The age of reason : financial decisions over the lifecycle

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Massachusetts

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Department

of

Economics

Working

Paper

Series

The

Age

of

Reason:

Financial

Decisions

Over

the

Lifecycle

Sumit Agarwal

John DriscoU

Xavier

Gabaix

David

Laibson

Working

Paper

07-March

15

2007

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E52-251

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Memorial

Drive

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MA

02142

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Paper

Collection at

The

Age

of

Reason:

Financial Decisions

Over

the

Lifecycle

Sumit

Agarwal,

John

C.Driscoll, Xavier Gabaix,

and David

Laibson*

CurrentVersion:

March

19,

2007

Abstract

Thesophistication of financial decisions varieswithage:middle-agedadultsborrowat lowerinterestratesand payfewerfeescomparedtoboth youngerandolder adults.

We

documentthispatterninten financialmarkets. Themeasuredeffectscan notbe explained by observedriskcharacteristics.Thesophistication of financial choicespeaksatabout age 53inourcross-sectional data. Ourresultsare consistentwiththehypothesisthat financial sophisticationrisesand thenfallswithage,althoughthe patterns thatweobserverepresent

amixofageeff'ectsandcohorteffects. (JEL:Dl, D4, D8, G2,J14).

Keywords: Household finance,behavioralfinance, behavioral industrial organiza-tion,aging, shrouding, autoloans,credit cards,fees,

home

equity,mortgages.

*_{Agarwal: Federal ReserveBankof}Chicago,sagarwal@frbchi.org. Driscoll: FederalReserve Board, john.c.driscoll@frb.gov. Gabaix: MIT,Princetonand

NBER,

xgabaix@princeton.edu. Laibson: Har-vardUniversityand

NBER,

dlaibson@harvard.edu. Gabaix andLaibson acknowledge support fromthe NationalScienceFoundation

(Human

andSocialDynamicsprogram). Laibson acknowledgesfinancial supportfromtheNationalInstitute on Aging (ROl-AG-1665). Theviews expressedin thispaperare thoseoftheauthorsand donot represent the policies or positionsoftheBoardofGovernors ofthe Federal ReserveSystem or the FederalReserve BankofChicago.

We

thank DavidCutler, Timo-thySalthouse,Fiona Scott-Mortonandparticipants at the InstituteforFiscal Studiesandthe

NBER

(Aging group)fortheircomments.

1

Introduction

Performance tends torise

and

then fallwithage. Baseball playerspeak in their late20s (Fair 2005b,

James

2003). Mathematicians, theoretical physicists,andlyric poets

make

their

most

importantcontributions aromid age30 (Simonton 1988). Chess players achieve their highestrankingintheirmid-30s (Charness and Bosnian 1990). Autocraticrulerslike

Queen

ElizabethI aremaximally effective in theirearly 40' (Simonton1988). Authorswritetheir

most

influentialnovelsaroundage 50(Simonton 1988).^

The

presentpaperstudiesan activitythatisrelevant totheentire adult population: per-sonalfinancialdecisionmaking.

Most

financialproductsare complex anddifficultto under-stand. Fees areshrouded

and

the true costs of afinancial servicesarenoteasilycalculated.

Making

the bestfinancial choices takesknowledge, intelligence,

and

skill.

This paper

documents

cross-sectional variationinthe prices that peoplepay forfinancial services.

We

find thatyounger adultsand older adultsborrowat higherinterestrates

and

pay

more

feesthan middle-agedadults controUingforallobservablecharacteristics, including measuresofrisk.

The hump-shaped

patternoffinancialsophisticationispresentin

many

markets.

We

study interestratesinsixdifferentmarkets: mortgages,

home

equityloans,

home

equitycreditlines,

auto loans, personal credit cards,

and

small businesscredit cards.

We

study the failure to optimally exploit balance transfercreditcard offers. Finally,

we

studythreekinds ofcredit cardfees: late

payment

fees, cash advance fees, and over limit fees. All ofthe evidence available to us implies a

hump-shaped

patternof financialsophistication, withapeakinthe early50s.

Age

effects provideaparsimonious explanationforthe

hump-shaped

pattern offinancial sophistication.

We

hypothesize that financial sophistication depends on a combination of analyticability

and

experientialknowledge. Researchoncognitiveaging implies that analytic ability follows a declining (weakly) concave trajectory after age 20.

We

hypothesize that experientialknowledge follows an increasingconcave trajectory due to diminishingreturns.

Adding

together these two factors implies thatfinancial sophistication shouldrise and then

fallwithage.

Cohorteffects

may

alsoexplain

some

oftheeffectsthat

we

observe. Differences in educa-tional levels

may

explain

why

older adults arelessfinanciallysophisticatedthan middle-aged adults. Naturally, such educationeffects willnot explain

why

young

adults (aroundage 30) are lesssophisticatedthan middle-aged adults. Additional

work

needstobedonetoidentify

'_{Whatabouteconomists?Tothe best}ofour knowledge, onlyNobel(Memorial) Prize winnersseemtohave beenstudied.Weinberg andGalenson (2005)findthat "conceptual" laureatespeakatage43,and

therelativecontributions ofageeffects

and

cohorteffects.

The

paper hasthe following organization. Section2discussesevidenceoncognitive

perfor-mance

fromthepsychologyliterature. Section 3 describes the basic structuretothe empirical sections.

The

next ten sections present results for interest rates onsix different financial products, threedifferentkinds of creditcardfeepayments,and onthe use ofbalancetransfer credit cardoffers. Section 14 usesalltensetsof resultstoestimate the ageofpeak sophistica-tion. Section 15 discusses other findingsontheeffectsofaging

and

thedifficulty inseparately identifyingageeffects

and

cohorteffects. Section 16 concludes.

2

Aging

and

cognitive

performance: Results

from

medical

and

psychological

research

Analytic ability can be measured in

many

different ways, including tasks that measure

memory,

reasoning,spatial visualization,

and

speed(seeFigure1).Analyticperformance shows a strong age patternincross-sectionaldatasets. Analyticperformanceisnegatively correlated withageinadultpopulations (Salthouse2005

and

Salthouse forthcoming): onaverage analytic performance fallsbytwotothreepercentofone standard deviation^ withevery incremental year ofageafterage20. Thisdeclineisremarkablysteadyfromage20 to age 90 (seeFigure

2).

The measured

age-related decline in analytic performance results from both age effects and cohort effects, but the panel datathat is available implies thatthedechne is primarily driven by ageeffects (Salthouse, Sclu-oeder

and

Ferrer2004).'^ Medicalpathologies represent' one important

pathway

for age effects. For instance, dementia isprimarily attributable to Alzheimer's Disease(60%)

and

vascular disease (25%).

The

prevalence ofdementiadoubles witheveryfive additionalyears oflifecycleage(Fratiglioni,

De

Ronchi, Agiiero- Torres, 1999). Age-drivendeclines inanalytic performancearepartially offsetbyage-driven increases in experience. Ifgeneral taskperformanceisa function of both analyticabilityandexperiential knowledge,thengeneraltaskperformanceshouldfirstincreasewithage (aspeopleaccumulate

more

earlylifeexperience),

and

thendecline (as experience saturates).'' Figure 3illustrates thismechanism.

The

currentpaperteststhehypothesis that general taskperformanceshould followa

hump-shapedpatternwithage.

We

focusonfinancialdecision-making. Because ourfinancialmarket

'Thisisastandard deviation calculatedfromtheentirepopulationof individuals. ''SeeFlynn(1984)fora discussionofcohorteffects.

''

SupposeAnalyticPerformance(AP)

=

a—faxage,andExperience

=

c-I-dxage,whiletotalperformance

Memory

study the followingwords andthienwriteas

manyasyoucanremember

Goat Door Fish Desk Rope Lake Boot Frog Soup Mule SpatialVisualization

Select the objecton theright thatcorrespondsto

the patternontheleft

cfa

_{Q B g}

Reasoning

Select thebestcompletion of the missingcell in

the matrix !

n A

D

A

1

A

1

A

D

O

!Z1

A

I

—

PerceptualSpeed

Classify thepairsassame(S) or different(D)as

quicklyas possible

Figure 1: Four

IQ

testsusedtomeasurecognitiveperformance. Source:Salthouse (forthcom-

ing)-dataspana short

number

ofyears,

we

areunableto

decompose

the relativecontributions of ageandcohorteffects.

3

Overview

We

document

a

U-shaped

curveinfinancial "mistakes" over the lifecyclein ten separate contexts:

home

equity loans

and

linesof credit; autoloans; creditcard interest rates; mort-gages; small business credit cards; creditcard late

payment

fees; creditcard over limit fees;

creditcardcashadvancefees;

and

use ofcreditcardbalancetransferoffers.

We

diagnose mistakesinthree forms: higher

APRs

(interest rates);higherfeepayments;

and

suboptimaluse ofbalancetransferoffers.

For eachapplication,

we

conductregression analysisthatidentifiesageeffectsandcontrols for observable factors that mightexplain patterns offee

payments

or

APRs

byage. Thus, unless otherwise noted,ineachcontext

we

estimate a regressionofthe type:

(1)

F —

a

+

/3X Spline{Age)

+

-yx Controls

+

e.

Salthouse Studies-MemoryandAnalyticTasks 1.5 1.0 -0.5 -0.0 -0.5 --1.0 --1.5 -2.0 V-

—

MatrixReasoning(N =2.440) SpatialRelations (N =1,611 PatternComparison(N = 6,547) 69 50 CD leS 7 20 30 40 50 60 70 80 CiironologicalAge

Figure2:

Age-normed

resultsfrom fourdifferentcognitivetests.

The

Z-score represents the age-contingentmean,

measured

inunits ofstandarddeviationrelativeto thepopulationmean.

More

precisely, the Z-scoreis (age-contingent

mean

minus population

mean)

_/ (population standarddeviation). Source: Salthouse (forthcoming).

Cognitive capital Task Performance Experiential capital

Performance

Analytic capital

Age

Figure3: Hypothesizedrelationbetweengeneral taskperformanceandage. Analytical capital declines with age and experiential capital increasewith age. Thisgenerates the hypothesis thatgeneral taskperformance (whichusesboth analytical

and

experientialcapital)firstrises

isa vector of control variables intended tocapturealternativeexplanationsineachcontext(for example, measuresofcredit risk),

and

S'pline{Age) is a piecewiselinear function that takes

consumer

age asitsargument(withknotpointsatages30, 40, 50,60

and

70).^

We

thenplot thefittedvaluesforthe splineonage. Regressions are eitherpooledpanel orcross-sectional, dependingonthe context.

Each

sectiondiscussesthenatureofthe mistake,briefly

documents

the datasets used, and presents the regressionresultsand graphs byage.

We

provide

summary

statistics forthedata sets intheAppendix.

4

Home

Equity

Loans

4.1

Data Summciry

We

use a proprietary panel dataset from a large financial institution that issued

home

equity loans

and

home

equitylinesofcredit nationally.

Between

March and December

2002, the lender offered a

menu

ofstandardized contracts for

home

equity credits.

Consumers

couldchoose betweenacreditloan

and

line;betweenafirst

and

secondlien;

and

couldchoose to pledge different

amounts

ofcollateral, withthe

amount

of collateral implying a loan-to-value

(LTV)

ratio ofless than 80 percent, between 80 and 90 percent,

and

between 90 an 100 percent) Ineffect, the lender offered twelvedifferent contractchoices. For 75,000 such contracts,

we

observe the contract terms, borrower demographic information (age, years at currentjob,

home

tenure),financialinformation (income

and

debt-to-incomeratio), andrisk characteristics (credit

(FICO)

score, and

LTV).

We

alsoobserveborrowerestimates oftheir housevalues

and

the loan

amount

requested.

4.2

Results

Table1reportstheresultsofestimating regressions of

APRs

(interest rates)on

home

equity loansona splinefor ageandcontrolvariables.

As

controls,

we

useallvariables observable to thefinancialinstitution thatmightaffect loanpricing, includingcredit risk measures, house andloancharacteristics,

and

borrowerfinancialand demographiccharacteristics.

The

control variablesall have theexpectedsign,

and most

arestatisticallysignificant, although

some

of

them

lackeconomicsignificance,perhapssurprisingly soin

some

cases.

The

measureof credit risk, the logofthe

FICO

score (lagged three

months

because it isonly updated quarterly), comes instatistically significant but witha negligiblemagnitude.

Our

understanding from discussionswithpeople

who

work

intheindustryisthatfinancialinstitutionsgenerally use the

'""Forinstance, inTable 1, the "Age30-40" splineis: max(30,min(40, /Ige)),the "Age

<

30" spline is

Home

EquityLoan

APR

byBorrower

Age

Borrower

Age

(Years)

Figure4:

Home

equityloan

APR

by

borrower age.

The

figureplotsthe residualeffectofage, aftercontrollingforother observablecharacteristics,suchaslog(income)

and

credit-worthiness.

FICO

scoretodetermine whethera loanofferismade, butconditionalontheofferbeingmade, donot use the score to dorisk-based pricing.

The

results here, andfor theotherconsumer credit products discussed below, are consistentwiththishypothesis.

Loan

APRs

dodepend stronglyontheabsenceofafirstmortgage (reducing the

APR),

and whetherthepropertyis

a second

home

ora condominium.

The

absenceofafirst mortgagereduces the probability of default andraises the

amount

thatmight be recovered conditionalon adefault. Second

homes

and

condominiums

are perceivedasbeingriskierproperties.

Log

incomeandlogyears

on

thejobalsohavelarge

and

negativeeffectson

APRs,

asexpected, sincetheyindicate

more

resources available topayofftheloan,

and

perhaps lessrisk inthelatter case.

The

largest effects on

APRs

come

from

dummy

variablesfor

LTV

ratios between80and90 percent and forratiosgreaterthan 90percent. Thisisconsistentwithdifferent

LTV

ratioscorresponding todifferentcontract choices.

Even

aftercontrollingforthesevariables,

we

findthattheagesplineshavestatistically

and

economicallysignificant effects. Figure 4 plots thefittedvaluesonthe splineforagefor

home

equity loans.

The

linehas apronounced U-shape, with

some

younger

and

olderborrowers paying100 basis points

more

than borrowersintheir late fortiesandearlyfifties. Forthis

and

the nine otherstudies,

we

presentinsection 14.2a formaltest fortheU-shape,whichthedata willpass.

Home

Equity

Loan

APR

Coefficient Std. Error Intercept 8.1736 0.1069

Log(FICO

Score) -0.0021 0.0001

LoanPurpose-Home Improvement 0.0164 0.0138 Loan Purpose-RateRefinance -0.0081 0.0113

No

FirstMortgage -0.1916 0.0097 Log(Months atAddress) 0.0021 0.0039 Second

Home

0.3880 0.0259

Condominium

0.4181 0.0165 Log(Income) -0.0651 0.0077 Debt/Income 0.0034 0.0002 Log(YearsontheJob) -0.0246 0.0039 SelfEmployed 0.0106 0.0161

Home

Maker -0.0333 0.0421 Retired 0.0355 0.0225 Age

<

30 -0.0551 0.0083 Age30-40 -0.0336 0.0043 Age40-50 -0.0127 0.0048 Age50-60 0.0102 0.0039 Age60-70 0.0174 0.0076 Age

>

70 0.0239 0.0103

LTV

80-90 0.7693 0.0099

LTV

90-t- 1.7357 0.0111

State

Dummies

YES

Number

ofObservations 16,683 Adjusted R-squared 0.7373

Table 1:

The

first

column

gives coefficient estimatesfor a regressionofthe

APR

ofa

home

equity loanona splinewithage asitsargument,financialcontrol variables

(Log(FICO)

credit risk score,income,

and

the debt-to-income-ratio),

and

other controls(statedummies,a

dummy

forloans

made

for

home

improvements,a

dummy

forloans

made

forrefinancing,a

dummy

for nofirstmortgageonthe property,

months

atthe address, yearsworked onthejob,

dummies

for self-emplyed,retiree,or

homemaker

status,

and

a

dummy

ifthepropertyisacondominium).

Home

EquityCreditLine

APR

byBorrower

Age

Borrower

Age

(Years)

Figure5:

Home

equity creditline

APR

by borrower age.^

The

figureplots the residualeffect ofage, aftercontrolling for other observablecharacteristics, such aslog(income) and credit-worthiness.

5

Home

Equity

Lines of

Credit

5.1

Data

Summary

Data

arethe

same

as describedinthe previoussection.

5.2

Results

Table2reportstheresultsof estimating regressions of

APRs

on

home

equitylinesof credit on asplineforage

and

the

same

control variables usedforthe

home

equity loans regression.

The

control variableshavesimilareffectson

home

equityline

APRs

asthey didfor

home

equity loan

APRs.

Fitted valuesontheagesplines,plottedinFigure5,continue tohavethe

same

pronounced U-shape, with

some

younger

and

older borrowers again paj'ing 100 basis point

more

than borrowersin their late fortiesandearly fifties. , .

5.3

One

Mechanism: Borrower

Misestimation

of

Home

Values

The amount

of collateralofferedbytheborrower,asmeasured bythe loan-to- value

(LTV)

ratio, is an important determinant ofloan

APRs.

Higher

LTVs

imply higher

APRs,

since

Home

Equity Line

APR

Coefficient Std. Error Intercept 7.9287 0.0570

Log(FICO

Score) -0.0011 0.0000

Loan Purpose-Home Improvement 0.0551 0.0051 Loan Purpose-RateRefinance -0.0386 0.0047

No

FirstMortgage -0.1512 0.0054 Log(MonthsatAddress) -0.0160 0.0019 Second

Home

0.3336 0.0132

Condominium

0.4025 0.0079 Log(Income) -0.1474 0.0037 Debt/Income 0.0044 0.0001 Log(YearsontheJob) -0.0164 0.0020 SelfEmployed 0.0135 0.0073

Home

Maker -0.0818 0.0215 Retired 0.0139 0.0109

Age

<

30 -0.0529 0.0050 Age30-40 -0.0248 0.0023 Age40-50 -0.0175 0.0022 Age50-60 0.0152 0.0035 Age60-70 0.0214 0.0064 Age

>

70 0.0290 0.0154

LTV

80-90 0.6071 0.0050

LTV

90+

1.8722 0.0079 State

Dummies

YES

Number

ofObservations 66,278 Adjusted R-squared 0.5890

Table2: Tliefirst

column

givescoefficientestimatesfora regression of the

APR

ofa

home

eq-uitylinesofcrediton a sphne withage asitsargument,financialcontrol variables

(Log(FICO)

credit risk score, income,

and

the debt-to-income-ratio),

and

other controls (state

dummies,

a

dummy

forloans

made

for

home

improvements, a

dummy

forloans

made

for refinancing,a

dummy

fornofirstmortgage onthe property,

months

atthe address, yearsworked onthejob,

dummies

forself-employed, retiree, or

homemaker

status,

and

a

dummy

iftheproperty is a

condominium)

.

the fraction ofcollateralislower. Atthisffnancial institution,borrowersestimatetheir

home

values,

and

askfora creditloan orhnefallingintooneofthree categoriesdepending onthe implied

LTV.

The

categoriescorrespond to

LTVs

of80percent orless;

LTVs

ofbetween80

and

90 percent;

and

LTVs

of90percent orgreater.

The

financialinstitutionseparatelyverifies thehousevalueusinganindustry-standard methodology.

Loan

pricingdepends

on

the

LTV

category theborrower falls into, and noton thespecific valuewithin that category; that is,

aloanwithan

LTV

of60has the

same

interest rateas a loanwith an

LTV

of70, holding borrowercharacteristicsfixed.

^

Iftheborrowerhasoverestimatedthe value of the house, so that the

LTV

isin facthigher thanoriginallyestimated, thefinancialinstitutionwilldirectthebuyertoadifferentloanwith a higherinterestratecorrespondingtothehigher

LTV.

Insuchcircumstances, the loanofficer

is alsogiven

some

discretionto departfromthefinancial institution'snormalpricingschedule to offer a higher interest rate than he or she would haveto aborrower

who

had

correctly estimated the

LTV.

Iftheborrower has underestimatedthevalue of the house,however, the financialinstitutionneednotdirectthebuyertoaloanwitha lowerinterestratecorresponding to the actual lower

LTV;

it

may

simply choose toofferthe same, higherinterest rate, for a lower-riskloan.'^

Since the

APR

paiddepends on the category the

LTV

falls in, andnot the

LTV,

home

value misestimation only leadsto higher interestrate

payments

if itcauses

LTVs

tochange in such a

way

that the loan

moves

intoa differentcategory. If, incontrast, theborrower's estimated

LTV

wereequal to 60,butthe true

LTV

were70, theborrowerwouldstillqualify for the highest quality loan category

and

wouldnotsufferan interestratepenalty.

We

define a Rate

Changing

Mistake

(RCM)

tohave occurred

when

a borrower'smisestimationofhouse value causes achangein

LTV

category

and

potentiallyachange ininterestrate paid.^

We

find that, on average,

making

an

RCM

increasesthe

APR

by 125 basis points forloansand 150 basis pointsforlines (controllingforothervariables,butnotage).

Ifthe probability of

making

a rate-changingmistakeisU-shaped withage,thena regression of

APR

onage conditioningonnothaving an

RCM

should

show

a nearlyflatpattern.^

We

haveverified thispracticein our datasctbyregressing the

APR

on boththe levelofthe

LTV

and

dummy

variables forwhetherthe

LTV

falls intooneofthe threecategories. Onlythecoefficients onthe

dummy

variableswerestatisticallyandeconomicallysignificant.

"^Notethatevenifthefinancial institution'sestimateofthe truehouse valueisinaccurate,that misestimation

willnotmatterfortheborroweraslongasotherinstitutionsusethesamemethodology.

*Specifically,

RCMs

occurwhentheborrower's estimationof hisorherhouse valueissuch that the

LTV

is lessthan80,whilethe true

LTV

isbetween80and90; ortheestimated

LTV

islessthan 80andthe true

LTV

isgreaterthan90;ortheestimated

LTV

isbetween80and90,but the trueislessthan80; ortheestimated

LTV

isbetween80and90,but the true

LTV

isgreaterthan90; orthe estimated

LTV

isgreaterthan90,but the true

LTV

islessthan80; ortheestimated

LTV

isgreaterthan90,but the true

LTV

isbetween80and90. ^Bucksand Pence (2006) present evidence that borrowersdonot generally have accurate estimatesof their

housevalues.

PropensityofMakingaRate-ChangingMistakeon

Home

EquityLoansbyBorrower

Age

Borrower

Age

(Years)

Figure 6: Propensityof

making

aRate

Changing

Mistakeon

home

equity loansby borrower age.

We

define a

Rate

Changing

Mistaketohave occurredwlien a borrower'smisestimation ofhousevaluecausesachangein

LTV

category

and

potentiallya changeininterestratepaid (see the textforafulldefinition).

The

figureplotsthe residualeffect ofage, aftercontrolling forotherobservablecharacteristics,suchaslog(income)

and

credit-worthiness.

PropensityofMakingaRate-ChangingIVlistakeon

Home

Equity Credit LinesbyBorrower

Age

90% 80% 70%

_\

^

60% C V O 50% -a> '^ 40%-

\

.

30%

\

^^^

20%

\

'

^^^^^^

10%

^"^-^

^^^--^'^^^

0%

Borrower

Age

(Years)

Figure 7: Propensity of

making

a Rate

Changing

Mistake on

home

equity credit lines

by

borrowerage.

We

definea

Rate

Changing

Mistaketohave occurred

when

a borrower's mises-timationofhousevahiecausesachangein

LTV

category

and

potentiallyachangein interest ratepaid (seethe textfor a fulldefinition).

The

figureplotsthe residualeffect ofage, after controllingforotherobservablecharacteristics,suchaslog(income) andcredit-worthiness.

Home

EquityLoan

APRs

forBorrowers

Who

DoNotMakea Rate-ChangingIVIistal<e

Borrower

Age

(Years)

Figure8:

Home

equity loan

APRs

forborrowers

who

donot

make

a rate-changing mistake.

The

figureplotsthe residualeffectofage, aftercontrollingforotherobservablecharacteristics, suchaslog(income) andcredit-worthiness.

Figures 6

and

7 plots the probabilityof

making

a rate-changingmistakebyagefor

home

equity loans

and

home

equitylines,respectively.

The

charts

show

U-shapesforboth. Borrow-ers atage 70havea 16(19)percentagepoint greaterchanceof

making

amistakethan borrowers at age 50 for

home

equity loans (lines); borrowersat age 20have a 35(41) percentage point greaterchance of

making

a mistake than borrowers at age 50.

The

unconditional average probability of

making

a rate-changingmistakeis24percentforloans

and

18percentforlines.

Figures 8

and

9plotthefittedvaluesfromre-estimatingthe regressionsintable3,but

now

conditioningontheborrowernot

making

anRCAi.

The

plotsshowsonlyslightdifferences in

APR

paidbyage.

The

APR

differencefora

home

equity loanforaborrowerat age70 over aborrowerat age50has shrunk from36 basis points to 8 basis points;fora

home

equityline ofcredit, it has slnrunkfrom 28 basis points to 4 basis points. For aborrower atage20, the

APR

differenceover aborrowerat age50 hasshrunk to 3basis pointsfor

home

equity loans and3basispointsfor

home

equitylinesofcredit.

This disappearanceofthe ageeffectisconsistentwiththecostofan

RCM

calculatedabove andthe additional probabilityof

making

an

RCM

byage. Forexample,a70-year old has a 16 and 19 percent additionalchanceof

making

an

RCM

forloans anlines. Multiplyingthisby the average

APR

cost ofan

RCM

for

home

equitylines

and

loans of150and 125 basis points, respectively, gives an expected in

APR

paid of26

and

23 basis points. Thesedifferences

Home

EquityCreditLine

APRs

forBorrowers

Who

DoNot Mal<e aRate-Changing Mistake

BorrowerAge(Years)

Figure 9:

Home

equity credit line

APRs

for borrowers

who

do not

make

a rate-changing mistake.

The

figure plots the residual effect ofage, after controlling for other observable characteristics,suchaslog(income)

and

credit-worthiness.

are,veryclosetotheestimateddifferencesof36-8=28 basispointsfor lines

and

28-5=23basis pointsfor loans.

6

Credit

Cards

6.1

Data

Summary

We

use aproprietarypanel datasetfroma large U.S.

bank

thatissuescredit cardsnationally.

The

dataset contains a representative

random

sampleofabout 128,000 credit card accounts followedmonthlyovera36

month

period(fromJanuary 2002 through

December

2004).

The

bulk ofthe data consists of the

main

billing information listed on each account's monthly statement, includingtotalpayment, spending, credit limit,balance, debt, purchasesandcash advance annualpercent rates (APRs), andfeespaid. At a quarterly frequency,

we

observe each customer's credit bureau rating

(FICO)

and a proprietary (internal) credit 'behavior' score.

We

havecreditbureau data aboutthe

number

ofothercreditcards held

by

theaccount holder,total credit card balances,

and

mortgagebalances.

We

have dataontheage,gender

and

incomeofthe accountholder, collected atthe timeofaccount opening. Furtherdetails

on

the data, including

summary

statisticsandvariable definitions, are availablein the data

Credit

Card

APR

Coefficient Std. Error Intercept 14.2743 3.0335 Age

<

30 -0.0127 0.0065 Age30-40 -0.0075 0.0045 Age40-50 -0.0041 0.0045 Age50-60 0.0023 0.0060 Age60-70 0.0016 0.0184 Age

>

70 0.0016 0.0364 Log(Income) -0.0558 0.0803 Log(FICO) -0.0183 0.0015

Home

Equity Balance 0.0003 0.0022 MortgageBalance -0.0000 0.0000

Number

ofObservations 92,278 Adjusted R-squared 0.0826

Table 3: This table givescoefficient estimates for a regression oftire

APR

ofa credit card ona splinewithage asitsargument,financialcontrol variables

(Log(FICO)

credit risk score, income, total

number

of cards, totalcard balance,

home

equity debt balance

and

mortgage balance).

appendix.

6.2

Results

Table 3 reports the results ofregressing credit card

APRs

on a spline with age as the argument

and

other controlvariables.

As

controls,

we

again use informationobservedbythe financialinstitutionthat

may

influencetheir pricing.

As

before,

we

findthatcreditscoreshave verylittle impacton creditcard

APRs.

APRs

rise withthe total

number

ofcards, though theeffectisnot statistically significant. Othercontrols, including thetotalcard balance, log income,andbalancesonother debt,donothave economicallyorstatisticallysignificant effects oncreditcard

APRs.

Figure??plotsthefittedvaluesonthe splineforage.

A

U-shapeispresent,though

much

lesspronounced thaninthe case of

home

equityloans.

7

Auto

Loans

7.1

Data

Summary

We

usea proprietarydatasetofautoloans originatedatseveral largefinancialinstitutions thatwerelateracquiredby anotherinstitution.

The

datasetcomprisesobservationson 6996 loans originatedforthepurchaseof

new and

usedautomobiles.

We

observe loan characteristics includingtheautomobilevalueandage,theloan

amount and

LTV,

themonthly payment,the

CreditCard

APR

byBorrower

Age

Borrower

Age

(Years)

Figure10: Credit card

APR

by borrowerage.

The

figureplotsthe residualeffectofage, after controllingforotherobservablecharacteristics,suchaslog(income)

and

credit-worthiness.

contractrate,

and

thetimeof origination.

We

alsoobserveborrowercharacteristicsincluding credit score,

monthly

disposableincome,

and

borrowerage.

7.2

Results

Table4reports theresultsofestimating a regression of the

APR

paidon autoloansona splinewithageastheargument andcontrolvariables.

FICO

credit riskscores againhavelittle

effectontheloan terms. Higherincomeslower

APRs

and

higherdebt-to-incomeratios raise them, though themagnitudes ofthe effects are neglige.

We

alsoinclude car characteristics, such astype

and

age, as one ofus has found those variables to matter for

APRs

inother

work

(Agarwal,

Ambrose

and Chomsisengphet, forthcoming)-though

we

note that thefinancial institutionsdonot conditiontheirloanson suchvariables.

We

alsoinclude loanage

and

state

dummies.

Figure 11 plots thefitted values

on

the splinefor age.

The

graph again shows arather pronounced U-shape.

Auto Loan

APR

CoefRcicnt Std. Error Intercept n.4979 1.3184 Age

<

30 -0.0231 0.0045 Age30-40 -0.0036 0.0005 Age40-50 -0.0054 0.0005 Age50-60 0.0046 0.0007 Age60-70 0.0031 0.0017 Age

>

70 0.0091 0.0042 Log(Income) -0.3486 0.0176 Log(FICO) -0.0952 0.0059 Debt/Income 0.0207 0.0020 JapaneseCar -0.0615 0.0270 European Car -0.0127 0.0038 LoanAge 0.0105 0.0005 CarAge 0.1234 0.0031 State

Dummies

YES

Quarter

Dummies

YES

Number

ofObservations 6,996 AdjustedR-squared 0.0928

Table4: Thistable givescoefficientestimatesfroma regressionofthe

APR

ofan autoloanona splinewithageasitsargument,financialcontrol variables

(Log(FICO)

creditriskscore,income,

and

the debt-to-income-ratio),

and

other controls (statedummies,

dummies

for whetherthe carisJapaneseorEuropean,loanage

and

carage).

AutoLoan

APR

byBorrower

Age

Borrower

Age

(Years)

Figure11:

Auto

loan

APR

by borrowerage.

The

figureplots the residualeffect ofage, after controllingforother observablecharacteristics, suchas log(incQme)

and

credit-worthiness.

8

Mortgages

8.1

Data

Summary

We

usea proprietarydatasetfroma largefinancial institutionthat originatesfirst mort-gagesinArgentina.

The

datasetcovers 4,867owner-occupied,fixedrate,firstmortgageloans originatedbetweenJune 1998

and

March

2000,and observed through

March

2004.

We

observe theoriginalloanamount,the

LTV

and

appraisedhousevalueatorigination,andthe

APR.

We

alsoobserveborrowerfinancialcharacteristics (includingincome, second income,yearsonthe job,wealthmeasures suchassecond house ownershipandcarownership

and

value),borrower riskcharacteristics (Veraz score(acreditscore similar tothe U.S.

FICO

score)

and

mortgage

payments

asapercentageofafter-taxincome),and borrower demographiccharacteristics(age, gender

and

maritalstatus).

8.2

Results

Table5reportsresultsof regressingthemortgage

APR

ona splinewithageasanargument andcontrolvariables.

As

controls,

we

again use variables observable to thefinancialinstitution that

may

affectloanpricing,includingriskmeasures(credit score,income,mortgage

payment

asa fraction ofincome, and

LTV),

andvariousdemographic

and

financialindicators(gender, maritalstatus, adumiriyvariableforcarownership,

and

several others; thesecoefficientsare not reported to save space).

The

coefficients onthe controls areagain of the expectedsign andgenerally statistically significant,thoughofsmallmagnitude.

The

coefficientsontheagesplineare positivebelowagethirty, thennegativethroughage 60

and

positivethereafter. Figure12 plotsthefittedvaluesonthe splineforage.

The

graph again generallyshowsaU-shape, though behaviorforyounger borrowersisratherdifferent.

9

Small Business Credit

Cards

9.1

Data

Summary

We

usea proprietary datasetofsmall business creditcard accounts originatedat several large institutions that issued suchcards nationally.

The

institutionswere later acquired by asingle institution.

The

paneldatasetcovers 11,254 accounts originated between

May

200

and

May

2002.

Most

ofthe business are very small,

owned

by asingle family, and have no formal financialrecords.

The

data sethas all information collected at the time ofaccount origination, including the borrower's self-reported personal income, yeai^s inbusiness of the firm,

and

borrowerage. Quarterly,

we

observe theaccountcreditbureauscore.

Mortgage

APR

Coefficient Std. Error Intercept 12.4366 4.9231 Age

<

30 0.0027 0.0046 Age30-40 -0.0023 0.0047 Age40-50 -0.0057 0.0045 Age50-60 0.0127 0.0093 Age60-70 0.0155 0.0434 Age

>

70 0.0234 0.0881 Log(Income) -0.2843 0.1303 Log( CreditScore) -0.1240 0.0217 Debt/Income 0.0859 0.2869 Loan

Term

-0.0114 0.0037 Loan

Term

Squared -0.0000 0.0000

Loan

Amount

-0.0000 0.0000

LoantoValue 0.1845 0.0187 YearsontheJob -0.0108 0.0046 Second

Home

0.1002 0.1014 Auto 0.1174 0.0807 AutoValue 0.0000 0.0000 Gender(l=Female) 0.0213 0.0706 Married -0.0585 0.0831

Two

Incomes -0.1351 0.1799 Married with

Two

Incomes -0.0116 0.1957 Employment: Professional -0.0438 0.1174 Employment:Non-Professional 0.0853 0.1041 Merchant -0.1709 0.1124

Bank

Relationship -0.2184 0.1041

Number

ofObservations 4,867 AdjustedR-squared 0.1004

Table5: Thistablereports theestimatedcoefficientsfroma regression ofmortgage

APR

ona splinewithage asits

argmnent and

financial

and

demographiccontrolvariables.

Mortgage

APR

byBorrowerAge

Borrower

Age

(Years)

Figure12:

APR

for Argentine mortgages by borrowerage.

The

figureplotsthe residualeffect ofage, after controlling for other observablecharacteristics, suchas log(income)

and

credit-worthiness.

9.2

Results

Table6reports theresultsofregressingthe

APR

forsmall businesscreditcardsonasphne with age as the

argument

and control variables.

As

with individual credit card accounts,

we

control forthe

PICO

score of the borrower, the total

number

ofcards,card balance,

and

cardlimit.

We

alsoinclude

dummy

variablesforyears inbusiness, and expect

APRs

tobe decreasing in this variable. All controls variables are statisticallysignificant and have the expectedsign, thoughonly the

dummies

foryearsinbusinesshavesubstantialmagnitudes.

APRs

aredecreasingintheageoftheborrowerthrough age60, andincreasingthereafter. Figure13 plotsthefittedvaluesonthe splinefor age.

The

graph showsapronounced U-shape.

10

Credit

Card

Fee

Payments:

Late

Fees

10.1

Overview

Certaincreditcard uses involve the

payment

ofafee.

Some

kindsof feesareassessed

when

termsofthecreditcard agreementareviolated. Otherkinds are assessedforuse ofservices. Inthe next threesections,

we

focusonthree importanttypes offees: late fees,over limit

Small Business Credit

Card

APR

Coefficient Std. Error Intercept 16.0601 0.6075 Age

<

30 -0.0295 0.0081 Age30-40 -0.0068 0.0040 Age40-50 -0.0047 0.0038 Age50-60 -0.0017 0.0055 Age60-70 0.0060 0.0209 Age

>

70 0.0193 0.0330 YearsinBusiness1-2 -0.5620 0.1885 YearsinBusiness2-3 -0.7463 0.1937 YearsinBusiness3-4 -0.2158 0.1031 YearsinBusiness4-5 -0.5100 0.0937 YearsinBusiness5-6 -0.4983 0.0931 Log(FICO) -0.0151 0.0008

Number

ofCards 0.1379 0.0153

Log(TotalCardBalance) 0.0000 0.0000 Log(TotalCardLimit) 0.0000 0.0000

Number

ofObservations 11,254 Adjusted R-squared 0.0933

Table6: Thistablereportstheestimatedcoefficients froma regression of the

APR

forsmall business credit cards

on

aspline with the business owner's age as its

argument

and other control variables

(dummies

for j^ears inbusiness,log(FICO)credit risk score,

number

ofcards, total card balance,and totalcardlimit).

SmallBusinessCreditCard

APR

byBorrower

Age

Borrower

Age

(Years)

Figure 13: Small business creditcard

APR

by borrowerage.

The

figure plots the residual effect ofage, after controlling for other observable characteristics, such aslog(income) and credit-worthiness

.

fees, and cash advancefees.-^°

We

describe thefeestructureforour datasetbelow.

1.

Late

Fee:

A

late fee ofbetween $30

and

$35isassessediftheborrower

makes

a

payment

beyond

theduedateonthecreditcard statement. Iftheborrowerislateby

more

than 60days once, orby

more

than 30days twicewithin ayear, the

bank

may

alsoimpose 'penaltypricing' byraisingthe

APR

to over 24 percent.

The bank

may

alsochoose to report late

payment

tocreditbureaus, adverselyaffecting consumers'

FICO

scores. If

theborrower does not

make

a late

payment

duringthe six

months

after thelastlate payment,the

APR

willrevert toitsnormal (thoughnotpromotional)level.

2.

Over

Limit

Fee:

An

overlimit fee, alsoofbetween $30 and$35, is assessedthe first

time theborrower exceedshis orher credit limit.

The same

penalty pricing asinthe late feeisimposed.

3.

Cash

Advance

Fee:

A

cash advance fee ofthe greater of 3 percent of the

amount

advanced,or$5,isleviedforeach cash advanceonthecreditcard. Unlike thefirsttwo fees,this feecanbeassessed

many

times permonth. Itdoes not cause the impositionof penaltypricingon purchasesor debt. However,the

APR

on cash advancesistypically greaterthanthaton pmxhases,

and

isusually 16percent ormore.

Payment

ofthesefees

may

be viewedas mistakesinthatfee

payment

may

beavoidedby small

and

relatively costlesschangesinbehavior.

We

use the

same

dataset as thatusedfor thecreditcard

APR

casestudydiscussedabove.

10.2

Results

Table 7 presents panel regressionsfor each typeoffee. In eachof the threeregressions,

we

regressa

dummy

variableequal to oneifafee ispaid that

month

ona splineforage

and

controlvariables;hencethecoefficientsgivethe conditionaleffectsoftheindependentvariables onthe propensity to payfees.

The

control variablesdiffer fromthose of the precedingsix examples, since

now

we

wish to control for other things that mightaffect thepropensity to

pay

afee, which arenot necessarily the

same

asthingsthatmightleadborrowerstodefault orotherwiseaffecttheirborrowingterms. "BillExistence" isa

dummy

variableequaltoone

ifabill wasissued lastmonth; borrowerswillonlybeeligibletopay alate fee ifabill was issued. "BillActivity" isa

dummy

variableequal tooneifpurchases or paymeiatswere

made

Othertypesof feesincludeannual,balancetransfer,foreign transactions,and pay byphone. All ofthese

fees are relatively lessimportanttoboththe-bankandthe borrower. Fewissuers(themostnotable exception beingAmericanExpress) continuetocharge annualfees,largely asaresultofincreased competitionfornew borrowers(Agarwaletal.,2005). Thecardsinourdatadonothave annualfees.

We

study balancetransfer

behavior using a separate datasetbelow. Theforeign transactionfeesandpayby phonefeestogether comprise

lessthan three percentofthetotal fees collectedbybanks.

onthe card; borrowerswillonlybeeligibleto payoverlimit orcashadvancefeesifthe card wasused. "Log(Purchases)" isthe log of the

amount

purchased onthe card, indollars;

we

would expectthat the propensity topayoverlimitandcashadvancefeeswould beincreasing with the

amount

ofpurchases.

"Log(FICO)"

isthecredit risk score,

and

"Log(Behavior)" is

aninternalriskscore createdbythe

bank

topredictlate

and

delinquent

payment beyond

that predictedbythe

FICO

score. Higherscores

mean

lessrisky behavior.

The

scores arelagged three

months

because they are only updated quarterly.

We

would expect the underlying behaviorleading to lowercredit riskscoreswouldlead tohigherfeepayment. "Debt/Limit"

isthe ratio of the balance ofcreditcarddebttothecredit limit;

we

would expectthathaving lessavailablecreditwould raisethepropensity topayoverlimit fees,

and

possibly otherfees.

For late fee payments,

column

one ofthe table, all control variables have the expected signs

and

arestatistically significant, though they arealso small in magnitude. Note that

some

control variables

may

partlycapturetheeffectsofage-related cognitive declineonfees.

Forexample,ifincreasingage

makes

borrowers

more

likelytoforgettopayfeesontime,that would bothincreasethe propensity topaylate fees anddecreasecredit and behaviorscores.

Hence

theestimatedcoefficientsonthe agesplines

may

understate

some

age-related effects. Coefficientsontheagesplinesareuniformlynegativeforsplinesthroughage50, negative orweaklypositiveforthe splinebetweenage 50and60, andpositivewithincreasing slopefor splinesaboveage50.

The

top line in Figure 14 plotsfitted valuesfor the age splinesfor the late fee

payment

regression.

11

Credit

Card

Fee

Payments:

Over

Limit

Fees

The

second

column

ofTable7 presents regressionresults forthe overlimitfee,onthe

same

controls

and

agesplines asforthelatefee. Results arevery similar to thoseforthelatefee.

The

bottom

lineinFigure14 plots fittedvaluesfor theage splines forthe overlimit fee

payment

regression.

12

Credit

Card

Fee

Payments:

Cash

Advance

Fees

The

second

column

ofTable7 presents regressionresults forthe cash advancefee, onthe

same

controls

and

agesplinesasforthelatefee. Results arevery similar to thoseforthelate fee

and

overlimitfee.

The

middlelineinFigure 14 plotsfittedvaluesfortheagesplines forthecashadvancefee

payment

regression.

Late

Fee

Over

Limit

Fee

Cash Adv.

Fee

Coeff. Std. Err. Coeff. Std. Err. Coeff. Std. Err. Intercept 0.2964 0.0446 0.1870 0.0802 0.3431 0.0631 Age

<

30 -0.0021 0.0004 -0.0013 0.0006 -0.0026 0.0011 Age30-40 -0.0061 0.0003 -0.0003 0.0001 -0.0004 0.0002 Age40-50 -0.0001 0.0000 -0.0002 0.0000 -0.0002 0.0000 Age50-60 -0.0002 0.0000 -0.0002 0.0000 -0.0003 0.0000 Age60-70 0.0004 0.0002 0.0003 0.0001 0.0004 0.0000 Age

>

70 0.0025 0.0013 0.0003 0.0001 0.0004 0.0000 BillExistence 0.0153 0.0076 0.0104 0.0031 0.0055 0.0021 BillActivity 0.0073 0.0034 0.0088 0.0030 0.0055 0.0021 Log(Purchases) 0.0181 0.0056 0.0113 0.0023 0.0179 0.0079 Log(Behavior) -0.0017 0.0000 -0.0031 0.0012 -0.0075 0.0036 Log(FICO) -0.0016 0.0007 -0.0012 0.0003 -0.0015 0.0005 Debt/Limit -0.0066 0.0033 0.0035 0.0013 0.0038 0.0012 Acct. FixedEff.

YES

YES

YES

Time

FixedEff.

YES

YES

^ES

Number

ofObs. 3.9Mill. 3.9Mill. 3.9Mill.

Adj. R-squarcd 0.0378 0.0409 0.0388

Table7: Thistablereportscoefficients-froma regression of

dummy

variablesforcreditcardfee

payments on

asphneforage, financialcontrol variables (log(FICO) credit risk score,internal

bank

behaviorriskscore,debtoverlimit)

and

other control variables

(dummies

forwhether a

billexistedlastmonth, forwhetherthecardwas usedlastmonth,dollar

amount

ofpurchases, account- andtime-fixed effects).

FrequencyofFeePaymentbyBorrowerAge 0.35 0,33

S

0.31 c o £0.29 g_0.27 2*0.25-C as 30.23 -CT

i

0.21 -O d)0.19 -u. 0.17 0.15

LateFee OverLimitFee

"

Cash AdvanceFee

BorrowerAge(Years)

Figure 14: Frequencyoffee

payment

by borrower age.

The

figureplots the residualeffect ofage, aftercontrollingfor other observable characteristics, suchas log(income) and credit-worthiness.

13

'Eureka'

Moments:

Balance Transfer Credit

Card

Usage

13.1

Overview^

Creditcard holders frequently receiveoffersto transfer account balancesontheircurrent cards to a

new

card. Borrowers paysubstantially lower

APRs

onthe balances transferred to the

new

card fora six-to-nine-month period (a 'teaser' rate). However,

new

purchaseson the

new

cardhavehigh

APRs.

The

catchisthatpayments onthe

new

cardgofirsttowards

paying

down

the (low interest) transferred balances,

and

only subsequently towards paying

down

the (highinterest) debt accumulated from

new

purchases.

The

optimalstrategyforborrowers,is to

make

all

new

purchasesontheir old creditcard

and

to

make

no

new

purchases withthe

new

cardto which balances havebeentransferred.

We

hypothesize that

some

borrowerswill figure this out before

making

anypurchases with the

new

card.

Some

borrowers

may

notinitially understandthe optimal strategy, andwill onlyfigureitoutbyobservingtheir (surprisingly) highinterestcharges.

Those

borrowerswill

make

purchasesfor oneor

more

months, then havea 'eureka'

moment,

after whichtheywill implementtheoptimalstrategy.

Some

borrowers willneveridentifytheoptimalstrategy.

13.2

Data

summary

We

usea proprietarypaneldatasetfromseverallargefinancial institutions, lateracquired by asingle financial institution, that

made

balancetransfer offers nationally.

The

dataset contains 14,798 accounts which accepted suchoffers over theperiod January 2000 tlirough

December

2002,

The

bulkofthedataconsists ofthe

main

bilhng informationlistedon each account'smonthlystatement, includingtotal payment,spending, credithmit, balance, debt, purchases and cash advance annual percent rates (APRs), and feespaid.

We

also observe the

amount

ofthe balance transfer, the start date of the balance transfer teaser rateoffer,

theinitialteaser

APR

onthebalancetransfer,

and

theenddateofthebalancetransfer

APR

offer.

At

aquarterly frequency,

we

observeeachcustomer'screditbureaurating

(FICO)

and a proprietary(internal)credit 'behavior'score.

We

havecreditbureau data aboutthe

number

of other credit cards held by the accountholder, total credit card balances,

and

mortgage balances.

We

have data on the age, gender

and

income ofthe account holder, collected at thetime ofaccount opening. Furtherdetails onthe data, including

summary

statistics

and

variabledefinitions, are availableinthedata appendix.

13.3

Results

About

onethird ofallcustomers

who

make

abalancetransferdo no spending onthe

new

card, thusimplementing the optimalstrategyimmediately. Slightly

more

than onethirdof customers

who make

a balance trairsfer spend every

month

duringthe promotional period, thus never experiencing a "Eureka"

moment.

Figure15 plots thefrequencyofEureka

moments

foreachage group.

The

plotofthose

who

never experience a "Eureka"

moment-that

is,

who

neverimplementtheoptimalstrategy-is a pronounced U-shape byage.

The

plot ofthose

who

implementthe strategyimmediately isa pronouncedinverted U-shape byage. Plots fortheother

months

arerelativelyflat.

Table8 reports theresults ofa regression of a

dummy

variablefor everhaving aEureka

moment

ona spline for age and controls for creditrisk (log(FICO)), education, gender

and

log(income).-''. Creditriskisincluded becausehigher scores

may

be associatedwithgreater financialsophistication. Similarly,

we

would expect borrowers withhigherlevelsofeducation tobe

more

likelytoexperienceEureka

moments

The

coefficientsontheage splineimplythat

young

adults

and

older adults arelesslikelytoexperienceEureka

moments.

Figure16 plotsfittedvalues forthe agesplines.

Note

that, unlike the otherfigures, higher values indicatea smaller propensity to

make

mistakes.

"Although wereportan

OLS

regressionforeaseininterpretingthecoefficients,wehavealsorun theregression

Fraction ofBorrowersinEachAge GroupExperiencinga EurekaIVloment,byiVIonth

50% ---MonthOne --- MonthFour NoEureka MonthTwo MonthFive MonthThree MonthSix 40%

\^,.

----"''

-^^

30%

;.--'^^^

20% 10%

,..___

0% 18to24 25to34 35to44 45to64 Over 65

BorrowerAgeCategory

Figure15: Fraction ofborrowersineachagegroupexperiencingspecific delays. Forexample, thedashed-bluelineplotsthe fraction ofborrowersexperiencingnodelay to aEureka

moment.

Thesesophisticatedborrowersrepresenta large fraction ofmiddle-aged households

and

a

much

smaller fraction ofyounger

and

olderhouseholds.

Propensity

of

Eureka

Moment

Coefficient Std. Error Intercept Age

<30

Age30-40 Age40-50 Age50-60 Age60-70 Age >70

Some

HighSchool HighSchoolGraduate

Some

College Associate'sDegree Bachelor'sDegree Graduate log(FICO) log(Limit) log(Income) 0.2587 0.0134 0.0019 -0.0001 -0.0029 -0.0035 -0.0083 -1.6428 -0.6896 -0.4341 -0.2439 0.3280 0.6574 0.0102 0.0120 -0.0044 0.0809 0.0026 0.0005 0.0000 0.0009 0.0008 0.0072 0.9570 0.8528 0.8944 0.4537 0.5585 0.3541 0.0019 0.0022 0.0067

Number

ofObservations Adjusted R-squared 3,622 0.1429

Table8: Thistablereportsestimatedcoefficientsfromapanel regressionoftlie

month

inwhich theborrowerdid no

more

spendingonthebalance transfercard (the 'eurekamoment')

on

a splinewithageas its

argument

and

other controlvariables.

14

Quantifying the

Performance

Pecik

14.1

Locating

the

Peak

of

Performance

Visual inspection of the agesplines fortheten case studies suggests thatfinancialmistakes areata

minimum

inthelate fortiesorearlj' fifties.

To

estimate the

minimum

more

precisely,

we

re-estimateeachmodel,replacingthesplinesbetween40and50

and

50

and

60withasingle splinerunningfrom40 to60, andthesquareofthatspline.

Inotherwords,

we

runthe following regression,where

F

isthe

outcome

associated respec-tivelywith eachofthe 10studies:

(2)

a

-(-/?X5'p/me(A(/e)4jg^[4o60]

+

7x Controls

+

e

+a

X Spline(A5e).45e6[40,60]

+

^'Spline

(^5'e)A3eel40,60]•

Here Spline{Age)isa piecewiselinearfunction that takes

consumer

ageasitsargument(with knotpoints atages 30,40, 60and 70). Spline{Age)j^gg^i^QQQ-^ representsthesplinesoutside ofthe[40,60] age range, while_{Spline {Age) y^^^^Q}QQ^ isthelinearsplinewithknot points at

asalogitandfoundsimilar results.

PropensityofEver ExperiencingaEureka

Moment

by Borrower

Age

Borrower

Age

(Years)

Figure 16: Propensity ofeverexperiencing a eurelca

moment

by borrower age.

The

figure plotsthe residual effect ofage, aftercontrolling forother observable characteristics, such as log(income), education,

and

credit-worthiness.

40

and

60. Hence, foragebetween 40and60,the aboveformulationisjust:

F =

Controls

+

a x

Age

+

bx

Age^

The

peak

ofperformanceisthevalue that minimizestheabovefunction, i.e.

(3)

Peak

=

-a/

(26)

We

calculatetheasymptotic standarderrorson

Peak

using the deltamethod,sothat s.e.{Peak)

isthestandarderrorassociatedwith thelinearcombination:

—

l/(26)-(Coefficientonage)

+

a/(26^)-(CoefHcientonage^).

In Table 9,

we

report the location ofthe 'age ofreason': the point at which financial mistakesareminimized.

The

mean

age of reasonappearsto beat 53.3years.

The

standard deviation across studiesis4.3 years.

Formalhypothesis testing (Hq: a

+

25x53

=

0)showsthatonly the location of theEureka

moment

isstatisticallydifferentfrom53years. Interestingly,theEurekataskisarguable the

most

"difficult" task,i.e. the

most

cognitively intensive one. It

makes

sense that thepeak age for that taskwould beearlierthantheother tasks. Since

we

donot havea rigorous measure

Age

of

Peak Performance

Standard Error

Home

Equity

Loans-APR

55.85 4.24

Home

EquityLines-APR 53.30 5.23

Credit

Card-APR

50.31 6.02

Auto

Loans-APR

49.63 5.03

Mortgage-

APR

61.75 7.92

Small Business Credit

Card-APR

56.04 8.01 CreditCardLate Fee 51.94 4.87 CreditCard OverLimitFee 53.97 5.02 CreditCardCash AdvanceFee 54.82 4.89

Eureka

Moment

45.81 7.93

Averageofthe 10 Studies 53.34

Table9;

Age

atwhichfinancialmistakes areminimized,foreachcasestudy

ofthe "difficulty"ofatask,the interpretation of the Eurekacaseremainsspeculative.

14.2

Formal

Test of

a

Performance

Peak

Effect

Table9allows usdoaformal test forapeakeffect. Inregression (2), the nullhypothesis ofa peakeffect is: (i) 6

>

0,

and

(ii)

Peak

=

—a/

(26) 6 [40,60]. Togetherthese conditions imply thatmistakesfollowaU-shape, withapeakthatisbetween40and60 years ofage.

Forcriterion(i),

we

note that theb coefficientsare positiveforall10studies. For9 ofthe 10 studiesbissignificantly differentfromzero (thecreditcard

APR

studyistheexception).-'^ For criterion (ii),Table9shows that apeak inthe 40-60agerangecannotberejectedforall

tenstudies.

15

Discussion

and

Related

Work

Age

effects offera unifiedparsimoniousexplanationforour findingsinall ten casestudies. However,our cross-sectional evidencedoesnot definitivelysupportthisinterpretation. In the currentsection,

we

review

some

possible alternativeexplanations.

Some

resultscouldbedrivenby unobservedvariationindefaultrisk. For instance, the U-shapeof

APRs,

couldbeduetoaU-shapeofdefaultbyage.

We

test thisalternativehypothesis byregressingdefault rates onagesplines for creditcards, autoloans,and

home

equity loans

and

creditlines.

We

plot fittedvaluesin Figure 17.

None

ofthegraphs isU-shaped.

On

the contrary,

home

equity loansandlines

show

apronouncedinverted-U-shape,implyingthat

'*To savespace,weonly report thet—statisticsassociatedwith theb coefficients. FollowingtlieorderofTable

9,theyare:2.20, 4.55, 7.80, 8.77, 17.05, 1.61, 4.57, 2.91, 3.08, 2.67.

Percent DefaultingbyBorrower

Age

8,00%

- -CreditCards ——AutoLoans HE-Loans

™„, HE-Lines ArgentinaMortgage '^'"^^"^-Small Business

700%

_-^-

\

6,00%

"-'^

"'"'--.,

4,00% «_—.

-"

300% u™^ ,.^^---"'-""^' "'"^^^^^^^^^^^^""•^^.^ .^.u-v—«"'""''*''*°*^'" "" '^^^^^^^S^*!r^ 2,00% 1,00%

^^

..^-^ 000%

^

Borrower

Age

(Years)

Figure17: Defaultfrequencyby borrowerage.

The

figureplotsthe residualefi'ectofage, after controllingforotherobservablecharacteristics,suchas income

and

credit-worthiness.

the

young

andoldhave lower defaultrates. Credit cards and autoloansalso

show

a slight invertedU-shape. Hence, Figure17 contradicts the hypothesis thatour resultsare drivenby an

unmeasured

defaultrisk. Also,notethatage-dependent defaultriskcould not explain the observedpatternsincredit cardfee

payments

orsuboptimaluseofbalancetransfers.

Some

ageeffectscouldbe generatedbyage-variationintheopportunitycost oftime[Aguiar

and

Hurst2005]. However, suchopportunity-costeffectswouldpredictthatretirees

make

fewer mistakes, whichisnot

what

we

observeinthe data.

The

presence ofage effects might also be interpreted as evidence for

some

kind ofage discrimination.

We

believe this to be unlikely, for two reasons. First, firms avoid age discriminationfor legalreasons. Penaltiesforage discrimination fromthe FairLending Act are substantial (as would bethe resulting negativepublicity). Second, theU-shaped pattern shows

up

in contexts such as fee

payments

and misuse ofbalance transfer offers in which discriminationisnot relevant (sinceallcard holdersfacethe

same

rules).

15.1

Related

Work

Other authorshavestudied theeffectsofagingonthe use offinancial instruments. Ko-rniotisand

Kumar

(2007) examine theperformance ofinvestors froma majorU.S. discount brokeragehouse.

They

usecensusdatatoimpute educationlevelsand data fromtheSurvey

ofHealth, Aging

and

Retirementin

Europe

to estimate a

model

ofcognitive abilities.

They

findthat investors withcognitive declinesearnannual returnsbetween3-5percentagepoints lower on arisk adjustedbasis. In a related paper,

Zinman

(2006) reports that older adults are

more

likelytoborrowathighinterestratesoncreditcard accounts, while simultaneously holdingliquid assets inlow-interest

bank

accounts.

Intheir

work on

financial hteracy, Lusardi

and

Mitchel findevidence consistent with an inverse-Ushapeoffinancial proficiency. Lusardi

and

Mitchell (2006)finda declineinfinancial knowledgeafterage50. Lusardi

and

Mitchell (2007)also findaninverseU-shapeinthemastery ofbasicfinancialconcepts, suchastheabilitytocalculatepercentages or simpledivisions.

After

some

ofour presentationsother researchershave offered tolook forage patterns of financialmistakesintheir

own

datasets. Lucia

Dunn

has reported to us that the

Ohio

State Survey on credit cards shows a U-shaped pattern ofcreditcard

APR

terms by age (Dunn, personal communication). Fiona Scott-Morton has reported thatin herdatasetof indirect autoloans (loans

made

by banks

and

financecompaniesusing the dealerasanintermediary;see Scott-Mortonetai,2003), loan

APR

terms

show

aU-shapedpattern(Scott-Morton, personal communication)

.

A

relationship between earning

and

performance has been noted in

many

non-financial^ contexts. Survey datasuggests that labor earningspeak aroundage50(GourinchasandParker, 2002) orafterabout30 years of experience

(Murphy

and Welch, 1990). Thisisconsistentwith ourhypothesis thateconomic performancedepends on both analyticabilities andexperience. Turning to purely noneconomic domains, thereis aliterature onestimatingperformance peaksinprofessionalathletics

and

other competitiveareas. Fair (1994, 2005a,2005b)estimates theeffectsofage declinesinbaseball

and

chess,

among

othersports.

James

(2003) estimates theage ofpeak performanceinbaseball tobe29.

A

burgeoningliterature inpsychology and economicsreportssystematic differencein "ra-tionality" between groupsof people. Benjamin,

Brown and

Shapiro(2006) findthat subjects withhighertest scores,orlesscognitiveload,displayfewerbehavioralbiases. Frederick (2005) identifies ameasure of "analytical IQ": people with higher scores oncognitive abilitytasks tend to exhibitfewer/weaker psychologicalbiases. While this literatureis motivated by ex-perimentaldata (whereit iseasier tocontrolfor unobservables),

we

rely onfielddatainour paper. Similarly, Massoud, Saunders and Schnolnick (2006) find that

more

educated people

make

fewer mistakesontheir credit cards.

A

number

ofresearchers have writtenabout consumercredit card use.

Our work most

closely overlaps with that of Agarwal et al. (2005),

who

useanother large

random

sample ofcredit cardaccounts to

show

that,onaverage, borrowers choosecreditcard contracts that minimize their total interestcosts net offeespaid.

About

40percent ofborrowersinitially choosesuboptimal contracts. While

some

borrowers incurhundredsofdollars ofsuchcosts,

most

borrowers subsequentlyswitch to cost-minimizing contracts.

The

resultsofourpaper

complement

those of

Agarwal

et al. (2005), since

we

find evidence of learning to avoidfees

and

interestcostsgiven a particular card contract.

Several researchers havelooked at theresponse ofconsumers to low, introductoi'y credit cardrates ('teaser' rates),

and

atthe persistence of otherwise highinterest rates. Shuiand Ausubel (2004)

show

that consumersprefer creditcard contractswith lowinitialrates for a shortperiod oftimetooneswith

somewhat

higher ratesfora longer period of time,even

when

thelatter is expost,

more

beneficial.

Consumers

alsoappear 'reluctant'to switch contracts. DellaVigna

and Malmendier

(2004) theorize thatfinancialinstitutionsset theterms ofcredit cardcontracts toreflectconsumers'poorforecastingabilityovertheirfutureconsumption.

Bertrand et al. (2005) find that randomized changes in the "psychological features" of

consumer

credit offers affect adoptionrates as

much

asvariations inthe interestrateterms. Ausubel(1991) hypothesizes thatconsumers

may

beover-optimistic,repeatedly underestimat-ingthe probability thattheywillborrow,thus possibly explaining thestickinessofcredit card interest rates.

Calem and

Mester (1995) use the 1989 Surveyof

Consumer

Finances (SCF) to argue that information barriers create high switching costs for high-balance credit card customers, leadingto persistence ofcreditcardinterest rates,

and

Calem,

Gordy and

Mester (2005) use the 1998

and

2001

SCFs

toarguethatsuchcosts continue tobeimportant. Kerr

and

Dunn

(2002) usedatafromthe 1998

SCF

toarguethathavinglargecreditcard balances raisesconsumers' propensity to searchfor lower creditcard interest rates. Kerr and

Dunn

(2004) use

SCF

datatoarguethatbanksofferbetterlendingtermstoconsumers

who

arealso

bank

depositors,

and

about

whom

the

bank

wouldthushave

more

information.

Other authors have usedcreditcarddatatoevaluate

more

generalhypotheses about con-sumption. Agarwal, Liu

and

Souleles (2004) usecreditcarddatato

examine

theresponse of consumersto the2001 tax rebates. Gross

and

Souleles (2002a) usecreditcarddatatoargue that default rates roseinthemid-1990sduetodeclining default costs, ratherthana deterio-ration in the credit-worthiness of borrowers. Gross andSouleles (2002b) findthat increases incredit limits

and

declinesininterestrates leadtolargeincreasesin

consumer

debt. Ravina (2005) estimates consumption Eulerequations for creditcard holders

and

findsevidence for habit persistence.

15.2

Some Open

Questions

for

Future

Resecirch

Our

findingssuggest several directionsforfuture research.

First,itwould beuseful tostudyageeffects inother decisiondomains.

We

havepresented a simpleprocedureforthis: (1) identifythe generalshapeofageeffects,asin (1),using controls

and agesplines; (2)estimate a linear-quadraticformtolocalizethepeakofperformance,as in

(2)-(3).

Second,it

may

bepossible todevelopmodelsthat predictthe location ofpeak performance. Thereisagrowing consensusthat analytically intensiveproblemsareassociatedwith younger

peak

ages-think aboutmathematics(see

Simonton

1988,Galenson2005,andWeinberg and Galenson 2006). Analogously,problemsthat are

more

experientially-relevanthaveolderpeak ages. Forinstance, Jones(2006)findsthatthepeakageforscientistshasdrifted higherinthe twentieth century.

More

knowledge

now

needstobeaccumulatedtoreach the cuttingedgeof thefield.

In our last case study,

we

found that

what

isarguably the

most

analytically

demanding

task- deducing the best

way

to exploit "interest-free" balance transfers-isassociated with theyoungestage of

peak

performance. Itwould beusefulto

know

ifthisassociationbetween analytically

demanding

problems

and

young

peakagesisgeneral.

Third, it would be useful to identify cost-effective regulations that would help improve financial decisions. Forceddisclosureis notitselfsufficient, since disclosing costsin thefine printwillhavelittleimpact ondistracted

and

boundedlyrationalconsumers.^'^

_Good

disclo-surerules willneedtobeeffectiveevenforconsumers

who

donot take thetimetoread thefine print or

who

havelimitedfinancialeducation.

We

conjecture thateffectiveregulationswould produce comparable

and

transparent products.

On

the otherhand,such homogenizationhas the

dynamic

costthatit

may

createaroadblockto innovation.

Fourth, studying cognitive lifecycle patterns should encourage economists to pay

more

attention tothe market for advice. Advice markets

may

not functionefficientlybecause of informationasymmetriesbetweentherecipientsandthe providers ofadvice (Dulleckand Ker-schbamer2006). It isparticularlyimportanttostudythe advicemarketforolderadults

who

are

now

required to

make

their

own

financialdecisions(e.g. by

making

decisionsabout401(k) rollovers, asset allocation,

and

decumulation).

16

Conclusion

We

findthat middle-age adults borrow at lower interestrates

and

paylower fees inten financialmarkets.

Our

analysis suggests thatthis factisnotexplainedby age-dependentrisk factors. Forexample,

FICO

scores

show

nopattern ofagevariation. Moreover,age variation indefault ratesactually predicts the opposite patternfromtheonethat

we

measure.

Age

effects parsimoniouslyexplain the patterns that

we

observe, but, cohort effects

may

also contribute to the observed findings.

Whatever

themechanism, thereappears tobe a robust relationship betweenage and financial sophisticationincross-sectional data. Future '^SeeGabaix, Laibson,Moloche andWeinberg(2006)andKamcnica(2007)formodelsofeconomicbehavior underinformation overload.