1 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Statistical Examination of Rounding 

Tendencies in the Consumer 

Expenditure Interview Survey

Taylor J. Wilson

Bureau of Labor Statistics

Joint Statistical Meetings (JSM)

Baltimore, Maryland

30 July 2017
2 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Research Question

Does the use of records help to reduce 

rounding in the Consumer Expenditure 

Interview Survey?
3 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Motivation

 Understanding the affect of respondent 

rounding on data quality. 

Reducing total survey error

 Encouraging the use of records in the CE.

Reducing rounding

Improving data accuracy

 Data on record use are available.

 “Heaped” values prevalent in the data. 
4 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Literature Review

 Response Heaping In InterviewerAdministered Surveys: A Cognitive Shortcut to 

Satisfice? (Holbrook et al, 2009)

 Encouraging Record Use for Financial Asset 

Questions in a Web Survey (Couper et al, 

2013)

 Heaping at Round Numbers on Financial 

Questions: The Role of Satisficing (Gideon et 

al, 2017)
5 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Identifying Rounded Values

 Guess (educated)

 Cut off points from psychological studies

Works with ratios

Extrapolated to small expenditures

 Heaped values

Highest probability of being rounded

Need systematic identification
6 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

What is a heaped value?

 “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.”

Wang, Hao, "Statistical methods for heaped data" 

(2009). Dissertations available from ProQuest. 

AAI3395726.
7 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov
8 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov
9 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov
10 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Properties of Heaping

 As a function of rounding

Order of magnitude effects and relative value

Use heaped data to identify rounded records

 As a function of natural prices

Common and uncommon price points for items

 More common in discrete data

CE data is already rounded to the dollar
11 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

How to identify heaping?

 Unique problems with order of magnitude 

effects related to expenditure data.

 The order of magnitude problem requires a 

more nuanced approach than the simple cutoff points that are typically suggested. 

 Relative value and rounded dollar amounts. 
12 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

How to identify heaping?

 Dynamic record evaluation

Programmatic solution 

Relativistic and non-arbitrary solutions

 How to determine sufficient concentration?

Deviation from typical heaped value

Relative to order of magnitude
13 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Average “Fall” Approach

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8 9 10 11

Frequency

Expenditure ($)

8

2

12
14 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Dynamic Evaluation

 Requires understanding your data

How many orders of magnitude does your expenditure 

cover?

 Compute the conditional mean

Grouped on order of magnitude

 Determine the standard deviation for non-zero 

distances to the left and right of a spike within the 

groups. 

 Loop through each observation and assign a t 

statistic to determine if it is significantly different 

from the norm. 
15 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Testing Significance

 The distance distributions constructed from 

the falls are generally non-normal right 

skewed. 

 68-95-99 Rule fails to provide accurate 

measure of significance. 

 Chebyshev’s Inequality as a benchmark for 

significance. 

Pr(|X − μ| ≥ kσ) ≤

1

k

2
16 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Record Use

 A household is said to have “used records” 

when the field representative notes that the 

household used records greater than 50% of 

the time. 

 Natural Error and Variance in response. 

 Hypothesis is that more record use implies 

less heaping. 
17 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Record Use

 About half of households have data for record 

use with a small variance depending on the 

selected time frame for analysis. 

 Of those who had data collected, about a 

fourth of these households used records over 

half the time (defined as a record user)

 Independent Variable of Interest
18 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Mann-Whitney U Test

 Non-parametric test for record use because of 

the non-normal underlying distributions. 

 Allows us to test the hypothesis that the 

probabilities of randomly selecting a value 

from two independent non-normal 

distributions are equal.

 Rank-Sum procedure on two expenditure 

types on a fixed order of magnitude value 

domain. 
19 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Mann-Whitney U Test

 Record use appears to be generally useful for 

smaller, large price-variance goods and 

services that aren’t purchased on a repeatable 

basis. 

 The following expenditure types were selected 

to exemplify the general behavior and to 

present this juxtaposition. 

Clothing and Accessories 

Subscriptions 
20 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Clothing and Accessories on Value Domain [0,99]

Two-sample Mann-Whitney U test

records | obs rank sum expected

-------------+---------------------------------------

0 | 291 60178 58345.5

1 | 109 20022 21854.5

-------------+---------------------------------------

combined | 400 80200 80200

H0: Pr(rounded value(records=0)) = Pr(rounded value(records=1))

z = 2.512

P value = 0.0120

The use of records dramatically decreased incidence of 

identified rounded values. Natural prices do not typically fall on 

highly divisible values in this expenditure category so the 

effect of records is expected to be greater. 
21 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Subscriptions on Value Domain [0,99]

Two-sample Mann-Whitney U test

records | obs rank sum expected

-------------+---------------------------------------

0 | 542 195798.5 195662

1 | 179 64482.5 64619

-------------+---------------------------------------

combined | 721 260281 260281 

H0: Pr(rounded value(records=0)) = Pr(rounded value(records=1))

z = 0.110

P value = 0.9123

The use of records did not decrease incidence of identified 

rounded values. Natural prices typically fall on highly divisible 

values in this expenditure category so the use of records is 

expected to be ineffectual. 
22 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

15 % of all 

observations
23 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

3 % of all 

observations
24 — U.S. BUREAU OF LABOR STATISTICS TATISTICS • bls.gov bls.gov

Conclusions

 Record use is helpful in improving data quality by 

reducing the coarseness of data for certain 

expenditure types.

 Recommendation is to repeat the analysis for every 

record type on a regular basis to evaluate any 

changes in consumer preferences or natural prices 

that may influence the effectiveness of records in a 

particular expenditure group.

 Spend resources targeting expenditure categories 

with record use incentives where you know record 

use makes a difference. 
Contact Information

25 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Taylor J. Wilson

Economist

Division of Consumer Expenditure Surveys

www.bls.gov/cex

202-691-6550

wilson.taylor@bls.gov