Calculating State Weights for the Consumer Expenditure Survey

Susan L. King

U.S. Bureau of Labor Statistics, 2 Massachusetts Avenue NE, Washington DC 20212

Abstract

The Consumer Expenditure Survey (CE) is designed to produce unbiased estimates of expenditures made 

by U.S. households at both the national and regional levels, but not at the state level. However, there is an 

increasing demand for state-level expenditure estimates and re-designing the survey to produce unbiased 

state-level estimates in all 50 states would be prohibitively expensive. This paper presents an experimental 

approach to calculating weights for selected states with a sufficient representation in the CE survey so that 

users can use the weights to calculate unbiased expenditure estimates for their research projects. The 

approach was first tested in New Jersey because in the sample design based on the 2000 Census, every 

county in the state was in CE’s sample. New Jersey’s sample was reduced by dropping counties, and 

expenditure estimates were calculated using both the full and reduced samples. There were no statistical 

difference in the expenditure estimates, indicating a successful approach. Then the approach was extended 

to Florida and California and again there were no statistical differences, so the state weighting algorithm 

was successful in all three test states.

Key words: base weights, stratification, Census tracts, constrained clustering, Consumer 

Expenditure Survey, sampling

1. Introduction

The Consumer Expenditure Survey (CE) is a nationwide household survey which collects data on the 

expenditures made, income earned, and taxes paid by American households. 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. Conversely, the 

CE Diary Survey collects detailed expenditure data on small, frequently purchased items such as food and 

apparel. Both surveys share the same sample design. 

CE data are used in a variety of ways. The Consumer Price Index (CPI) is the primary customer of the CE 

Survey and CPI uses the 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. The Internal 

Revenue Service (IRS) and the Supplemental Poverty Measure (SPM) are also customers of the CE Survey. 

The IRS uses CE’s data to derive sales tax tables for taxpayers to use in the itemized deductions section of 

their tax returns. The SPM, which is an additional and not the official poverty measure, uses CE’s data to 

derive poverty thresholds based on the amount of money consumers report spending on a basic set of goods 

that includes food, clothing, shelter, and utilities, and a small additional amount to allow for other needs. 

CE uses a two-stage sample design to select a sample of households from the civilian non-institutional 

population.1 In the first stage, single counties or groups of adjacent counties are assigned to Primary 

 

1 The civilian noninstitutional population covers approximately 98 percent of the U.S. population and 

includes people living in houses, condominiums, and apartments, as well as people living in group quarters 

such as college dormitories or boarding houses. However, it excludes the non-civilian and institutional 

portions of the population, such as military personnel living on base, nursing home residents, and prison 

inmates.

335
Sampling Units (PSUs) and a representative sample of PSUs is selected for the survey. In the second stage 

of the sample design, a representative sample of addresses isselected by systematic random sampling within 

each PSU.

CE redesigns its survey after every decennial census to reflect population changes, and to improve both 

coverage and sample selection procedures. CE has 91 PSUs in its sample which are distributed across the 

United States. Some of the PSUs are large metropolitan areas and are included in every design, whereas the 

other PSUs may enter and leave the sample with a design change after a decennial census. Some states may 

not have a PSU or only one or more rural PSUs, while other states such as New Jersey, may have every 

county in the sample. The sampling weights for each household are calibrated to national and regional 

population totals, but not state population totals. This means that the expenditure estimates are statistically 

valid at the national and regional levels, but not at the state level.

One approach to providing state-level estimates is for CE to calculate estimates for major expenditure 

categories for all 50 states, including the states without PSUs, and publish the tables. Another approach is 

to calculate weights for select states with PSUs that continue regardless of sample design changes and 

provide the user with weights so that they can produce expenditure estimates for their research projects. 

The latter approach was selected. The objective is to develop a state weighting algorithm for calculating 

respondent weights at the state level which parallels current procedures for estimating respondent weights 

at the national and regional levels. The state-level weights will be put on a separate public database so that 

the state weights can be merged with CE’s Public Use Microdata (PUMD) files, allowing researchers to 

calculate state expenditure estimates for their projects. 

New Jersey was selected as a test state because every county was included in a sampled PSU in Design 

2000, the sample design based on the 2000 Census. Every county in New Jersey was included in either the 

New York or Philadelphia PSU. Therefore, expenditure data was available in every county of New Jersey, 

allowing for the calculation of the state’s “true” expenditures. In Design 2010, the sample design based on 

the 2010 Census, five counties were dropped from the sample design. In this experiment, data from the 

sampled New Jersey counties in the 2010 Census were retained in the 2000 database and the state 

expenditures re-calculated. Thus, Design 2000 was treated as “truth” and Design 2010 was treated as an

experiment, allowing a comparison of expenditure estimates from every county in the state with expenditure 

estimates from a subset of the counties. The estimates from the two designs were found not to be statistically 

different and found to be similar to estimates from CE’s Philadelphia and New York Metropolitan Statistical 

Areas (MSAs). CE’s large urban PSUs are also referred to as MSAs. Also, CE and the American 

Community Survey (ACS) ask similar questions for two expenditure categories, Electricity and natural gas 

and Rented dwellings. The ratio of the CE to ACS estimates at the national level were almost identical to 

the state level estimates, indicating that the New Jersey estimates were of the same quality as the national 

estimates. 

This experimental technique for calculating state weights and expenditure estimates was then applied to 

Florida and California where only a subset of the counties in the state are included in sampled PSUs. The 

state expenditure estimates for Florida and California also compared favorably to expenditure estimates 

from state MSAs and for the two expenditure categories from the ACS. In conclusion, the results from the 

three states indicate that the technique for computing state weights is promising.

2. Overview of CE’s Sample Design 

It is important to understand CE’s national sample design and weighting because the calculation of state 

weights is a modification of the national procedures (Neiman et al., 2015). 

336
2.1 First Stage Sample Design 

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). 

In the first stage, all 3,143 counties in the United States are assigned to PSUs. Urban PSUs are defined by 

the U.S. Office of Management and Budget (OMB) by assigning counties surrounding an urban core to 

geographic entities called Core Based Statistical Areas (CBSAs) where 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 CBSAs: metropolitan CBSAs which are CBSAs that have an urban core with more 

than 50,000 people, and micropolitan CBSAs which are CBSAs that have an urban core with 10,000 to 

50,000 people. All other counties are rural, and OMB does not group rural counties into small clusters of 

adjacent counties. CE defines its own rural PSUs using an adjacency matrix and zero-one integer linear 

programming (King 2012). In general, rural PSUs have their state’s identity suppressed on CE’s PUMD 

file because they have fewer than 100,000 people and there is a risk of identifying individual respondents. 

As a result, in most states, rural PSUs cannot be used for their state estimates.

After defining PSUs, each PSU is assigned to a stratification cluster based on its size-class and Census 

Region or Division. 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 Census Region or 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. 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 property value, median household 

income, latitude, and longitude. Median household income and median household property value correlate 

with expenditures and are calculated for each PSU from five-year ACS estimates. 

After stratification, one PSU is selected to represent the PSUs in the stratification cluster 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, selfrepresenting 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. The smaller metropolitan and 

micropolitan PSUs are stratified together in Design 2010, but stratified separately in Design 2000. 

2.2 Second Stage Sample Design 

After selecting the PSUs, a representative sample of addresses within each PSU is selected using systematic

random sampling. The interest is in consumer units (CUs), 2 which are groups of people in households who 

pool their incomes to make joint expenditure decisions, but since there is usually one consumer unit per 

household and one household per address, the terms “address,” “household,” and “consumer unit” are often 

used interchangeably. 

The first 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 91 sampled PSUs such that the variance of CE’s 

 

2 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.

337
most important statistic, the average annualized expenditure per consumer unit nationwide on all items, is 

minimized (Neiman et al., 2015). This objective is accomplished by allocating the nationwide sample to 

individual PSUs proportional to the number of people they represent, i.e., their stratum’s population. After 

the sample has been allocated, a representative sample of addresses within each PSU is selected with 

systematic random sampling, where the within PSU sampling interval for each PSU is the number of 

addresses on the sampling frame in the PSU divided by the number of sample addresses allocated to the 

PSU.

3. Weighting for CE’s Survey and State Weights 

After drawing a representative sample of addresses in every PSU, each CU is assigned a base weight, which 

is the number of addresses in the population represented by the selected CU. The base weight is adjusted 

for subsampling in the field, noninterviews, and finally calibrated to known population totals. 

3.1 Base Weights for the National Estimates 

CE has a two-stage sample design which is reflected in the base weights. For Design 2000, the base weights 

are defined as:

( ) 1 Base Weight 2 Within PSU Sampling Interval Probability of Selecting PSU = × ×

where

 PSU Population Probability of Selecting PSU = Stratification Cluster Population

The probability of selection is calculated in the first stage of the sample design after the PSUs have been 

stratified and selected. The within PSU sampling interval is from the second sampling stage and is 

multiplied by two because a single sample is drawn for the combined Diary and Interview Survey with the 

sampled addresses alternately assigned to the Diary and Interview Survey. Beginning in 2018, the factor 

“2” will no longer be required since the sample of addresses will be drawn separately.

3.2 Base Weights for the State Estimates

The base weights for the state estimates are calculated similar to the national estimates. The primary 

difference is that. U.S. Census tracts replace PSUs for determining the probability of selection. Census 

tracts are small contiguous areas within a county or county equivalent that are relatively permanent from 

census to census. Ideally, Census tracts are approximately 4,000 people but can range from 1,200 to 8,000 

people. Census tracts vary in geographical size, depending on population density, and range from a few 

blocks in densely populated areas to hundreds of square miles in sparsely populated areas. 

Census tracts for a state are stratified using the same procedure for stratifying PSUs. For state estimates, 

the number of clusters is set to five, corresponding to the number of income quintiles. Only two clustering 

variables are used for state estimates: median household property value and median household income, 

which correlate with expenditures and are calculated for each Census tract from five-year ACS estimates.

Latitude and longitude are not used as clustering variables for state-level estimates.

The same “within PSU sampling interval” is used for both state and national estimates, hence for the state 

weights, the base weights are calculated for each stratum as:

338
( )

Sum of the Tract Populations in State in a Stratum State Base Weight = Sum of CE's Tract Populations in a Stratum

Within PSU Sampling Interval

x

     

3.3 Weighting Control Factor 

The weighting control factor adjusts for subsampling in the field, which occurs when a data collector visits 

a particular address and discovers multiple housing unit where only one housing unit was expected. The 

weighting control factor is generally 1.0, since subsampling is infrequent.

3.4 Noninterview Adjustment

The noninterview adjustment factor adjusts for interviews that cannot be conducted in occupied housing 

units due to a consumer’s refusal to participate in the survey or the inability to contact anyone at the housing 

unit in spite of repeated attempts. For the national estimates, the sample CUs are partitioned into cells and 

an initial noninterview adjustment factor is calculated for each cell using a cell weighting procedure, where 

the cells are defined by five variables: the month in which the data was collected, the region of the U.S., 

the average adjusted gross income in the CU’s zip code, the consumer unit size, and the number of contact 

attempts made by interviewers. The initial noninterview adjustment factor is calculated for each cell, but 

when there is an insufficient number of CUs in a cell, the factor is adjusted using a hierarchical cell 

collapsing procedure where cells are collapsed together using two of the five cell-defining variables: the 

consumer unit size and the number of contact attempts made by interviewers. Cells are not collapsed by 

month, the four regions of the U.S. (Northeast, Midwest, South, and West), or the three income groups 

(bottom 10%, middle 80%, and top 10%) which are formed using the average adjusted gross income in the 

CU’s zip code according to a publicly available database from the IRS.

For state estimates, the noninterview adjustment is also calculated for each CU using the cell weighting 

procedure along with the hierarchical cell collapsing procedure. However, the procedure is run at the state 

level instead of at the regional level and run quarterly instead of monthly. The state’s sample size is too 

small for monthly processing. A surrogate variable, ACS’s median household income for each CU’s Census 

tract replaced the average adjusted gross income in the CU’s zip code.

3.5 Calibration 

The final weight adjustment is calibration which adjusts the STAGE1WTs of the respondent CUs to sum 

to 24 “known” population totals to account for frame undercoverage. STAGE1WT is the product of the 

base weight x weighting control factor x noninterview adjustment factor. CE uses Lagrange multipliers to 

select the weights that minimize the amount of change made to the STAGE1WTs so that the calibrated 

weights multiplied by the number of CU members in each of the 24 demographic groups sum to the 24 

population totals. The 24 population totals are from the Current Population Survey (CPS) and are: the total 

number of households in the U.S.; the total number of homeowning households in the U.S.; the total number 

of people in the four regions of the U.S.; the total number of people in the urban areas of those four regions; 

and the total number of people in 14 age x race categories. The population totals are updated every quarter 

from CPS.

At the state level, the same procedure is used, except only 9 “known” population totals are used in the 

Lagrange multiplier algorithm: the total number of households in the state; the total number of homeowning 

households in the state and the total number of people in 7 age categories. In most states, there is an 

insufficient number of black people in the sample for the calibration algorithm to converge, especially in 

the Diary Survey, which is the reason the 14 age x race categories were reduced to 7 age categories. On 

occasion, there was also an insufficient number of people in the 75+ age category, and when that occurred 

the 65-74 and 75+ age categories were combined into a single 65+ age category.

339
There are infinitely many set of weights that sum to the 24 (or 9) “known” population totals. The 

algorithm sets limits on the amount the STAGE1WTs can change, between 0.5 and 4, and the final 

weights are the product of the STAGE1WT x calibration factor. 

4. Variance 

Both the expenditure means and variances are calculated using the final weights from calibration using 

complete interviews. CE has a complex sample design and for the national estimates, balanced repeated 

replication (BRR) is used to generate an unbiased estimate of the sampling variance for expenditure means. 

CE assigns its PSUs to 43 rows of a Hadamard matrix, which are balanced by population, and the CUs 

within each stratum are randomly assigned to one of two half samples. For the state estimates, it is not 

possible to assign Census tracts to rows on a Hadamard matrix, so the jackknife, another method for 

estimating variances in a complex sample design, is applied (Valliant et al., 2013). 

In applying the jackknife, one unit is deleted within a stratification cluster at a time. A unit is a county tract 

combination. Census tracts are unique within a county, but their codes may be duplicated in other counties 

so it is useful to create a new variable, CTY_TRACT, by concatenating county and tract. Some 

CTY_TRACTs are void of CUs and these are not used in the jackknife. Other CTY_TRACTs have one or 

more CUs, usually less than twelve. In the jackknife, each CTY_TRACT, i, is deleted one-at-a-time within 

a stratification cluster, h. Let nnh be the number of CTY_TRACTs in cluster h. All CUs in the deleted 

CTY_TRACT have their state weights set to zero. The other (nnh − 1) CTY_TRACTs in stratification 

cluster h have their state weights multiplied by nnh⁄(nnh − 1) to represent the full stratification cluster. CUs 

in other stratification clusters retain their original state weight. Each deletion is a replicate, θθ�(hii) ,with a 

mean expenditure estimate for each of the over 800 expenditure categories and there is a replicate for each 

CTY_TRACT. The mean for the full sample is �θθ. The variance for each expenditure category is calculated

using the following formula. 

VV�θθ�� = �nnh − 1

nnh

5

h=1

�� θθ�(hii) − θθ��

2

nnh

ii=1

5. State Estimates-Data

Five quarters of data from the Interview Survey and four quarters of data from the Diary Survey are required 

to calculate one-year estimates of consumer expenditures. Respondents for the Interview Survey are queried 

about their expenditures over a three-month period and interviews conducted in the first quarter of a year 

have expenditures from the previous year; therefore, five quarters of data are required to capture all 

expenditures that occurred in a single calendar year. Respondents for the Diary Survey are queried about 

their expenditures for the current week and there is no overlap for the previous year. Interview and Diary 

data from 2013 and quarter 1 of 2014 were selected for this project. Design 2010 was not implemented until 

2015, so the data for this project uses Design 2000. 

Other required variables include Census tract population, median household income and median household 

property value. The source of these variables is the 5-year, 2010-2014, estimates from the ACS. 

340
6. State Estimates–New Jersey

New Jersey was selected as a test state because in Design 2000, every county was in a sampled PSU: either 

the Philadelphia or New York PSU. Therefore, expenditure data was available in every county of New 

Jersey, allowing for the calculation of the state’s “true” expenditures. In Design 2010, three counties in 

southern New Jersey in the Philadelphia PSU (Atlantic, Cumberland, and Cape May) and two counties in 

the northern New Jersey in the New York PSU (Warren and Mercer) were dropped. Using the same data 

from Design 2000, data from the sampled New Jersey counties in the 2010 Census were retained, reweighted, and a new set of state weights calculated. An evaluation of the differences between Design 2000 

and Design 2010 expenditures gives an indication of the procedure’s effectiveness when extended to other 

states where a smaller portion of the population is sampled. 

Each Census tract in New Jersey was assigned to one of five stratification clusters using a heuristic 

stratification algorithm and two clustering variables from five-year ACS estimates: median household 

property value and median household income. These two clustering variables correlate with expenditures 

and are an indication of wealth. It is helpful to examine the distribution of wealth, as indicated by the 

mapping of the 2,010 Census tracts in New Jersey by stratification cluster, Figure 1. The varying geographic 

size of the clusters is evident in Figure 1. Smaller Census tracts in geographic size represent denser 

populations. The population is denser and more affluent in Northern New Jersey. Approximately 76% of 

the CUs in New Jersey are in the New York PSU. Consequently, the expenditure estimates are closer to 

New York than Philadelphia. 

Figure 1. The Census tracts in New Jersey are mapped by their cluster stratification assignment and the 

cluster centers are provided below the map. The first coordinate is the median household property value 

and the second coordinate is median household income. The clusters are ordered in increasing median 

household property value. The higher median household property value and income tracts predominate in 

Northern New Jersey. The tract size indicates population density. 

341
For both designs, New Jersey state-level expenditure estimates and their corresponding standard errors 

(SEs)and coefficient of variations (CVs) for 2013 are given in Table 1. Also, MSA-level expenditure 

estimates for 2013-2014 for the Philadelphia and New York MSAs are provided in the table for comparison.

Currently, CE plans to publish state level estimates for New Jersey using one year of data, but currently 

publishes MSA-level expenditure estimates every year using two years of data.

From Table 1, both designs have similar mean expenditures. For Average annual expenditures, the 

difference between the two designs is $112 for a $65,000 expenditure. Housing, Transportation, and Food 

are major expenditure categories and the difference in the two designs are: $11, $59, and $107, respectively. 

In general, as expected, the standard errors increase with the reduced sample size in Design 2010, but the 

difference in SEs are small. The difference in SEs between the two designs for Average annual 

expenditures, Housing, Transportation, and Food are: $254, $23, $116, and $32, respectively. Another 

method of comparison, which accounts for the magnitude of the expenditures, is coefficient of variation, 

which is the ratio of the SE to the mean. For both designs, the CVs are of the same magnitude. For Average 

annual expenditures, the CV is 3.70% for Design 2000 and 4.08% for Design 2010. The coefficient of 

variation is highest for Education, a highly variable expense, since not all CU’s have education expenses. 

These statistics indicate that the expenditure estimates from the reduced sample, Design 2010, are as reliable 

as the expenditure estimates from the full sample, Design 2000. 

Also from Table 1, it is evident that CE’s Design 2000 and 2010 estimated state expenditure means are 

closer to the means for the New York MSA than to the means for Philadelphia MSA. An exception is 

Transportation, which is closer to the Philadelphia MSA. Although, the Philadelphia and New York MSAs 

include counties outside of New Jersey, the closeness of CE’s mean expenditure estimates to the MSAs 

mean expenditure estimates provides confidence that the state weighting algorithm is working correctly.

Another approach to evaluating the procedure for calculating state weights is to compare CE’s expenditure

estimates to those from other government surveys, which ask questions on a subset of topics covered by the 

CE Survey. CE is always interested in how the estimates from other surveys compare with CE’s estimates. 

CE compared two of its expenditure categories, Electricity and natural gas and Rented dwellings, with the 

data in ACS’s PUMD files. The comparison was made for the New Jersey estimates as well as for the 

national estimates. It is difficult to compare the estimates from two surveys due to conceptual differences 

in the questions, as well as differences in their target populations, sample designs, and interviewing 

procedures. 

A comparison of the two surveys’ estimates for two expenditure categories, Electricity and natural gas and 

Rented dwellings, is presented in Table 2. CE’s Design 2000 expenditure estimates are lower than the 

ACS’s expenditure estimates. For Electricity and natural gas, the CE/ACS ratio for the nation and New 

Jersey are 0.86 and 0.87, respectively. However, for Rented dwellings, the CE/ACS ratio is lower for the 

nation than for New Jersey, 0.79 and 0.87. The CE/ACS ratios are similar for Design 2010. Since, the 

CE/ACS ratios for New Jersey are as high as the CE/ACS ratios for the nation, this indicates that the New 

Jersey estimates are of equal quality as that for the nation and that the state weighting algorithm is working 

correctly.

In summary, several approaches were taken to evaluating the state expenditure estimates for New Jersey. 

Design 2000, with expenditure data from CUs in all counties, was compared to Design 2010, with 

expenditure data from CUs in a subset of the counties. Design 2000 and Design 2010 means and SEs were 

close to each other and the CVs were of the same magnitude as well. Because the New Jersey population 

is denser and more affluent in the portion of the state in the New York PSU, the New Jersey estimates are 

closer to the New York MSA estimates, as expected. Finally, the CE/ACS ratios for New Jersey were of 

equal quality as the national estimates. These results indicate that the state weighting algorithm will be 

effective in states where only a subset of the state’s counties is included in the survey.

342
Table 1. New Jersey State means, SEs, CVs, and Philadelphia and New York MSA means for primary expenditure categories 

 CE's Estimated State Expenditures for 2013 Coefficient of Variation CE's MSA Tables for 2013-2014

 Design 2000 Design 2010 Design Design Philadelphia New York

Expenditure Category Mean ($) SE ($) Mean ($) SE ($) 2000 (%) 2010 (%) Mean ($) Mean ($)

Average annual 

expenditures 65,165 2,408 65,277 2,662 3.70 4.08 57,907 63,193

Food 7,842 524 7,735 556 6.68 7.19 7,263 7,329

Alcoholic beverages 588 90 589 104 15.40 17.73 636 541

Housing 25,064 850 25,074 827 3.39 3.30 20,475 25,046

Apparel and services 2,600 379 2,631 399 14.59 15.15 2,193 2,334

Transportation 9,177 790 9,118 906 8.61 9.93 9,500 8,442

Healthcare 3,857 228 3,945 260 5.92 6.59 4,386 3,937

Entertainment 2,584 197 2,491 191 7.61 7.66 2,730 2,597

Personal care products and 

services 778 80 747 82 10.22 10.99 676 748

Reading 110 23 108 23 20.91 21.52 105 100

Education 3,238 1,063 3,502 1,366 32.84 39.01 2,003 2,575

Tobacco products and 

smoking supplies 289 45 277 44 15.62 16.03 343 230

Miscellaneous 547 83 527 89 15.26 16.86 561 652

Cash contributions 1,543 205 1,505 230 13.30 15.28 1,237 1,669

Personal insurance and 

pensions 6,950 469 7,030 487 6.74 6.93 5,800 6,993

Table 2. CE and ACS comparison of New Jersey Design 2000 expenditures 

National New Jersey

Expenditure Category CE ($) ACS ($) CE/ACS ($) CE ($) ACS ($) CE/ACS ($)

Electricity and Natural Gas 1,814.16 2,117.00 0.86 2,308.24 2,667.57 0.87

Rented Dwellings 3,323.61 4,220.06 0.79 4,507.20 5,167.57 0.87

343
7. State Estimates–Florida

Florida provides a different scenario to test the state weighting algorithm because it has both selfrepresenting and non-self-representing PSUs. In Design 2010, PSUs are self-representing if they have more 

than 2.5 million people, so Miami and Tampa are self-representing PSUs and the other PSUs in the state 

are non-self-representing. By contrast, in Design 2000 the self-representing threshold was 2.7 million 

people, so Miami was the only self-representing PSU and the other PSUs in the state (including Tampa) 

were non-self-representing. 

Self-representing PSUs have larger within-PSU sampling intervals than non-self-representing PSUs, which 

has an impact on the state base weight, see Section 3.2. The first factor in the base weight equation is 

calculated at the state and not at an individual PSU level. Consequently, the base weights are higher for 

self-representing PSUs than for non-self-representing PSUs, but the number of interviews in a non-selfrepresenting PSUs is approximately the same as in a self-representing PSU. Thus, in the state estimates, 

households in self-representing PSUs have more weight than households in non-self-representing PSUs. 

The stratification cluster algorithm uses zero-one integer linear programming in which the number of 

decision variables is equal to the number of stratification clusters (five) times the number of Census tracts. 

Thus, Florida has 4,245 Census tracts, and 21,225 decision variables whereas, New Jersey had 2,010 Census 

Tracts and 10,050 decision variables. It was important to test the stratification cluster algorithm, a vital 

component of the state weighting algorithm, on a problem of this size. The zero-one integer linear 

programming component solved the assignment problem and the mapping of Census tracts by stratification 

cluster.is shown in Figure 2. The cluster centers are provided below the map. The first coordinate is the 

median household property value and the second coordinate is median household income. 

Table 3 shows both the state expenditure means and SEs for Florida and the MSA means for Miami. The 

state means and Miami MSA means are of the same magnitude, but in general, the state expenditures are 

slightly higher. However, residents in Miami spend more on Housing, Personal care products and services, 

and Education than the state average.

The difference between the state expenditures and Miami expenditures is not unexpected. Approximately 

22% of the Florida CUs are from the Miami PSU, so the state is not dominated by Miami. Also, Miami is 

not an affluent metropolitan area. In 2010-2014, income after taxes in Miami ($48,310), which affects 

expenditures, is lower than the regional income after taxes for the South ($53,566) and for the United States 

($57,364) (Dotson). 

The CE and ACS comparison for two Florida expenditure categories, Electricity and natural gas and Rented 

dwellings, are presented in Table 4. For Electricity and natural gas, the CE/ACS Florida ratio is 0.88, which 

is slightly higher than the national CE/ACS ratio of 0.86. For Rented dwellings, the Florida CE/ACS ratio 

is 0.85 which is higher than the national CE/ACS ratio of 0.79. As with New Jersey, the state CE/ACS 

ratios are as good or better than the national CE/ACS ratios indicating that the state weighting algorithm is 

effective.

344
Figure 2. The Census tracts in Florida are mapped by their cluster stratification assignment and the cluster 

centers are provided below the map. Highly populated tracts are small geographic areas which appear grayblack and predominate along the coast.

Table 3. Florida state expenditure means and SEs and Miami MSA means

CE's Estimated State 

Expenditures for 2013

Miami MSA

for 2013-2014

Expenditure Category Mean ($) SE ($) Mean ($)

Average annual expenditures 45,944 1,787 43,066

Food 6,142 370 5,610

Alcoholic beverages 383 68 375

Housing 16,719 591 16,981

Apparel and services 1,392 209 1,350

Transportation 8,304 629 7,243

Healthcare 2,976 177 2,433

Entertainment 1,970 161 1,565

Personal care products and services 647 97 712

Reading 69 11 54

Education 480 111 632

Tobacco products and smoking 

supplies 232 30 172

Miscellaneous 494 166 376

Cash contributions 1,243 260 739

Personal insurance and pensions 4,895 427 4,823

345
Table 4. CE and ACS comparison of Florida expenditures 

Florida

Expenditure Category CE ($) ACS ($) CE/ACS 

Electricity and natural gas 1,671.94 1,905.32 0.88

Rented dwellings 3,605.01 4,229.70 0.85

8. State Estimates–California

California has the largest number of Census tracts of any state in the United States, 8,057 and it was 

important to test whether the stratification cluster algorithm could solve a problem with 40,285 decision 

variables. The algorithm successfully assigned Census tracts to stratification clusters and the mapping is 

shown in Figure 3. The high-income and densely populated areas are primarily along the coast.

Figure 3. The Census tracts in California are mapped by their cluster stratification assignment and the 

cluster centers are provided below the map. The first coordinate is the median household property value 

and the second coordinate is median household income. The higher income and property value tracts 

predominate along the coast and the interior Census tracts have lower population, median household 

property value, and median household income. 

California has three self-representing PSUs and several non-self-representing PSUs. The self-representing 

PSUs are: San Francisco, San Diego, and Los Angeles and its suburbs. Approximately 76% of California’s 

346
population resides in these three PSUs and a survey designed specifically for California would be heavily 

concentrated in Los Angeles, San Diego, and San Francisco. 

Table 5 shows the state expenditure means and SEs for California and the MSA means for Los Angeles, 

San Diego, and San Francisco. The California state expenditure estimates are within the range of the three 

MSA expenditure estimates, which is expected because of the predominance of the three large metropolitan 

areas in the survey and state. 

Table 5. California state and MSA means for CE’s primary expenditure categories 

CE Estimated Weights CE's MSA Tables for 2013-2014

Expenditures for 2013 Los Angeles San Diego San Francisco

Expenditure Category Mean ($) SE ($) Mean ($) Mean ($) Mean ($)

Average annual expenditures 58,583 1,358 55,546 63,189 68,765

Food 7,441 258 7,278 6,936 8,152

Alcoholic beverages 552 50 478 681 721

Housing 22,574 519 21,501 23,774 25,663

Apparel and services 1,901 124 1,920 1,977 2,227

Transportation 8,566 372 8,315 10,319 9,404

Healthcare 3,352 149 3,178 4,395 4,459

Entertainment 2,661 114 2,427 2,894 3,329

Personal care products and services 791 39 781 744 850

Reading 115 9 79 162 161

Education 1,558 185 1,601 1,068 1,900

Tobacco products and smoking 

supplies 193 19 163 232 187

Miscellaneous 554 62 608 1,091 813

Cash contributions 1,868 387 1,291 1,752 2,460

Personal insurance and pensions 6,457 250 5,926 7,162 8,438

The CE and ACS comparison for two California expenditure categories, Electricity and natural gas and 

Rented dwellings, are presented in Table 6. For Electricity and natural gas, the CE/ACS California ratio is 

0.84, which although lower than the national CE/ACS ratio of 0.86, is not of concern. For Rented dwellings, 

the California CE/ACS ratio is 0.88 which is higher than the national CE/ACS ratio of 0.79. In conclusion, 

the CE/ACS ratios are as good or better than the national CE/ACS ratios indicating that the state weighting 

algorithm is effective.

Table 6. CE and ACS comparison of California expenditures 

California

Expenditure Category CE ($) ACS ($) CE/ACS 

Electricity and natural gas 1,449.44 1,723.91 0.84

Rented dwellings 6,315.01 7,148.09 0.88

9. Conclusion

The primary difference in the calculation of state versus regional or national expenditure estimates is the 

probability of selection. Both use the same assignment algorithm to either assign Census tracts or PSUs to 

stratification clusters, which are constrained by population bounds. Both procedures use noninterview

347
adjustment and calibration to adjust the weights to known population counts from the Current Population 

Survey. The state estimates use jackknife to calculate the variances, whereasregional and national estimates 

are calculated using BRR.

The states selected, New Jersey, Florida, and California, have a range of number of Census tracts as well 

as PSU coverage. In New Jersey, every county was in a self-representing PSU, allowing for the dropping 

of counties, re-calculating the CU weights and expenditure estimates, and comparing with the expenditure 

estimates using all counties. The estimates were close, indicating that the state weight algorithm will 

produce accurate state expenditure estimates for states with less sampled population. Florida has one selfrepresenting PSU, Miami, and multiple non-self-representing PSU. California has multiple selfrepresenting PSUs and one or more non-self-representing PSUs. For all three states, the expenditure 

estimates are similar to CE’s two-year MSA tables. It is important, but often difficult to compare CE’s 

estimates to other surveys. The survey purposes are different, and the other survey may oversample in 

certain demographics. It is seldom an exact comparison. For the two expenditure categories: Electricity and 

natural gas and Rented dwellings, CE’s estimates were consistently lower than ACS’s estimates. The state 

CE/ACS ratios were equivalent or better than the national level ratios, indicating that the quality of the state 

estimates is equal to the national estimates.

It might be beneficial to calculate state estimates using two years of data. This would increase the sample 

size, making the mean and variance more precise. 

Although, the procedure to calculate state weights is experimental, it is a promising approach, producing 

consistent expenditure estimates under varying PSU coverage.

10. Disclaimer

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

Labor Statistics.

11. References

Dotson, M. (2016). Eating and Drinking in Miami: consumer expenditures 2010-2014, Beyond the 

Numbers: Regional Economies, vol. 5, no. 11 (US Bureau of Labor Statistics), 

https://www.bls.gov/opub/btn/volume-5/eating-and-drinking-in-miami-consumer-expenditures2010-14.htm.

King, S., Schilp, J., and Bergmann, E. (2011). Assigning PSUs to a Stratification PSU. Proceedings of the 

American Statistical Association, Section on Survey Methods Research, 2235-2246. 

King, S. (2012). A “First-Cut” at Forming Rural PSUs. Proceedings of the American Statistical Association, 

Section on Survey Methods Research, 4055 -4066. 

Murphy, P., (2008). An Overview of Primary Sampling Units (PSUs) in Multi-Stage Samples for 

Demographic Surveys. Proceedings of the American Statistical Association, Section on Government 

Statistics, 2856-2863. 

Neiman, D, King, S., Swanson, D., Ash, S., Enriquez, J., and Rosenbaum, J. (2015). Review of the 2010

Sample Redesign of the Consumer Expenditure Survey. Proceedings of the American Statistical 

Association, Section on Survey Methodology, 2522-2536. 

348
Valliant, R., Dever, J., and Kreuter, F. (2013). Practical Tools for Designing and Weighting Survey 

Samples. Springer, New York.

349