Attachment P - Selecting a Sample Household

Selecting a Sample
of Households for the
Consumer Expenditure
Survey

Susan L. King and
Sylvia A. Johnson-Herring

Susan L. King is a mathematical statistician in
the Division of Price Statistical Methods, Branch
of Consumer Expenditure Surveys, U.S. Bureau
of Labor Statistics.
Sylvia A. Johnson-Herring is a mathematical
statistician in the Division of Price Statistical
Methods, Branch of Consumer Expenditure
Surveys, U.S. Bureau of Labor Statistics.

Introduction
The Consumer Expenditure Survey
(CE) is a nationwide household survey designed by the U.S. Bureau of
Labor Statistics (BLS) to find out how
Americans spend their money. The CE
consists of two separate surveys, the
Diary and Quarterly Interview surveys.
Each quarter of the year, approximately
3,200 households are visited in the Diary survey and approximately 15,000
households are visited in the Interview
survey to collect information on the expenditures of American households. A
question frequently asked by the survey
respondents is “How was my household selected to be in this survey?”
This article answers that question by
looking at the CE’s sample design and
the selection process.
Survey description
The CE is an important economic survey. One of the primary uses of its data
is to provide expenditure weights for
the Consumer Price Index (CPI). The
CPI affects millions of Americans by
its use in cost-of-living wage adjustments for many workers, cost-of-living adjustments to Social Security
payments, and inflation adjustments to
Federal income-tax brackets. CE data
also are used to compare expenditure
patterns of various segments of the

14 Consumer Expenditure Survey Anthology, 2008

population, such as elderly versus nonelderly people. In addition, the data are
being used by the Federal Government
in a new experimental poverty index.
The purpose of the Diary survey is
to obtain detailed expenditure data on
small, frequently purchased items such
as food and apparel. The purpose of the
Interview survey is to obtain detailed
expenditure data on large items such as
property, automobiles, and major appliances; and on recurring expenses such
as rent, utilities, and insurance premiums. Under contract with BLS, field
representatives from the U.S. Census
Bureau personally visit the households
in the Diary and Interview surveys’
samples to collect the data.
Each household in the Diary survey
is asked to record all of the expenditures it makes during a 2-week period.
Field representatives visit each household in the sample three times. On the
first visit, the field representatives introduce themselves, explain the survey,
and leave a diary in which the household members are asked to record all
their expenditures for a 1-week period.
On the second visit, the field representatives pick up the first week’s diary,
ask whether there are any questions,
and leave another diary for the second
week. On the third visit, the field representatives pick up the second week’s

diary and thank the household for participating in the survey. After participating in the survey for 2 weeks, the
household is dropped from the survey,
and it is replaced by another household.
Each household in the Interview
survey is interviewed every 3 months
for 5 consecutive quarters. Trained
field representatives ask household
members about their expenditures over
the previous 3 months. Responses are
entered into a laptop computer. Each
interview takes approximately 70 minutes to complete. Expenditure information obtained in the first interview
is used only for “bounding” purposes,
which address a common problem in
which survey respondents tend to report expenditures to have been made
more recently than they actually were
made. Thus, expenditure information
from the first interview is not used.
Only expenditure information from the
second through fifth interviews is used
in the CE’s published estimates. The
households in the Interview survey are
on a rotating schedule, with approximately one-fifth of the households in
the sample being new to the survey
each quarter.
Sample design
The selection of specific households to
participate in the CE survey is carried
out in multiple stages. The first stage
of sampling is defining and selecting
a random sample of geographic areas called “primary sampling units”
(PSUs) from across the United States.
In this stage, all of the counties in the
United States are divided into small
groups of counties (called PSUs), and a
representative sample of them is selected to be in the survey. After the PSUs
are defined and selected, the second
stage of sampling involves determining
the number of households to be visited
in each PSU. The CE’s budget allows
for a certain number of households to
be visited each year nationwide, and,
in this stage, that number is allocated
to the individual PSUs selected for the
survey. The final stage of sampling is
selecting specific households to be vis-

ited within the PSUs. Households are
selected using a systematic selection
procedure to ensure that each category
of households is well represented in the
survey. This is a brief summary of the
CE’s sample design. The rest of this
article describes these steps in more
detail.
Defining and selecting the PSUs
In the first stage of sampling, PSUs
are defined and selected for the survey.
PSUs are counties or groups of counties grouped together into geographic
entities called “core-based statistical
areas” (CBSAs) by the U.S. Office of
Management and Budget. CBSAs were
defined for use by Federal statistical
agencies in collecting data and tabulating statistics.
There are two types of CBSAs,
metropolitan and micropolitan. Metropolitan CBSAs consist of one or more
counties with at least one urban area of
50,000 or more people, while micropolitan CBSAs consist of one or more
counties centered around an urban area
with 10,000–50,000 people. Both include the adjacent counties that have
a high degree of social and economic
integration with the area’s core as measured by commuting ties. Areas outside
CBSAs are called “non-CBSA” areas
and are mostly rural.
After the PSUs are defined, they are
categorized according to their population and region of the country. There
are four regions of the country (Northeast, Midwest, South, and West), and
four PSU “size classes”:

• “A” PSUs, which are metropolitan CBSAs with a population
over 2 million people
• “X” PSUs, which are metropolitan CBSAs with a population
between 50,000 and 2 million
people
• “Y” PSUs, which are micropolitan CBSAs
•

“Z” PSUs, which are non-CBSA
areas and are often referred to as
“rural” PSUs

By definition, the “A” PSUs are
“self-representing” and, therefore, have
a 100 percent probability of selection in the survey. The “X,” “Y,” and
“Z” PSUs are “non-self-representing.”
The non-self-representing PSUs are
grouped together into groups of PSUs
(called “strata”) according to a 5-variable
geographic model whose variables are
latitude, longitude, latitude squared,
longitude squared, and percent of the
population in the PSU who live in an
urban area. A typical stratum has approximately 10 PSUs, and all of the
PSUs are in the same “region-size
class.” After the PSUs are grouped into
strata, one PSU per stratum is randomly selected with probability proportional to its population. The PSU that is
randomly selected represents the whole
stratum.
For example, table 1 shows stratum
X344, which is a group of eight “X”

Table 1. The PSUs in stratum X344
PSU

Population

Charlotte, NC-SC

1,114,808

Charleston-North Charleston, SC

549,033

Greenville, SC

379,616

Fayetteville-Fort Bragg, NC

302,963

Columbus, GA-AL

274,624

Gastonia, NC

190,365

Wheeling, WV-OH

153,172

Warner Robbins, GA
Total

134,433
3,099,014

Consumer Expenditure Survey Anthology, 2008 15

PSUs in the South. According to the
2000 Census, their populations ranged
from 134,433 to 1,114,808, for a total
stratum population of 3,099,014 people. One PSU was randomly selected to
represent the entire stratum. The PSU
was Greenville, South Carolina. It had
12.25 percent of the stratum’s population
(0.1225=379,616/3,099,014);
hence, it had a 12.25 percent chance of
being selected, and a random number
generator selected it.
PSU definitions for the current CE
sample are based on information from
the 2000 Census. Prior to 2005 (1996–
2004), PSUs were defined based on
information from the 1990 Census.
The two sample designs are called the
“2000 Census-based sample design”
and the “1990 Census-based sample
design,” respectively. The original
2000 Census-based sample design consists of 102 PSUs, of which 86 urban
PSUs are designated as “CPI areas.”
The CE and CPI share the sample
design, with the exception of the “Z”
PSUs. The CE survey covers the entire
Nation (“A,” “X,” “Y,” and “Z” PSUs),
while the CPI survey covers only the
urban portion of the Nation (“A,” “X,”
“Y,” but not “Z” PSUs.) See table 2
for the number of PSUs by region and

size class in CE’s original 2000 Census-based sample design.
Shortly after this sample design was
implemented, newly imposed budget
constraints forced the CE and CPI to
eliminate 11 “X” PSUs from the sample, and to change the size class of 7
“A” PSUs to the “X” category. As a result, the sample of PSUs currently used
by the CE has 91 PSUs, of which 75 urban PSUs also are used by the CPI. The
CE began collecting data in the original
2000 Census-based sample design in
2005 and in the revised 2000 Censusbased sample design in 2006. (See table 3 for a summary of the revised 2000
Census-based sample design.)
A map of the PSUs in the revised
2000 Census-based sample design is
shown in figure 1.
Allocating the national sample
of households to individual PSUs
Once the PSUs are selected, the number of households to be visited in each
PSU must be determined. In the original 2000 Census-based sample design,
CE’s budget allowed for 7,700 household interviews per year in the Diary
survey and 7,700 household interviews
per quarter in the Interview survey (interviews 2–5 only) at the national level.

Table 2. Original 2000 Census-based sample design (102 PSUs)
PSU
size
class

Region
Northeast

Midwest

South

West

Total

A

6

5

7

10

28

X

4

12

18

8

42

Y

2

4

6

4

16

Z

2

4

6

4

16

14

25

37

26

102

Total

Table 3. Revised 2000 Census-based sample design (91 PSUs)
PSU
size
class

Region
Northeast

Midwest

South

West

Total

A

5

4

6

6

21

X

4

10

16

8

38

Y

2

4

6

4

16

Z
Total

2

4

6

4

16

13

22

34

22

91

16 Consumer Expenditure Survey Anthology, 2008

In this stage of sampling, those 7,700
households are allocated (divided)
among the 102 PSUs in the original
2000 Census-based sample design.
The first step in determining the number of households to visit in each PSU is
to group the “X,” Y,” and “Z” PSUs by
region and size class. Cross-classifying
the four regions of the country (Northeast, Midwest, South, and West) with
the three non-self-representing PSU
size classes (“X,” Y,” and “Z”) yields
12 region-size classes, which are treated like the 28 self-representing (“A”)
PSUs. This gives 40 self-representing
geographic areas.
The objective of this stage of sampling is to allocate the 7,700 households
to the 40 areas in a way that minimizes
the standard error of CE’s published expenditure estimates at the national level.
This can be accomplished by allocating
the households in a manner that is directly proportional to the population
that each area represents; this allocation
method is a standard statistical technique
that comes very close to minimizing the
standard error at the national level.
Without any modifications, proportional allocation would have given
7,034 households to the urban (“A,”
“X,” and “Y”) areas and 666 households to the rural (“Z”) areas. However,
research indicated that increasing the
number of households in urban areas
to 7,300 and decreasing the number of
households in rural areas to 400 would
have a significant impact on lowering
CPI’s standard error but would have
only a minimal impact on CE’s standard error. Since the CPI is the CE’s
primary customer, the allocation process was modified to allocate exactly
7,300 households to the 36 urban areas,
and exactly 400 households to the four
rural areas. Further, to guarantee that
enough interviews are collected to satisfy CPI’s publication requirements in
each of the 36 urban areas, the sample
of 7,300 households is allocated in a
way that at least 80 interviews are obtained in each area. Operationally, the
7,700 households were allocated to
the 40 areas by solving the following
nonlinear programming problem:

Figure 1. Spatial distribution of CE PSUs across the United States. The “A” PSUs correspond to the large population
centers. The southern United States has a large number of “X” PSUs, and there are parts of the western United States without representation.
Given values of pi and p, find values of xi that…
40





i =1

 7,700

2

x
p
minimize
∑  i − i 
p

(0)

36

subject to
∑ xi = 7,300

(1)

40

(2)

i =1

∑x

i = 37

i

= 400

xi >80
i = 1, 2,…, 36
(3)
xi > 0
i = 37,…, 40
(4)

where xi = the number of households allocated to geographic ‘area i’
pi = the population represented by geographic ‘area i’
p = p1 + p2 + … + p40

The output from this nonlinear
program is an allocation of the 7,700
households to the individual geographic areas. The objective function (0)
minimizes the sum of squared differences between each area’s share of the
national population and its share of the
national sample of households. This
allocates the sample of households as
close to population proportionality
as possible. Constraint (1) limits the
sample of the 36 urban areas to 7,300
households. Constraint (2) limits the
sample of the four rural areas to 400
households. Constraint (3) allocates
at least 80 households to each urban
area to ensure that the CPI’s survey
estimates are accurate enough to pub-

Consumer Expenditure Survey Anthology, 2008 17

lish. Constraint (4) makes sure that the
remaining areas are assigned nonnegative numbers of households.
After the 7,700 households are allocated to the 40 geographic areas, the
households allocated to the 12 “X,”
“Y,” and “Z” areas are suballocated to
individual PSUs according to their proportion of the area’s population.
Continuing the example from
above, the nonlinear program allocated
1,342.32 out of 7,700 households to
the “X” areas in the South. There are
18 “X” strata in the South, and stratum
X344 has 6.20 percent of its population; hence, it was suballocated 6.20
percent of the sample. Thus, stratum
X344 is given a target sample size of
83.22 interviewed households (83.22 =
1,342.32 x 0.0620).
Adjusting the PSU’s
target sample sizes for
nonparticipation
Unfortunately, not all households selected for the survey participate in it.
Some households cannot be contacted;
some households are contacted but
refuse to participate; and some households are ineligible for the survey. As
a result of this “nonparticipation,” the
actual number of households designated for the survey must be larger
than the target number of interviewed
households. The designated number of
households to be visited in each PSU
is determined by adjusting the target
sample size that was identified by the
expected survey participation rate.
For example, the participation rate
in stratum X344 is estimated to be 60
percent based on data from 1999–2001.
Approximately 20 percent of the households are “out of scope” (the housing
units are unoccupied, demolished, converted to nonresidential use, located on
a military base, etc.), and 20 percent of
the households are “in scope” but do
not participate, leaving 60 percent of
the households participating in the survey. Thus, the sample size inflation factor for stratum X344 is 1.66 (= 1/0.60),
which means 166 households need to
be selected for every 100 completed
interviews that are wanted. Finally, the

inflated target sample size is multiplied
by 2 to account for the two surveys, Diary and Interview. This yields a “designated sample size” for each PSU. In
stratum X344, the designated sample
size is 276.29 households:
Designated = (Target Sample Size) x
Sample Size (Nonparticipation Inflation
Factor) x 2

= 83.22 x 1.66 x 2

= 276.29

This means that, each year, the U.S.
Census Bureau selects 276.29 households in the Greenville, South Carolina, metropolitan area in order to collect
data from 83.22 households per year in
the Diary survey and 83.22 households
per quarter in the Interview survey (interviews 2–5 only).
The revised sample allocation
As mentioned, shortly after the original 2000 Census-based sample design
was implemented, newly imposed
budget constraints caused the CE and
CPI to eliminate 11 “X” PSUs from
the sample and to change the size class
of 7 “A” PSUs to the “X” category.
When this change was implemented,
a decision was made to keep the target
sample sizes for the PSUs in the 2000
Census-based sample design and to
drop the 642 households that had been
allocated to the 11 eliminated PSUs.
This effectively reduced the national
target sample size from 7,700 to 7,058.
Computations to reallocate the national
sample were not carried out. Instead,
the CE’s original sample size was simply reduced by the sample sizes that
were allocated to the 11 eliminated
PSUs.
Selecting the households to visit
After determining the number of
households to visit in each PSU, the
final stage of sampling is selecting
specific households to visit. The U.S.
Census Bureau has a list of households
across the Nation (called the “sampling
frame”), and the specific households to
visit are selected from that list.

18 Consumer Expenditure Survey Anthology, 2008

The sampling frame is divided into
four “segments”: Unit, area, permit,
and group quarters. The “unit” segment
has about 80 percent of the households,
and it consists of regular housing units
with “city-style addresses” (street
name, house number, apartment number, etc.). The “area” segment has about
10 percent of the households, and it
consists of housing units that are physically located and listed by Census field
personnel prior to sample selection.
Most households in the “area” segment
are in rural areas. The “permit” segment
has about 9 percent of the households,
and it consists of housing units that were
constructed after April 1, 2000 (the date
of the last census). Finally, the “group
quarters” segment has about 1 percent
of the households, and it consists of
housing units in which the occupants
share their living arrangements.
Within each PSU, a “systematic
sample” of households is selected from
each of the four segments. The households are sorted by variables that are
correlated with their expenditures: Urban/rural; the market value of the home
(for owners) or the rental value of the
apartment (for renters); the number
of people in the household; etc. This
ensures that every kind of household
is well represented in the survey. Although the specific variables used to
sort the households differ slightly in
each of the four segments, the procedures for selecting the sample are the
same.
Once the list of households is sorted, a systematic sample of households
is selected. The first household selected
from the list is randomly selected using
a random number generator to select
one of the first k households on the list.
Then, the remaining households are selected by taking every kth household on
the list after the first one. The number
k is called the “sampling interval,” and
it is computed independently for each
PSU by dividing the total number of
households in the PSU by the number
of households in the PSU that will be
visited.
For example, in stratum X344
(Greenville, South Carolina), the sam-

pling frame has 176,654 households,
and the CE draws a sample of 276.29
households per year in that area; hence,
the sampling interval is k = 639.38:
k = PSU sampling interval

= (Number of Households in the
PSU) / (Designated sample
size)

= 176,654 / 276.29

= 639.38

This means that the first household
selected for the sample is one of the
first 639 households on the list. After
the initial household is randomly selected, every 639th household on the

list is selected for the sample as well.
Thus, if the rth household on the list is
randomly selected (1< r < 639), then
the other households will be r + 639,
r + (2 x 639), r + (3 x 639), etc. The
selected households are assigned to the
Diary and Interview surveys on an alternating basis.
Conclusion
This article describes the CE’s selection
of a representative sample of American
households to participate in a survey
about their expenditures. The first stage
of sampling is defining geographic areas
called “PSUs,” which are small groups
of counties. The PSUs are grouped into

“strata,” and one PSU is randomly
selected from each stratum. Each randomly selected PSU represents itself
plus the other nonselected PSUs. Then,
the number of interviewed households
targeted for the entire Nation is allocated to the individual PSUs, and those
numbers are inflated to account for
survey “nonparticipation.” Finally,
the specific households to be visited
are selected from the complete list
of households (called the “sampling
frame”) using a systematic selection
procedure. The three-stage sampling
process provides the CE with a wellbalanced and representative sample
of American households.

Consumer Expenditure Survey Anthology, 2008 19