Statistical Examination of Rounding Tendencies in 

the Consumer Expenditure Interview Survey 

Taylor Wilson1 and Safia Abdirizak2

1U.S. Bureau of Labor Statistics, Washington, DC 20212

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

Abstract

Based on the results from the 2015 Consumer Expenditure Field Staff Survey Analysis 

Report, 98.4% of Field Representatives stated that record use improves the accuracy of 

the interview. The primary purpose of this project is to conduct research regarding the use 

of records as it relates to the rounding effect of recall interviews. This paper tests two 

hypotheses, [1] the use of records reduces the rounding effect and, as a result, increases 

data accuracy and quality and [2] the rounded expenditure amounts and non-rounded 

expenditure are significantly different. The hypotheses are important in aiding large survey 

programs in understanding how respondent rounding will affect the underlying data 

quality of the survey responses. 

We employ a unique approach to isolate values which are most likely heaped—a coarse 

data property in which the respondents tend to converge their answers on ‘round numbers.’ 

This method examines the frequency of numbers represented in a domain of discrete values 

and examines the likelihood of observing any given value versus the rest of the values in 

that domain. The values which are statistically over represented by pre-defined threshold 

are heaped and thus more likely to be rounded. By identifying those values which have the 

highest probability of being a rounded value, we make an assumption that those values 

have actually been rounded. The findings will be of interest to survey methodologists and 

practitioners working in large scale survey operations with recall survey components and 

specific data quality goals. 

Key Words: Record Use, Data Quality, Rounding, Reporting Behavior 

All views expressed in this paper are those of the authors and do not necessarily reflect the 

views or policies of the U.S. Bureau of Labor Statistics 

1. Background 

Defining and identifying rounding in large scale interviewer-administered surveys has been 

a key focus for researchers in assessing how rounding affects the data quality of the results. 

The Consumer Expenditure Survey (CE) is a nationwide household survey conducted by 

the U.S. Bureau of Labor Statistics (BLS) to find out how Americans spend their money. 

Its primary customer is the Consumer Price Index, which uses CE data for its expenditure 

weights. Other customers include the Department of Defense which uses CE data to help 

determine cost-of-living allowances for military personnel, and the Department of 

Agriculture which uses CE data to calculate the annual cost of raising a child. 

The CE consists of two sub-surveys, an Interview survey (CEQ) and a Diary survey (CED), 

collected for the BLS by the U.S. Census Bureau. The purpose of the Diary survey is to 

collect detailed expenditure data on small, frequently purchased items such as food and 

894
apparel. The purpose of the Interview survey is to collect detailed expenditure data on large 

items such as property, automobiles, and major appliances, as well as on recurring expenses 

such as rent, utilities, and insurance premiums. The data from the two surveys are then 

combined to provide a complete picture of consumer expenditures in the United States. 

In recent years CE has engaged an effort to redesign the survey. That redesign plan, the 

“Gemini Project”, introduces a records based interview to comply with specific 

recommendations by researchers to optimize the use of records in the CE. The stated goal 

of records according to the Gemini Redesign Proposal Report is to acquire precise and 

accurate information. Recent CE research by Elkin, Kopp, McBride, and Tan (2015), 

suggest that incidences of rounding are an indication of poor reporting quality. As 

expected, the findings from this report also show that recall data had a higher percent of 

rounded values. Similarly, in efforts to evaluate data quality, Murphy (2015) conducted a 

split sample experiment in the Community Advantage Panel Survey to explore the effects 

of record use. The sample consisted half of telephone respondents and half of in-person 

household interview respondents who were both encouraged to check records. As a result, 

the act of checking records was associated with lower levels of rounding, which is 

consistent with literature related to the use of records in interviewer and self-administered 

surveys.

Survey methodologists have conducted research to understand the mental process of 

answering survey questions, similar to the CEQ. The survey response model found in the 

second edition of Groves (2009) textbook on survey methodology describes the cognitive 

process of how respondents formulate responses. The first stage of the response model 

begins with “comprehension” in which the respondent interprets the question. The second 

stage, “retrieval”, is when respondents recall the necessary information needed to answer 

the question. The third stage of the process “judgment” is a combination of estimating and 

summarizing the information recalled during the retrieval stage. Finally, in the “reporting” 

stage, respondents formulate their final response. During the reporting stage, respondents 

may adjust their response based on their ability to retrieve stored information during the 

recall stage. 

This paper approaches detection of inaccurate data from the perspective of respondent 

rounding as opposed to strictly fabricated responses. To detect possible fabricated data, 

Swanson, Cho, and Eltinge (2003) provide insight on methods by applying Benford’s Law. 

Benford’s law suggests that leading (or left-most) digits follow a certain distribution. Thus 

by identifying the distribution of the leading digits, one can detect if the data may be 

fraudulent or error-prone if the leading digits do not follow the expected distribution 

evident in Benford’s law, shown in Swanson, Cho, and Eltinge (2003). Further discussion 

of detecting possible inaccurate data in surveys can be found in Manski (2010). Manski 

notes that responses typically follow a certain pattern. Five percent intervals are more 

common (i.e., 5, 10, ..., 90, 95), with responses more bunched at 50 percent than at adjacent 

round values (40, 45, 55, 60). 

The motivation behind the subsequent research is to identify the extent of rounded 

responses in the CEQ and understand how respondents who consult records may differ 

from those who do not. In addition, the findings from the analyses will inform which 

sections of the CEQ will benefit from encouraging record use. This will lead to a more 

efficient use of resources and help to minimize the burden to respondents by requesting the 

use of additional records in the interview. 

895
2. Data 

For the purpose of our research, we utilize the CEQ because we are interested in examining 

the impact of rounding and record use in this sub-survey. The CEQ is designed to obtain 

data on the types of expenditures respondents can recall for a period of three months or 

longer. In contrast, the CED includes records of daily expenditures collected over a twoweek period. Most of the expenditures recorded are for “small-ticket” items, such as 

detailed groceries (lettuce, potatoes, dishwashing soap), for which long recall is not 

expected. Therefore, there is little opportunity to assess rounding for expenditures with 

wide-ranging costs. 

Record use is collected as part of a post-interview questionnaire that the interviewer fills 

out following each interview. The interviewer can report one of four categories related to 

the frequency of record-use (1 “Always or almost always”, 2 “Most of the time”, 3 

“Occasionally”, 4 “Never or almost never”). For the purposes of this analysis, households 

that are recorded as a one or two are called record users and a three or four are called nonrecord users. To examine the effects of rounding in the CEQ, we explore a wide range of 

expenditures to evaluate the differences in the prevalence of rounding. Thus, the CEQ is 

an ideal source of data because the survey collects large expenditures, such as property and 

vehicles, and those that occur on a regular basis, such as rent or utilities. 

In order to evaluate the effects of rounding in the CEQ, we utilized pre-processed data to 

look at raw respondent reported expenditure values. CE only collects integer responses in 

the CEQ, so a minor amount of rounding is already imposed by the instrument itself. Preprocessed data are data that CE receives from the Census Bureau before any CE processing 

has been done. The primary limitation of the data with respect to this analysis is that the 

overall record use question is based on the interviewer’s recollection and is asked at the 

end of the interview. For this analysis, a year of data are constructed from the monthly 

files between November 2015 and November 2016 using Stata 15/SE. 

3. Methodology 

3.1 Defining a Rounded Value 

In order to provide a reasonable and workable definition of a rounded value, it is important 

to consider the trade-off between arbitrary definitions of roundedness and the analytic 

power those definitions provide. The more relaxed the definition of roundedness, the more 

biased any analysis will be in its conclusions. This is primarily due to the increased 

likelihood of a false positive that arises from these arbitrary definitions. Consider the 

application of a loose roundedness rule to a dataset with discrete numeric values. For 

example, every value evenly divisible by five will be called a rounded value. This rule will 

cover many numbers that are not empirically being rounded to by respondents of the 

survey—even if that same rule does capture the values which are being rounded to. This 

addition of noise could result in inconclusive, insignificant, or incorrect results simply 

because the definition of roundedness was not well specified. Considering the purpose of 

this study is to examine the effects of records on respondent rounding, properly defining 

the dependent variable (i.e. roundedness) in the data is paramount to achieving meaningful 

results. As such, the analysis attempts to move away from a priori definitions of rounding 

toward an empirical posteriori approach. 

Based on a review of literature related to rounding in large-scale surveys, rounded values 

are typically defined as any value with 00, 25, 50, or 75 as the trailing digits for 

896
expenditures. This is the “round number” approach which has some foundation in 

psychological studies regarding the way individuals think about dividing large values into 

smaller parts1. Another way to approach the rounded value definition is by simply dividing 

all expenditure values by 5 or 10 and any number that is evenly divisible will be considered 

rounded. Both of these methods are highly arbitrary and will likely contain false positives 

or will miss values to which respondents are rounding. 

For the analysis of the CEQ, “heaped” values in the dataset are examined as a measure of 

coarseness. From Hao Wang’s 2009 paper “Statistical Methods for Heaped Data”, 

“Heaping is a common type of measurement error emerging when data are collected with 

various degrees of coarseness. We say that a dataset is heaped when it contains a mixture 

of exact and rounded-off values.”2 These spikes in frequency at certain numbers in the 

datasets strongly suggest heaping. It is important to also be able to call an individual 

number heaped as opposed to calling the entire dataset heaped in order to determine 

roundedness for a given number. The relationship between heaping and roundedness is 

ambiguous at best. Many of these frequency spikes are made up of a combination of factual 

expenditure amounts and rounded ones. These actual expenditure amounts are the effect of 

what we call “natural prices” of particular items. A simple example would be to consider 

an item, purchasable for 50 dollars per unit in a market of similar items that vary in price 

(e.g. 52 dollars, 48 dollars, etc.). Respondents display a propensity to round these varied 

prices near the “round number” to 50. Some of the 50 dollar responses will actually be 50 

dollar purchases despite the over-representation of 50 in the dataset due to this rounding 

propensity. When markets have round natural prices, the argument that heaping implies 

roundedness becomes weaker and reports for each value on the domain can be 

hypothetically split into a proportion of rounded values and natural prices. The assumption 

is that values with a more pronounced spike (i.e. sufficiently higher than the typical spike) 

have a higher proportion of rounded values in them relative to their neighbors. We call 

these highly spiked values rounded by assuming the proportion of natural prices are 

comparatively low. The real challenge is deciding when a frequency spike at a certain 

number can be considered more severely heaped relative to its neighbors. 

In order to accomplish this, it is necessary to characterize these spikes in a way which is 

objectively comparable. For this we use a method we call the “average fall approach.” The 

approach begins by assigning the number of times an expenditure was reported to be a 

dollar amount d, denoted as nd. Next the approach examines every possible integer along 

a domain and identifies the difference in the frequency of that integer from its left and right 

neighbor, DL and DR respectively, represented in equation (1) and (2). 

DL = nd - nd−1(1)

DR = nd - nd+1(2)

Lastly, we define the threshold for which the joint distances are great enough that they can 

be considered different enough from the mean drop over the whole distribution to identify 

a value as heaped. Almost all expenditure distributions are right skewed or log-normal. 

This is due to a lower bound at zero for their domains and the relative infrequency of large 

individual expenditures in the data for most expenditure types. Because of this inherent 

 

1

 See Groves (2009) 

2

 For more information see, Wang (2009) 

897
skew, the empirical rule whereby 95% of all observations fall within approximately two 

standard deviations of the mean does not automatically apply. The justification for 

selecting two standard deviations as the threshold in spite of the skews comes from 

Chebyshev’s Inequality, represented here as equation (3). 

Pr(|X − μ| ≥ kσ) ≤

1

k

2

(3)

This states that the probability of an observation less the mean value of a distribution being 

greater than k standard deviations is less than or equal to the reciprocal of the square of the 

number of standard deviations. Taking k = 2, the probability that an observation is outside 

two standard deviations from the mean is at most 0.25. This implies that at least 75% of 

the observations lie within two standard deviations of the mean for a wide class of 

probability density functions. The more normal the distribution, the more observations two 

standard deviations will capture--up to 95% of the distribution. This implies that a 

sensitivity can be chosen that guarantees a set percentage of observations will be covered. 

Since most expenditure distributions fall somewhere between normal and a right skew, two 

standard deviations are selected as the threshold for analysis guaranteeing a coverage from 

75% to 95%. The condition for an expenditure value being identified as heaped and 

therefore rounded is specified in equation (4), where μ is the mean of the average drop 

along a specified domain. 

DL,DR ≥ μ + 2σ (4)

3.2 Order of Magnitude Effects 

The definition of a rounded value specified here can be considered for specific orders of 

magnitude. Many expenditure value domains cover multiple orders of magnitude. For 

example, the clothing and accessories expenditure type has many expenditures valued 

between 1 and 100 dollars as well as many expenditures valued at over 1,000 dollars. 

However, given the right skew of the distributions, the frequency of the reported 

expenditures naturally approach zero because it becomes very unlikely to observe very 

large expenditure amounts in any frequency. This implies that using the method specified 

in the previous section, frequency differences in the higher orders will tend to be smaller 

and thus reduce the mean distance of the drops in the whole domain. Additionally, the 

relatively large frequency spikes in the smaller orders will obscure rounding behaviors in 

the larger domains where frequency spikes are less likely to be identified as being 

significantly different. Doing a simple logistic regression involving each order of 

magnitude as a predictor for observing a rounded value, while not previously restricting 

the sample to each order when doing the identification, will demonstrate this behavior. 

Table I reports the odds ratios from a logistic analysis of the rounded value identification 

procedure across the whole domain for Clothing and Accessories. 

Table 1. Odds Ratios from Logistic Analysis of Whole Sample Rounding 

Identification Procedure

Odds Ratio Standard Error Z - Statistic

Order One (n x 101) 11.14 0.91 29.67***

Order Two (n x 102) 7.26 0.52 27.89***

Source: CE Microdata – Clothing and Accessory Section

898
Compared to the third order expenditure values (n x 103

), the odds of observing a rounded 

value in the first order is 11 times more likely and the odds of observing a rounded value 

in the second order is 7 times more likely. To assess the real incidence of rounding behavior 

in all domains, it is necessary to restrict the domain to each order of magnitude in which 

expenditures occur. Repeating the procedure separately for each order of magnitude will 

appropriately classify values as rounded within its local area. This will dramatically 

increase the number of values identified as being rounded, especially in the higher valued 

domains where there is relative scarcity of reported expenditures and smaller variance in 

the drops. We can see this by repeating the logistic analysis of these split samples presented 

in table II. 

Table 2. Odds Ratios from Logistic Analysis of Split Sample Rounding Identification 

Procedure

Odds Ratio Standard Error Z - Statistic

Order One (n x 101) 0.47 0.03 -10.49***

Order Two (n x 102) 0.59 0.03 -9.85***

Source: CE Microdata – Clothing and Accessory Record Type

The odds ratios show that it is half as likely to observe a rounded value in order one relative 

to order three and sixth tenths as likely to observe a rounded value in order two relative to 

order three. To understand this result, consider that the largest frequency records are in 

orders one and two for the Clothing and Accessories record type. Because of this, the 

average fall in the distribution is much larger in order one and two than it is in the higher 

domains making it easier for a value to be considered rounded in the higher domains. When 

considering the whole sample, it was virtually impossible for a third order value to be 

considered rounded because of the influence of first order frequencies. After identifying 

values in comparison to their peers, the results are much more indicative of respondent 

behavior. There is no optimal odds ratio between the orders that should be expected. As 

long as the expenditures are being properly identified relative to their peers, the odds ratios 

can be any non-negative number. It may be possible in some expenditure sections for 

rounding to not occur in one order and occur frequently in another. In this case, the odds 

ratios would only show the relative difference in the frequency of the identified values. 

Figure I shows the behavior of one of these expenditure distributions as it approaches the 

higher orders. Evaluating expenditure values relative to their peers captures the smaller 

spikes at the right hand side of the frequency distribution. 

899
Figure 1. Histogram of Reported Clothing and Accessories Values

3.3 Odds Ratios for Evaluating the Impact of Records

To determine the odds of observing a rounded value in the records group versus the nonrecords group, odds ratios are computed from a logistic regression where records use is the 

independent variable and the identified rounded values are the dependent variable. Orders 

of magnitude are incorporated when identifying the rounded values in the procedure 

described in section 3.2. This ensures that the rounded values are appropriately identified 

relative to their peers as opposed to the whole sample. This allows us to predict the odds 

of observing a rounded value if a respondent utilized records. The resulting odds ratio will 

be in comparison to the baseline group of records equal to zero (non-record users). The 

null hypothesis is that records do not reduce the incidence of rounding in the data. The 

alternative hypothesis is that records reduce the incidence of rounding in the data. 

Therefore, we expect to observe an odds ratio that is less than one for all tested expenditure 

categories. Odds that are not significantly different from one imply that records do not 

impact rounding in the expenditure category in a statistically significant way. 

3.4 Mann-Whitney u Test 

The Mann-Whitney u test is used to test the significant differences in the expenditure 

distributions between the record using group and the non-record using group. This provides 

insight into whether or not the values reported are affected by the introduction of records. 

The primary advantage of this test over a standard t test is that the u test is non-parametric 

and does not require the data be normally distributed. The u test requires that two 

independent samples are compared, in this case record and non-record users, and that the 

data be ordinal. In order to compare the majority and non-majority record user groups, the 

response of the interviewer is considered. That is, the interviewer reports whether or not a 

household used records with varying degrees of frequency. That response is recoded into 

a 1 for respondents who used records 50 percent or more of the time and a 0 for respondents 

900
who used records less than 50 percent of the time. The data are then ranked against each 

other by which value is greater and those identified ranks for each independent sample are 

added up. The u statistic based on the sum of ranks and the standard deviation are then 

computed from the two independent samples. From this it is possible to determine whether 

one distribution is significantly different from another. Procedural details are outlined in 

the 1947 paper by Mann and Whitney.3 This test does not assess whether medians between 

the groups are significantly different. For that, a chi-squared statistic is computed for a 

nonparametric equality-of-medians hypothesis test. It is possible for one of these tests to 

be insignificant while the other is significant. Mann-Whitney u tests look at shape and 

location of the distribution while the equality of medians test examines differences in the 

median value of the expenditures.4 

4. Results 

The analysis of responses provides results consistent with other recall surveys in that there 

is an observed heaping pattern that occurs in all record types. Figure II shows examples 

from four of the observed record types. Value domains are restricted to 1000 for clarity of 

presentation. 

Figure 2. Frequency Histograms Demonstrating Heaping Patterns for Four Record Types

Given the proposed definition of a rounded record defined in the above section, the ratio 

of rounded values to non-rounded values will indicate the relative frequency of this 

behavior in the data. Respondent rounding varies across record type in frequency. The use 

of records in all examined cases lowers the frequency of rounded values with the notable 

exception of Renter’s Insurance, which is not significantly different between the groups. 

In certain cases, record use improves the data distributions, resulting in more varied 

 

3

 For more information see, Mann, H. B. (1947) 

4

 For more information on these tests, see: 

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1120984/ 

901
responses and less heaping. Evidenced by the statistically significant reduction in rounding 

in most cases. Most record types follow this pattern. In certain cases, the effect of record 

use is less pronounced. The subscriptions record type experiences a smaller reduction of 

rounded values when records are used in the interview. The survey does not capture 

whether or not a record was used on a particular response so it is possible that a records 

respondent is still rounding some of their expenditures for which they did not have a record. 

Table III shows these figures for a selection of record types in the Interview Survey. 

Table 3. Comparison of CU rounded expenditures Non-Record vs. Record User

Non-Record Record Odds 

Ratio

Expenditure 

Section

# 

Rounded

# 

Total

% 

Rounded

# 

Rounded

#

Total

% 

Rounded

Owned Housing 

(MRTPMTX) 1,405 3,561 39 312 1,205 26 0.54***

Utilities 

(UTLCHGX2) 1,740 8,938 19 223 2,609 9 0.39***

Rented Vehicles 

(RENTEXPX) 222 509 44 83 246 34 0.67***

Non-health 

Insurance 

(INSNEXXB)

 Life 614 2,126 29 167 857 19 0.61***

 Automobile 1,384 4,924 28 319 1,093 23 0.79***

 Homeowners' 497 1,536 32 374 1,526 25 0.68***

 Renter's 267 710 38 66 168 39 0.95***

Health Insurance 

(HHIRPMXB) 1,480 5,112 29 322 1,680 19 0.59***

Medical 

(MEDPMTX) 1,551 4,981 31 298 1,586 19 0.52***

Clothing 

(CLOTHXA) 2,110 6,721 31 397 1,958 20 0.57***

Subscriptions 

(SUBEXPX) 415 2,892 14 81 637 12 0.76***

Source: CEQ Survey Unbox Data (November 2015- November 2016)

*p<.05; **p<.01; ***p<0.001 | Most Appropriate Order of Magnitude Selected

While some of the heaping observed can be attributed to respondent rounding, a portion of 

the heaping is due to the underlying natural prices of the items that make up that category. 

Because of this, some of those values will align with the actual expenditure amount paid 

by the consumer for the item. In distributions where the typical pre-tax prices of items tend 

to align with what we define as a rounded value, the introduction of a record will not add 

any new information for the respondent. This typically occurs with large ticket items where 

companies apply marketing practices when pricing. If a company does the rounding for the 

902
consumer (e.g. 500 dollar washing machine), then that record type will report a higher 

frequency of these expenditures. 

The literature also suggests that recurring expenditures are easier to remember for recall 

surveys. When comparing aggregate CE data with administrative sources, categories like 

rent typically tend to match very well.5 Despite categories like mortgage payments being 

recurring, they also are rarely round numbers to which a respondent would choose to round. 

This implies that the introduction of records will still provide new information (i.e. the 

actual amount paid) for the respondent and therefore a more accurate value. In the case of 

the subscriptions category which is typically composed of smaller expenses, the natural 

price effect is influencing the outcome whereby the expenses are both repeatable and 

similar to what a respondent may choose to round to anyway (e.g. 10 dollar Netflix 

subscription). Adding records may not add much information in this case, which is 

demonstrated by the comparatively small two percentage point difference between the 

record group and non-record group. Opposite to this, there are those expenditure categories 

that naturally have items priced very differently from the rounded value definition. These 

will typically be smaller expenditures where the prices are situated toward the lower end 

of the value distribution and are non-repeated (e.g. Clothing and Accessories). These 

expenditure categories are expected to be greatly influenced by the introduction of records. 

This is confirmed by percentage decreases and the significance of the odds ratios. 

Generally, survey methodologists prefer decreasing the amount of heaping in the dataset 

yields higher quality data. Given the general finding from the literature that households 

tend to underreport the value of many of their expenditures6,7, it is reasonable to expect that 

any significant differences in medians by the introduction of records would result in a 

higher reported value for record users. Table IV reports the median expenditures for each 

expenditure type by record and non-record users and records the difference between the 

values. The significance of these differences are tested in the following section. 

Table 4. Medians by Group – Values in USD

Expenditure Section N Record Users Non-Record 

Users Difference

Owned Housing (MRTPMTX) 4,766 $2188 $2300 -$112

Utilities (UTLCHGX2) 11,547 325 277 48

Rented Vehicles 

(RENTEXPX) 755 235 238 -3

Non-health Insurance 

(INSNEXXB)

Life 2,983 106 100 6

Automobile 6,017 228 240 -12

Homeowners' 3,062 182 190 -8

Renter's 878 35.5 40 -4.5

 

5

 The estimated aggregate rent in CE is 98 percent of the aggregate estimated in the 2015 

National Accounts. https://www.bls.gov/cex/cepceconcordance.htm 

6

 See Tucker et al (2005), https://www.bls.gov/cex/research_papers/pdf/st040070.pdf 

7

 See McCully et al (2013), https://www.bls.gov/osmr/pdf/ec130020.pdf 

903
Health Insurance 

(HHIRPMXB) 6,792 262 242.5 19.5

Medical (MEDPMTX) 6,567 225 170 55

Clothing (CLOTHXA) 8,679 271 240 31

Subscriptions (SUBEXPX) 3,529 40 36 4

Source: CEQ Unbox Data (November 2015- November 2016)

Most Appropriate Order of Magnitude Selected

Each record type was examined for equality of medians and similarity of distributions to 

determine what effect, if any, records have on the reported expenditure values. The MannWhitney u test is used to test the null hypothesis that values from each group are drawn 

from the same expenditure distribution. The median test is used to test the null hypothesis 

that the medians of both groups are equal. Unequal medians may suggest that record use 

may have an effect on the magnitude of reported expenditures. Both tests are run for all 

examined record types and the results are reported in table V. 

Table 5. Mann-Whitney u Test and Equality-of-Medians Test for Each Expenditure

Mann-Whitney u Test

(Record v. Non-Record)

Equality of Medians

(Record v. Non-Record)

Expenditure Section N Z Statistic P Value Chi 

Squared P Value

Owned Housing 

(MRTPMTX) 4,766 2.117 0.034* 2.981 0.084

Utilities 

(UTLCHGX2) 11,547 -8.257 0.000*** 45.089 0.000***

Rented Vehicles 

(RENTEXPX) 755 0.737 0.461 0.099 0.753

Non-health Insurance 

(INSNEXXB)

 Life 2,983 -0.495 0.621 0.414 0.520

 Automobile 6,017 1.749 0.080 2.573 0.109

 Homeowners' 3,062 0.020 0.984 0.349 0.555

 Renter's 878 0.600 0.549 0.766 0.382

Health Insurance 

(HHIRPMXB) 6,792 -2.468 0.014* 5.913 0.015*

Medical 

(MEDPMTX) 6,567 -7.050 0.000*** 32.135 0.000***

Clothing 

(CLOTHXA) 8,679 -3.852 0.000*** 12.098 0.001**

Subscriptions 

(SUBEXPX) 3,529 -2.403 0.016** 1.483 0.223

Source: CEQ Unbox Data (November 2015- November 2016)

*p<.05; **p<.01; ***p<0.001 | Most Appropriate Order of Magnitude Selected 

Subscriptions and mortgage payments are the most interesting result from these tests. The 

results show that these expenditure types have medians that are not statistically different, 

904
but distributions that are significantly different. Non-health insurance and rented vehicle 

expenditure types produce insignificant results in both tests despite having significant odds 

ratios. This shows that the incidence of rounding significantly decreased but the general 

shape of the distribution and the median was preserved. The remaining expenditure types 

have significant differences in the medians and in distributions, showing that the record 

use changed the shape of the data and also the median value in a significant way. 

Differences in the inherent qualities of a record user and a non-record user may also have 

an effect on their spending and reporting style. For all significant differences in medians, 

the use of records has generated higher values overall. This is also evident from the 

negative z-scores produced by the test. Negative z-scores indicate that the median of the 

record users was higher than the median of the non-record users. 

5. Conclusion 

The use of the average fall approach to identify rounded records has enabled testing of 

whether record use significantly impacts the coarseness of data in the Consumer 

Expenditure Interview Survey. Eleven expenditures (e.g. Health Insurance, Subscriptions, 

etc.) were tested using this method. All expenditures displayed significant decreases in the 

likelihood of observing a rounded value when records were introduced, with the exception 

of renter’s insurance. Further testing on the equality of medians showed that for all 

expenditure types where there was a significant difference in medians, records increased 

the median value of the expenditure. Changes in distributions were more common among 

expenditure categories. This is likely due to the redistribution of the heaped values to other 

values in the distribution. This lends credibility to the claim that rounding by the respondent 

or by a decision rule in processing could change the distributions in significant ways. Some 

expenditure types benefit more in terms of roundedness reduction from the use of records 

while others only have marginal benefits. It will be necessary to explore in future work 

whether the trade-off in increased respondent burden from record use for the observed 

changes in medians and distributions is worth it. Overall, the use of records appears to have 

a positive effect on the accuracy of the data and produces a higher quality product from the 

survey. 

905
References 

Bar, Haim, and Dean Lillard. "A Heap of Trouble? Accounting for Mismatch Bias in

 Retrospectively Collected Data on Smoking." Health, Econometrics and Data

 Group, 2010. 

Battistin, Erich. "Errors in Survey Reports of Consumption Expenditures." 2003. 

Dominitz, Jeff, and Charles F. Manski. "Perceptions of Economic Insecurity: Evidence

 from the Survey of Economic Expectations." Public Opinion Quarterly 61, no. 2

 (1997) 

Elkin, Ian, Brandon Kopp, Brett McBride, and Lucilla Tan. "Results from the Consumer

 Expenditure Surveys’ Individual Diary Feasibility Test." 2015. 

Fischhoff, Baruch, and Wändi Bruine De Bruin. "Fifty–Fifty=50%?" Journal of

 Behavioral Decision Making 12, no. 2 (1999) 

Geisen, Emily, Ashley Richards, and Charles Strohm. "U.S. Consumer Expenditure

 Records Study." 2011. 

Gideon, Michael, Joanne Hsu, and Brooke McFall. "Eliciting financial information on

 surveys: rounding in reported mortgage balances." FCSM, 2015. 

Gideon, Michael, Brooke Helppie-Mcfall, and Joanne W. Hsu. "Heaping at Round

 Numbers on Financial Questions: The Role of Satisficing." Finance and

 Economics Discussion Series 2017, no. 006 (2017).

Groves, Robert M. Survey methodology. New York: J. Wiley, 2009. 

Hart, Anna. “Mann-Whitney Test Is Not Just a Test of Medians: Differences in Spread

 Can Be Important.” BMJ : British Medical Journal 323.7309 (2001): 391–393. 

Lillard, Lee A. , and Robert J. Willis. "Cognition and Wealth: The Importance of

 Probabilistic Thinking." SSRN Electronic Journal. 

Mann, H. B., and D. R. Whitney. “On a Test of Whether one of Two Random Variables

is Stochastically Larger than the Other.” The Annals of Mathematical Statistics,

 vol. 18, no. 1, 1947, pp. 50–60., doi:10.1214/aoms/1177730491. 

Manski, Charles F. "Measuring Expectations." Econometrica 72, no. 5 (2004) 

Manski, Charles F., and Francesca Molinari. "Rounding Probabilistic Expectations in

 Surveys." Journal of Business & Economic Statistics 28, no. 2 (2010) 

McCully, Clinton, Thesia I. Garner, William Passero. “Understanding the Relationship:

 CE Survey and PCE.” Bureau of Labor Statistics. 2013. 

Moore, Jeffrey, Linda Stinson, and Edward Welniak. "Income Measurement Error in

 Surveys: A Review." 1999. 

Murphy, J., J. Rosen, A. Richards, S. Riley, A. Peytchev, and M. Lindblad. "Financial

 Record Checking in Surveys: Do Prompts Improve Data Quality?" Field

 Methods 28, no. 3 (2015) 

Pudney, Stephen. "Heaping and leaping: Survey response behaviour and the dynamics of

 self-reported consumption expenditure." Institute for Social and Economic

 Research University of Essex, 2008. 

906
Swanson, David, Moon Jung Cho, and John Eltinge. "Detecting Possibly Fraudulent or

 Error-Prone Survey Data Using Benford’s Law." 

Tucker, Clyde, Paul Biemer and Brian Meekins (2005), “Estimating the Level of

 Underreporting of Expenditures among Expenditure Reporters: A Micro-Level

 Latent Class Analysis,” American Statistical Association 2005 Proceedings of the

 Section on Survey Research Methods,, Washington, D.C., American Statistical

 Association. 

Tversky, A., and D. Kahneman. "Judgment under Uncertainty: Heuristics and Biases."

 Science 185, no. 4157 (1974) 

Wang, Hao, "Statistical methods for heaped data" (2009). Dissertations available from

ProQuest. AAI3395726. http://repository.upenn.edu/dissertations/AAI3395726

907