Chapter 16.
Consumer Expenditures and Income

Sample Design

Selection of households
The Consumer Expenditure Survey is a nationwide household survey designed to represent the total U.S. civilian noninstitutional population. The selection of households begins with the definition and selection of primary sampling units (PSUs). PSUs are counties (or parts thereof), groups of counties, or independent cities grouped together into geographic entities called “core-based statistical areas” (CBSAs). The sample of PSUs currently used in the survey consists of 91 areas, of which 75 urban areas are also used by the Consumer Price Index program.

The 91 PSUs are classified into four categories:

• 21 “A” PSUs, which are metropolitan CBSAs with a population over 2.7 million people
• 38 “X” PSUs, which are metropolitan CBSAs with a population under 2.7 million people
• 16 “Y” PSUs, which are micropolitan CBSAs, defined as areas that have at least one urban cluster of at least 10,000 but less than 50,000 population, plus adjacent territory that has a high degree of social and economic integration with the core as measured by commuting ties
• 16 “Z” PSUs, which are non-CBSA areas, and are often referred to as “rural” PSUs

The population represented by the survey is the total U.S. civilian noninstitutional population, both urban and rural. It includes people living in houses, condominiums, apartments, and group quarters such as college dormitories. It excludes people such as military personnel living on base, nursing home residents, and people in prisons.

The U.S. Census Bureau selects a sample of approximately 12,000 addresses per year to participate in the Diary Survey. Usable diaries are obtained from approximately 7,100 households at those addresses. Diaries are not obtained from the other addresses due to refusals, vacancies, ineligibility, or the nonexistence of a housing unit at the selected address. The actual placement of diaries is spread equally over all 52 weeks of the year.

The Interview Survey is a rotating panel survey in which approximately 14,000 addresses are contacted in each calendar quarter of the year. One-fifth of the addresses contacted each quarter are new to the survey and provide “bounding” interviews that provide baseline data, which are not used to compute the survey’s published expenditure estimates. Excluding these bounding interviews and interviews not completed due to refusals, vacancies, ineligibility, or the nonexistence of a housing unit at the selected address, usable interviews are obtained from approximately 7,100 households each quarter. After a housing unit has been in the sample for five consecutive quarters, it is dropped from the survey and a new housing unit is selected to replace it.

Note: The sample design described above with 91 PSUs is based on information collected in the 2000 Census, and has been in use since 2006. The original 2000 census-based sample design was introduced in 2005 and consisted of 102 PSUs: 28 “A” PSUs, 42 “X” PSUs, 16 “Y” PSUs, and 16 “Z” PSUs. However, budget cuts in 2006 forced seven “A” PSUs to be changed to the “X” category, and 11 “X” PSUs to be dropped from the sample. Dropping 11 “X” PSUs from the sample reduced the number of sampled addresses and interviewed households by approximately 8 percent. Otherwise the original and current 2000 census-based sample designs are the same.

Cooperation levels
Response data for the 2005 Consumer Expenditure Survey are shown in table 1. For the Interview survey, the totals refer to housing units in the second through fifth quarters of the survey (the non-bounding interviews), with each unique housing unit providing up to four usable interviews. For the Diary Survey, the totals refer to housing units in weeks 1 and 2 of the survey, with each unique housing unit providing up to two usable interviews. Most Diary respondents participate for both weeks.

There are three general categories of nonresponse:

• Type A nonresponses are refusals, temporary absences, and noncontacts
• Type B nonresponses are vacant housing units, housing units with temporary residents, and housing units under construction
• Type C nonresponses are destroyed or abandoned housing units, and housing units converted to nonresidential use

Response rates are defined to be the percent of eligible housing units (that is, the designated sample less Type B and Type C nonresponses) from which usable interviews are collected. In the 2005 Interview Survey there were 39,988 eligible housing units from which 29,804 usable interviews were collected, resulting in a response rate of 74.5 percent. In the 2005 Diary Survey there were 21,309 eligible housing units from which 15,126 usable interviews were collected, resulting in a response rate of 71.0 percent.

Estimation methodology
The estimation of population quantities of interest, such as the average expenditure per consumer unit on a particular item, is achieved through the use of weights. Each consumer unit in the survey is assigned a weight, which is the number of similar consumer units in the U.S. civilian noninstitutional population the sampled consumer unit represents. Using these weights, the average expenditure per consumer unit on a particular item category is estimated by

where

= average expenditure per consumer unit on the item category,

y_i = expenditure made by the i ^th consumer unit on the item category,

w_i = weight of the i ^th consumer unit in the sample, and

s = sample of consumer units that participate in the survey.

For example, if y_i is the expenditure on butter made by the i ^th consumer unit in the sample during a given time period, then is an estimate of the average expenditure on butter made by all consumer units in the U.S. civilian noninstitutional population during that time period.

If one wanted to estimate the proportion of consumer units that purchased butter during a given time period, then the same formula is applied, where y_i is set equal to 1 if the i ^th consumer unit purchased butter during the time period, and 0 if it did not. When this 1/0 definition of y_i is used, is an estimate of the proportion of all consumer units in the U.S. civilian noninstitutional population that purchased butter during the given time period.

Several factors are involved in computing the weight of each consumer unit for which a usable interview is received. Each consumer unit is initially assigned a base weight, which is equal to the inverse of the consumer unit’s probability of being selected for the sample. Base weights in the Consumer Expenditure Survey are typically around 10,000, which means that a consumer unit in the sample represents 10,000 consumer units in the U.S. civilian noninstitutional population—itself plus 9,999 other consumer units that were not selected for the sample. The base weight is then adjusted by the following factors to correct for certain nonsampling errors:

Weighting control factor. This adjusts for subsampling in the field. Subsampling occurs when a data collector visits a particular address and discovers multiple housing units where only one housing unit was expected.

Noninterview adjustment factor. This adjusts for interviews that cannot be conducted in occupied housing units due to a consumer unit’s refusal to participate in the survey or the inability to contact anyone at the sample unit in spite of repeated attempts. This adjustment is based on region of the country, household tenure (owner/renter), consumer unit size, and race of the reference person.

Calibration factor. This adjusts the weights to 24 “known” population counts to account for frame undercoverage. These “known” population counts are for age, race, household tenure (owner/renter), region of the country, and urban/rural. The population counts are updated quarterly. Each consumer unit is given its own unique calibration factor. There are infinitely many sets of calibration factors that make the weights add up to the 24 “known” population counts, and the Consumer Expenditure Survey selects the set that minimizes the amount of change made to the “initial weights” (initial weight = base weight x weighting control factor x noninterview adjustment factor).

Precision of the estimates
The precision of the estimator is measured by its standard error. Standard errors measure the sampling variability of the Consumer Expenditure Survey estimates. That is, they measure the uncertainty in the survey estimates caused by the fact that a random sample of consumer units from across the United States is used instead of collecting data from every consumer unit in the nation.

Standard errors are estimated using the method of “balanced repeated replication.” In this method the sampled PSUs are divided into 43 groups (called strata), and the consumer units within each stratum are randomly divided into two half samples. Half of the consumer units are assigned to one half sample, and the other half are assigned to the other half sample. Then 44 different estimates of are created using data from only one half sample per stratum. There are many combinations of half samples that can be used to create these “replicate” estimates, and the Consumer Expenditure Survey uses 44 of them that are created in a “balanced” way with a 44 x 44 Hadamard matrix. The standard error of is then estimated by

^,

where _r is the rth replicate estimate of .

The coefficient of variation is a related measure of sampling variability. It measures the variability of the survey estimate relative to the mean. It is defined by the equation

and usually is expressed as a percent.

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