Attachment T - Review of the 2010 Sample Redesign

Review of the 2010 Sample Redesign of the
Consumer Expenditure Survey
Danielle Neiman1, Susan King2, David Swanson2, Stephen Ash1,
Jacob Enriquez1, Joshua Rosenbaum1
1
U.S. Census Bureau, 4600 Silver Hill Rd, Washington DC 20233
2
U.S. Bureau of Labor Statistics, 2 Massachusetts Avenue NE, Washington DC 20212

Abstract
The Consumer Expenditure Survey (CE) is a nationwide household survey conducted
jointly by the U.S. Bureau of Labor Statistics and the U.S. Census Bureau to investigate
how Americans spend their money. Every ten years the survey updates its sample of
geographic areas around the country as well as its sample of households in those
geographic areas based on the latest decennial census to ensure the sample accurately
reflects shifts in the American population. This paper describes CE’s latest sample
design that will be used over the next ten years (2015–2024), including research that went
into its decisions. Topics include the coordination of CE’s household sample with other
household surveys conducted by the Census Bureau, and a new annual sampling
methodology used by all Census Bureau household surveys.
Key Words: Sample-design stratification, sample selection, sample allocation, first-stage
sample design, second-stage sample design, Consumer Expenditure Survey
1. Introduction
The Consumer Expenditure Survey (CE) is a nationwide household survey which collects
data on the expenditures made by American households. After every decennial census,
CE redesigns its survey to reflect population changes, and to improve both coverage and
sample selection procedures. This paper explains the new design implemented in 2015
which uses the 2010 Decennial Census (Design 2010) and compares it to the design
implemented in 2005 after the 2000 Decennial Census (Design 2000).
1.1 Survey Description
The CE Survey consists of two independent surveys: the CE Interview Survey and the CE
Diary Survey. The CE Interview Survey collects detailed expenditure data on large
expenditures such as property, automobiles and major appliances; and on recurring
expenditures such as rent, utilities, and insurance premiums. Each household is
interviewed every three months for four consecutive quarters by a field representative
from the U.S. Census Bureau. Each interview takes approximately an hour. Conversely,
the CE Diary Survey collects detailed expenditure data on small, frequently purchased
items such as food and apparel. A household completes two one-week diaries requiring
three visits from the field representative. Both surveys share the same sample design.
CE data is used in a variety of ways. The Consumer Price Index (CPI) is the primary
customer of the CE Survey and uses consumer expenditure data to select new “market
baskets” of goods and services for the index, to determine the relative importance of its
components, and to derive cost weights for the baskets. CE also uses consumer

expenditure data to calculate poverty thresholds for the Supplemental Poverty Measure,
which is an additional measure and not the official poverty measure. The Internal
Revenue Service uses consumer expenditure data to calculate alternate sales tax standard
deductions. The Department of Defense uses consumer expenditure data to determine
cost-of-living allowances for military personnel living off military bases. Also, market
researchers find consumer expenditure data valuable in analyzing the demand for various
groups of goods and services.
1.2 Overview of the Sample Selection Process
CE’s universe of interest is the U.S. civilian non-institutional population, which includes
people living in houses, condominiums, apartments, and group quarters such as college
dormitories. However, military personnel living on base, nursing home residents, and
prison inmates are excluded. The civilian non-institutional population represents more
than 98 percent of the population of the United States. The unit of interest is the
consumer unit, a group of people who pool their incomes to make joint expenditure
decisions. Consumer units include families; groups of unrelated people who live together
and pool their incomes to make joint expenditure decisions; and single persons who live
alone or with other individuals but who are financially independent of the other
individuals. There can be multiple consumer units in a household, but generally a
consumer unit and a household are equivalent.
CE uses a two-stage sample design to select a sample of households from the civilian
non-institutional population. In the first-stage, single counties or groups of adjacent
counties are assigned to Primary Sampling Units (PSUs). There are two types of PSUs:
urban and rural. Every county in the United States is assigned to an urban or a rural PSU,
but only a subset of the PSUs is selected for sampling. As mentioned above, a primary
customer of CE is the Consumer Price Index (CPI) and the two surveys worked together
on selecting a common set of urban PSUs in Design 2010, allowing CPI to collect prices
in the same areas that CE collects expenditure data. CE also selects a sample of rural
PSUs to collect household expenditure data, but CPI does not collect prices in rural areas.
In the second-stage of the sample design, addresses are selected by systematic sampling
within each PSU. The second-stage design is a joint effort by the Bureau of Labor
Statistics and the Census Bureau and the selected households are interviewed by a
representative of the Census Bureau. The addresses are selected in conjunction with
other household surveys including the Current Population Survey (CPS), Survey of
Income and Program Participation (SIPP), National Crime Victimization Survey
(NCVS), and American Housing Survey (AHS) which make up the Demographic
Household Surveys of the Census Bureau. The Demographic Household Surveys share
the same sampling frames and the same sampling systems to minimize overlap between
the surveys and to reduce the probability that a household is asked to participate in
multiple surveys during the lifetime of the design.
1.3 Changes in the Survey
Previously, each household in the Interview Survey was interviewed every three months
for five consecutive quarters. The first interview was used only for “bounding” purposes
to address a common problem in which survey respondents tend to report expenditures
more recent than actually occurred. The bounding interview was never used in
calculating expenditure estimates and was dropped to reduce respondent burden and the
survey’s cost (Ryan 2013). In Design 2010, there are only four consecutive interviews.

Another change is the source of demographic variables used in the creation of the new
sample design. In Design 2010, both stages of the sample design switched to using
demographic variables found in the American Community Survey (ACS), a continual
monthly survey, which makes frequent demographic updates possible. Previously, the
demographic variables came from the long form of the decennial Census, which is no
longer conducted.
2. First Stage Sample Design: Defining and Selecting a Sample of PSUs
There are three major tasks in the first stage of a multi-stage stratified sample design:
defining PSUs, stratifying PSUs, and selecting PSUs (Murphy 2008).
2.1 Defining PSUs
The U.S. Office of Management and Budget (OMB) assigns counties surrounding an
urban core to geographic entities called Core Based Statistical Areas (CBSAs). The
assignment is based on each county’s degree of economic and social integration to the
urban core as measured by commuting patterns. There are two types of urban CBSAs:
metropolitan and micropolitan. A metropolitan CBSA has an urban core with more than
50,000 people and a micropolitan CBSA has an urban core of between 10,000 and 50,000
people. CBSAs form the urban PSUs in the CE Survey and may cross state borders.
Counties which are not part of a metropolitan or micropolitan CBSA are rural and are
sampled by CE. Since OMB does not group rural counties into small clusters of adjacent
counties, CE defines its own PSUs. CE requires a rural PSU to be within a state border,
to consist of adjacent rural counties, have a land area less than 3,000 miles and have a
minimum population of 7,500 people. The last two constraints are guidelines used by the
Census Bureau for establishing the maximum workload for a single field representative
(Murphy 2008). Prior to Design 2010, there was no formal procedure for assigning
adjacent rural counties to a PSU, so an algorithm was developed for Design 2010 using
an adjacency matrix and zero-one integer linear programming (King 2012).
2.2 Self-Representing and Non-Self Representing PSUs
All 3,143 counties in the United States are assigned to a PSU and each PSU is assigned to
a stratum based on its size-class. Then one PSU is selected to represent all of the PSUs in
the stratum with probability proportional to size. Very large metropolitan PSUs are
assigned to their own stratum and are selected with probability of one. Consequently,
these PSUs are referred to as self-representing. In Design 2010, self-representing PSUs
have populations greater than 2.5 million people, whereas in Design 2000, the population
cut-off was 2.7 million. The remaining PSUs are non-self-representing. In Design 2010,
the non-self-representing metropolitan and micropolitan PSUs are stratified together.
The rural PSUs have their own stratum in both designs.
In Design 2010, the self-representing PSUs are called “S” PSUs; the non-selfrepresenting metropolitan and micropolitan PSUs are called “N” PSUs; and the rural
PSUs are called “R” PSUs. In Design 2000, the self-representing PSUs were called “A”
PSUs; the non-self-representing metropolitan PSUs were called “X” PSUs; the
micropolitan PSUs were called “Y” PSUs; and rural PSUs were called “Z” PSUs. Thus,
the number of size-classes was reduced from four to three in the new sample design.
For stratification, Alaska and Hawaii are separated from the continental United States
because they have homogeneous markets with unique pricing behaviors and weak

correlation with price changes of the other non-self-representing PSUs in the western
United States. For this reason, in the earlier designs, both Anchorage, AK and Honolulu,
HI were self-representing PSUs even though their populations were below the cut-off. In
the new design, the four CBSAs in Alaska were grouped into a state stratum and
Anchorage was selected to represent the state stratum. Likewise, the four CBSAs in
Hawaii were grouped into a state stratum and Honolulu was selected to represent the
stratum.
The total number of self-representing and non-self-representing PSUs in the sample are
determined by budgets and other factors including sampling variance and bias. Based on
these criteria, it was decided that both CE and CPI would have 75 urban PSUs and CE
would have 16 rural PSUs, which is the same as CE’s Design 2000. There are 23 selfrepresenting PSUs including Anchorage and Honolulu and 52 non-self-representing
PSUs in the sample. The 52 stratification clusters for those PSUs are divided among the
nine Census Divisions.
2.3 Stratifying Non-Self-Representing PSUs
The non-self-representing PSUs are stratified by size-class and geographic division.
There are two size-classes which are the “N” and “R” categories mentioned above, and
nine geographic divisions. The Census Bureau divides the United States into four
geographic regions (Northeast, Midwest, South, and West), and each region has two
divisions except the South which has three divisions, which makes a total of nine
divisions. Previously CE and CPI stratified by region, but stratifying by division allows
the CPI to increase the number of inflation rates it publishes. Then, after the non-selfrepresenting PSUs are stratified within their size-class and geographic division, one PSU
per stratum is randomly selected to represent the stratum.
The primary objective of PSU stratification is to minimize the between-PSU component
of sampling variance (Murphy 2008). In other words, the PSUs within each stratification
cluster should be as homogenous as possible with respect to the survey variable,
expenditures, but there should be variability between the stratification clusters. Also,
within each division, each stratification cluster should have approximately the same
population to minimize variance. This is a constrained clustering problem and is solved
using heuristic algorithms.
Traditional clustering algorithms find homogenous
stratification PSUs, but do not balance the population. In the previous design, the
Friedman-Rubin hill climbing algorithm was used to assign PSUs to stratification
clusters, but in Design 2010 a new heuristic stratification algorithm was developed which
uses k-means clustering and zero-one integer linear programming (King et al., 2011). In
Design 2010, four clustering variables were used: median household income, median
household property value, latitude and longitude. Median household income and median
property value correlate with expenditures and are calculated for each PSU from fiveyear ACS estimates.
2.4 Selecting Non-Self-Representing PSUs
After the non-self-representing PSUs are assigned to stratification clusters, 16 rural PSUs
are selected with probability proportional to size to represent their strata. However, the
52 non-self-representing metropolitan and micropolitan PSUs are stratified together and
selected using maximum overlap and controlled selection.
Since there are significant costs both financial and in loss of expertise when opening and
closing field offices, it is desirable to retain as many of the current PSUs as possible in

the new sample (Ernst et al., 2007 and Johnson et al., 2012). Maximum overlap
procedures attempt to retain as many of the PSUs from the old sample design as possible
and are done in a way that preserves the unconditional selection probabilities in the new
design. In Design 2010 it was conducted at the stratum level. All overlap methods
create and use conditional probabilities based on their overlap rules. Only non-selfrepresenting metropolitan PSUs are overlapped in Design 2010. All of the PSUs in the
stratum are used in the calculation of the conditional probabilities of selection. In Design
2000, the Perkins (1970) method of maximum overlap, a heuristic procedure, was used,
whereas in Design 2010, the Ernst (1986) method, which uses linear programming, was
used. The Ernst method determines the set of conditional probabilities that maximize the
expected unconditional number of PSUs that will be re-selected. The two procedures
have different assumptions and the overlap is larger in the Ernst method, lowering the
cost of the new design.
The actual sample of PSUs is selected using controlled selection, and it is based on the
PSUs’ conditional probabilities that were derived from the overlap maximization process
described above. In each Census Region, there are several strata and one PSU is selected
from each stratum. Certain combinations of PSUs or patterns are preferred because they
lower the sample variance or more evenly distribute the sample according to constraints
such as the number of PSUs per state, or the percentage of micropolitan and metropolitan
PSUs in the region. Thus, controlled selection controls for interaction between PSUs
across strata by increasing the probability of selecting a preferred pattern. Mathematical
optimization techniques are often used in control selection. In Design 2010, the non-selfrepresenting metropolitan and micropolitan PSUs are in the same stratum. Since CPI
found a difference in price change behavior in metropolitan and micropolitan areas, the
number of metropolitan and micropolitan PSUs are controlled. In Design 2000,
controlled selection was performed at the Census Region level and controls were on the
number of overlap PSUs and PSUs per state.
Although, conditional probabilities are used in the overlap maximization and controlled
selection process to select the 52 non-self-representing PSUs for the sample, the
unconditional probability of selection, the selected PSUs population divided by its
stratum population, is used in weighting.
3. Second-Stage Sample Design: Selecting a Sample of Households
Once a sample of PSUs is selected, the next stage of the sample design is selecting a
representative sample of households within the PSUs. This involves several sub-steps,
which include: determining the survey’s total nationwide sample size based on the
survey’s total available budget, allocating the sample to all of the individual PSUs, and
selecting a systematic sample of addresses. The goal of this process is to select a sample
which minimizes the variance of CE’s most important statistic, the average annualized
expenditure per household nationwide on all items.
There are many second-stage changes to Design 2010. In prior designs, the civilian noninstitutional population was represented by four frames and those frames were shared by
the Demographic Household Surveys 1 of the Census Bureau. In Design 2010, the
1

The Demographic Household Surveys of the U.S. Census Bureau include the Current Population
Survey, Survey of Income and Program Participation, American Housing Survey, and the National
Crime Victimization Survey.

Demographic Household Surveys made the decision to move towards a two frame sample
design which incorporates annual sampling and moves away from the once-a-decade
sampling of Design 2000. Another change from the last design was the discontinuation
of the decennial census long-form which caused a change in the variables used to stratify
households in the systematic sample. The new variables are from the ACS and this new
process allows more up-to-date information about the U.S. population to be included in
the sample selection process annually. Also, the optimization program used to select the
sample size for each PSU was modified.
3.1 Sample Allocation and Sample Size
The first sub-step of selecting a sample of addresses within each PSU is determining the
survey’s nationwide sample size and allocating it to the sample PSUs. CE’s budget
allows 12,000 addresses to be selected per year for the Interview Survey and 12,000
addresses per year for the Diary Survey.
The objective of the allocation process is to allocate the 12,000 addresses to the PSUs in
a way that minimizes CE’s nationwide variance. It uses a two-step population-based
technique: stratify the 91 sample PSUs into 41 “index areas” defined by CPI, allocate the
nationwide sample of 12,000 addresses directly proportional to the population
represented by each of the CPI index areas, and then sub-allocate the sample to individual
PSUs in the index areas. The 41 index areas consist of the 23 self-representing PSUs
plus the 18 non-self-representing division size-classes (9 Census divisions x 2 sizeclasses). This model was first used in Design 2000, and recent research by BLS and
Census confirmed that this method is still the simplest and most effective way of
producing expenditure estimates with small variances at the nationwide level (Swanson et
al., 2011 and 2012).
The allocation is accomplished by solving the following nonlinear optimization problem:
Given the values of 𝑝𝑝𝑖𝑖 and 𝑟𝑟𝑖𝑖 for every index area i, find the values of 𝑛𝑛𝑖𝑖 that
Minimize
Subject to:

41

𝑛𝑛𝑖𝑖 𝑟𝑟𝑖𝑖 𝑝𝑝𝑖𝑖 2
��
− �
𝑁𝑁𝑁𝑁 𝑝𝑝
𝑖𝑖=1
41

� 𝑛𝑛𝑖𝑖 = 12,000
𝑖𝑖=1

𝑛𝑛𝑖𝑖 𝑟𝑟𝑖𝑖 ≥ 80, for 𝑖𝑖 = 1 𝑡𝑡𝑡𝑡 32

𝑛𝑛𝑖𝑖 𝑟𝑟𝑖𝑖 ≥ 40, for 𝑖𝑖 = 33 𝑡𝑡𝑡𝑡 41

where
𝑝𝑝𝑖𝑖 = population of the i-th index area;
𝑟𝑟𝑖𝑖 = participation rate (eligibility rate times the response rate) of the i-th index area;
𝑛𝑛𝑖𝑖 = number of addresses allocated to i-th index area;
𝑝𝑝 = ∑41
𝑖𝑖=1 𝑝𝑝𝑖𝑖 is the population of the United States;
𝑛𝑛𝑖𝑖 𝑟𝑟𝑖𝑖 = expected number of interviewed households in the i-th index area;
𝑁𝑁𝑁𝑁 = ∑𝑖𝑖 ∈𝑈𝑈𝑈𝑈𝑈𝑈 𝑛𝑛𝑖𝑖 𝑟𝑟𝑖𝑖 is the expected number of interviewed households nationwide.

As mentioned above, CE’s budget allows 12,000 addresses to be selected per year for the
Interview Survey and 12,000 addresses per year for the Diary survey. The objective is to

allocate the 12,000 addresses in a way that minimizes CE’s nationwide variance. The
objective function shown above minimizes the sum of squared differences between each
index area’s share of the national population and its share of the addresses, which is a
good approximation to minimizing the nationwide variance. The total U.S. population, p,
is known as well as the population of each index area, 𝑝𝑝𝑖𝑖 . The expected number of
interviewed households is 𝑛𝑛𝑖𝑖 𝑟𝑟𝑖𝑖 , where 𝑛𝑛𝑖𝑖 is the number of addresses and is the decision
variable to be determined in the optimization model and 𝑟𝑟𝑖𝑖 is the participation rate for
index area i. The total number of interviewed households is NR. The first constraint is
linear and restricts the number of addresses to 12,000. The lower bound constraints
require at least 80 addresses in each of the 32 urban index areas (i = 1 to 32) and 40
addresses in each of the 9 rural index areas (i = 33 to 41).
The participation rate is the response rate times the eligibility rate. The response rate for
each index area is calculated from CE data over the most recent five year period, whereas
the eligibility rate is the percent of addresses on the sampling frame with occupied
housing units and is calculated using the most recent five years of data from the ACS,
which also uses the Master Address File (MAF) as its frame. Since the response rates are
different for the Interview and Diary Surveys, an optimization model is run for each
survey. In Design 2010, the number of addresses is calculated annually using the most
current response and eligibility rates.
A similar nonlinear optimization model was used in the previous design, with a subtle
difference (King et al., 2008). The decision variable was the number of usable
interviews, around 7,000, and not the number of addresses, which is 12,000. In the new
design addresses are allocated instead of usable interviews. This change moves the
nonresponse adjustment to an earlier step in the process. In the past a nonresponse
adjustment was made to inflate the number of usable interviews up to the number of
usable addresses that needed to be selected. Also, in the previous design, the sample size
was determined once, and there were two linear constraints on the number of usable
interviews: one for urban index areas and the second constraint for rural index areas.
Other updates to the sample design were considered through research projects conducted
prior to the new sample design implementation. However, a decision was made to not
include them because the results of the research did not provide enough evidence of
improvement to the sample design. For example, one of the research projects suggested
that cost savings could be obtained if the sample was clustered, where two, three or four
neighbors would be in sample at the same time. However, it was concluded that even
though there is some cost savings associated with clustering (Reyes-Morales et al., 2008)
there would have to be an overall sample size increase to maintain the current variance on
the key survey estimate due to the correlation between neighbors’ expenditures which
would require an increased budget (Ash et al., 2010).
3.2 New Sampling Frames and Sample Coordination
After determining the sample size for every PSU, the next step is selecting a sample of
households in them and that requires sampling frames. The sampling frames for Design
2010 are new and are especially designed to meet the needs of the Demographic
Household Surveys of the Census Bureau. The surveys have the same population of
interest: the civilian non-institutionalized population of the United States and therefore
able to share the same sampling frames and sampling systems. The new sampling frames
are designed to meet the surveys requirement of sample coordination and allow a more
frequent, survey-specific, sampling process.

In Design 2010 the Census Bureau has three sampling frames that are shared by all of its
Demographic Household Surveys, including CE: the Unit, Group Quarters (GQ), and
Coverage Improvement frames. All three frames are created from the Census Bureau’s
MAF, which is basically a list of all residential addresses identified in the 2010 census
plus biannual updates from the U.S. Postal Service (Nguyen et al., 2011).
The Unit frame is the largest frame and it contains both existing housing units and new
growth units. It has over 98% of the MAF’s addresses. The GQ frame is also created
from the MAF, but it is much smaller. It is a list of housing units that are owned or
managed by organizations for residents who live in group arrangements such as college
dormitories and retirement communities. The Coverage Improvement frame is also
created from the MAF, but it is supplemented by additional housing units identified
through address canvassing procedures. It contains housing units that are primarily in
rural areas where there is a high concentration of non-city-style addresses 2 , but CE
decided not to use it.
In Design 2010, there is a major change in the updating method of the Unit Frame. Prior
to Design 2010, the frame was a static list of addresses that was updated once per decade,
but now it is a dynamic list of addresses that is updated twice per year with information
from the Postal Service. That allows the sampling frequency to be increased from once
per decade to once per year. The frame also allows for mid-year growth to be
incorporated into the samples via an extension of the frame called a skeleton, a set of
empty records, which are filled-in with new growth during the six month update of the
frame. The skeleton is sampled during the regular annual sampling process using the
same sampling rate as the Unit frame. The skeleton sample becomes active only when
filled with new growth during the mid-year frame update.
Conversely, the GQ frame does not have a growth component and is updated every three
years. If a new GQ is created after the frame creation, that GQ will not be included into
the sample until the next frame creation process. If the size of a selected GQ changes,
those changes are taken into account during the GQ sampling process.
In Design 2000, four frames represented the civilian non-institutional population: Unit,
Group Quarters (GQ), Area, and Permit. Most addresses in the United States are covered
by the Unit and GQ frame. The Unit frame is the largest frame and represents regular
housing units. The GQ frame represents group living arrangements such as a college
dormitory. The Permit and Area frames identified new addresses or new growth. The
permit frame was a skeleton frame, a list of empty cells, which was filled in with new
growth identified by building permit offices throughout the life of the design. The Area
frame was used in locations with high concentrations of non-city-style addresses or no
building permits were available and required a field listing procedure to capture new
growth. These frames were created once, at the beginning of the design and the sample
was selected for the next ten years.
The sample coordination between the Demographic Household Surveys was an easy
implementation in Design 2000 because the sampling was done once. For Design 2010,
the sample coordination is more complex because the sample selection is done annually.
2

A non-city-style address is one whose format uses a rural route and box number, or a post office
(PO) box, instead of a house number and a street name.

In order to achieve this sample coordination, the surveys enacted a set of common
sampling rules and controls on the actual frames to facilitate this process. For example,
the need to sample both births (new growth) and deaths (demolished units) during the
sample selection process by all the surveys is a new sampling requirement. This is now
necessary in the new design so that in the future, those units are sampled at the same rates
as the existing units. Then once the sample is prepared for interviewing, their status is
evaluated prior to being sent out for interview and at this time, the deaths are filtered out
of the sample. Another frame issue is ensuring that once a survey selects a sample of
housing units, the sample “resting period”, or the 5-year time period needed between a
households last scheduled interview and next possible selection for a new survey, is the
same for all selected housing units and is independent of whether or not the household
was actually sent out for interview. This ensures that the left over frame universe
maintains its properties as an unbiased universe. For example, some surveys sample the
frame at a higher rate and then implement a subsampling process in order to target
specific populations. The sampling rules would force the initial sample to have the same
resting period as the sample that was actually sent out for interview. To ensure that there
is enough sample on the sampling frames for all surveys during the life of the sample
design, all of the sampling fractions of the surveys are evaluated prior to each round of
sample selection. During this evaluation, changes to every surveys sampling fraction
could occur to reduce the amount of sample being selected from the frame, within a
particular county. The limits are imposed on all surveys that are in the affected county,
and these limits control the amount of sample that could be selected. Any adjustments
are recorded and incorporated into the sample weights for each survey.
3.3 Within-PSU-Stratification
Even though the sampling frames are shared by all of the Demographic Household
Surveys, each survey selects an efficient sample differently. The CE Survey orders the
households on the sampling frame in such a way that when a systematic sample is
selected, households from every economic stratum are well-represented in the survey.
Households on the frame are sorted by variables whose values are known for every
household on the frame and which are correlated with the surveys main variable of
interest, the average annualized total expenditure per household on all items. Sorting the
households this way has the effect of stratifying the frame and since the sorting procedure
is done independently within each PSU, it is called “within-PSU-stratification.”
CE draws its sample from two frames (Unit and GQ), but only the Unit frame uses a CEspecific variable to sort the households from poor-to-rich before drawing a sample of
them. The GQ frame uses a generic variable common to all Census Bureau Demographic
Household Surveys. In the Unit frame, the stratification variable (the sorting variable) is
created from the number of occupants in each household, their housing tenure
(owner/renter), and the market value of their home (for owners) or the rental value of
their apartment or home (for renters). These variables are used because they are
correlated with expenditures: households with more people tend to be wealthier than
those with fewer people; homeowners tend to be wealthier than renters; and people living
in high-price housing units tend to be wealthier than those living in low-price housing
units.
The number of household occupants and their housing tenure come from the 2010
decennial census and are on the MAF, while monthly rental and property values come
from the households surveyed by ACS and are on its 5-year data file. In Design 2010 the
stratification variables are updated annually incorporating the most up-to-date ACS

estimates. Table 1 shows the Design 2010 within-PSU-stratification for geocoded
addresses with complete tenure and vacancy information.
Table 1. Design 2010 Within-PSU Stratification Value Assignment

Estimated Monthly Rent
for Renters(quartiles)

Estimated Market Value
of Home for Homeowners
(quartiles)

Housing
Value
Quartile
1
2
3
4
1
2
3
4

Number of Household Occupants
1

2

0

3

4+

10
25
30
45

11
24
31
44

12
23
32
43

13
22
33
42

14
21
34
41

50
65
70
85

51
64
71
84

52
63
72
83

53
62
73
82

54
61
74
81

The monthly rental and property values are aggregated into four quartiles, which are
defined separately by county using data collected by ACS. The Census Bureau partitions
every county into a large number of “blocks,” and then CE staff aggregates those blocks
into a small number of contiguous geographic “domains” having 50-100 renters who
were in the ACS survey. Their median rental value is then computed using their ACS
data and the median value is assigned to every household in the domain that reported
being a renter in the 2010 census. The process generated a few dozen geographic
domains per county, each of which had its own median rental value, and then quartiles
were formed by stratifying the domains into four groups. Then the process was repeated
for homeowners.
In Table 1, all of the renters are at one end of the stratification and all of the owners are at
the other end of the stratification. The renters and owners are subdivided into quartiles
because monthly rental and property values vary by geographic area and quartiles provide
a more equal distribution of the addresses than raw dollar amounts. Vacant housing units
are put in the middle column because although they were vacant at the time of the
decennial census, when CE’s field representatives visit them they could be in any of the
four non-zero categories. The serpentine sorting order guarantees a good mixture of
expenditure levels in the sample. This makes sample selection efficient for the CE
surveys and minimizes the variance in the second-stage.
The within-PSU-stratification variable for the Design 2000 Unit frame was similar to the
Design 2010 stratification variable described above, but their data came from different
sources. In Design 2000, the number of occupants and tenure came from the 2000
decennial census short form, while the rental and property value came from its long form.
In Design 2010, the number of occupants and their tenure still came from the decennial
census, but since the long form was discontinued the rental and property value was taken
from ACS (Steinberg et al., 2009). Also, in Design 2000, vacant units (0 occupants) were
placed in the leftmost column instead of the middle column because 0 normally comes
before 1, 2, 3, and 4; and the rows alternated between renters and owners, placing poor
renters next to poor homeowners to keep poor people together. Similarly, rich renters
were placed next to rich homeowners to keep rich people together. However, research
showed that renters tend to be uniformly poorer than homeowners (the richest renters are

poorer than the poorest homeowners), which led to a decision to completely separate the
renters from the owners in Design 2010 (Lineback et al., 2009).
The within-PSU-stratification variable used in the GQ frame is pre-defined and not
unique for each survey. It uses a geographic and block level sort on “percent of college
housing.” The college housing population is very different than the rest of the GQ
population (Jonas et al., 2012), so using it as the within-PSU-stratification variable
produces a more representative systematic sample of GQ housing. For Design 2010, the
GQ frame is re-created every three years and at that time any newly discovered GQs will
be included in the next round of GQ sampling (Nguyen et al., 2011). By contrast, in the
previous design, the GQ sample was selected for the entire decade at the beginning of the
sample design.
3.4 Selecting a Systematic Sample of Households
The Interview and Diary households are selected jointly, in one sample selection process
for each frame. The GQ frame sampling selects three years of sample in one round of
sampling, and the unit frame sampling selects enough sample for one year. The sample
sizes for the combined selection are created by first taking the larger sample size
generated by the optimization program described in Section 3.2. The larger sample size
for the PSU from either the Diary Survey or Interview Survey is doubled to ensure that
enough sample is selected for both surveys. The selection is planned such that alternating
sample units are used in the Interview Survey or Diary Survey, and to achieve the survey
specific sample sizes, a sample reduction process is planned to randomly remove housing
units from the survey which required the smaller sample.
Each county has its own sample selection process. Once the list of housing units within a
county are sorted using the within-PSU-stratification, the first housing unit is randomly
selected using a dependent random number generator. The dependent random number
generator is used in the sample selection process to ensure that the randomness
introduced by the number generator does not affect the overall desired sample size. Then
the remaining housing units are selected by taking every kth housing unit on the ordered
list. The number k is the sampling interval for the county and it is computed
independently for each PSU by dividing the total number of housing units from the MAF
by the desired sample size.
The effects of the sample coordination of the CE sample with the other household
surveys could also affect the sample selection process if a particular county that CE
selects sample from is flagged as being “crowded.” The term “crowded” identifies a
county in which the combined survey sampling rate, across all surveys, for that particular
county was identified to be too much for the county to handle. Once a county is flagged,
the sampling rates allowed for that county are capped for all surveys to ensure that there
are enough housing units for all the surveys to sample from. These adjustments to the
sampling rates are rare but would affect the overall sample sizes at the PSU level for all
the coordinated sample surveys.
4. Sample Administration and Maintenance
The last part of the second-stage sample design is the planning that occurs after sample
selection. Each survey has its own method of planning how each sampled housing unit
will enter the interview process and how the new design will be introduced into the
current interview cycle.

Sample coding is the process of assigning each housing unit in the sample to either the
Diary or the Interview Survey. The housing units are labeled with sample codes to
identify their assigned survey. The sample coding process also assigns the housing units
to: (1) a time frame for interviewing; (2) half-samples, which are used in variance
estimation; and (3) sample reduction codes.
When assigning the sample codes, it is necessary to order the selected units, called hits,
by original sort order. The goal of the code assignments is for each separate sample code
and sample code combination to be a subsample of the overall systematic random sample.
Furthermore, the subsample must be a systematic random sample with hits that are equidistant to each other (Ash 2011).
Sample designations are sample codes that identify whether a housing unit is assigned to
the Diary Survey or the Interview Survey. Sample designations also indicate if a housing
unit is a production unit or a reserve unit. Reserve units are supplemental housing units
that are set aside for special research projects. All other housing units are called
production units and are a part of the main sample. The four sample designations are
Interview Production (Q), Interview Reserve (X), Diary Production (D), and Diary
Reserve (E). In the previous design, both the production and reserve sample designations
were in the same hit string. However, in Design 2010, the Diary reserve sample is
included with the Interview production sample and the Interview reserve sample is
included with the Diary production sample. This structure ensures the reserve sample for
either the Diary or Interview Survey will not be geographically close to its production
sample, if it is used (hits are geographically close due to the sort order). A number is
appended to the sample designation to indicate the year in which the sample was selected.
For the Diary Survey, the Diary Placement Day is the earliest day of the year when the
diary is to be placed. This is determined by uniformly assigning the sample codes quarter,
week, and day. For the Interview Survey, the interview dates are determined from two
sample codes called panel and rotation. The rotation sample code is the quarter of the
year when the sample designation is introduced. The panel represents the month of the
quarter when the sample units are interviewed. There are several other sample codes of
lesser importance such as reduction groups and half-samples. Reduction groups are
numbers between 1 and 101 assigned to every household in the sample that are used to
reduce the sample. To reduce the sample by 1%, a reduction code is randomly selected,
and units with that reduction code are excluded from the sample. The half-sample code is
a special sample code that splits the sample into equally sized groups and is used in
estimating the variance.
The sample codes are systematically assigned after sorting the housing units in a specific
order. For example, in assigning the sample designations, the file is first sorted by the
original hit order, and then housing units are sequentially assigned to the following
samples: Diary Production, Interview Reserve, Interview Production, and Diary Reserve.
The other sample codes are assigned similarly but with different sort orders. The sort
order is important to prevent correlations from being generated between some of the
coded variables. For example, the housing units are sorted to avoid assigning all the odd
numbered half samples to the same quarter, or the even numbered half samples to the
same panel group.

The Design 2010 Diary Survey sample was introduced in January 2015, and the
Interview Survey sample was gradually phased-in over the eleven-month period of
February through December 2015.
5. Other Changes and Summary
In Design 2010, there were improvements to the frames and timing of the sample
selection process. Although not specific to CE, these changes are briefly discussed.
The MAF was updated with Global Positioning System (GPS) coordinates that were
collected during Decennial 2010 address canvassing operations. Most of the addresses
on the MAF have GPS coordinates (94 percent) and these GPS coordinates will be passed
to field representatives as an additional method to use when trying to locate their case
assignments (Winstead et al., 2011).
The coordination of the Demographic Household Surveys into one on-going sample
selection system has the added bonus of being able to in-activate and re-activate sample
units after a pre-determined resting period that is specific to each survey. This allows a
sample unit that has already been selected for interview, to have a pre-defined resting
period which prevents the unit from being selected again within that time period (Nguyen
et al., 2011).
As a summary, Table 2 provides a quick reference to highlight some of the changes
between the old and new design discussed in the previous sections.
Table 2. Design 2000 vs Design 2010 for the CE Surveys
Sample Design Element

Design 2000 Details

Design 2010 Details

PSU Selection Frequency

Every 10 years

Every 10 years

PSU Name
1st letter
2nd letter
3rd letter
4th letter

A, X, Y, Z
Census Region
3rd and 4th digits are
Stratum Indicators

S, N, R
Census Region
Census Division
Stratum Indicator

First Stage PSUs

75 non rural PSUs
16 rural PSUs

75 non rural PSUs
16 rural PSUs

Second Stage Frames

4 Frames:
Unit, Area, Permit, GQ

2 Frames:
Unit, GQ

Second Stage Stratification
Clusters
New Growth

41 Strata

47 Strata

Area, Permit: ongoing

Unit: every 6 months
GQ: every 3 years

Frame Creation and Second
Stage Sampling Frequency

Every 10 years

Unit Frame: Yearly
GQ Frame: Every 3 Years

6. Future Research
CE plans a major revision to both the Interview and Diary Surveys in Design 2020. The
proposed design includes two waves of data collection twelve months apart. The two
surveys will combine and the same household will participate in both waves. Each wave
is composed of two visits with a household member serving as a respondent. The first
visit is an in-person interview in which the field representative collects easily recalled
expenditures from the previous three months. The field representative will ask the
respondent to collect records for expenditures such as utilities for the three month period
prior to the second interview. Also, on the first visit, the field representative will train all
eligible household members on using the electronic diary, which individual expenditures
will be entered for the next week. During the second interview, which occurs one week
after the first visit, the diaries will be reviewed for missed expenditures and then large
expenditures from requested records at the first interview will be recorded. Twelve
months later, the process will be repeated with the same interview structure. Hopefully,
the new design change will increase response rates by reducing respondent burden. The
new design will alleviate the repetitive collection of some expenditure like mortgage
payments which do not change from month to month. One of the downsides of the new
design is that four continuous quarters of data from the same household will not be
available for research projects. The new design will have minimal impact on the sample
selection procedures discussed in this paper.
7. Disclaimer
The views expressed in this paper are those of the authors and do not necessarily reflect
the policies of the U.S. Census Bureau and the U.S. Bureau of Labor Statistics.
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