Underreporting of Purchases in the U.S. Consumer Expenditure Survey

Stephanie Eckman

Fellow

Survey Research Division

RTI International

Washington DC 20005

United States

seckman@rti.org

Acknowledgements: The research reported here was supported by an ASA-NSF-BLS 

Fellowship. The author thanks Laura Erhard, Parvati Krishnamurty, Adam Safir, Lucilla Tan, 

and Erica Yu for discussion on the ideas behind this research, help with data processing, and 

comments on draft versions of the paper. Ruben Bach, Ashley Amaya and Jill Dever also 

provided comments.

Forthcoming in Journal of Survey Statistics and Methodology

Abstract

Motivated misreporting occurs when respondents give incorrect responses to survey 

questions to shorten the interview; studies have detected this behavior across many modes, 

topics, and countries. This paper tests whether motivated misreporting affects responses in a 

large survey of household purchases, the U. S. Consumer Expenditure Interview Survey. The 

data from this survey inform the calculation of the official measure of inflation, among other 

uses. Using a parallel web survey and multiple imputation, this paper estimates the size of the 

misreporting effect without experimentally manipulating questions in the survey itself. Results 

suggest that household purchases are underreported by approximately 5 percentage points in 

three sections of the first wave of the survey. The approach used here, involving a web survey 

built to mimic the expenditure survey, could be applied in other large surveys where budget or 

logistical constraints prevent experimentation.

Statement of Significance

Household purchases may be underreported in the first wave of the U. S. Consumer 

Expenditure Interview Survey. The approach used here, involving a web survey built to mimic 

the expenditure survey, could be applied in other large surveys where budget or logistical 

constraints prevent experimentation.
1 Introduction

Researchers are increasingly aware of the shortcuts that respondents take to make surveys 

less burdensome: when the structure of the questions allows respondents to learn which 

responses trigger additional questions, they can avoid giving those responses. This phenomenon, 

called motivated misreporting, has been detected in surveys across several modes, countries, and 

topics, suggesting it is a wide-spread phenomenon (Duan et al. 2007; Kreuter et al. 2011; 

Eckman et al. 2014; Tourangeau et al. 2015). In previous studies of motivated misreporting, the 

most vulnerable questions concern clothing purchases or other routine household purchases 

(Kreuter et al. 2011; Eckman et al. 2014; Bach and Eckman, 2018). The Consumer Expenditure 

Interview Survey (CE) asks hundreds of such questions. The collected data are used in the 

calculation of the Consumer Price Index (CPI) and other important economic analyses. The 

survey’s reliance on filter questions has led researchers to worry about underreporting of 

purchases in the CE (Bosley et al. 1999; Shields and To 2005; Yan and Copeland 2010; McBride 

2013; Clark-Fobia et al. 2018). The National Research Council (2013, pp. 84-85) mentioned the 

risk of motivated misreporting in its review of the CE:

It seems likely that respondents learn quickly...that the interview will last longer if 

they answer “yes” to these [filter] questions.... Fifty percent of field 

representatives said [this] happened frequently or very frequently.

This study investigates the amount of the measurement error introduced by motivated 

misreporting in the first wave of the CE. Using a web survey which experimentally varied 

question order, and data from the CE itself, the study imputes the responses that would be 

obtained in a hypothetical version of the CE. The results in this paper will be of interest to users 

of CE data and to many other surveys that use filter questions. In addition, the approach taken in 

this study could be applied to other large ongoing surveys that cannot launch full-scale 

experiments of alternative methods but nonetheless want to estimate and understand 

measurement error in their current questionnaire.

2 Relevant Literature

This study builds on the literature on motivated misreporting. Because experimentation in 

the CE was not possible, the study relies on multiple imputation to estimate the hypothetical 

responses in a different version of the CE instrument. The two subsections below summarize the 

relevant research on motivated misreporting and multiple imputation.

Motivated Misreporting

The literature on motivated misreporting demonstrates that some respondents will give 

incorrect answers in surveys to reduce the length or burden of the interview. Motivated 

misreporting occurs in three types of questions: filter, looping, and screening questions 

(Tourangeau et al. 2015). Both filter and looping questions are present in the CE, although this 

study focuses on filter questions.
Filter questions can be asked in two formats: grouped and interleafed. The interleafed 

format asks the follow-ups after each filter. The grouped format asks all filter questions at the 

start of the section and then asks all relevant follow-up items. Although the questions asked in 

each format are the same, the order is different, which affects the experience of the respondent. 

The interleafed format allows a respondent to learn the consequences of a “yes” answer and 

adjust her reporting to reduce the burden of the survey. The grouped format collects all responses 

to the filter questions before the respondent realizes that the follow-up questions are coming. 

Numerous experimental studies have found that filters in the grouped format collect more “yes” 

responses than those in the interleafed format (see for example: Kreuter et al. 2011, Eckman et 

al. 2014, Eckman and Kreuter 2018, Bach et al. 2019). These studies suggest that respondents 

underreport in the interleafed format to reduce the burden and length of the survey, and 

comparison of filter responses to administrative records supports this explanation (Eckman et al. 

2014).

Another way to order the filter and follow-up questions would be to ask all filters (in all 

sections) first and then all the follow ups: the grouped-overall format. Previous research, 

associated with the study behind Eckman et al. (2014) but not reported there, suggested that the 

grouped-overall format is quite awkward for both interviewers and respondents. It requires 

respondents to first think about vacations, then about clothing, then about furniture, and later to 

return to each topic to answer the follow up questions: “thinking back to the vacation that you 

said a household member took in the last three months...” This format is seldom used in surveys.

Looping questions are similar to filter questions. They ask a series of follow-up questions 

about each event a respondent has experienced: degrees, jobs, purchases. These questions can 

also be asked in two formats. In the how-many format, the respondent first reports how many 

events she has experienced and then answers the follow-up questions about each one. This 

format is similar to the grouped format: the respondent does not realize that the follow-up 

questions are coming before reporting the number of events. In the go-again format, the 

respondent answers the follow-up questions about one event and then is asked if he has another 

event of that type to report. The go-again format is similar to the interleafed format, because the 

respondent experiences the follow-up questions before deciding to report another event. The 

how-many format collects more event reports than the go-again format (Eckman and Kreuter 

2018).

Motivated misreporting has been detected across several topics, from mental health 

(Duan et al. 2007; Kessler et al. 1998) to employment (Eckman et al. 2014) and in several 

countries (Kreuter et al. 2019). The effect also exists in all tested modes. In a small face-to-face 

study (n = 304) in Maryland, Bach et al. (2019) found underreporting by 3.3 percentage points 

(t = 1.84;p = 0.066) in the interleafed format. A U.S. web survey found a larger format effect, 

11.4 percentage points (p < 0.001; n = 1,215; Kreuter et al. (2019)).

The CE asks filter questions in the interleafed format in many sections, leading to the 

concern that purchases are underreported. Previous research has explored motivated misreporting 

in filter questions in the CE. Bosley et al. (1999) found no evidence of motivated misreporting, 

although the study involved only 24 participants and looked at responses in the second wave. 

McBride (2013) investigated whether reports of purchases decreased over the length of the CE 
interview detecting some evidence for this trend. In cognitive interviews using CE items, 

respondents preferred the interleafed condition because it allowed them to think about one item 

at a time, rather than jumping between items as in the grouped format (Clark-Fobia et al. 2018). 

Other studies have investigated underreporting of purchases in later waves of the CE, finding 

little evidence that data quality worsens over waves (Shields and To 2005; Yan and Copeland 

2010; Bach and Eckman 2019). However, none of these studies provide strong evidence of 

motivated misreporting in the first wave of CE, a gap in the literature that this paper addresses.

Thus, there is a contradiction in the literature: studies robustly find motivated misreporting in 

many surveys, yet the phenomenon has not been conclusively demonstrated in the CE, a long 

survey which uses many filter questions in the interleafed format. 

Multiple Imputation

To estimate motivated misreporting in the CE, this study imputes the responses that CE 

respondents would give if the filter and follow-up questions were asked in the grouped format. 

Imputation is most often used to fill in item missing data in surveys. For example, respondents 

may skip or refuse a question about their income. To impute these missing values, researchers 

might use regression imputation, which involves building a model to predict income from the 

other variables in the survey. On the cases where income is not missing, income is modeled as a 

function of the available characteristics (for example, age, home ownership, and marital status). 

The model can then predict income for the cases where it is missing. Other imputation methods, 

such as hot deck, are also possible.

The concern with all methods of single imputation is that analysis of the imputed data set 

does not account for the uncertainty in the imputed values. To correctly account for this 

uncertainty, researchers use multiple imputation, filling in several values for each missing 

response. The values might be multiple predictions from one model or predictions from several 

models. The result is multiple complete data sets. The final analyses then account for the 

uncertainty in the imputed values by capturing the variation across the data sets (Rubin 1987).

More recently, researchers have expanded the use of multiple imputation beyond item 

missing data. The cross-survey imputation of Rendall et al. (2013) involves collecting all 

variables of interest in one survey (the “impute-from” survey) and a subset of those variables in 

the other survey (the “impute-to” survey), which is generally larger or higher quality. In the 

paper’s application, shown in Table 1a, the background variables (X1) and the outcome variable, 

Y, were observed (shown with “O”) in both surveys. However, one crucial explanatory variable, 

X2 was observed in only the impute-from survey. The authors imputed X2 in the impute-to survey 

(shown with “I”) and used the multiply-imputed data in analysis. An important condition of this 

approach is that all variables of interest are collected in one survey: the variables are jointly 

observed.

Other researchers have taken these ideas further and relaxed the jointly-observed 

requirement. Several studies have used multiple imputation to predict how respondents would 

have responded in an alternative mode (Powers et al. 2005; Christensen et al. 2006; Peytchev 

2012; Kolenikov and Kennedy 2014; Park et al. 2016). The approach is shown in Table 1b: 

respondents in Source 1 responded in Mode A (YmodeA) and those in Source 2 responded in Mode 
B (YmodeB). The hypothetical responses of Source 2 respondents in Mode A were filled in via 

multiple imputation. The goal of these studies is to remove the mode effect when combining 

responses from the two sources. Importantly, in most of these studies, no cases respond in both 

modes; responses in the two modes are not jointly observed.

Two recent papers used a nonprobability survey to impute a substantive variable missing 

from a probability data set (Kim et al. 2020; Chen et al. 2020). Researchers collected background 

variables (X) and the outcome of interest (Y) with a nonprobability web survey and then imputed 

Y on the probability survey: see Table 1c. In these studies, the X and Y variables were jointly 

observed.

The approach in this paper combines elements from the mixed-mode approach (Table 1b) 

and the nonprobability approach (Table 1c). Section 3 gives details of the nonprobability web 

survey and the CE, and Section 4 describes the imputation approach in detail.

Table 1: Three Uses of Imputation

Data Source X1 X2 Y

Impute-to Survey O I O

Impute-from Survey O O O

(a) Rendall et al. Approach

Data Source X YmodeA YmodeB

Source 1 O O

Source 2 O I O

(b) Mixed-Mode Approach

Data Source X Y

Probability O I

Nonprobability O O

(c) Nonprobability Approach

X = background variables; Y = variable of interest

O = observed data; I = imputed data
3 Data

Data from a web survey designed to mimic portions of the CE support the imputation of 

counterfactual responses in the CE: how CE respondents would have answered filter questions 

about purchases if they were asked in the grouped rather than the interleafed format. The two 

subsections below describe the web and CE data sets used in the imputation.

Web Survey

The web survey was conducted September 27–October 9, 2019, with members of the 

Lightspeed opt-in panel; 2,198 completed the survey. The median response time was 10.7 

minutes (mean 13.7). The panel did not report the number of cases invited to the survey, so no 

response rate or participation rate is available. The web survey’s questionnaire consisted of six 

sections and was modeled after the CE questionnaire. It contained three sections of background 

questions: Section 1 asked about demographics, Section 2 about housing unit characteristics, and 

Section 6 about household income. See the Open Science Framework (https://osf.io/a5vpe/) for 

question wording. These variables are strongly correlated with purchases and thus are needed for 

the imputation models described below. The order of these sections matched the order in which 

they are asked in the CE and did not vary across respondents.

Sections 3, 4, and 5 of the questionnaire contained questions from three purchase sections 

of the CE: utilities, clothing, and non-health insurances. The 16 filter questions in these sections 

asked about recent household purchases of (or payments for) items such as electricity, shoes, and 

life insurance. Each filter question in these sections, if answered with a “yes,” triggered followup questions. In the utilities section, the follow-ups asked about the amount paid, the billing 

period, and whether any portion was a deductible business expense. In the clothing section, the 

follow-ups asked about the cost, the month of the purchase, and for whom the purchase was 

made. In the insurance section, the follow-ups again asked for the amount, the frequency, and 

whether any portion of the premiums was paid by the household. The wording of all questions is 

available at the link in the previous paragraph. Table 2 shows the number of filters and followups in these three sections. These sections were chosen in consultation with CE staff to reflect 

the diversity of topics included in the CE and because they do not depend on answers in other 

sections. Questions based on the clothing section have been used in several previous studies 

(Kreuter et al. 2011; Eckman et al. 2014).

Table 2: Number and Characteristics of Questions in Filter Question Sections, by Section

Section # Filters # Follow-Upsa Go-Again Loop

Utilities 5 4 No

Clothing 6 5 Yes

Insurance 5 5 Yes

a per filter question

The web survey contained two manipulations. The first randomly assigned respondents to 

receive the filters in the interleafed format (51% of respondents) or the grouped format (49% of 
respondents). The grouped format was grouped within each section: respondents answered all 

filters and follow-ups in one section before moving on to the next. Because of this awkwardness

of the grouped-overall format, it was not used in this study. If the grouped-overall format collects 

more reports of purchases than even the grouped (within-section) format, and these additional 

purchases are correct, then the version of the grouped format implemented in this study may 

underestimate underreporting in the CE. The second manipulation randomized the order of the 

three purchase sections. Between 16% and 17% of respondents answered the sections in each of 

the six possible orderings. Both randomizations, format and section order, were successful. The 

mean household size does not differ significantly between the two formats (F(1,3129) = 28.36;p 

< 0.001). The distribution of 21 of the 22 categorical variables shown in Table 4 also did not 

differ at the 5% level of significance between the formats or the section orders. Only household 

receipt of self-employment income showed significant deviation between the two formats (χ

2

(2) 

= 7.97; p = 0.019), which is not unexpected with multiple tests of significance.

In the clothing and insurance sections, the CE uses a go-again loop to collect information 

about additional purchases of a given item. The web survey included go-again loops in these 

sections as well (Table 2). However, although the CE allows respondents to report many 

purchases of each item, the web survey was limited to only two purchases, to limit the 

complexity of the web survey programming. In preparing the data for analysis, all purchases after 

the first for each item in both the CE and web data were discarded. That is, if the respondent 

reported having two life insurance policies, the filter for that item is still coded as “yes” and not 

two.

Throughout the questionnaire, explicit don’t know and prefer not to say responses were 

available. In the CE, these response options are not explicitly offered, but respondents can tell the 

interviewer they do not know an answer or do not wish to answer a question. In the web mode, 

this approach of allowing such responses without making the options explicit does not work. 

Even when explicit response options are offered, online panel participants tend to answer all 

questions (Hillygus et al. 2014; Kaplan and Edgar 2018). To try to make the web survey 

participants’ behavior similar to the CE participants’, the survey included explicit don’t know and 

refused options on most questions. The survey also displayed text at the beginning calling 

respondents’ attention to these options, following Kaplan and Edgar (2018). Web respondents 

could also simply skip past most questions without answering. Across the 35,168 filters (2,198 

respondents ×16 items), 3.9% of responses were “don’t know” responses and 1.3% were “prefer 

not to say.” In addition, 0.53% of filters were simply skipped. To match how the CE works 

(described below), all filter responses other than “yes” were recoded to “no” for analysis.

Consumer Expenditure Interview Survey

The CE is conducted every month in the United States by Census Bureau interviewers. 

Selected housing units remain in the sample for four waves, but only data from the first wave are 

used in this study, because the mechanism of response is likely different in later waves when 

respondents know that each reported purchase leads to follow-ups (see Bach and Eckman 2019, 

for a discussion of motivated misreporting in later waves of the CE). During the interview, a 

household informant reports on purchases by all household members in the previous 3 months. 
The instrument contains 23 sections. Several collect background information about the household 

and its members. The majority ask about purchases using filter and looping questions. There are 

sections on spending on trips and vacations, appliances, home furnishings, vehicle expenses, and 

more. The Bureau of Labor Statistics prefers that the survey be administered in person, but 

respondents can choose to do a telephone interview. About 75% of first wave interviews are 

conducted in person. In 2018, the median length in the first wave was 75 minutes (Hubener et al. 

2019).

To match the web survey as closely as possible, the analysis uses data from September 

and October 2019. In these months, 932 respondents completed the first wave of the survey, 55% 

of all eligible cases. (The CE does not calculate response rates for each month and wave.) The 

data used in this study are available to researchers outside of the Bureau of Labor Statistics only 

via the onsite visiting researcher program. The data do not include any imputations or editing.

In the CE, interviewers can administer the sections in any order but usually stick to the 

default order. Data about the order of administration are captured only in the instrument trace 

files, which were not available for this study. The imputation models discussed below assume 

that all CE respondents received the six sections used in the web surveys in the default order: 

demographics, housing unit characteristics, utilities, clothing, non-health insurance, income.

The filter questions in the CE are asked in the interleafed format, but in an unusual way 

that the self-administered web survey was not entirely able to replicate. For example, during the 

insurance section, interviewers read a list of the insurance types of interest: life, homeowner’s, 

renter’s, car, and other. The respondent should mention which of the insurance types she has. For 

each type reported, the follow-up questions are asked. If the respondent does not mention a given 

item, such as renter’s insurance, then that item simply does not appear in the data set for that 

respondent. That is, “no” responses to the filter questions are not recorded in the CE data. To 

make the CE match the web survey, “no” responses were filled in for items that were missing in 

the raw data. With this edit and the recoding of missing responses to filter question in the web 

survey to “no,” the two surveys should be aligned. Thirty-one cases (3.33%) reported no 

purchases in the 16 items used in this study, which is a close match for a same percentage in the 

web survey (3.37%).

If the household purchased more than one of a given item, the respondent first answers 

the follow-up questions about one purchase and then can indicate additional purchases and 

answer follow-ups about each one. As mentioned above, each item was coded as purchased (1) 

or not (0), even if a respondent reported more than one purchase of a given item. In the CE, 

respondents reported two or more purchases to 5.9% of the clothing items and 2.7% of the 

insurance items. In the web, these percentages were 10.2% and 7.0%. These results are in line 

with generally higher reporting in these two sections by the web respondents, as shown in 

Section 5. Collapsing multiple purchases makes the analysis in this paper similar to other studies 

of motivated misreporting.

4 Methods

The ideal design to test for motivated misreporting in the CE would randomly assign 

respondents to the interleafed or grouped formats, while holding constant other study 
characteristics. The difference in the number of reported purchases between the formats would be 

the measure of motivated misreporting. Although this approach has worked well in earlier 

studies, experimentation is not feasible in the CE because of budget constraints and the 

importance of the CE data. However, the importance of the CE also means that it is crucial to 

know whether motivated misreporting is taking place.

Instead, this study uses multiple imputation to estimate the extent of motivated 

misreporting in Wave 1 of the CE. Table 3 illustrates the approach. The CE is conducted in the 

interleafed format and collected background variables (X) as well as purchase data (Y interleafed). 

The web survey collected the same background variables and asked the purchase questions in 

both formats. However, no cases responded in both the interleafed and grouped format: the 

variables X, Y interleafed, and Y grouped are never jointly observed. The web survey did not administer 

the questions in both formats to the same respondents because those answering the purchase 

questions twice would likely respond differently the second time or even break off. Just as in the 

multimode imputation studies discussed in Section 4, joint observation of the Y

interleafed and 

Y

grouped is not possible. Responses by the CE respondents to the filter questions in the grouped 

format are imputed from the observed cells.

Table 3: Design for Imputation of CE Responses in Grouped Format

Data Source X Y

interleafed Ygrouped

Consumer Expenditure O O I

Web Survey O O

O O

O = observed data; I = imputed data

Twelve imputation models are used to impute the responses in the grouped format, 

marked “I” in Table 3. Each model predicts multiple responses (yes or no) to the filter questions 

about household purchases. The following subsections compare the responses of the CE and web 

respondents, describe the imputation models, and detail the analysis approach.

Comparison of CE and Web Survey Respondents

There are many differences between the web and CE surveys. The CE is an intervieweradministered survey: interviewers can provide motivation to complete the interview and to 

provide higher quality answers. The CE contains many more sections and items than the web 

survey. The CE respondents are recruited from a probability sample of the U.S. household 

population; the web respondents are members of the Lightspeed panel who take surveys in 

exchange for payment. The extent to which the models can accurately predict the responses of 

CE respondents in the grouped format depends on how similar the respondents to the two 

surveys are. If the web respondents are very unlike the CE respondents, in ways that influence 

purchasing behavior, then the web survey data cannot be used to impute the purchases of the CE 

respondents.

About half of the length of the web survey was devoted to collecting background 

information about each case. The variables fall into three categories: demographics, housing unit 
characteristics, and household income. The full list of background variables is given in Table 4. 

These variables are the predictors in the imputation models. Although there may be additional 

variables that would also be related to household purchases, the imputation models can only use 

variables collected in the CE.

Table 4 compares the CE and web survey respondents on the background variables. 

Missing responses (don’t know, refused, and simply skipped) are combined and shown as a 

category. (The seven “HU has” variables are exceptions: each has only two response categories: 

“yes” and “no”: missing responses in the CE are not permitted. To match this behavior, all 

missing responses to these questions in the web survey were recoded as “no.”) Statistical 

comparisons between the two surveys require an assumption about the selection process in the 

nonprobability web survey. Following guidance from the American Association for Public 

Opinion Research (AAPOR 2016), the comparisons in Table 4 assume that the web respondents 

are a simple random sample from the Lightspeed panel; no weights, clustering, or stratification 

are used in the calculation of standard errors. Seventeen of the 23 variables show significant 

differences, after Bonferroni correction for multiple testing and adjustment for the geographic 

clustering of the CE cases. However, there is no concern about overlap: the characteristics of the 

CE respondents are well represented among the web respondents, indicating that the weak 

version of the overlap (or common support) assumption needed for the approach in this paper is 

met (Cunningham 2021, Section 5.1.4). To formally test this assumption, the propensity to be in 

the CE data set versus the web data set was predicted from the variables shown in Table 4 using 

a logistic model (Cunningham 2021, Section 5.4). The predicted propensities demonstrate that 

there is sufficient overlap between the two data sets: propensities range from 0.000148 to 0.979 

in the web data set and from 0.0460 to 0.996 in the CE data set.

Imputation models can control for differences between the web and CE respondents in

the variables in Table 4. More concerning are the differences that exist after controlling for these 

variables. The imputation approach described below rests on the assumption that there are no 

relevant differences between the CE and web survey respondents after adjusting for these 

characteristics. This assumption, called the conditional independence or unconfoundedness 

assumption in the causal inference literature, is common yet fundamentally untestable (Angrist 

and Pischke 2009, Section 3.2.1; and Wooldridge 2010, Section 21.3).
Table 4: Comparison of Demographics of CE and Web Respondents

Mean/Proportion (SE) Prob. of F 

Testa

Variable Category CE Web

HH members NAb2.43 (0.0084) 2.73 (0.0075) < 0.0001

HU has pool No 0.95 (0.0081) 0.80 (0.0085) < 0.0001

Yes 0.053 (0.0081) 0.20 (0.0085)

HU has offstreet parkingNo 0.52 (0.020) 0.33 (0.010) < 0.0001

Yes 0.48 (0.020) 0.67 (0.010)

HU has porch No 0.47 (0.018) 0.21 (0.0087) < 0.0001

Yes 0.53 (0.018) 0.79 (0.0087)

HU has 

apartment

No 0.99 (0.0028) 0.90 (0.0064) < 0.0001

Yes 0.01 (0.0028) 0.10 (0.0064)

HU has central 

air

No 0.57 (0.022) 0.30 (0.0098) < 0.0001

Yes 0.43 (0.022) 0.70 (0.0098)

HU has 

window air

No 0.88 (0.014) 0.69 (0.0099) < 0.0001

Yes 0.12 (0.014) 0.31 (0.0099)

HU has solar 

panels

No 0.98 (0.0050) 0.93 (0.0053) < 0.0001

Yes 0.018 (0.0050) 0.065 (0.0053)

HU single 

family

No 0.36 (0.018) 0.37 (0.010) 0.0007

Yes 0.64 (0.018) 0.61 (0.010)

Missing 0 (NA) 0.016 (0.0027)

No. bedrooms 1 0.12 (0.011) 0.096 (0.0063) 0.001

2 0.25 (0.016) 0.24 (0.0091)

3 0.39 (0.016) 0.40 (0.011)

4 0.17 (0.012) 0.18 (0.0082)

5+ 0.057 (0.0087) 0.053 (0.0048)

Missing 0.0054 (0.0023) 0.029 (0.0036)
No. bathrooms 1 0.44 (0.020) 0.39 (0.010) < 0.0001

2 0.43 (0.020) 0.43 (0.010)

3+ 0.12 (0.012) 0.14 (0.0074)

Missing 0.0043 (0.0021) 0.037 (0.004)

R owns home No 0.37 (0.016) 0.44 (0.011) < 0.0001

Yes 0.63 (0.016) 0.54 (0.011)

Missing 0 (NA) 0.023 (0.0032)

R age 18-34 0.12 (0.012) 0.51 (0.011) < 0.0001

35-49 0.22 (0.013) 0.16 (0.0079)

50-64 0.24 (0.015) 0.16 (0.0077)

65+ 0.38 (0.015) 0.15 (0.0076)

Missing 0.032 (0.0061) 0.20 (0.003)

R White No 0.22 (0.021) 0.19 (0.0083) 0.15

Yes 0.77 (0.022) 0.80 (0.0086)

Missing 0.010 (0.0034) 0.017 (0.0028)

R Black No 0.89 (0.012) 0.85 (0.0077) 0.024

Yes 0.10 (0.012) 0.14 (0.0073)

Missing 0.010 (0.0034) 0.017 (0.0028)

R Asian No 0.93 (0.016) 0.94 (0.0051) 0.24

Yes 0.059 (0.016) 0.044 (0.0044)

Missing 0.010 (0.0034) 0.017 (0.0028)

R Hispanic No 0.88 (0.016) 0.90 (0.0063) 0.22

Yes 0.11 (0.015) 0.085 (0.0059)

Missing 0.011 (0.0035) 0.011 (0.0022)

R married No 0.50 (0.018) 0.52 (0.011) 0.037

Yes 0.50 (0.018) 0.47 (0.011)

Missing 0.0043 (0.0026) 0.015 (0.0026)

R never 

married No 0.79 (0.015) 0.58 (0.011) < 0.0001

Yes 0.20 (0.014) 0.41 (0.011)

Missing 0.0043 (0.0026) 0.015 (0.0026)

R education No HS degree 0.085 (0.0012) 0.043 (0.0043) < 0.0001

HS degree 0.24 (0.015) 0.21 (0.0087)
Some college 0.22 (0.013) 0.21 (0.0087)

Associate’s 

degree 0.11 (0.0010) 0.013 (0.0071)

Bachelor’s 

degree

0.21 (0.015) 0.27 (0.0095)

Master’s or 

higher 0.12 (0.011) 0.13 (0.0071)

Missing 0.17 (0.0045) 0.0091 (0.002)

HH wage 

income No 0.30 (0.015) 0.30 (0.0097) 0.0009

Yes 0.67 (0.016) 0.63 (0.0103)

Missing 0.027 (0.0085) 0.073 (0.0056)

HH has selfemployment

income

No 0.87 (0.013) 0.81 (0.0083) 0.0104

Yes 0.10 (0.011) 0.14 (0.0073)

Missing 0.027 (0.0085) 0.049 (0.0046)

HH income < $30k 0.37 (0.018) 0.17 (0.0081) < 0.0001

$30k-$50k 0.086 (0.0087) 0.13 (0.0072)

$50k-$70k 0.058 (0.0073) 0.098 (0.0063)

$70k-$90k 0.083 (0.0090) 0.085 (0.0060)

$90k-$120k 0.066 (0.0081) 0.067 (0.0053)

≥ $120k 0.17 (0.012) 0.10 (0.0065)

Missing 0.17 (0.016) 0.34 (0.0010)

a F statistic for test of hypothesis that means/proportions not equal 

b Continuous variable; all others categorical

F tests control for geographic clustering of CE cases
The household income variable was collected slightly differently in the two surveys. The 

CE collects income at the household member level. It first asks for the amount earned by each 

member. If the respondent does not give an answer, it asks for income in ranges: less than 

$5,000; [$5,000, $10,000); [$10,000, $15,000); [$15,000, $20,000); [$20,000, $30,000); 

[$30,000, $40,000); [$40,000, $50,000); [$50,000, $70,000); [$70,000, $90,000); [$90,000, 

$120,000); $120,000 and greater. The web survey used a different approach. Income is among 

the most sensitive questions asked in surveys (Tourangeau and Yan 2007). Without the 

motivation provided by an interviewer and the backing of an official government survey, the web 

survey was unlikely to be able to collect income for each household member. For these reasons, 

the web survey asked for household income in ranges (the same ranges given above). To make 

the income data collected in the two surveys comparable, the CE income data were aggregated to 

the household level. For those households where amounts were reported for each member (68% 

of households), household income is the sum of the reported amounts. For those households 

where ranges were reported for all members (5.9% of households), the minimum and maximum 

income was calculated for each member from the reported range. These two numbers were 

summed across all household members to capture the minimum and maximum possible 

household income. The household income was set to the mean of these two numbers. For those 

households where a mix of ranges and amounts were reported (8.8% of households), income for 

those members reported in ranges was set to the midpoint of the range and income was then 

summed across all household members. For the remaining CE households (17.1%), income was 

set to missing. For all three types of households, the resulting household income was then 

collapsed into larger ranges. The web survey respondents were more likely not to answer the 

income question (Table 4). The wage income and self-employment income indicators were also 

asked at the person level in the CE and at the household level in the web survey. When 

aggregating the CE data to the household level, a household was marked as having wage income 

(or self-employment) income if any member was reported to have that income type. These 

indicators differ significantly in the two sets of respondents but not meaningfully.

Figure 1 compares the percentage of CE respondents who answered with “yes” to each 

item’s filter question with the percentage among web respondents in the interleafed format. 

Thirteen of the 16 items show significantly different purchase rates (with Bonferroni correction 

and clustering adjustment). However, the correlation between the percentages is 0.93, indicating 

that the reported purchase rates are similar. Web respondents are more likely to be insured and 

less likely to have expenses for water and sewage and garbage and recycling. Although there are 

differences between the two groups of respondents, the broad overlap between them supports the 

imputation approach used below.
Figure 1: Comparison of Web and CE Respondents on Reported Purchases

NOTE: Only web survey respondents in interleafed format included
Imputation Models

The other factor influencing the accuracy of the imputed values is how well the models 

explain purchases of the 16 items. Twelve logistic imputation models were fit at the case-item 

level on all data from the CE and web surveys. In each model, the dependent variable is the filter 

response, “yes” or “no.” The independent variables in the models are the format (grouped or 

interleafed), the survey (CE or web), the item (1 through 16), the order of the sections (1 through 

6; fixed for CE respondents), and the background variables shown in Table 4. Unfortunately, no 

information about the CE interviewers was available for inclusion in the models. The models do 

not account for the clustering of observations into primary sampling units in the CE or into 

respondents in the web survey. However, analysis of the imputed data does, as discussed in the 

next subsection.

Table 5 shows the interactions included in each model. Together these models cover all 

interactions likely to affect purchases. The full set of all interactions could not be fit in one 

model, because of sparse cells, so the models differ in the interactions they include. In each 

model in the table, all variables indicated with an “a” in a given column were interacted with 

each variable with a “b” in that column. When interactions were included in a model, main 

effects were also included. Variables indicated with an “x” were included without any 

interactions. Model 1 interacts the grouped (versus interleafed) indicator with each of the 

background variables to capture how respondent and household characteristics impact the 

difference between the two formats. Model 2 interacts the survey indicator (CE versus web) with 

the background variables, because the demographic makeup of the two surveys differs (Table 4). 

Model 3 contains no interactions. Model 4 interacts the grouped (versus interleafed) indicator 

with the item indicator, because the two formats may behave differently with some items. Model 

5 includes the interaction of the survey indicator and the item, because the mode effect 

(interpreted broadly to include representation and measurement differences) may differ by item. 

And Model 6 interacts the item indicator with each of the background variables. Models 7–12 are 

identical to Models 1–6 but exclude household income because of the challenges in constructing 

comparable household income measures. As indicated in Table 5, all models include main effects 

for all variables. Table 6 shows that the models fit the data reasonably and about equally well. 

The best fitting model is Model 5, according to both the AIC and BIC measures.
Table 5: Specification of Logistic Imputation Models

Variable Model

1 2 3 4 5 6 7 8 9 10 11 12

Grouped (vs. Interleafed) a x x a x x a x x a x x

CE (vs. Web) x a x x a x x a x x a x

Item (1-16) x x x b b a x x x b b a

Section Order x x x x x x x x x x x x

HH members* b b x x x b b b x x x b

HU has pool b b x x x b b b x x x b

HU has off-street parking b b x x x b b b x x x b

HU has apartment b b x x x b b b x x x b

HU has central air b b x x x b b b x x x b

HU has window air b b x x x b b b x x x b

HU has solar panels b b x x x b b b x x x b

HU single family b b x x x b b b x x x b

HU bedrooms b b x x x b b b x x x b

HU bathrooms b b x x x b b b x x x b

HH has wage income b b x x x b b b x x x b

HH has self-employment income b b x x x b b b x x x b

HH income b b x x x b

R owns home b b x x x b b b x x x b

R age b b x x x b b b x x x b

R white b b x x x b b b x x x b

R African-American b b x x x b b b x x x b

R Asian b b x x x b b b x x x b

R married b b x x x b b b x x x b

R never married b b x x x b b b x x x b

R Hispanic b b x x x b b b x x x b

R education b b x x x b b b x x x b

NOTE: Case base for each model is 50,080 filter questions. “x” indicates variables included 

without any interactions. In each column, every variable shown with “a” is interacted with every 

variable shown with “b.”

* Continuous variable; all others categorical
Table 6: Measures of Fit of Imputation Models

Fit Measure

Model

1 2 3 4 5 6 7 8 9 10 11 12

AUC 0.798 0.798 0.796 0.798 0.801 0.798 0.797 0.797 0.795 0.8 0.801 .08

AIC 52446.6 52428.8 52569.7 52320.6 51991.7 52365.5 52518.5 52495.4 52631.3 52381.1 52052.1 52482.3

BIC 53434.6 53390.3 53151.9 53035.1 52706.2 53212.4 53400.7 53351.1 53160.6 53042.7 52713.1 53222.2

n 50080 50080 50080 50080 50080 50080 50080 50080 50080 50080 50080 50080

AUC = Area Under Receiver Operating Curve

AIC = Akaike’s information criterion

BIC = Bayesian information criterion
Figure 2: Comparison of Predicted Probabilities (0-100) from Imputation Models

NOTE: Only predictions for CE case-items in the grouped format shown (n=14,912 in each 

subplot)
The scatterplot matrix in Figure 2 compares the predicted probabilities from each model 

for the CE cases in the grouped format. The probabilities estimate how likely each case is to 

purchase each item. The horizontal axis of every subplot ranges from 0 to 100. The main 

diagonal of the matrix shows the density of the predicted probabilities from each model in a 

kernel density plot. The vertical axis of the subplots below the diagonal also ranges from 0 to 

100. In the subplots below the diagonal, the wider the distribution of points, the more those two 

models disagree about the probability that a given case would report a purchase of a given item 

in the (hypothetical) grouped format. The pairwise correlations between the models’ predication 

are all greater than 95%. The smallest correlation is between models 2 and 11.

Estimation of Motivated Misreporting Effect

Twenty responses to each filter question were imputed from each model representing how 

CE respondents would respond in the grouped format. The main outcome of interest is the 

motivated misreporting effect in the CE (MM), which is the difference between the percentage of 

filters answered with “yes” in the observed interleafed format p

interleafed and the percentage of 

filters answered with “yes” in the imputed grouped format p

grouped:

MMm = p

interleafed − pm

grouped

 (1)

The m subscript refers to the imputation model. Each model gives a different estimate of p

grouped 

and a different motivated misreporting effect. The standard error on p

grouped

m and on MMm should 

account for the uncertainty in the imputations. If the format effect in Wave 1 of the CE is similar 

to that observed in previous studies, MMm will be negative, indicating underreporting in the 

interleafed format. Using a specification curve (Simonsohn et al. 2019), the results section 

compares the estimates of MMm across the 12 imputation models to understand how robust they 

are to model specification. Using 12 models, which vary in their predictions, and making 

multiple imputations from each one, captures the uncertainty both within and between models. 

The results section reports estimates from an analysis that combines the imputations from all 

models (240 imputations in total) to produce a thirteenth estimate of MM.

All models and analyses were run in Stata 15.1 (StataCorp LP 2017) and are unweighted. 

Analyses of the imputed data account for the clustering of the case-item observations within 

primary sampling units in the CE and within respondents in the web survey.

5 Results

The outcome of interest is the percent of filters answered with “yes” in the interleafed 

format minus the percent answered with “yes” in the grouped format (Equation 1). In the web 

survey, the grouped format collects more “yes” responses to the filter questions than the 

interleafed format does. Purchases are underreported by 6.1 percentage points in the interleafed 

format relative to the grouped format, across all sections and items (standard error 0.80; see the 

left side of Table 7). The motivated misreporting effect occurs in each of the three sections and 

varies from 9.4 percentage points in the clothing section to 3.0 percentage points in the insurance 

section. These results regarding the motivated misreporting effect are as expected from previous 

research (Kreuter et al. 2011; Eckman et al. 2014; Tourangeau et al. 2015; Bach and Eckman 
2018). The order of the section also significantly impacted the probability of responding “yes” to 

the filter questions. The second and third sections garnered 3.9% and 5.5% fewer “yes” 

responses than the first section (all differences significant at 5% level). Because the order of the 

section was randomized in the web survey, these are true order effects and not topic effects.

In the CE, the 12 imputation models each provide a different set of responses to the filter 

questions in the grouped format and a different estimate of the motivated misreporting effect in 

Equation (1). Figure 3 shows the estimated motivated misreporting effects from each model, 

overall and for the three sections: utilities, clothing, and insurance. This specification curve 

captures the sensitivity of the results to the different models. In the overall subplot, 10 of the 12 

models report a significant effect in the expected direction: the percentage of filter questions 

answered with a “yes” in the interleafed format is lower than it would be if the questions were 

asked in the grouped format. In the utilities section, the results have no clear sign, and half the 

models predict no significant difference in the grouped and interleafed format. In the CE, the 

order of the section is not recorded but most respondents answer the utility section before the 

clothing or insurance section. The results shown in the upper right subplot of Figure 3 may be the 

result of an order effect more than a topic effect. In the clothing section, all models report a 

significant motivated misreporting effect, and the size of the effect is largest in this section. 

Models 5, the best-fitting model according to Table 6, reports significant and negative effects 

overall and in each section.

The right side of Table 7 shows the percentage of filters answered with “yes” in each 

format, overall and by section in the CE, after imputation. The reported imputed estimates come 

from the combination of all 12 models and 20 imputation from each one, for 240 total 

imputations. In the interleafed format, 33.8% of the filter responses were “yes.” In the grouped 

format, 38.7% were imputed “yes.” The difference between the two formats is −4.9 percentage 

points (standard error −2.15), slightly smaller than the difference in the web survey (−6.1, 

standard error 0.80).

6 Discussion

Because experimental manipulation of the questions in the CE was not possible, this 

paper has used a different approach. Members of a nonprobability panel were randomly assigned 

to answer CE filter questions about household purchases in the grouped or interleafed format. 

Multiple imputation was used to understand how CE respondents would have answered in the 

grouped format. Most models show that respondents underreport purchases by approximately 

five percentage points to avoid the follow-up questions.
Table 7: Motivated Misreporting Effects in Web and CE

Web CE

Section Interleafed

% Yes

Grouped 

% Yes

Difference

% Points

Interleafed

% Yesa

Grouped 

% Yesab

Difference

% Pointsa

Overall 36.8

(0.53)

42.9

(0.60)

-6.1*

(-0.80)

33.8

(0.73)

38.7

(2.10)

-4.9*

(-2.15)

Utilities 40.5

(0.75)

45.7

(0.84)

-5.2*

(-1.1)

47.4

(1.12)

46.6

(3.51)

0.82

(3.67)

Clothing 32.7

(0.80)

42.1

(1.0)

-9.4*

(1.3)

24.5

(0.95)

34.8

(3.63)

-10.2*

(-3.71)

Insurance 37.9

(0.66)

40.9

(0.74)

-3.0*

(-1.0)

31.3

(0.81)

35.7

(1.88)

-4.4*

(-1.97)

Standard errors in parentheses

* Difference significant at 5% level

a Standard errors adjust for clustering of observations 

b

Imputed from all models; standard errors adjust for multiple imputation 
Figure 3: Estimates of Motivated Misreporting Effects across Imputation Models

Difference in “Yes” Percentages: Interleafed – Grouped (see Equation 1)

95% confidence intervals shown, adjusted for multiple imputation and clustering of observations

It is not possible to say what the effects of this motivated misreporting might be on the 

CPI. The CE data contribute to the weights used to construct the market basket for the CPI. 

Underreporting may affect the assigned weights. If the motivated misreporting effect is larger 

toward the end of the questionnaire (which this paper has not tested), and the rate of price 

increases on goods in those sections is higher or lower than the overall rate of price increases, 

then bias in the CPI is possible. The ultimate effect of motivated misreporting on the CPI is too 

complex to speculate on in this paper. However, the CE data are used for many other purposes by 

policy researchers and academics. Some of these other studies may be more vulnerable to bias 

because of motivated misreporting. Researchers should carefully think through how 

underreporting of purchases in the CE could bias their analyses.

To reduce the motivated misreporting effect in the CE, the survey could do several things. 

First, the CE could switch to a grouped by section or even a grouped-overall approach. In 

discussions, researchers at the Bureau of Labor Statistics are hesitant to make this change. Many 

respondents find the grouped approaches difficult because they require jumping from one item to 

the next in the filter questions and then going back to each purchased item: respondents prefer to 

think about items one at a time (Clark-Fobia et al. 2018). Another option would be to interview 

more respondents but ask fewer questions of each one to reduce the burden and length of the 
survey. Imputation could fill in the missing responses (Gonzalez and Eltinge 2008). This 

approach would likely increase data collection costs, however, and thus is also not ideal. Future

research should focus on identifying techniques to minimize motivated misreporting in the 

interleafed format, which would benefit the CE and many other important surveys.

The results in this paper depend strongly on the imputation models. The models explain 

purchases rather well but not perfectly, as shown in Table 5. The models control for the observed 

differences between the web and CE respondents (Table 4 and Figure 1) but cannot control for 

unobserved differences. In addition, this study relies on a nonprobability survey; a more 

representative set of web respondents may result if different imputations and different 

conclusions. Income data were collected differently in the CE and the web survey. And no 

interviewer characteristics were available in the CE: controlling for the clustering of cases by 

interviewer may alter the results.

Nevertheless, these results are the strongest evidence to date that motivated misreporting 

is taking place in the first wave of the CE. Furthermore, the approach used here is one that other 

large surveys may find useful. When experimental manipulation in a given survey is not possible, 

because of budget or practical constraints, a parallel web survey offers a way to estimate how 

questionnaire changes would affect the collected data.
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