Attachment R - Assessing Non Response Bias

Section on Survey Research Methods – JSM 2009

Assessing Nonresponse Bias in the Consumer Expenditure
Interview Survey
Susan L. King∗

Boriana Chopova
Dave E. McGrath

Jennifer Edgar
Jeffrey M. Gonzalez
Lucilla Tan

Abstract
The Consumer Expenditure Interview Survey (CE) is a nationwide survey conducted by the
U.S. Bureau of Labor Statistics to estimate the expenditures made by American households. The
response rate for the survey has varied between 74.5 and 78.6 percent over the past six years. In
2006, the Office of Management and Budget (OMB) issued a directive for any household survey with
a response rate below 80 percent to conduct a study determining whether nonresponse introduces
bias into the survey estimates. This paper is a synthesis of four studies undertaken to respond to
OMB’s directive. The four studies are: a comparison of response rates between subgroups of the
survey’s sample; a comparison of respondent demographic characteristics between the CE and the
American Community Survey, an analysis of nonresponse bias using ’harder-to-contact’ respondents
as proxies for nonrespondents; an analysis of nonresponse bias using intermittent respondents and
attritors as proxies for nonrespondents. Collectively, the studies show no meaningful bias in the
survey’s estimates even though the nonresponse is not missing completely at random.
Key Words: Continuum of resistance, intermittent respondent, missing data, panel survey, proxy
nonrespondent

1. Introduction
The Office of Management and Budget (OMB) is concerned with the decreasing unit response rates in household and establishment surveys. To address this concern, OMB (2006)
issued new standards and guidelines for federal statistical surveys. These guidelines require
that, for any survey with a response rate below 80 percent, the data are analyzed to determine whether the missing values are missing completely at random (MCAR), and that an
estimate of the nonresponse bias be provided.
The Consumer Expenditure Interview Survey (CE) is a nationwide household survey
conducted by the U.S. Bureau of Labor Statistics (BLS) to estimate expenditures made by
American households, and it is one federal statistical survey with a response rate below 80
percent. The response rate for the CE ranged from 74.5 percent to 78.6 percent between
years 2002 and 2007. The design includes a rotating panel in which approximately 14,000
households are visited each quarter of the year, and each is contacted for an interview every
three months for five consecutive quarters. Expenditure information from the first interview
is excluded from published estimates and is only used for inventory and bounding purposes.
This addresses a common problem in panel surveys in which respondents erroneously recall
and report events (in this case, expenditures) to have occurred more recently than they
actually did. Only expenditure information from the second through fifth interviews is used
in the published estimates.
To evaluate nonresponse bias in the CE, four studies were completed: a comparison of
response rates among subgroups of the survey’s sample; a comparison of socio-demographic
characteristics to the American Community Survey (ACS); an analysis of nonresponse bias
using ‘harder-to-contact’ respondents as proxies for nonrespondents; and, an analysis of
nonresponse bias using intermittent respondents and attritors as proxies for nonrespondents.
These studies were designed to answer the questions: (1) Are the data in the CE MCAR?
(2) What are the demographic characteristics of the nonrespondents? and, (3) What is the
level of nonresponse bias in the CE?
∗ King.Susan@bls.gov

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

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2. Methodology: Common Approaches across Studies
2.1

Data

For comparability of results, the four studies used a common analysis file, based on data
collected for interview waves 1, 2, and 5 from April 2005 through June 2006. This time
period was selected because the Contact History Instrument (CHI) was first available in
April 2005. CHI data were used in the identification of proxy nonrespondents in one of the
studies. The unit of analysis in these studies is a consumer unit (CU), which in most cases
is a household. The common data file consists of one record per wave per CU for waves 1,
2, and 5. For each record, there are CU-level variables as well as variables for the survey
respondent.
2.2

Weighting

The CE sample design is a nationwide probability sample of addresses. Most addresses
consist of one CU, but some addresses have more than one. Each interviewed CU represents itself as well as other CUs; therefore, each interviewed CU must be weighted properly
to account for all CUs in the target population. The U.S. Bureau of the Census selects
the sample and provides the base weights, which are the inverse of a CU’s probability of
selection. Each CU in a Primary Sampling Unit (PSU)1 has the same base weight. BLS
makes three types of adjustments to the base weights: an adjustment if the interviewer
finds multiple housing units where only a single housing unit was expected; a noninterview
adjustment; and, a calibration adjustment. These weighting adjustments are made to each
CU. The noninterview adjustment accounts for nonresponse by increasing the weight of
the respondents in socio-demographic classes that are thought to be associated with nonresponse. Calibration adjusts the weights to Census population controls in order to account
for frame undercoverage. All studies presented here use base weights, but additional analyses using the nonresponse and calibration weights are provided in the study comparing CE
respondents to ACS respondents.
2.3

Nonresponse Bias Formula

For the estimates of nonresponse bias in the two proxy nonrespondent studies, relative
nonresponse bias was computed instead of an estimate of exact nonresponse bias. The
reason is that the dollar amounts vary substantially across expenditure categories; thus,
making comparisons among them difficult. Relative nonresponse bias is a more appropriate
statistic for comparisons across categories. The following formula was used to compute
relative nonresponse bias, denoted as RelBias(Z¯R ), in the base-weighted sample mean:

 ¯

Z¯R − Z¯T
NN R
ZR − Z¯N R
B(Z¯R )
¯
=
=
RelBias(ZR ) = ¯
N
ZT
Z¯T
Z¯T
where:
• B(Z¯R ) is the absolute nonresponse bias in the base-weighted respondent sample mean;
• Z¯R is the base-weighted respondent mean of expenditures;
• Z¯T is the base-weighted all CU mean of expenditures;
• Z¯N R is the base-weighted proxy nonrespondent mean of expenditures;
• NN R is the base-weighted number of proxy nonrespondent CUs; and,
• N is the base-weighted total number of CUs.
1 In the CE a PSU is a geographic entity that consists of several counties. The average number of counties
in a PSU is about five.

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2.4

Variance Estimation and Significance Testing

Estimates of means, frequencies, and variances were made using procedures designed for
R
complex sample surveys. Means and frequencies were calculated using SAS
9: PROC
SURVEYMEANS and SURVEYFREQ. For comparisons on categorical variables, the test
statistic used was the adjusted Rao-Scott chi-square (SAS Institute Inc., 2004). For twoway comparisons, the null hypothesis tested was “no association between response status
and subgroup”. For the comparison of CE sample characteristics to the ACS, the one-way
comparison null hypothesis, assuming that the ACS distribution is the truth, is that both
distributions are similar. Since the variance for relative nonresponse cannot be expressed in
closed-form, the random groups method (Wolter, 1985) was used to estimate the variance of
the relative nonresponse bias for each expenditure category mean. 95% confidence intervals
for the relative nonresponse bias estimates were calculated in a standard manner but using
the random groups variance estimate.
3. Individual Studies
In this section, the basic methods and the key findings of each study are highlighted.
Detailed results (e.g., estimates and significance tests) from most studies are omitted here
due to space constraints, but they are available upon request from the authors. Conclusions
about CE respondents drawn collectively from all four studies are presented in Table 3 and
estimates of relative nonresponse bias in Table 2.
3.1

Comparisons of Response Rates Across Subgroups

This study examined the response rates among subgroups that could be identified for both
respondents and nonrespondents. The goal was to determine whether the survey’s respondents and nonrespondents had the same distribution on various characteristics. The
subgroups analyzed were: region of the country (Northeast, Midwest, South, West), urbanicity (urban, rural), type of PSU, housing tenure (owner, renter, other), and housing values
for owners and renters2 .
Base-weighted response rates were calculated for each subgroup separately for waves 1,
2, and 5. Base-weighted response rates answer the question: “What percent of the survey’s
target population do the respondents represent?” These response rates were computed as
the sum of base-weighted interviewed units divided by the sum of base-weighted interviewed
units plus the units with Type A noninterviews. Type A noninterviews occur when no
interview is completed at an occupied eligible housing unit3 .
The base-weighted response rates suggest that response rates differ within all of the
subgroups examined. In particular, statistically significant differences (p < 0.05) were
found in the following pairwise comparisons within the subgroups:
• across regions, CUs in the Northeast and West have lower response rates than those
in the Midwest and South;
• across types of PSU, CUs in metropolitan Core Based Statistical Areas (CBSAs) with
a population of more than 2 million people have lower response rates than those in
other types of PSUs;
• renters in the third and fourth quartiles of housing values have lower response rates
than renters in the lower quartiles in the Unit and Area frames4 , with a similar trend
among homeowners; and,
• CUs in urban areas have lower response rates than those in rural areas.
2 The information on housing values is from the 2000 decennial census instead of the CE. This means that
the information is available for every CU, including both respondents and nonrespondents, but is slightly
out-of-date.
3 When possible, neighbors or field interviewers provide demographic information for nonrespondents.
However, the quality of this data has not been evaluated.
4 The unit frame has complete addresses, whereas the area frame has incomplete addresses. The unit
frame covers most of the population.

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Although there is evidence of an association between housing tenure and survey participation, there were no statistically significant differences between the pairwise comparisons
of owners and renters participation in waves 2 and 5 (respondents who do not own or
rent their homes had significantly higher response rates, but the number of these ‘other’
respondents is very small and the difference is not thought to be substantively meaningful).
In general, response rate differences among subgroups suggest that the data are not
MCAR because the respondent and nonrespondent CUs are not simple cross sections of the
original sample.
3.2

Comparisons of the CE Respondents to the ACS

Another approach to analyzing nonresponse bias is to compare the distribution of sociodemographic characteristics of respondents to that of a recent census or other ‘gold standard’
survey (Groves, 2006). The ‘gold standard’ survey chosen for this study was the 2005 ACS.
The ACS satisfied three important criteria: (1) its estimates are considered to be very
accurate; (2) it has key socio-demographic variables available; and, (3) it was conducted in
a time period very close to that which was used to analyze the CE. The ACS is a mandatory
survey with a response rate of 97.3% and a coverage rate of 95.1% (Census Bureau, 2006).
CE and ACS respondents were compared on the following characteristics: gender, age,
race, educational attainment, household size, tenure, the number of rooms in the dwelling
unit, housing value, rent, and CU income. Statistically significant differences (p < 0.055 )
were found between the two distributions for all comparisons and all types of weighting with
only two exceptions, calibration-weighted age and housing. The majority of the statistically
significant differences were smaller than six percentage points. However, larger differences
were found for race and rent. The ACS reported 74.9% of the population as white, whereas
the base, noninterview, and calibration weighted percentage of whites was 82.3%, 83.3%,
and 81.4%, respectively. From the ACS, 20.5% of the population had a monthly rent less
than $500, whereas the interview survey reported 38.7%, 38.5%, and 38.4%. This indicates
that the CE data are probably not MCAR.
There are several factors (e.g., the extremely large sample size) beyond the characteristics of the respondents that make differences likely to be statistically significant. For
example, differences in proportions of subgroups of less than 1.5% between the ACS and
CE distributions for the characteristics of gender, education attainment, and CU size were
found to be statistically significant. In addition, the CE and the ACS collect data differently, the two surveys use different data collection modes, and the wording of the questions
are different. As a result, the strength of the comparison to the ACS is limited by the extent
to which the survey designs are truly comparable.
In short, the first study found that the data are not MCAR, and this study provided
further evidence to substantiate that conclusion.
3.3

‘Harder-to-Contact’ Respondents as Proxies for Nonrespondents

The third study uses ‘harder-to-contact’ respondents as proxies for nonrespondents. It draws
on a theory known as the ‘continuum of resistance’ to identify a subset of respondents to
serve as proxy nonrespondents. This theory suggests that sample units can be ordered across
a continuum by the amount of interviewer effort exerted in order to obtain a completed
interview and those requiring the most effort should be similar to actual nonrespondents
(Groves, 2006).
Using CHI data, a respondent was classified as ‘harder-to-contact’ when over 45 percent
of their contact attempts resulted in noncontacts. This cut-off was selected to yield a
response rate slightly under 80 percent, which is similar to the CE’s actual response rate
during the study period. Also, the noncontact rate was chosen as the classification variable
because this measure standardizes the amount of effort exerted by an interviewer to make
contact across all sample units.
As an example, consider the contact history of a CU that had 6 contact attempts (Table
1). In this example, of the 6 contact attempts that were made, 2 resulted in contacts and
5 All

differences were significant at the α = 0.001 level.

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Table 1: Classification of contact attempts

1.
2.
3.
4.
5.
6.

Contact attempt

Classification

No one home
No one home
Got answering machine/service
No one home
Respondent too busy, appointment set
Complete case - ready to transmit

Noncontact
Noncontact
Noncontact
Noncontact
Contact
Contact

4 noncontacts, for a 67% noncontact rate. Since the noncontact rate is greater than 45%,
this particular CU was classified as ‘harder-to-contact.’
In this study respondents and proxy nonrespondents were compared at each wave on the
following socio-demographic characteristics: gender, marital status, race/ethnicity, age, educational attainment, household tenure, Census Region (Northeast, Midwest, South, West),
urbanicity (urban, rural) and CU size. Statistically significant differences between the two
groups (p < 0.05) across the three waves were found for respondent age, marital status,
CU size, and census region. Other statistically significant differences occurred at individual
waves for race, educational attainment, and housing tenure. Collectively, these differences
suggest, once again, that the CE data may not be MCAR.
This study also estimated the relative nonresponse bias for total expenditures and for
13 expenditure categories. Table 2 shows the relative nonresponse bias estimates along
with their 95% confidence intervals for waves 2 and 5. In wave 2, estimates of relative
nonresponse bias for total expenditures [-0.14%, 95% CI: (-1.4%, 1.12%)] and 11 expenditure categories were not significantly different from zero. Two relative nonresponse bias
estimates that were significantly different from zero were Health expenditures [3.68%, 95%
CI: (1.80%, 5.56%)] and Reading materials expenditures [3.82%, 95% CI: (0.51%, 7.13%)].
Similar results were found for wave 5. It is worth noting that Health and Reading materials
expenditures represent only 6% and 0.3%, respectively, of total spending; thus, the impact
of any nonresponse bias from them is probably very small.
3.4

Pattern of Participation while in the Sample

The fourth study is based on the premise that nonrespondents are similar to respondents
who failed to complete the entire panel of interviews (Reyes-Morales, 2003; 2007). Attritors and intermittent respondents were classified as proxy nonrespondents, and then these
proxy nonrespondents were compared to respondents on socio-demographic variables and
expenditures.
The study was based on a single cohort of CUs who had their first interview in April-June
2005, their second interview in July-September 2005, and their last interview in April-June
2006. The cohort had 3,071 unique CUs out of which 2,468 were used in this study. The
CUs were then divided into three groups according to their pattern of participation in waves
2 through 56 : complete respondents (CUs who participated in the survey in all contiguous
waves of the survey period), attritors (CUs who participated in the first wave for which
they were eligible, and possibly completed the second and third waves [if eligible] but then
refused to participate in all subsequent waves for which they were eligible), and intermittent
respondents (CUs who participated in at least one but not all waves for which they were
eligible). These groups comprised 78.6%, 14.1%, and 7.3% of the cohort, respectively.
The following set of demographic characteristics were analyzed in this study: household
tenure (owner, renter), marital status, gender, respondent age, race, Hispanic origin, CU
size, educational attainment, region, and urbanicity (urban, rural). Missing demographic
information for proxy nonrespondents was imputed using a method similar to the ‘last observation carried forward’, where any missing values for a particular CU were imputed by
6 For any wave, only CUs who resided at addresses eligible for inclusion in the sample were considered
for the construction of the 3 analysis groups.

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copying the values recorded for that CU in a previous interview (Verbeke and Molenberghs,
2000). This assumes that the demographic characteristics do not change from one wave
to the next. Statistically significant differences (p < 0.05) were found between intermittent respondents and complete respondents with respect to age and Hispanic origin; while
attritors were found to differ from complete respondents only with respect to age.
For relative nonresponse bias computations, we combined attritors and intermittent respondents to form one group of proxy nonrespondents and averaged expenditures across
waves 2 through 5 for each expenditure category (Table 2). Estimates of relative nonresponse bias for total expenditures [-0.54%, 95% CI: (-2.31%, 1.24%)] and 10 expenditure
categories were not significantly different from zero. However, relative nonresponse bias
was significantly different from zero in three expenditure categories: Entertainment [3.46%,
95% CI: (0.35%, 6.57%)]; Personal insurance [3.82%, 95% CI: (1.72%, 5.93%)]; and, Transportation [-5.65%, 95% CI: (-9.11%, -2.19%)]. These categories represent 5.1%, 10.3%, and
19.1%, respectively.
4. Conclusions
All of the studies found that the data are not MCAR. Significantly different response
propensities were found for various demographic characteristics in the studies on subgroup
comparisons, respondent characteristics compared to the ACS, as well as the two proxy
nonrespondent studies. Because statistically significant differences were found in each of
these studies, we concluded that the data are not MCAR. Any characteristic for which a
statistically significant difference was observed suggests that the respondent sample disproportionately represents particular subgroups of the survey’s target population. Common
findings across the studies are summarized in Table 3 and indicate that blacks are underrepresented among the respondents while those age 65 and over tend to be overrepresented.
Both proxy nonrespondent studies found no evidence of relative nonresponse bias in
total expenditures. Between them, these studies found significant relative nonresponse bias
estimates in expenditures on health, reading materials, entertainment, personal insurance,
and transportation. With the exception of transportation and personal insurance, the other
expenditures comprised less than 10% of total expenditures. In addition, because each study
identified different categories to have a significant relative nonresponse bias and since some
bias could be expected to occur at random, we conclude that the expenditure estimates
derived from the CE are not subject to high levels of nonresponse bias.
No study by itself provides a definitive answer to the questions raised in this research.
Taken together, the four studies indicate that nonresponse bias is not a significant problem
for CE estimates, even though respondents and nonrespondents tend to be demographically
dissimilar and the data not missing at random. The findings contradict the commonly
held belief that if a survey’s missing data are not MCAR, then its estimates are subject
to nonresponse bias. From the nonresponse bias equation provided by OMB (2006), a
mean estimate’s nonresponse bias disappears if there is complete response or if the mean
expenditure is similar for respondents and nonrespondents. For the CE, the absence of
meaningful bias in total expenditures in spite of nonresponse suggests that the bias in an
underrepresented group (e.g., blacks) is offset by a similar bias in an overrepresented group
(e.g., the over-65 age group).
5. Acknowledgments
The views expressed in this paper are those of the authors and do not necessarily reflect the
policies of the U.S. Bureau of Labor Statistics. The authors would like to thank Karen Goldenberg and Dave Swanson for helpful discussions of nonresponse bias and earlier versions
of this paper.
REFERENCES
Groves, R. M. (2006). Nonresponse rates and nonresponse bias in household surveys. Public Opinion
Quarterly, 70, 646-675.

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Office of Management and Budget (OMB) (2006). Standards and guidelines for statistical surveys. Washington, D.C. Retrieved September 11, 2007 from www.whitehouse.gov/omb/inforeg/statpolicy/standards.pdf.
Reyes-Morales, S.E. (2003). Characteristics of complete and intermittent responders in Consumer Expenditure Quarterly Interview Survey. Internal BLS Report.
Reyes-Morales, S.E. (2007). Characteristics of complete and intermittent responders in Consumer Expenditure Quarterly Interview Survey: 2001-2006. Internal BLS Report.
SAS Institute Inc. (2004). SAS/STAT user’s guide, version 9.1. Cary, NC: SAS Institute Inc.
Verbeke, G. & Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data. New York: SpringerVerlag.
Wolter, K.M. (1985). Introduction to Variance Estimation. New York: Springer-Verlag.

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0.81
2.88
3.90
1.90
5.10
13.40
6.00
33.13
0.63
10.32
0.29
0.72
19.12

Relative
Bias (%)
-0.14
-0.96
0.96
2.09
-3.74
0.49
0.19
3.68
-0.28
0.32
-0.51
3.82
-0.27
-1.96

Table 2: Estimates of relative bias in the CE for expenditure categories using proxy nonrespondents
‘Harder-to-Contact’ respondents as proxy nonrespondents
Pattern of Participation
Wave 2
Wave 5
Across waves
Share of total
Expenditure Category
expenditures (%)
Lower
Upper Relative
Lower
Upper Relative
Lower
Upper
95% CI 95% CI Bias (%) 95% CI 95% CI Bias (%) 95% CI 95% CI
-1.40
-1.12
-0.10
-1.18
0.98
-0.54
-2.31
1.24
-3.74
-1.82
-2.82
-6.18
0.54
-2.37
-9.09
4.36
-3.48
5.40
0.37
-1.85
2.59
-0.01
-5.24
5.21
-2.60
6.78
0.73
-2.02
3.48
4.24
-0.98
9.46
-10.83
3.35
1.86
-6.08
9.80
-2.27
-11.81
7.28
-2.49
3.47
0.40
-2.43
3.23
3.46
0.35
6.57
-0.83
1.21
0.76
-0.06
1.58
0.09
-1.35
1.53
1.80
5.56
3.21
0.88
5.54
1.03
-2.76
4.82
-1.40
0.84
-0.89
-1.94
0.16
-0.56
-2.26
1.14
-2.24
2.88
0.59
-0.91
2.09
1.95
-0.74
4.65
-2.72
1.70
-0.68
-2.36
1.00
3.82
1.72
5.93
0.51
7.13
3.41
0.28
6.54
4.22
-1.16
9.60
-4.07
3.53
-1.51
-3.43
0.41
2.51
-1.79
6.81
-5.04
1.12
-0.53
3.59
2.53
-5.65
-9.11
-2.19
Total Expenditures
Alcoholic beverages
Apparel and services
Cash contributions
Education
Entertainment
Food
Health
Housing
Personal care
Personal insurance
Reading materials
Tobacco
Transportation

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Urbanicity

Census region

Marital status

Housing tenure

Education level

Race

Age

Gender

Characteristic

-

urban underrepresented

Midwest, South
overrepresented

-

renters overrepresented

-

-

-

-

Response Rate
Across Subgroups

2-4 person CUs
underrepresented

-

-

-

renters underrepresented

HS graduate
underrepresented

blacks underrepresented

55+ overrepresented

males underrepresented

Comparison to
ACS

2-, 4-person CUs
overrepresented

inconclusive

West overrepresented

not married
underrepresented

renters underrepresented

inconclusive

blacks underrepresented

55+ overrepresented

inconclusive

‘Harder-to-Contact’
as Nonrespondents

inconclusive

inconclusive

inconclusive

inconclusive

inconclusive

inconclusive

blacks underrepresented

65+ overrepresented

inconclusive

Pattern of
Participation

inconclusive

inconclusive

inconclusive

inconclusive

inconclusive

inconclusive

blacks underrepresented

55+ overrepresented

inconclusive

Conclusion

Table 3: Summary of significant differences in characteristics of respondents across studies

CU size

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