Statistical Association, to appear.

BLS Handbook of Methods (Bulletin 2490, April 1997), Washington, D.C.: Bureau of Labor

Statistics, pp. 57-69.

Ernst, L. R. (1989), "Weighting Issues for Longitudinal Household and Family Estimates," in

Panel Surveys, eds. D. Kasprzyk, G. Duncan, G. Kalton, and M. P. Singh, New York: John

Wiley & Sons, pp. 139-159.

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

the Bureau of Labor Statistics.