Heaping at Round Numbers

on Financial Questions: 

The Role of Satisficing 

Michael Gideon (U.S. Census Bureau)

Joanne Hsu (Federal Reserve Board)

Brooke Helppie McFall (University of Michigan)

FCSM

December 3, 2015

The analysis and conclusions set forth are those of the authors and do not indicate concurrence

with other members of the research staff or the Board of Governors of the Federal Reserve

System or any other insNtuNons, including the U.S. Census Bureau.
ID 

0 

C! 

..;-

0 

0 

(') 

0 

~o 

·u; 

C 

Q) 

0 

C\I 

0 

0 

0 

C! 

0 

0 100 200 300 400 500 

Actual balances of first mortgages ($1 000s) 

Line at 100k. Source: FRBNY CCP/Equifax 2013 

600 700 

0 

C\I 

·u; 

co 

Q) 

0 

ID 

0 .....,_,...,....,...,,-,...,...-,-,.....-,--,-,.....-,...,....,...,-,....,..-,-,.....-,--,-,.....-,--,-.,...,,-,...,...,...,.....,....,..-,.-

0 100 200 300 400 500 

Balances of first mortgages ($1 000s) 

Line at 100k. Source: SCF 2013 

600 700 

Administrative vs. survey data: mortgages 

AdministraNve (Credit reports) Survey of Consumer Finances

ObservaNon: “exact values” on survey data show a lot more heaping than administraNve data
Background 

• Self-reported financial data oWen treated as exact, true values.

• Evidence of heaping at round numbers

• Earnings (Schwabish 2007)

• Self-reported consumpNon expenditure (Pudney 2008)

• Wealth quesNons in SIPP data (Eggleston 2015)

• Why do we care?

• Inference using coarse data are sensiNve to assumpNons about

coarsening mechanism (Heitjan and Rubin, 1990).

• If you know something about the process, beber inferences

• Using thresholds, e.g. IRS determining non-filing rates using

survey data
Research questions 

1. Do paberns of heaping vary across quesNons and

surveys?	

2. Is heaping consistent with saNsficing?

End goal: Do round “exact values” provide more or less

precision than range/bracket alternaNves in surveys? What is

the impact of round “exact numbers” in applied analyses?
Conceptual framework: Satisficing 

• Response behavior that yields “good enough” response, but

not the “opNmal” response

• Krosnick (1991):

(task difficulty)

P(satisficing) =

(ability) ×(motivation)

• If rounding is a result of saNsficing,

1. Higher ability & moNvaNon à less	rounding	

2. More difficult tasks à more rounding
Data 

• Survey of Consumer Finances (2013)

• NaNonally	representaNve of all American households. CAPI. Contains

detailed data about household income, assets and debts. N~6000	in survey

analysis N=2096.	Sponsored by Federal Reserve Board, data collected b

NORC.	

• CogniNve Economics Study (2011)

• NaNonal	sample, older adults, panel (2008-). Self-administered, web and mail

modes. Asset/debt quesNons about household level. Contains detailed data

about income, assets and debts. Less-detailed than SCF.	N~900;	analysi

N=304.	

• Analyze quesNon-respondent level data

• Variety of quesNons about financial values

• Restricted to value responses (excludes ranges and item

non-responders)	

• Random effects regressions
	 	

Measurement: roundness of responses 

(m − n)

rounding =

(m −1)

•n = # o significant digit reported

•m=ma possibl significant digit (magnitude)

•rounding betwee 1

•mor trailin zeros à higher valu of rounding
Examples 

Ex 1: response of $3,000

(m − n) (4 −1)

rounding = = =1

(m −1) (4 −1)

Ex 2: response of $53,000

(m − n) (5− 2)

rounding = = = 0.75 (m −1) (5−1)

Ex 3: response of $53,233

(m − n) (5− 5)

rounding = = = 0

(m −1) (5−1)
0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0.0 

Q,~ 

(; C 

Rounding across questions on SCF 2013 
Rounding across Qs on CogEcon (2011) 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

1 
Measurement: task difficulty by question type 

• Knowable	quesNons: single account

• Value of a single checking account

• Knowable	quesNons: aggregated

• Total income (wages + interest + ...)

• Unknowable quesNons

• Home values

• Differences can arise at any stage of response (Tourangea

1984

1. Comprehension	

2. InformaNon retrieval

3. IntegraNon

4. Response formulaNon
Measurement: task difficulty (2) 

STAGES OF RESPONSE

(1) Comprehension

(2) InformaHon	

retrieval

(3) IntegraHon

(4) Response

formulaHon

Knowable,	

Aggregate

NA

MulNple pieces

of informaNon

Concretedifficult

Privacy less

important

QUESTION TYPE	

Knowable,	

Single

NA

One piece of

informaNon

Concrete-easy

Privacy more

important

Unknowable

NA

MulNple

uncertain pieces

of informaNon

Abstract-difficult

Privacy less

important
SCF: Categorizing questions into types 

• Unknowable: Home value; Food at home; Food away from

home

• Knowable, single account: Mortgage; Checking; Savings;

Social Security income

• Knowable, aggregate: Credit cards (new charges); credit

cards (balance outstanding)
0.8 

0.7 

0.6 

Overall Unknowable Knowable-single Knowable-aggregated 

account 

Rounding across Q type: SCF 
CogEcon: Categorizing questions into types 

• Unknowable: Home value; Food at home; Food away from

home

• Knowable, single account: Social Security income; Pension

income; Mortgage

• Knowable, aggregate: Total household income; Earnings;

Assets in tax-favored reNrement accts; Assets outside taxfavored ret accts; Check, Savings, CDs; credit card (balance

outstanding); other non-housing debt; 401(k) contribuNons;

health insurance; health spending out-of-pocket
0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

Overall Unknowable Knowable-single Knowable-aggregated 

account 

Rounding across Q type: CogEcon 
Rounding as a response strategy 

• Run random effects regressions for all quesNons, then for

each quesNon type

• Intraclass correlaNon tells us the level of correlaNon in

rounding within respondents

• Results:

• Higher for knowable and single-account quesNons

• Lower correlaNon when we include the individual specific

predictors, evidence that observable characterisNcs

explain some but not all of the correlaNon within

respondents.
	 	

Measurement: ability & motivation 

• Ability

• Proxy with educaNon (SCF and CogEcon)	

• Direct measures of cogniNon: Number	Series; memory

score (CogEcon)**	

• CFO—most knowledge person in household (CogEcon)	

• MoNvaNon

• Need for	CogniNon (CogEcon)**	

• ConsulNng records (SCF and CogEcon)	

• Response latencies (CogEcon)	

**All CogEcon respondents also completed a comprehensiv

personality and cogniNve assessment (CogUSA)	
	 	

	 	

Ability 

• EducaNon: no clear relaNonship (SCF, CogEcon)	

• Household CFO: most knowledgeable person in the

household	àround less (CogEcon)	

• Number	Series: no clear relaNonship (CogEcon)	

• Episodic Memory: beber memory à less	rounding

(CogEcon)	

• Bobom line: Not	all forms of ability contribute equally to

response	process
	 	

Motivation 

• Need	for CogniNon: higher moNvaNon à less	rounding

(CogEcon)	

• Respondent consulted records à less	rounding	(SCF, CogEcon)	

• ConsulNng records has larger effect for knowable quesNons

• Records only help increase precision when they contain

informaNon needed to answer the quesNon
0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0.0 

Food 

away 

----, 

Food SP SocSec R SocSec CC still 

home 

-+-cogEcon 

-+-SCF 

Checking Mortgage Home 

Value 

Motivation (2) 

• QuesNon order: moNvaNon may wane as survey progresses

• Similar quesNons in completely different order, but exhibit

similar rounding paberns
Alternative hypothesis: sensitivity? 

• Another explanaNon: people round to blur answers to

sensiNve quesNons	

• Analyze response Nmes by quesNon (CogEcon)	

• SaNsficing: round answers take shorter Nme (cogniNve

shortcut)

• SensiNvity: round answers do not take shorter Nme (blur

answers at final stage of response)

• Results: Longer Nme à less	rounding.	

• Consistent with rounding as a cogniNve shortcut
Alternative hypothesis: sensitivity? (2) 

• Single vs. aggregated amounts:

• SaNsficing: least rounding for single-account Qs

• SensiNvity: most rounding for single-account Qs, since

aggregaNon shields amount in individual accounts

• Results: Single-account Qs à less	rounding	

• Consistent with rounding as a cogniNve shortcut.

• Caveat: analysis mostly on variaNon within respondent.

• Need	further analysis to assess variaNon across

respondents (more sensiNve types of people)
Conclusion 

• Rounding largely consistent wit saNsficing

• More difficult quesNons à more rounding	

• MoNvated à less	rounding	

• Higher ability: mixed results

• No	evidence that rounding is related to sensiNvity/privacy

• Mode could maber

• Endogenous choice of info retrieval strategy?

• Memory vs. consulNng records: Related to abilit and

moNvaNon
Next steps 

• SIPP 2008 and redesigned 2014 to unpack quesNon difficulty

• Use Nme on survey before presented with a Q to test whether

faNgue is associated with greater rounding

• ImplicaNons for survey design: trade-off between precision and

respondent burden?
Thank you! 

Michael Gideon michael.s.gideon@census.gov

Joanne Hsu joanne.w.hsu@frb.gov

Brooke McFall bhelppie@umich.edu

Acknowledgments:

The NaNonal	InsNtute on Aging (grant number NIA	P01 AG026571) for

support of the CogniNve Economics Study.

The NaNonal	InsNtute on Aging (grant number NIA	P01 AG026571) for

research support for McFall.	

The NaNonal	InsNtutes of Health, including the NaNonal	InsNtute on

Aging (T32AG000243; P30AG012857) for research support for Gideon.