ASSIGNING PERMANENT RANDOM NUMBERS TO THE BUREAU OF LABOR STATISTICS 

LONGITUDINAL (UNIVERSE) DATA BASE 

Shail Butani, Kenneth W. Robertson, Kirk Mueller 

Shail Butani, BLS, 2 Massachusetts Ave., NE Room 4985, Washington, DC 20212-0001 

KEY WORDS: Sampling Frame, Sampling Units, Permanent Random Numbers, Collocated Permanent Random 

Numbers 

I. Introduction 

The U.S. Bureau of Labor Statistics (BLS) routinely 

conducts several large-scale establishment surveys in 

a Federal/State cooperative environment. The major 

ones are: the Current Employment Statistics (CES) 

Survey, commonly known as the monthly payroll 

survey; the Occupational Employment Statistics 

(OES) Survey; and the Occupational Safety and 

Health (OSH) Survey. At present, the CES and OES 

Surveys are going through major redesigns. A major 

feature of the redesigns calls for centralized 

processing of the sample allocation and selection in 

order to achieve efficiency and to spread the response 

burden more evenly among the businesses; the OSH 

Survey already has centralized processing. 

Additionally, the BLS is in the process of designing a 

longitudinal database (LDB) for its Business 

Establishment List (BEL). These opportunities 

presented an ideal time to begin the use of permanent 

random numbers (PRN) at BLS. 

We first describe the BEL that serves as a sampling 

frame for BLS’ business surveys. Next, we discuss 

PRNs and collocated PRNs. An outline of some of 

the complexities of assigning PRNs when surveys 

have different designs with respect to sampling units, 

stratification, allocation and selection cells is also 

given in this section. In Section IV, we give a brief 

summary of the sample designs for the CES, OES, 

and OSH Surveys. The methodology of assigning 

PRNs and collocated PRNs to the initial frame is 

discussed in Section V. This is followed by a 

discussion of assigning collocated PRNs to new 

businesses in a manner that will ensure proper 

representation for ongoing surveys. In Section VI, 

we present some data as to how well the collocated 

PRNs technique is working. Finally, we conclude 

with a brief summary. 

II. Business Establishment List (BEL) 

The primary source of the BLS’ BEL is the quarterly 

contributions reports filed by employers for each 

unemployment insurance (U.I.) account with their 

state unemployment insurance agency. The data for 

both private and public sector workers are delivered 

to BLS after they go through several stages of 

refinement by the employment security agencies of 

50 states and the District of Columbia as part of the 

Covered Employment and Wages, or ES-202, 

Program. For the purposes of this paper, geography 

is restricted to these jurisdictions. Employment 

covered under the U.I. laws provides a virtual census 

(98 percent) of employees on nonfarm payrolls. This 

rich and comprehensive database has about seven 

million records. Among other data elements, each 

record has a Standard Industrial Classification (SIC) 

code, a state code, a county code that can be mapped 

into a Metropolitan Statistical Area (MSA), 

employment for each month of the quarter, and total 

quarterly wages. A record usually represents the 

worksite or establishment level for each U.I. account. 

BEL is also currently going through a major revision. 

Among other things, this revision involves improved 

methodology for linking records both within and 

across quarters. This allows us to better track data 

on job creations, destruction, and wages, etc. at the 

establishment as well as at the U.I. account level over 

time. The new frame called the longitudinal database 

(LDB) will for each multi-establishment employer 

have a record at the U.I. account level as well as a 

record associated with each worksite. (The current 

universe database has records only at the worksite 

level.) 

III. Permanent Random Numbers 

Objective--Primary purposes for using permanent 

random numbers (PRNs) are: (1) to achieve the 

amount of sample overlap desired within a survey 

from one time period to another; and (2) to minimize 

the overlap in samples between different surveys. 

Because the business population is dynamic, it is also 

important to update the sample in order to take into 

account changes to the frame due to births (new 

businesses), deaths (out-of-businesses), mergers, 

acquisitions, and changes in employment size, 

geography, and industry of a unit. 

PRN Methodology—A detailed description on 

various variations of the PRNs methodology is given 

in Ohlsson (1995). In this paper, we describe a 

simplistic version of PRNs and collocated PRNs. In 

its very basic form, we assign PRNs that are 

uniformly distributed over the interval [0, 1) to every 
record on the frame; we carry out the PRN to 12 

decimal places in order to minimize the number of 

ties that could occur in seven million records. Let Xi

denote the random number for unit i in a stratum; 

next in each selection stratum, we order the 

population in ascending order of the Xi’s. Then, 

selecting the first n units on the list should constitute 

the desired simple random sample without 

replacement. 

 

Births are assigned new PRNs independent of 

existing units and PRNs; deaths are removed from 

the frame together with their PRNs; and units that 

move from one stratum to another due to changes in 

MSA, SIC, size, etc. (“strata jumpers”) keep their 

previously assigned PRNs. (It is worth noting that 

survey data should not be used to update the frame as 

it may lead to a biased sample.) Thus, we are 

drawing the sample for the next survey round from an 

up-to-date frame. 

At BLS, the use of PRNs originated with the CES 

redesign. In the various sample design simulations 

that were conducted, we used the PRNs methodology 

to: update the probabilities of selection; include new 

U.I. accounts (business births); remove old U.I. 

accounts (deaths); handle units that have changed 

size class, MSA, or SIC (strata jumpers); and perform 

sample rotation. The main reasons for using PRNs in 

CES are to achieve the desired sample overlap from 

previous survey year to the next and to properly 

represent births in the sample. 

Overlap between surveys--Let us assume that the 

CES, OES, and OSH Surveys have essentially the 

same sample designs and sample sizes. Let us further 

assume that we want to minimize the overlap 

between the three surveys. Then, we could divide the 

interval [0,1) into three equal parts, say [0.00, 0.33), 

[0.33, 0.66), and [0.66, 1.00), and take the first n 

units in each interval. 

Overlap within a survey--In the above example, 

suppose we desire to rotate one-third of the sample in 

each of the three surveys. To achieve this, in each 

sampling stratum, we select the {(n/3) + 1}th through 

the (4n/3)th units in each of the three intervals in 

[0, 1); where, n is the desired sample size for that 

stratum. It should be noted that the realized overlap 

in the sample is approximately equal to the desired

one. This is because births and deaths rarely offset 

each other exactly and because of “strata jumpers”. 

Complications in use of PRNs--In the real world, 

things are rarely as simple as in the above example. 

In our case, the sampling unit is not the same for the 

three surveys; the allocation and selection cells vary 

across the surveys; the amount of overlap desired 

from one period to the next within each survey also 

differs. 

The major issue with the assignment of PRNs 

pertains to over-stratification leading to small 

numbers of population units in most allocation and 

selection cells. Although there are about seven 

million establishments on the frame, allocation and 

selection cells became thin when one considers 

stratifying by geography (state or MSA), industry 

(major industry division, 2- or 3-digit SIC), and 

employment size class. If the number of units were 

large, then simply assigning permanent random 

numbers would suffice. Another complexity 

involved proper representation of births. Births tend 

to be small relative to the continuous population in 

the stratum. To alleviate the problems, collocated 

permanent numbers are used to distribute the 

units evenly on the interval [0,1). Collocation, 

however, raises many other issues. Do we collocate 

at the U.I. account or at the worksite level; what 

level of geography, industry to use; which 

definition of size class? These and other 

complexities are discussed in the section following 

the sample design. 

 Collocated PRN Methodology-- Collocated PRNs, 

CXi’s, are computed as {(Ri –ε)/N}, where, Ri is 

the rank of Xi in the sorted list for the stratum, N 

is the number of units in the frame for that 

stratum, and ε is a random number that is 

uniformly distributed on the interval [0,1]. Note that 

the same value of ε is used for every unit in that 

stratum. With this transformation, the CXi’s are 

evenly spaced in [0,1). As with PRNs, ε and 

collocated PRNs were carried out to 12 decimal 

places. 

Again, let us suppose that there are only three units 

on the frame in a selection cell and we desire to take 

one unit for each of the three surveys. If the PRNs 

are not collocated, then there is a 1/27 chance that all 

three units fall in the interval [0.00, 0.33). Hence, the 

first unit in this interval will be selected for all three 

surveys since the second and third intervals have no 

units (sequential selection wraps-around). Similarly, 

there is a 1/27 likelihood that all three units are in the 

second or third interval; overall, the probability is 

3/27 that any one of the three unit will be selected in 

all three surveys. Collocation of PRNs ensures that 

three different units will be selected for the three 

surveys. In a similar manner, collocation ensures that 

each quarter’s births are evenly dispersed within each 

stratum. In the interval [0,1) collocation of PRNs for 
birth units is performed independently of the 

continuous units. 

IV. Sample Designs for CES, OES, and OSH 

Surveys 

 

CES Survey Redesign--The CES is a monthly survey 

designed to produce estimates of employment, 

payroll, and hours worked by various levels of 

industrial details for the Nation, 50 States plus D.C., 

and MSAs. The primary advantage of the CES 

estimates is their timeliness. Because the primary 

purpose of CES is to measure the monthly change, 

both the current and the new samples are designed to 

have over 90 percent sample overlap between two 

consecutive months. A detailed description of the 

redesign with respect to goals, sample design 

parameters, features, and characteristics are described 

in Butani, Stamas and Brick (1997). 

OES Survey Redesign--The OES is an annual survey; 

the redesign calls for the survey to measure 

employment and wages for over 750 occupations by 

various levels of industrial activity for the Nation, 50 

States plus D.C. and for over 350 Metropolitan areas. 

A detailed description of the OES sample redesign is 

given in an internal document (BLS, 1998). 

OSH Survey--Like the OES, the OSH Survey is an 

annual survey; it is designed to estimate the number 

and frequency of work-related injuries and illnesses 

by detailed industry for the Nation and for Sates 

participating in the survey. For a detailed 

description, see the BLS Handbook of methods. 

Summary of the three designs--The important 

features of the three sample designs are summarized 

below. Note: Some surveys include Puerto Rico, 

Virgin Islands, and other U.S. Territories. For the 

purposes of this paper, we will concentrate only on 

fifty States plus the District of Columbia.

Sample Design for CES, OES, and OSH Surveys 

Feature CES-R OES-R OSH 

Frequency Monthly Annual Annual 

Sampling Unit U.I. account Worksite Worksite 

Sample Size 250,000 U.I. accounts or 

650,000 worksites 

400,000 worksites 200,000 worksites 

Allocation Cells ST/Major Industry Divisions/8 

Size Classes 

MSA/3-digit SIC/7 Size 

Classes 

ST/Varying Industry/ 

5 Size Classes 

Selection Cells Major Industry Divisions/8 

Size Classes/MSA within a 

State 

11 X 8 X 350 

MSA/3-digit SIC/ 

7 Size Classes 

350 X 377 X 7 

ST/Varying Industry/ 

5 Size Classes 

51 X 100 –300 X 5 

Desired Annual Overlap Over 90% Zero over 3 years Independent Samples 

Treatment of Births Quarterly Update Annual Annual 

Frame Maintenance Annual Annual Annual 

Employment Size Class Definitions 

CES-R OES-R OSH 

1-9 1-4 (Beginning with 98 

Survey) 

10-19 5-9 1-10 

20-49 10-19 11-49 

50-99 20-49 

100-249 50-99 

250-499 100-249 50-249 

500-999 250 + (Certainty) 250-999 

1000+ (Certainty) 1000 + 

V. Assignment of PRNs and Collocated PRNs 

Initial Assignment of Collocated PRNs--We begin by 

assigning collocated PRNs to each worksite (7 

million records) on the 1995 second quarter 

frame, and collocating PRNs within the MSA/3-digit 

SIC/OES size class strata. For initialization 

purposes, we chose OES selection cells because OES 

has the largest sample size, rotates the fastest, the 

industry level is fixed and is at a low level (3-digit 

SIC). 

To handle the CES survey, we aggregated all 

worksites belonging to a multi-establishment 

employer to their U.I. account level. These multiestablishment U.I. accounts were then assigned a 

PRN and were collocated separately from the single 

establishment U.I. accounts at the MSA/3-digit 

SIC/OES size class level. In the CES sample, this 

procedure was beneficial in distributing the multiestablishment and single establishment accounts 

according to their proportion in the population. 
Assignment of Collocated PRNs to Birth Units--Birth 

units are most important to the CES Survey because 

of the contribution they make to over-the-year change 

in employment. For this reason, with each quarterly 

update of the frame, the new units are first assigned 

PRNs at the U.I. account level and collocated at the 

ST/Major Industry Division/ 8 CES size classes level 

(CES allocation cells). Generally, there are few birth 

units each quarter and the allocation and selection 

cell levels are the same for the supplemental sample 

of births each quarter. Additionally, the vast majority 

of birth units are single establishments; thus, the 

worksite and U.I. account levels are the same for 

these units. PRNs are also assigned to the worksites 

for the occasional birth units that are multiestablishment accounts and to the expansion 

worksites for multi-establishment accounts; these 

PRNs are also collocated separately at the CES 

allocation cell level. 

Starting Points for Each Survey-- Another issue is 

what should be the starting points for each survey? 

Given the above sample designs, there is really no 

clean way to determine the optimal starting points for 

the three surveys. The determination of starting 

points is complicated since the sampling fractions 

vary by allocation cells and the allocation cells 

themselves are different for each survey. Based on 

the rotation period for each survey and on several 

approximations including sampling fractions, the 

proposed starting points for each survey and size 

class as determined by the Bureau’s Office of Survey 

Methods Research (BLS, 1996) are given in the table 

below. 

 

Starting Points 

Size 

Class 

CES-R OSH OES-R 

1-9 0 0.20 0.25 

10-49 0 0.45 0.55 

50-249 0 0.40 0.50 

250-999 0 0.66 0 

1000+ 0 0 0 

VI. Distribution of Universe and Samples 

At present, CES and OES have begun using 

collocated PRNs in selecting the samples; OSH is 

expected to start using them with the implementation 

of the LDB in 1999. The universe and sample 

distribution for CES pertaining to multiestablishment accounts and birth units are 

summarized in the first two tables below, while the 

overlap between the OES and CES samples is given 

in Table 3. 

Table 1. CES Universe and Sample Distributions-–1st Quarter 1997 Frame 

Distribution of UI Accounts, by Size and UI Type, 

CES – National - Wholesale Trade

 Multis Singles Total UIs 

 Size 1 % Popl’n 0.099 99.901 415,707

 Employment 1-9 % Sample 0.067 99.933 5,997

 Size 2 % Popl’n 0.922 99.078 74,376

 Employment 10-19 % Sample 0.925 93.075 2,270

 Size 3 % Popl’n 6.622 93.378 49,499

 Employment 20-49 % Sample 6.875 93.125 2,720

 Size 4 % Popl’n 21.893 78.107 15,320

 Employment 50-99 % Sample 23.050 76.950 1,436

 Size 5 % Popl’n 37.078 62.921 7,530

 Employment 100-249 % Sample 36.227 63.773 1,129

 Size 6 % Popl’n 51.671 48.329 1,736

 Employment 250-499 % Sample 48.134 51.876 453

 Size 7 % Popl’n 65.411 34.589 584

 Employment 500-999 % Sample 64.706 35.294 204

 Size 8 % Popl’n 80.258 19.742 233

 Employment 1000 + % Sample 80.258 19.742 233

 
Table 2. CES Universe and Sample Distributions—1st Quarter 1997 Frame 

Distribution of UI accounts, by Size and Age, CES 

 Original PRNDATE 96-2 PRNDATE 96-3 PRNDATE 96-4 PRNDATE 97-1 PRNDATE Total 

Size % Popl’n 86.42 3.18 3.14 3.39 3.87 3,897,244 

1-9 % Sample 86.43 3.23 3.21 3.34 3.80 78,818 

Size % Popl’n 94.05 1.72 1.56 1.35 1.31 773,131 

10-19 % Sample 94.28 1.67 1.50 1.30 1.26 31,083 

Size % Popl’n 95.26 1.38 1.25 1.08 1.04 507,497 

20-49 % Sample 95.23 1.42 1.30 1.00 1.05 38,172 

Size % Popl’n 96.15 1.09 1.01 0.82 0.93 175,164 

50-99 % Sample 96.14 1.09 1.02 0.73 1.02 23,703 

Size % Popl’n 96.93 0.86 0.82 0.61 0.78 102,828 

100-249 % Sample 96.83 0.90 0.81 0.64 0.82 24,023 

Size % Popl’n 97.75 0.59 0.62 0.38 0.66 31,418 

250-249 % Sample 97.64 0.61 0.67 0.42 0.67 12,137 

Size % Popl’n 98.04 0.46 0.39 0.39 0.71 14,519 

500-999 % Sample 97.71 0.51 0.46 0.46 0.86 8,014 

Size % Popl’n 98.45 0.40 0.35 0.18 0.62 10,646 

1000+ % Sample 98.45 0.40 0.35 0.18 0.62 10,646 

Table 3. Overlap between OES and CES sample 

National

 Size 1 Size 2 Size 3 Size 4 Size 5 Size 6 Size 7 Size 8 Total 

Mining % overlap 26.51 37.56 45.44 55.78 64.37 74.48 89.47 100.00 42.04

 OES sample 2674 1898 2207 1011 640 243 95 33 8801

Construction % overlap 5.70 5.43 10.57 22.21 38.64 58.11 86.25 100.00 11.33

 OES sample 29666 20042 21824 10285 4963 776 211 30 87797

Dur/Non/Durable % overlap 6.95 9.51 12.04 20.00 32.96 56.05 76.48 100.00 19.07

 OES sample 37462 29533 37290 24431 22098 8601 3615 1794 164824

TPU % overlap 11.57 17.63 25.24 36.59 50.63 66.63 80.71 100.00 26.19

 OES sample 18967 14137 17150 9535 6642 1876 783 477 69567

Wholesale % overlap 5.05 9.21 13.35 20.46 30.87 50.38 71.72 100.00 12.49

 OES sample 31722 25566 29678 12821 6368 1298 336 74 107863

Fire % overlap 16.31 28.22 30.58 36.30 44.96 60.32 75.59 100.00 27.79

 OES sample 29703 17111 16262 8475 5304 1681 799 464 79799

Services % overlap 6.90 10.98 16.04 25.47 40.72 61.17 79.81 100.00 17.89

 OES sample 106749 74578 74632 37317 30058 9546 3934 2499 339313

 

Total % overlap 8.99 13.63 19.17 29.12 43.94 62.13 78.61 100.00 20.27

VII. Summary 

From the above data, it appears that the collocated 

PRNs technique is working reasonably well in 

achieving the desired overlap within a survey while 

maintaining a representative sample selected from an 

up-to-date frame. It is also performing reasonably 

well in reducing overlap between the two surveys. 

In the future, the BLS would evaluate the use of U.I. 

account as the sampling unit for OES and OSH 

Surveys. This should somewhat simplify the 

collocation process and coordination between 

surveys. 

Any opinions expressed in this paper are those of the 

authors and do not constitute policy of the Bureau of 

Labor Statistics.
References 

1. Butani, S., G. Stamas and M. Brick (1997), 

“Sample Redesign for the Current Employment 

Statistics Survey”, Proceedings of the Section on 

Survey Research Methods, American Statistical 

Association. 

2. Bureau of Labor Statistics, Office of Survey 

Methods Research, 1996. “Collocated Random 

Number Assignment”. BLS internal report, 

December. 

 

3. Bureau of Labor Statistics (1997), Handbook of 

Methods, Washington, D.C., U.S. Department of 

Labor, Bulletin 2490, pp. 70-79. 

4. Bureau of Labor Statistics, Statistical Methods 

Division, 1998. “Survey Method and Reliability 

Statement for the 1996 OES Survey”. BLS 

internal report, March. 

5. Ohlsson, E. (1995), “Coordination of Samples 

Using Permanent Random Numbers”, In B.G. 

Cox et al., Business Survey Methods, New York: 

 Wiley, pp. 153-183.