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Massachusetts Institute of Technology
Department of Economics
Working Paper Series
THE AGE OF REASON:
FINANCIAL DECISIONS OVER THE LIFECYCLE
Sumit Agai"wal
John Driscoll
Xavier Gabaix
David Laibson
Working Paper 07-1
March 15, 2007
Revised: June 7, 2007
Room E52-251
50 Memorial Drive
Cambridge,
MA 021 42
This paper can be downloaded without charge from the
Social Science Research Network Paper Collection at
http;//ssrn.com/abstract=973790
The Age
of Reason: Financial Decisions
Over the Lifecycle
Sumit Agarwal, John C. DriscoU, Xavier Gabaix, and David Laibson*
June
7,
2007
Abstract
The
sophistication of financial decisions varies with age: middle-aged adults borrow at lower
interest rates
and pay fewer
fees
compared
pattern in ten financial markets.
characteristics.
data.
falls
Our
The
to
both younger and older adults.
The measured
effects
this
sophistication of financial choices peaks around age 53 in our cross-sectional
results are consistent with the hypothesis that financial sophistication rises
with age, although the patterns that we observe represent a mix of age
effects.
We document
cannot be explained by observed risk
effects
and then
and cohort
(JEL: Dl, D8, G2, J14).
Keywords: Household finance, behavioral finance, behavioral industrial organization,
aging, shrouding, auto loans, credit cards, fees,
home
equity, mortgages.
Federal Reserve Bank of Chicago, sagarwal@frbchi.org. Driscoll: Federal Reserve Board,
Gabaix: New York University and NBER, xgabaix@stern.nyu.edu. Laibson: Harvard University and NBER, dlaibson@harvard.edu. Gabaix and Laibson acknowledge support from the
National Science Foundation (Human and Social Dynamics program). Laibson acknowledges financial support from the National Institute on Aging (ROl-AG-1665). The views expressed in this paper are those of
the authors and do not represent the policies or positions of the Board of Governors of the Federal Reserve
For their comments we thank Marco Basetto, Stephane
System or the Federal Reserve Bank of Chicago.
Bonhomme, David Cutler, Ray Fair, Luigi Guiso, Gur Huberman, Ulrike Malmendier, Mitch Petersen, Rich
Rosen, Timothy Salthouse, Fiona Scott Morton, Jesse Shapiro, Paolo Sodini, Nick Souleles, Jon Zinman,
and participants at the Bank of Spain, Chicago Fed, the Federal Reserve Board, Princeton, the Institute
for Fiscal Studies and the NBER (Aging and Behavioral Economics groups), the Yale Behavioral Economics
'Agarwal:
john.c.driscoll@frb.gov.
conference.
Introduction
1
Performance tends to
rise
and then
Baseball players peak in their late 20s
with age.
fall
(James 2003). Mathematicians, theoretical physicists, and
contributions around age 30 (Simonton 1988).
mid-30s (Charness and Bosnian 1990).
Authors write
(Simonton 1988).
The
their
most
Making the best
This paper documents
is
though
less august,
Many
it is
relevant to the entire adult
financial products are
complex and
financial choices takes knowledge, intelligence,
cross-sectional variation in the prices that people
find that younger adults
and older adults borrow
than middle-aged adults controlling
fees
in their
difficult
Fees are sometimes shrouded and the true costs of financial services are not always
easily calculated.
We
most important
their
around age 50 (Simonton 1988).^
influential novels
population: personal financial decision making.
vices.
make
Autocratic rulers are maximally effective in their early 40s
present paper studies an activity that
to understand.
poets
lyric
Chess players achieve their highest ranking
for all
pay
and
skill.
for financial ser-
at higher interest rates
and pay more
observable characteristics, including measures of
risk.
The hump-shaped
pattern of financial sophistication
interest rates in six different markets: mortgages,
loans, personal credit cards,
and small business
exploit balance transfer credit card offers.
payment
fees,
cash advance
hump-shaped pattern
Age
We
and over
We
credit cards.
Finally,
we study
limit fees.
many
home
study the failure to optimally
three kinds of credit card fees: late
peak
in the early 50s.
hump-shaped pattern
for the
We
effects
may
explain
also explain
why
some
ability follows
hypothesize that experiential knowledge
Adding together these two
an increasing concave trajectory due to diminishing returns.
may
of financial
hypothesize that financial sophistication depends on a combination of analytic
factors implies that financial sophistication should rise
Cohort
and then
of the effects that
we
fall
with age.
observe.
Differences in educational
older adults are less financially sophisticated than middle-aged adults.
Naturally, such education effects will not explain
why young
phisticated than middle-aged adults. Additional
work needs
adults (around age 30) are less soto be
done to identify the
contributions of age effects and cohort effects.
The paper has
study
All of the evidence available to us implies a
one parsimonious explanation
a declining (weakly) concave trajectory after age 20.
follows
We
markets.
equity credit lines, auto
and experiential knowledge. Research on cognitive aging implies that analytic
ability
levels
present in
is
equity loans,
of financial sophistication, with a
effects provide
sophistication.
fees,
home
relative
'
the following organization. Section 2 discusses evidence on cognitive performance
from the psychological and medical
literature.
Section 3 describes the basic structure of the
'What about economists? Oster and Hamermesh (1998) find
may simply reflect lower motivation with
sharply with age. This
that economists' output in top publications dechnes
age.
More
and Galenson (2005)'s study of Nobel (Memorial) Prize winners. They
43, and "experimental" ones at age 61.
Weinberg
peak at age
optimistic data arc reported in
find that "conceptual" laureates
empirical analysis.
The next
ten sections present results for interest rates on six different financial
products, three different kinds of credit card fee payments, and on the use of balance transfer credit
card
offers.
Section 14 uses
all
ten sets of results to estimate the age of peak sophistication.
15.1 discusses other findings on the effects of aging
effects
2
and cohort
effects.
and the
Section
difficulty in separately identifying
age
Section 16 concludes.
Motivating Evidence on Aging and Cognitive Performance from
Medical and Psychological Resccirch
Analytic cognitive capabilities can be measured in
many
different ways, including tasks that
evaluate working memory, reasoning, spatial visualization, and cognitive processing speed (see
Figure
1).
Analytic performance shows a robust age pattern in cross-sectional datasets.
performance
is
Salthouse, forthcoming).
On
average analytic performance
falls
by two to three percent of one
standard deviation" with every incremental year of age after age 20.
steady from age 20 to age 90 (see Figure
The measured
This decline
effects (Salthouse,
is
remarkably
2).
age-related decline in analytic performance results from both age effects and
cohort effects, but the available panel data implies that the decline
pathway
Analytic
strongly negatively correlated with age in adult populations (Salthouse, 2005 and
Schroeder and Ferrer,
for age effects.
For instance, dementia
(60%) and vascular disease (25%).
years of lifecycle age (Fratiglioni,
is
primarily driven by age
Medical pathologies represent one important
2004).'^
is
primarily attributable to Alzheimer's Disease
The prevalence
of dementia doubles with every five additional
De Ronchi,
Agilero- Torres, 1999). There
is
a growing literature
that identifies age-related changes in cognition (see Park and Schwarz 1999, Denburg, Tranel and
Bechara 2005), including the
result that older adults
appear to pay relatively
less attention to
negative information (Carstensen 2006).
Age-driven declines in analytic performance are partially
rience.
a car.
Most day-to-day
offset
by age-driven increases
tasks rely on both analytic and experiential
For such tasks, we hypothesize that task performance
is
human
capital
-
in expe-
e.g.
buying
hump-shaped with respect to
age.'*
Figure 3 illustrates this case.
The current paper
pattern with age.
"This
is
We
tests the prediction that general task
focus on financial decision-making.
performance follows a hump-shaped
Because our financial market data span
a standard deviation calculated from the entire population of individuals.
'Sec Flynn (1984) for a discussion of cohort effects.
""This happens for instance under the following set of sufficient conditions:
(i)
general task performance
is
deter-
mined by the sum of analytic capital and experiential capital, (ii) experiential capital is accumulated in diminishing
amounts over the lifecycle, and (iii) analytic capital falls linearly (or concavely) over the lifecycle (see Figure 2).
Then general task performance will under be hump-shaped with to respect to age under simple conditions, e.g., if
experiential capital rises fast enough early in life, and slowly enough late in life.
3
''
,
Memory
Reason ng
study the following words and then write as
many
as you can
Select the best completion of the missing
remember
ceil
the matrix
n A
n A
Goat
i
i
Fish
A
Desk
1
Rope
Lake
Boot
^
A
Frog
A
Soup
1
Mule
Perceptual Speed
Spatial Visualization
Select the object on the nght that corresponds to
the pattern on the
Classify the pairs as
same
(S) or different (D) as
quickly as possible
left
[Z]_[Z]
Figure
1:
Four IQ tests used to measure cognitive performance. Source: Salthouse (forthcoming).
a small number of years,
effects,
we
are unable to
decompose the
and leave that analysis to future research with
The main
contribution of the paper
cross-sectional datasets: a
hump-shaped
note that this hump-shaped pattern
do not have any direct evidence
is
is
to
relative contributions of age
different
data
document a robust empirical
relationship between age and
and cohort
sets.
regularity in
all
of our
financial sophistication.
consistent with the aging evidence described above, but
for this cognitive/aging
We
we
mechanism. Other explanations - including
cohort effects and other mechanisms - are also plausible. For instance, the outcomes we document
could arise as a result of optimal endogenous accumulation of
the old might calculate that
it is less
the stakes are smaller for them.
middle-aged adults are generally
valuable to acquire relevant
Another channel might be
in social
human
human
capital.
capital,
social networks.
The young and
perhaps because
It is
plausible that
networks that give them more sophisticated advice about
the management of their finances, perhaps because they have greater access to financially-minded
coworkers.
Salthouse Studies - Memory and Analytic Tasks
l.fa
1
84
1.0
^-..
*-^
^^fe^^ar
0.5
0.0
-
69
-
50
~^\-
^-^
-
0.5
^>
1.0
-
V
1.5
-
—
2:
Age-normed
results
o
160
Word
Recall (N = 2,230)
Matrix Reasoning (N = 2,440)
7
Pattern Comparison (N = 6.547)
40
30
50
60
Chronological
Figure
to
.
Spatial Relations (N = 1,618)
—20
31-^
||-i
from four
70
80
90
Age
different cognitive tests.
The Z-score
represents the age-
contingent mean, measured in units of standard deviation relative to the population mean.
precisely, the Z-score
is
(age-contingent
mean minus population mean)
/ (population
More
standard
deviation). Source: Salthouse (forthcoming).
Cognitive
bxperientiai
capital
capita!
Tasl<
Performance
Performance
Analytic
capital
Age
Figure
3:
Hypothesized relation between general task performance and age.
Analytical capital
and experiential capital increase with age. This generates the hypothesis that
general task performance (which uses both analytical and experiential capital) first rises and then
declines with age
declines with age.
.
.
Overview^
3
In the
body
Such mistakes
We
of the paper,
reflect the
we document a U-shaped
age-related curve in financial "mistakes."
hump-shaped sophistication pattern discussed
study ten separate contexts:
home
payment
interest rates; mortgages; small business credit cards; credit card late
over limit
We
fees; credit
card cash advance
fees;
diagnose mistakes in three forms:
rates); higher fee
in the previous section.
equity loans and lines of credit; auto loans; credit card
and use of
higher
fees; credit
card
credit card balance transfer offers.
APRs
(Annual Percentage Rates,
payments; and suboptimal use of balance transfer
i.e.,
interest
offers.
For each application, we conduct a regression analysis that identifies age effects and controls
APRs
observable factors that might explain patterns of fee payments or
for
otherwise noted, in each context we
(1)
F=
'
Here
F
is
the level of the
by age.
Thus, unless
estimate a regression of the type:
+
a + P X Spline{Age)
APR paid by the borrower
'y
X Controls
+
e.
(or the frequency of fee
payment). Controls
is
a
vector of control variables intended to capture alternative explanations in each context (for example,
measures of credit
its
risk),
and Spline{Age)
argument (with knot points
the spline on age.
is
a piecewise linear function that takes consumer age as
at ages 30, 40, 50, 60
Each section discusses the nature
We
Appendix.
Home
4
We
70).^
of the mistake, briefly
presents the regression results and graphs by age.
in the
and
then plot the fitted values
provide
documents the datasets used, and
summary
statistics for the
.-'
..-.
'
.
home
equity loans and
home
subprime loans or other market segments.
a
menu
and
of standardized contracts for
line;
'
Equity Loans
We use a proprietary panel dataset constructed with records from a national
that has issued
data sets
'
.
.
Data Summary
4.1
for
Regressions are either pooled panel or cross-sectional, depending on the context.
between a
first
home
equity lines of credit.
The
Between March and December 2002, the lender
equity credits.
Consumers chose between a
and second hen; and could choose to pledge
different
with the amount of collateral implying a loan-to- value (LTV) ratio of
80 and 90 percent, and between 90 an 100 percent.
^For instance, in Table 1, the "Age 30-40" spline
and the "Age,> 70" spline is max {70, Age).
financial institution
lender has not specialized in
is:
less
amounts
offered
credit loan
of collateral,
than 80 percent, between
In effect, the lender offered twelve different
max (30,min
(40, Age)), the
"Age < 30" spline
is
min(30, Age),
For 75,000 such contracts, we observe the contract terms, borrower demographic
contract choices.^
home
information (age, years at current job,
income
ratio),
and
estimates of their house values and the loan
and debt-to-
tenure), financial information (income
(FICO)
risk characteristics (credit
amount
and LTV).
score,
We also observe
"^
borrower
requested.
Results
4.2
Table
1
reports the results of estimating regressions of
loans on a spline for age and control variables.
financial institution that
characteristics,
might
and borrower
have the expected
financial
significance, surprisingly so in
The measure
people
some
and demographic
who work
is
on home equity
(interest rates)
we use
all
variables observed
The
characteristics.
control variables
FICO
score (lagged three
months because
but with a negligible magnitude.
is
made, but conditional on the
The
results here,
and
offer
for the other
only
it is
Discussions with
FICO
in the industry reveal that financial institutions generally use the
the score to do risk-based pricing.
all
cases.
statistically significant
to determine whether a loan offer
by the
house and loan
although some of them lack economic
statistically significant,
of credit risk, the log of the
updated quarterly),
APRs
controls,
affect loan pricing, including credit risk measures,
and most are
sign,
As
score
being made, do not use
consumer credit products
discussed below, are consistent with this hypothesis.
Loan APRs do depend strongly on the absence of a
whether the property
is
a second home or a condominium.
Second homes and condominiums are perceived as
also have large
mortgage (reducing the
The absence
of a
first
and negative
effects
riskier properties.
Log income and
APRs come
from
dummy
greater than 90 percent.
variables for
This
is
LTV
default.
log years
on APRs, as expected, since they indicate more
resources available to pay off the loan and perhaps less risk in the latter case.
on
APR) and
mortgage reduces
amount that might be recovered conditional on a
the probability of default and raises the
on the job
first
The
largest effects
between 80 and 90 percent and
ratios
consistent with different
LTV
for ratios
ratios corresponding to different
contract choices.^
Even
after controlling for these variables,
APR as
we
find that the age splines have statistically
and
the sign of a mistake for four reasons.
First, contracts do not differ in points charged
Second, even conditioning on contract choice some borrowers pay higher APRs
Third, we control for borrower rislt characteristics. Fourth, in section 5.3, we show that the residual
''We interpret a high
or in other charges to the borrower.
than others.
variation in
'We do
APRs
is
explained by the propensity to
make an
identifiable mistake in the loan acquisition process.
not have internal behavior scores (a supplementary credit risk score) for these borrowers.
Such scores are
performance-based, and are thus not available at loan origination.
^We
estimate three variants as a specification check.
to have quadratic and cubic terms.
This allows us to
First,
make
we allow the FICO
scores, income,
not a consequence of omission of potential nonlinear effects of other control variables.
the splines to have knot points at every
five years,
caused by the use of ten-year splines does not
qualitatively or quantitatively changed.
and
LTV
ratios
we see are
Second and third, we allow
sure that the nonlinear effects with age that
and have a
artificially create
dummy
for
a U-shape.
each age, to ensure that the smoothing
In
all
three cases, our results are not
Home
Equity Loan
APR
|
8.1736
0.1069
-0.0021
0.0001
0.0164
0.0138
-0.0081
0.0113
No
-0.1916
0.0097
First
Mortgage
Log(Months
Second
at Address)
Home
Condominium
0.0077
0.0034
0.0002
-0.0246
0.0039
0.0106
0.0161
-0.0333
0.0421
0.0355
0.0225
30
-0.0551
0.0083
30-40
-0.0336
0.0043
40-50
-0.0127
0.0048
50-60
0.0102
0.0039
60-70
0.0174
0.0076
>
70
0.0239
0.0103
80-90
0.7693
0.0099
90-H
1.7357
0.0111
Employed
Home Maker
Retired
<
LTV
LTV
YES
Dummies
Number of Observations
16,683
Adjusted R-squared
0.7373
State
The
first
0.0259
0.0165
Log(Years on the Job)
Age
Age
Age
Age
Age
Age
0.0039
0.3880
0.4181
Debt/Income
Self
0.0021
-0.0651
Log(Income)
1:
Std. Error
Log(FICO Score)
Loan Purpose-Home Improvement
Loan Purpose-Rate Refinance
Intercept
Table
Coefficient
column
gives coefficient estimates for a regression of the
loan on a spline with age as
its
APR
of a
home
equity
argument, financial control variables (Log(FICO) credit risk score,
dummy for loans made
dummy for no first mortgage
income, and the debt-to-income-ratio), and other controls (state dummies, a
for
home improvements, a dummy
for loans
made
for refinancing,
a
on the property, months at the address, years worked on the job, dummies
or homemaker status, and a dummy if the property is a condominium).
for self-emplyed, retiree,
Home
Equity Loan
APR by
Borrower Age
Borrower Age (Years)
Figure
4:
Home
equity loan
APR by
borrower age. The figure plots the residual
controlling for other observable characteristics, such as log(income)
economically significant
equity loans.
The
in section 14.2 a
line
effect of age, after
and credit-worthiness.
Figure 4 plots the fitted values on the spline for age for
effects.
home
has a pronounced U-shape.^ For this and the nine other studies, we present
formal hypothesis test for the U-shape.
To anticipate those
results,
we
reject the
null hypothesis of a flat age-based pattern in 9 out of 10 cases.
Home
5
Equity Lines of Credit
Data Summary
5.1
The
dataset described in the previous section
is
used here.
Results
5.2
Table 2 reports a regression of the
same
APRs from home
equity lines on a spline for age and the
control variables used for the home" equity loans regression.
Mortgage and other long-term
explanation
of the
period.
for
interest rates
the observed pattern
sample period.
is
were generally
falling
The
control variables have similar
during this period.
Thus, another possible
that younger and older adults disproportionately borrowed at the beginning
However, we found no time-variation
in the
age distribution of borrowers over the sample
Home
Equity Credit Line
APR
by Borrower Age
Borrower Age (Years)
Figure
5:
Home
equity credit line
APR by
borrower age. The figure plots the residual
after controlling for other observable characteristics, such as log(income)
effects
on home equity
line
APRs
as they did
on home equity loan APRs. APRs.
Fitted values on the age splines, plotted in Figure
The amount
ratio,
is
of collateral offered
continue to reveal a pronounced U-shape.
estimate their
home
is
At the
lower.
values,
and ask
for
The
LTVs
of
Home
Values
Higher
LTVs imply
higher
The bank then
verification process.
Loan
LTV
estimate.
The
categories correspond to
between 80 and 90 percent; and LTVs of 90 percent or
LTV
constructs a bank-generated
The bank-LTV can
pricing depends on the
since the
a credit loan or credit line falling into one of three categories
financial institution then independently verifies the house value using
methodology.
APRs,
financial institution that provided our data, borrowers first
depending on the implied borrower-generated
of 80 percent or less;
of
by the borrower, as measured by the loan-to-value (LTV)
an important determinant of loan APRs.
fraction of collateral
'
5,
One Mechanism: Borrower Misestimation
5.3
effect of age,
and credit-worthiness.
LTV
LTV
LTVs
greater.
an industry-standard
based on the bank's independent
therefore differ from the borrower-LTV.^°
category that the borrower
value within that category; for example, a loan with an
falls
LTV
into
and not on the
of 60 has the
same
Bucks and Pence (2006) present evidence that borrowers do not generally have accurate estimates of
values.
10
specific
interest
their house
Home
Equity Line
APR
|
Intercept
Log(FICO Score)
Loan Purpose-Home Improvement
Loan Purpose-Rate Refinance
No
0.0000
-0.0386
0.0047
-0.1512
0.0054
-0.0160
0.0019
0.3336
0.0132
0.4025
0.0079
Log( Income)
-0.1474
0.0037
Debt/Income
0.0044
0.0001
-0.0164
0.0020
0.0135
0.0073
-0.0818
0.0215
0.0139
0.0109
First
Mortgage
at Address)
Home
Log(Years on the Job)
Self
Employed
Home Maker
Retired
Age
<
30
-0.0529
0.0050
Age
Age
Age
Age
Age
30-40
-0.0248
0.0023
40-50
-0.0175
0.0022
50-60
0.0152
0.0035
60-70
0.0214
0.0064
>
70
0.0290
0.0154
80-90
0.6071
0.0050
90-1-
1.8722
0.0079
LTV
LTV
YES
Dummies
Number of Observations
66,278
Adjusted R-squared
0.5890
State
The
risk score,
for loans
no
first
first
0.0570
0.0051
Condominium
2:
7.9287
0.0551
Second
lines of credit
Std. Error
-0.0011
Log(Months
Table
Coefficient
column
gives coefficient estimates for a regression of
on a spline with age as
its
tfie
APR
of a
home
equity
argument, financial control variables (Log(FICO) credit
dummy
dummy for
income, and the debt-to-income-ratio), and other controls (state dummies, a
made
for
home improvements,
a
dummy
for loans
made
for refinancing,
a
mortgage on the property, months at the address, years worked on the job, dummies
homemaker status, and a dummy if the property is a condominium).
self-employed, retiree, or
11
for
LTV
rate as a loan with an
loans are less than 80. '^
bank-LTV
of 70, holding borrower characteristics fixed, since the
If
LTVs
both
of
the borrower has overestimated the value of the house, so that the
higher than borrower-LTV, the financial institution will direct the buyer to a different
is
loan with a higher interest rate corresponding to the higher bank-LTV. In such circumstances, the
loan officer
also given
is
some
discretion to depart
from the
financial institution's
normal pricing
schedule to offer a higher interest rate than the officer would have offered to a borrower
correctly estimated her
LTV.
If
who had
the borrower has underestimated the value of the house, however,
the financial institution need not direct the buyer to a loan with a lower interest rate corresponding
bank-LTV (which
to the
may
lower in this case than the borrower-LTV); the loan officer
is
simply
choose to offer the higher interest rate associated with the borrower-LTV, instead of lowering the
rate to reflect the lower bank-LTV.'^
APR paid
Since the
of the borrower-LTV.
was
70, the
not
suflfer
occurred
payments
tlie
still
LTV
on average, making a
bank-LTV
estimated
LTV
We
of 85 but the
value misestimation
differs
was
60,
qualify for the highest quality loan category
from the category
bank
(LTV<80) and would
bank-LTV category -
calculates an
RCM increases the APR by
LTV
LTV
but the true
define a Rate-Changing Mistake
the borrower-LTV category differs from the
borrower estimates an
home
category and not the LTV,
the category of the
effective interest rate penalty.
when
find that,
if
in contrast, the borrower's
If,
borrower would
an
LTV
depends on the
leads to higher interest rate
(RCM)
to have
when
for instance,
We
of 75 (or vice versa). ^'^
125 basis points for loans and 150 basis
points for lines (controlling for other variables, but not age).
To
highlight the importance of
ROMs, we
Table
1
and
2,
APR
The
paid by age.
at age 70 over a borrower at age 50 has
equity line of credit,
APR
who do
APR
the
APR
is
for
from re-estimating the regressions
not make a
difference for a
RCM. The
home
has shrunk from 28 basis points to 4 basis points.
home
plots
equity lines of credit.
essentially ffat with age.
for
a
home
For a borrower at age 20,
shrunk to 3 basis points
We
in
show only
equity loan for a borrower
shrunk from 36 basis points to 8 basis points;
difference over a borrower at age 50 has
and 3 basis points
RCM,
it
APR for consumers who do not make a
fitted values
but now conditioning on borrowers
slight differences in
the
study the
first
Rate-Changing Mistake. Figures 6 and 7 plot the
for
home
equity loans
conclude that, conditional on not making a
So the U-shape of the
APR
is
primarily driven by the
Rate-Changing Mistakes.
We
next study
who makes
changing mistake by age
"We
dummy
dummy
have
for
verified this practice in
variables for whether the
a
RCM.
home
Figures 8
equity loans and
and 9
home
our dataset by regressing the
bank-LTV
falls
plot the probabihty of
making a
equity lines, respectively.
APR
on both the
into one of the three categories.
level of the
Only the
The
rate-
figures
bank-LTV and
coefficients
on the
variables were statistically and economically significant.
Even if the financial institution's estimate of the true house value is inaccurate, that misestimation
matter for the borrower as long as other institutions use the same methodology.
"Recall that the categories are less than 80, 80 to 90, and greater than 90.
12
will
not
Home
APRs for Borrowers Who Do Not Make a
Rate-Changing Mistake
Equity Loan
Borrower Age (Years)
Figure
6:
Home
equity loan
APRs
for
borrowers
who do not make
a rate-changing mistake. The
figure plots the residual effect of age, after controlling for other observable characteristics, such as
log(income) and credit-worthiness.
Home
Equity Credit Line
Make
APRs
for
Borrowers
Who Do
Not
a Rate-Changing Mistake
Borrower Age (Years)
Figure
The
7:
Home
equity credit line
APRs
for
borrowers
who do
not
make a rate-changing
mistake.
figure plots the residual effect of age, after controlling for other observable characteristics, such
as log(income)
and credit-worthiness.
13
Propensity of Making a Rate-Changing Mistake on
Equity Loans by Borrower Age
Home
Borrower Age (Years)
Figure
We
8:
Propensity of making a Rate Changing Mistake on home equity loans by borrower age.
define a
Rate Changing Mistake
value causes a change in
for
a
full definition).
The
LTV
to have occurred
when a
borrower's misestimation of house
category and potentially a change in interest rate paid (see the text
figure plots the residual effect of age, after controlling for other observable
characteristics, such as log(income)
and credit-worthiness.
Propensity of Making a Rate-Clianging Mistake on
Equity Credit Lines by Borrower
^
C
O
Home
Age
60'
50'
Borrower Age (Years)
home equity credit lines by borrower
Rate Changing Mistake to have occurred when a borrower's misestimation of
house value causes a change in LTV category and potentially a change in interest rate paid (see
Figure
age.
9:
We
Propensity of making a Rate Changing Mistake on
define a
the text for a
full definition).
The
figure plots the residual effect of age, after controlling for other
observable characteristics, such as log (income) and credit- worthiness.
14
show U-shapes
Borrowers at age 70 have a 16 (19) percentage point greater chance of
for both.
making a mistake than borrowers
at age 50 for
home
equity loans (lines); borrowers at age 20 have
The
a 35 (41) percentage point greater chance of making a mistake than borrowers at age 50.
unconditional average probability of making a rate-changing mistake
percent for
for loans
and 18
with the cost of a RCM calculated above and the additional probRCM by age. For example, a 70-year old has a 16 and 19 percent additional
a RCM for loans and hues, respectively. Multiplying this by the average APR
effect is consistent
making a
chance of making
cost of a
24 percent
lines.
This age
ability of
is
RCM for home equity lines and loans of about 150 and 125 basis points, respectively, gives
APR paid of about 26 and 23 basis points. These differences are very
an expected incremental
close to the estimated differences of
about 23 basis points
about 28 basis points for lines (reported in Figure
We
for the
home
conclude that in the example of
APR
U-shape of the
Figure 4) and of
for loans (reported in
5).
equity hnes and loans,
we have
identified the channel
as a function of age (as always, controlling for other characteristics).
Younger and older consumers have a greater tendency to misestimate the value
which leads to a Rate-Changing Mistake, which leads them to borrow
the other hand, for consumers
independent of age. Hence,
and older
who do
this
not
at
of their house,
an increased APR.
On
APR is essentially
APR paid by younger
make a Rate-Changing Mistake, the
channel explains quantitatively the higher
adults.
Given the large costs associated with a Rate-Changing Mistake, one might ask why borrowers
do not make greater
effort to
may
potential borrowers
are aware of this fact, they
aspect of loan pricing
more accurately estimate
not be aware that credit terms
may
may
not
know how much
their house values.
will differ
by
LTV
One
possibility
is
that
category; or, even
if
they
the terms differ by category.
This particular
thus be a shrouded attribute.
"Eureka" Moments: Balance Transfer Credit Card Usage
6
Overview
6.1
Credit card holders frequently receive offers to transfer account balances on their current cards
to a
new
Borrowers pay substantially lower
card.
APRs
card for a six-to- nine- month period (a 'teaser' rate).
The catch
have high APRs.
transferred balances,
new purchases.
The optimal
on her old
is
that payments on the
on the balances transferred to the new
However, new purchases on the new card
new card
and only subsequently pay down the (high
'
pay down the (low
interest) debt
interest)
accumulated from
'
strategy during the teaser-rate period,
credit card
first
and to make
all
is
for the
borrower to make
payments to her old card.
15
all
The optimal
new purchases
strategy implies
that the borrower should
make no new purchases with the new card
to which balances have been
transferred (unless she has already repaid her transferred balances on that card).
We
hypothesize that some borrowers will identify this optimal strategy immediately - before
malcing any purchases with the
Some borrowers may not
pay cycles
new
Some borrowers
card.
will
never identify the optimal strategy.
the optimal strategy, but will discover
initially identify
it
after
one or more
Those borrowers
after observing their (surprisingly) high interest charges.
will
make
purchases for one or more months, then have a "eureka" moment, after which they will implement
the optimal strategy.^"*
Data Summary
6.2
We
use a proprietary panel data set from several large financial institutions, later acquired by
a single financial institution, that
14,798 individuals
who
December 2002.
The bulk
made
The data
balance transfer offers nationally.
set contains
accepted such balance transfer offers over the period January 2000 through
of the data consists of the
main
information listed on each'
billing
account's monthly statement, including total payment, spending, credit limit, balance, debt, purchases, cash
advance annual percentage rates (APRs), and
fees paid.
We
also observe the
amount
of the balance transfer, the start date of the balance transfer teaser rate offer,, the initial teaser
APR
on the balance
frequency,
transfer,
and the end date of the balance transfer
we observe each customer's
We
credit 'behavior' score.
APR
and income
At a quarterly
(internal)
have credit bureau data about the number of other credit cards held
by the account holder, total credit card balances, and mortgage balances.
age, gender,
offer.
bureau rating (PICO) and a proprietary
credit
We
have data on the
of the account holder, collected at the time of account opening.
In this
sample, borrowers did not pay fees for the balance transfer. Further details on the data, including
summary
statistics
and variable
definitions, are available in the
Appendix.
Results
6.3
About one
third of
all
customers
who make
a balance transfer do no spending on the
thus implementing the optimal strategy immediately.
who make a balance
transfer spend every
riencing a "Eureka"
moment.
moments between the
first
month during the promotional
The remaining
period, thus never expe-
and sixth months.
never experience a "Eureka"
(the
"Month One"
We
thank Robert Barro
for
moment The
age.
line) is
card,
nearly one-third of customers experience "Eureka"
Figure 10 plots the frequency of Eureka moments for each age group.
pronounced U-shape by
new
Shghtly more than one third of customers
that
is,
plot of those
who
who implement
plot of those
Plots for Eureka,
this type of potentially tricky financial product.
16
who
is
a
the optimal strategy immediately
a pronounced inverted U-shape by age.
drawing our attention to
The
never implement the optimal strategy -
moments
in Each Age Group Experiencing a
Eureka Moment, by IVlonth
Fraction of Borrowers
-
- "
Month One
Month Two
Monlh Three
Monlh Five
Month Six
No Eureka
Month Four
^^^^
50%
\
S2
I
40%
_...-•
"-
o
CO
30%
''
o
c
a
/-'"'^
'
-
20%
a
10%
,
, __.,
_
18
to
25
24
to
35
34
to
45
44
to
64
Borrower Age Category
Figure
Fraction of borrowers in each age group experiencing specific delays.
10:
the dashed line plots the fraction of borrowers experiencing no delay to a Eureka
sophisticated borrowers represent a large fraction of middle-aged households and a
fraction of younger
time space (that
The No Eureka
is
Eureka moments that occur
smaller
strictly after
Month One)
groups with the greatest frequency of maximal
line implies that the
confusion are younger adults and older adults.
is
much
and older households.
in the interior of the
are flat.'^
For example,
moment. These
The group with the
greatest frequency of optimality
middle-aged adults.
dummy
Table 3 reports the results of a regression of a
on a
spline for age
Credit risk
Similarly,
is
and controls
for credit risk
included because higher scores
may be
we would expect borrowers with higher
Eureka moments The
less likely to
coefficients
variable for ever having a Eureka
moment
(log(FICO)), education, gender, and log(income).^^.
associated with greater financial sophistication.
levels of
education to be more
likely to
experience
on the age spline imply that young adults and older adults are
experience Eureka moments.
Figure 11 plots the fitted values of the age splines for the propensity of ever experiencing a
"Eureka" moment. Note that, unlike the other figures, higher values indicate a smaller propensity
make
to
mistakes. Consistent with the evidence so
far,
we observe a performance peak
in
middle
'^Although the average percent of borrowers for each of the intermediate categories is small-on the order of five
percent-summing over all the months yields a fraction of borrowers equal to the one-third of total borrowers.
Although we report an OLS regression for ease in interpreting the coefficients, we have also run the regression as
a logit and found similar results.
'
17
Propensity of ever experiencing a "Eureka"
Intercept
0.2587
0.0809
< 30
0.0134
0,0026
30-40
0.0019
0.0005
40-50
-0.0001
0.0000
50-60
-0.0029
0.0009
60-70
-0.0035
0.0008
-0.0083
0.0072
-1.6428
0.9570
High School Graduate
-0.6896
0.8528
Some
-0.4341
0.8944
Associate's Degree
-0.2439
0.4537
Bachelor's Degi'ee
0.3280
0.5585
Graduate Degree
0.6574
0.3541
Log(FICO)
0.0102
0.0019
Log (Limit)
0.0120
0.0022
-0.0044
0.0067
Age
Age
Age
Age
Age
Age > 70
Some High
School
College
Log (Income)
Number
of Observations
Adjusted R-squared
Table
3:
Moment
Std. Error
Coefficient
3,622
0.1429
This table reports estimated coefficients from a panel regression of the month
in
which the
borrower did no more spending on the balance transfer card (the "Eureka" moment) on a sphne
with age as its argument and other control variables.
age.
Credit Cards
7
Data Summary
7.1
We
use a proprietary panel dataset from several large financial institutions that offered credit
cards nationally, later acquired by a larger financial institution.
tive
random sample
The dataset contains a
of about 128,000 credit card accounts followed
(from January 2002 through December 2004).
The bulk
representa-
monthly over a 36 month period
of the data consists of the
main
billing
information listed on each account's monthly statement, including total payment, spending, credit
limit, balance, debt,
purchases and cash advance annual percent rates (APRs), and fees paid.
a quarterly frequency,
we observe each customer's
(internal) credit 'behavior' score.
We
credit
have credit bureau data about the number of other credit
cards held by the account holder, total credit card balances, and mortgage balances.
on the age, gender and income of the account holder, collected
Further details on the data, including
At
bureau rating (FICO) and a proprietary
summary
statistics
18
at the
and variable
We
have data
time of account opening.
definitions, are available in
Propensity of Ever Experiencing a "Eureka"
Moment by
Borrower Age
Borrower Age (Years)
Figure 11: Propensity of ever experiencing a "Eureka"
moment by borrower
The
age.
figure plots
the residual effect of age, after controlling for other observable characteristics, such as log(income),
education, and credit- worthiness.
the data Appendix.
Results
7.2
Table 4 reports the results of regressing credit card
and other control
institution that
credit card
significant.
variables.
may
APRs.
As
controls,
influence pricing.
APRs
rise
As
APRs on
a spline with age as
before,
we
with the total number of cards, though the effect
is
on
not statistically
Other controls, including the total card balance, log income, and balances on other
Figure 12 plots the fitted values on the spline for age.
weaker than the age-based patterns that we document
8.1
financial
find that credit scores have little impact
debt, do not have economically or statistically significant effects on credit card
8
argument
its
we again use information observed by the
A
U-shape
is
APRs.
present, though
it is
much
for other financial products.
Auto Loans
Data Summary
We
use a proprietary data set of auto loans originated at several large financial institutions
that were later acquired by another institution.
loans originated for the purchase of
The data
set
new and used automobiles.
19
comprises observations on 6,996
We
observe loan characteristics
Credit Card
APR
|
Coefficient
Intercept
14.2743
3.0335
Age < 30
-0.0127
0.0065
Age 30-40
-0.0075
0.0045
Age 40-50
-0.0041
0.0045
Age 50-60
0.0023
0.0060
Age 60-70
0.0016
0.0184
Age
>
70
0.0016
0.0364
Log(Income)
-0.0558
0.0803
Log(FICO)
-0.0183
0.0015
0.0003
0.0022
-0.0000
0.0000
Home
Equity Balance
Mortgage Balance
Number
of Observations
92,278
Adjusted R-squared
Table
4:
total
0.0826
This table gives coefficient estimates
spline with age as
number
its
Std. Error
for
a regression of the
APR
of a credit card on a
argument, financial control variables (Log(FICO) credit
of cards, total card balance,
home
Credit Card
risk score,
income,
equity debt balance and mortgage balance).
APR by Borrower Age
Borrower Age (Years)
Figure
12:
Credit card
APR
by borrower age.
The
figure plots the residual effect of age, after
controlling for other observable characteristics, such as log(income) and credit-worthiness.
20
Auto Loan
APR
|
Coefficient
11.4979
1.3184
30
-0.0231
0.0045
Age 30-40
-0.0036
0.0005
Age 40-50
-0.0054
0.0005
Age 50-60
0.0046
0.0007
Age 60-70
0.0031
0.0017
0.0091
0.0042
Log (Income)
-0.3486
0.0176
Log(FICO)
-0.0952
0.0059
Debt/Income
0.0207
0.0020
Japanese Car
-0.0615
0.0270
European Car
-0.0127
0.0038
Loan Age
0.0105
0.0005
Car Age
0.1234
0.0031
Intercept
Age
Age
<
>
70
YES
YES
Dummies
Quarter Dummies
Number of Observations
State
6,996
Adjusted R-squared
Table
5:
Std. Error
0.0928
APR of an auto loan on a
(Log(FICO) credit risk score, income,
dummies, dummies for whether the car is
This table gives coefficient estimates from a regression of the
spline with age as its argument, financial control variables
and the debt-to-income-ratio), and other controls
Japanese or European, loan age and car age).
(state
including the automobile value and age, the loan
contract rate, and the time of origination.
credit score,
8.2
We
amount and LTV, the monthly payment,
the
also observe borrower characteristics including
monthly disposable income, and borrower
age.
Results
Table 5 reports the results of regressing the
and control variables.
incomes lower
FICO
APRs and
effects are small.
We
APR
paid for auto loans on an age-based spline
credit risk scores again have little effect
on the loan terms.
Higher
higher debt-to-income ratios raise them, though the magnitudes of the
also include car characteristics, such as type
found those variables to matter
for
APRs
in other
and age, as one
of us has
work (Agarwal, Ambrose, and Chomsisengphet,
forthcoming)-though we note that the financial institutions do not directly condition their loans
on such variables.
We
also include loan age
and state dummies.
Figure 13 plots the fitted values on the spline for age.
21
The graph shows a pronounced U-shape.
Auto Loan
APR
by Borrower Age
Borrower Age (Years)
Figure 13:
Auto loan
APR
by borrower age.
The
figure plots the residual efTect of age, after
controlling for other observable characteristics, such as log(income)
9
9.1
credit- worthiness.
Mortgages
Data Summary
We
,
.
use a proprietary data set from a large financial institution that originates
Argentina.
first
mortgages
in
Using data from one other country provides suggestive evidence about the international
applicability of our findings.
The data
set covers 4,867
loans originated between June 1998 and
observe the original loan amount, the
We
and
also observe
LTV
owner-occupied, fixed rate,
first
March 2000 and observed through March
and appraised house value
at origination,
mortgage
We
2004.
and the APR..
borrower financial characteristics (including income, second income, years on the
job, wealth measures such as second house ownership, car ownership
characteristics (Veraz score, a credit score similar to the U.S.
as a percentage of after-tax income),
FICO
and value), borrower
score,
risk
and mortgage payments
and borrower demographic characteristics
(age, gender,
and
marital status).
9.2
Results
Table 6 reports results of regressing the mortgage
variables.
As
controls,
we again use
variables observed
APR
on an age-based spline and control
by the financial institution that
loan pricing, including risk measures (credit score, income, mortgage
22
payment
may
affect
as a fraction of
Mortgage
APR
by Borrower Age
1275
,^ 12
c
o
u
V
0^
50
12,25
^^-—"^ ^^
a:
0.
^/
< 12.00
11,75
11,50
-
Borrower Age (Years)
Figure
14:
APR
for
Argentine mortgages by borrower age. The figure plots the residual
age, after controlling for other observable characteristics, such as log(income)
and
effect of
credit- worthiness.
income, and LTV), and various demographic and financial indicators (gender, marital status, a
dummy
variable for car ownership, and several others - these coefficients are not reported to save
The
space).
significant,
The
coefficients
on the controls are again of the expected sign and generally
statistically
though of small magnitude.
coefficients
positive thereafter.
on the age spline are positive below age
Figure 14 plots the
fitted values
30,
then negative through age 60 and
on the sphne
for age.
The
figure provides
only partial support for the U-shape hypothesis.
Small Business Credit Ccirds
10
Data Summary
10.1
We
use a proprietary data set of small business credit card accounts originated at several large
institutions that issued such cards nationally.
institution.
Most
The panel data
of the business are very small,
The data
set
has
all
The
institutions were later acquired
set covers 11,254 accounts originated
owned by a
single family,
between
May
by a
200 and
and have no formal
May
single
2002.
financial records.
information collected at the time of account origination, including the business
owner's self-reported personal income, the number of years the business has been in operation, and
the age of the business owner.
We
observe the quarterly credit bureau score of the business owner.
23
Mortgage
Coefficient
Std. Error
12.4366
4.9231
30
0.0027
0.0046
Age 30-40
Age 40-50
-0.0023
0.0047
-0.0057
0.0045
Age 50-60
0.0127
0.0093
Age 60-70
0.0155
0.0434
0.0234
0.0881
Log(Income)
-0.2843
0.1303
Log(Crcdit Score)
-0.1240
0.0217
Intercept
<
Age
Age
>
70
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
0.1845
0.0187
-0.0108
0.0046
0.1002
0.1014
Auto
0.1174
0.0807
Auto Value
0.0000
0.0000
Gender (l=Female)
0.0213
0.0706
Married
-0.0585
0.0831
Two
-0.1351
0.1799
-0.0116
0.1957
-0.0438
0.1174
0.0853
0.1041
Merchant
-0.1709
0.1124
Bank Relationship
-0.2184
0.1041
Loan
to Value
Years on the Job
Second
Home
Incomes
Married with
Two Incomes
Employment: Professional
Employment:Non-Professional
Number
of Observations
4,867
Adjusted R-squared
Table
6:
APR
0.1004
This table reports the estimated coefficients from a regression of mortgage
spline with age as its
argument and
financial
and demographic control
24
variables.
APR
on a
Small Business
C redit Card APR
|
Coefficient
Std. Error
Intercept
16.0601
0.6075
Age < 30
-0.0295
0.0081
Age 30-40
Age 40-50
Age 50-60
-0.0068
0.0040
-0.0047
0.0038
-0.0017
0.0055
Age 60-70
Age > 70
0.0060
0.0209
0.0193
0.0330
Years in Business 1-2
-0.5620
0.1885
Years in Business 2-3
-0.7463
0.1937
Years in Business 3-4
-0.2158
0.1031
Years in Business 4-5
-0.5100
0.0937
Years
-0.4983
0.0931
-0.0151
0.0008
in
Business 5-6
Log(FICO)
Number
of Cards
0.1.379
0.0153
Log(Total Card Balance)
<0.0001
<0,0001
Log(Total Card Limit)
<0.0001
<0.0001
Number
of Observations
11,254
Adjusted R-squared
Table
7:
This table reports the estimated coefficients from a regression of the
credit cards
on a spline with the business owner's age as
(dummies for j'ears in business, log(FICO)
and total card limit).
10.2
0.0933
credit risk score,
APR for small business
argument and other control variables
number
of cards, total card balance,
Results
Table 7 reports the results of regressing the
based spline and control variables.
FICO
its
score of the business owner, the total
also include
dummy
we expect APRs
to
variables for the
fall for
statistically significant
APR
for small business credit cards
As with individual
number
number
credit card accounts,
of cards, card balance,
on an age-
control for the
and card
limit.
We
of years the small business has been operating -
businesses with longer operating histories.
and have the expected
we
sign,
All control variables are
though only the dummies
for years in business
have substantial magnitudes.
APRs
are decreasing in the age of the borrower tlurough age 60
15 plots the fitted values on the spline for age.
and increasing thereafter. Figure
The graph shows a pronounced U-shape.
25
Small Business Credit Card
APR
by Borrower Age
Borrower Age (Years)
Figure
15:
Small business credit card
APR by
borrower age. The figure plots the residual
age, after controlling for other observable characteristics, such as log(income)
effect of
and credit-worthiness.
Credit Card Fee Payments: Late Fees
11
11.1
Overvie^v
Certain credit card uses involve the payment of a
terms of the credit card agreement are violated.
In the next three sections,
and cash advance
1.
Late Fee:
fees.^'^
A
We
we
Some
fee.
Other
kinds of fees are assessed
focus on three important types of
fees: late fees,
late fee of
between $30 and $35
is
assessed
credit card statement.
If
if
the borrower
the borrower
APR
to over 24 percent.
The bank may
make a
late
fees,
payment during the
six
months
makes a payment
late
also
by more than 60
impose 'penalty
also choose to report late
payments to credit bureaus, adversely affecting consumers' FICO
does not
is
may
days once or by more than 30 days twice within a year, the bank
by raising the
over limit
describe the fee structure for our data set below.
beyond the due date on the
pricing'
when
fees are assessed for use of services.
scores.
after the last late
If
the borrower
payment, the
APR
All of these fees
'^ Other types of fees include annual, balance transfer, foreign transactions, and pay by phone.
bank and the borrower. Few issuers (the most notable exception being
American Express) continue to charge annual fees, largely as a result of increased competition for new borrowers
(Agarwal et al., 2005). The cards in our data do not have annual fees. We study balance transfer behavior using
a separate data set below. The foreign transaction fees and pay by phone fees together comprise less than three
percent of the total fees collected by banks.
are relatively less important to both the
26
normal (though not promotional)
will revert to its
2.
Over Limit
An
Fee;
over limit fee - also between $30 and $35 -
Over
the borrower exceeds his or her credit limit.
that
3.
analogous to the penalty pricing that
is
Cash Advance
fees, this fee
purchases, and
Payment
it
many
imposed
as a result of late fees.
amount
the greater of 3 percent of the
is
times per month.
APR
time
first
on cash advances
It
is
Unlike the
first
two
does not cause the imposition of
typically greater
than the
APR
on
usually 16 percent or more.
of these fees
may
assessed the
is
limit violations generate penalty pricing
levied for each cash advance on the credit card.
is
However, the
is
is
cash advance fee - which
can be assessed
penalty pricing.
Tibet,
A
Fee:
advanced, or $5 -
level.
is
For example,
not generally a mistake.
if
a card holder
not be optimal to arrange a credit card payment for that month.
vacationing in
payment can often be avoided by small and
of fees are sometimes mistakes, since the fee
costless changes in behavior.
is
However, payments
For instance, late fees are sometimes due to
memory
relatively
lapses that
could be avoided by putting a reminder in one's calendar.
We
11.2
use the
same data
set as that
used
APR
case study discussed above.
Results
Table 8 presents panel regressions for each type of
regress a
dummy
variables.
variable equal to one
Hence the
propensity to pay
The
card
for the credit
if
a fee
is
fee.
paid that
coefficients give the conditional effects of the
fee,
variable equal to one
if
issued.
a
bill
was issued
"Bill Activity"
were made on the card; borrowers
will
card was used.
is
"Log(Purchases)"
last
is
a
risk score created
FICO
score.
"Log(FICO)"
mean
control for factors
borrowers
Existence"
"Bill
be
will only
variable equal to one
if
is
eligible to
a
dummy
pay a
is
limit
fees
if
the
card, in dollars;
we
would be increasing with
the credit risk score, and "Log(Behavior)"
late
is
an internal
and delinquent payment beyond that predicted by
less risky
because they are only updated quarterly.
amount purchased on the
and cash advance
late
purchases or payments
only be eligible to pay over limit or cash advance fees
the log of the
by the bank to predict
Higher scores
month;
dummy
would expect that the propensity to pay over
the amount of purchases.
Now we
which are not necessarily the same as factors that might
lead borrowers to default or otherwise affect their borrowing terms.
the
independent variables on the
control variables differ from those of the preceding six examples.
was
and control
spline
fees.
that might affect the propensity to pay a
fee if a bill
we
In each of the three regressions,
month on an age-based
We
behavior.
The
scores are lagged three
months
would expect the underlying behavior leading
lower credit risk scores would lead to higher fee payment.
27
"Debt/Limit"
is
to
the ratio of the balance
Late Fee
Coeff.
Over Limit Fee
Cash Adv. Fee
Coeff.
Coeff.
Std. Err.
0.0446
0.1870
0.0802
0.3431
0.0631
30
-0.0021
0.0004
-0.0013
0.0006
-0.0026
0.0011
30-40
-0.0061
0.0003
-0.0003
0.0001
-0.0004
0.0002
40-50
-0.0001
0.0000
-0.0002
0.0000
-0.0002
0.0000
50-60
-0.0002
0.0000
-0.0002
0.0000
-0.0003
0.0000
60-70
0.0004
0.0002
0.0003
0.0001
0.0004
0.0000
>
70
0.0025
0.0013
0.0003
0.0001
0.0004
0.0000
Existence
0.0153
0.0076
0.0104
0.0031
0.0055
0.0021
Bill Activity
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
<
Age
Age
Age
Age
Age
Age
Bill
Time Fixed Eff.
Number of Obs.
YES
YES
YES
YES
YES
YES
3.9 Mill.
3.9 Mill.
3.9 Mill.
Adj. R- squared
0.0378
0.0409
0.0388
Acct. Fixed
Eff.
This table reports coefficients from a regression of
8:
Std. Err.
0.2964
Intercept
Table
Std. Err.
payments on a spline
for age, financial control variables
dummy
variables for credit card fee
(log(FICO) credit risk score, internal bank
behavior risk score, debt over limit) and other control variables (dummies for whether a
last
month,
for
whether the card was used
last
bill
existed
month, dollar amount of purchases, account- and
time- fixed effects).
of credit card debt to the credit limit;
we would expect
the propensity to pay over limit
and possibly other
fees,
that having less available credit would raise
fees.
For late fee payments - column one of the table -all control variables have the expected signs
and are
statistically significant,
variables
may
though they are also small
in
magnitude.
increasing age
makes borrowers more
likely to forget to
pay
fees
on the age sphnes may understate some age-related
Coefficients
weakly positive
on the age
For example,
if
on time, that would both increase
the propensity to pay late fees and decrease credit and behavior scores.
coefficients
Note that some control
partly capture the effects of age-related cognitive decline on fees.
Hence the estimated
effects.
splines are uniformly negative for splines through age 50, negative or
for the spline
between age 50 and
60,
and positive with increasing slope
for
sphnes
payment
regres-
above age 50.
The top
line in
Figure 16 plots fitted values for the age splines
for the late fee
sion.-^^
Gabaix and Laibson (2006), we study
payment of past fees, and forgetting.
'^In Agarwal, DriscoU,
learning from the
28
this propensity of paying fees as the interaction of
Frequency of Fee Payment by Borrower Age
Borrower Age (Years)
Figure 16; Frequency of fee payment by borrower age.
The
figure plots the residual effect of age,
after controlling for other observable characteristics, such as log(income)
12
Credit Card Fee Payments:
The second column
controls
and age
and credit-worthiness.
Over Limit Fees
of Table 8 presents regression results for the over limit fee,
splines that were used for the late fee.
on the same
Results are similar to those generated in
analysis of the late fee.
The bottom
line in
Figure 16 plots fitted values of the age splines for the over limit fee payment
regression.
13
Credit Card Fee Payments:
The second column
controls
and age
payment
of Table 8 presents regression results for the cash advance fee,
splines that were used for the late fee.
analysis of the late fee
The middle
Cash Advance Fees
line in
and the over
on the same
Results are similar to those generated in
limit fee.
Figure 16 plots fitted values of the age splines for the cash advance fee
regression.
29
The Peak
14
of PerformEince
Locating the Peak of Performance
14.1
Visual inspection of the age splines for the ten case studies suggests that financial mistakes are
at a
minimum
in the late
40s or early 50s.
To estimate the minimum more
precisely,
we re-estimate
each model, replacing the splines between 40 and 50 aiid 50 and 60 with a single spline running
from 40 to
60,
and the square of that
This enables us to more precisely estimate the local
spline.
properties of the performance curve.
In other words,
we run
the following regression, where
F
is
the outcome associated respectively
with each of the 10 studies:
F = a + (3
(2)
+a
Here Spline{Age)
is
X Spline{Age) ^gg^^iQQQj
X Spline (Age) ^g^^^^Qf^^^
+
+7
b
[40,60] age range, while Spline (Age) ^^^uq
F=
of performance
is
Controls
q^i
is
+
a x
Age +
age)
+
is
b
implicitly quadratic in age:
x Age}
(26)
Peak
calculate the asymptotic standard errors on
is
argument (with
the linear spline with knot points at 40 and 60.
Peak = -a/
Peak
its
defined as the value that minimizes the above function:
(3)
error of
•
5'p/me(A5e)^pe^|40_6o] represents the sphnes outside of the
70).
Hence, for age between 40 and 60, the above formulation
We
+e
a piecewise linear function that takes consumer age as
knot points at ages 30, 40, 60 and
The peak
x Controls
Spline (^5e)^4gee|40,60]
using the delta method, so that the standard
the standard error associated with the linear combination:
— l/(26)-(Coefficient on
a/ (26^) -(Coefficient on age").
In Table
9,
are minimized.
we report the
location of the 'age of reason': the point at which financial mistakes
The mean age
of reason appears to be at 53.3 years.
calculated by treating each study as a single data point
Formal hypothesis testing (Hq: a
moment
is
statistically different
+
26 x 53
from 53
most dependent on analytic capacity and
transfer offers that
we study were new
=
0)
is
deviation
shows that only the location of the Eureka
years. Interestingly, the
least
The standard
4.3 years.
Eureka task
is
arguable the most
dependent on experience (since the kinds of balance
financial products
when our data was
collected).
It is
not
surprising that the peak age for succeeding at that task would be earlier than the peak age for the
other tasks.
However, since we do not have a rigorous measure of the
interpretation of the Eureka case remains speculative.
30
"difficulty" of
a task, the
Age
Peak Performance
Standard Error
55.9
4.2
53.3
5.2
Eureka Moment
45.8
7.9
Card-APR
Auto Loans-APR
50.3
6.0
49.6
5.0
Mortgage-APR
56.0
8.0
Credit Card Late Fee
6L8
5L9
4.9
Credit Card Over Limit Fee
54.0
5.0
Credit Card Cash Advance Fee
54.8
4.9
Average over the 10 Studies
53.3
Home
Home
Equity
of
Loans-APR
Equity Lines-APR
Credit
Card-APR
Small Business Credit
Table
Age
9:
at
which financial mistakes are minimized,
each case study
for
Formal Test of a Peak of Performance Effect
14.2
Table 9 allows us do a formal test for a peak
peak
7.9
effect
(i)
is:
6
>
0,
and
(ii)
Peak — —a/
mistakes follow a U-shape, with a peak that
For criterion
(i),
10 studies, b
is
For criterion
(ii).
we note that the
significantly different
effect.
(26)
is
G
In regression (2), the null hypothesis of a
[40,60].
Together these conditions imply that
between 40 and 60 years of age.
b coefficients
are positive for
from zero (the credit card
For 9 of the
10 studies.
all
APR
study
is
the exception). ^^
Table 9 shows that a peak in the 40-60 age range can not be rejected
for all ten
studies.
14.3
A
What
Possible Interpretation of the Location of the Performance Peak
determines the age of peak performance?
tween experience (that
is
linearly after age 20), the sooner people start
of
If
peak performance
reflects
accumulated with diminishing returns) and analytic
a trade-off be-
ability (that declines
experimenting with the product, the
earlier
peak
performance should be. For instance, take the simple functional forms presented
in section 2.
= a—
age/f3. Sup-
Suppose Analytic Capital declines
pose that Experiential Capital
Capital
=
\n{age
and -yageo
effective age
<
is
—
ageo
less
'yageo),
is
is
linearly
with age, so that Analytic Capital
accumulated with diminishing returns -
where ageo
is
the effective age at
for instance. Experiential
the actual age at which people start using the product,
which people
start using the
product (so 7 <
1).
The
than the actual age since consumers get indirect experience (observation and
advice) as a result of their interactions with slightly older individuals
To save space, we only report the f— statistics associated with the
they are: 2.20, 4.55, 7.80, 8.77, 17.05, 1.61, 4.57, 2.91, 3.08, 2.67.
31
who
6 coefficients.
use the product.
The
Following the order of Table
9,
model implies that peak performance occurs
later
when people
To evaluate
Peak — P + jageo. Hence, peak performance
at
start using the product later in
this hypothesis for
is
life.
each financial product, we
first
construct the distribution of the
ages of the users of this product in our data set and calculate the age at the 10th percentile of the
distribution,
which we
the product.
We
33
+
We
call "agei[)% "
0.71x0(7610%, (i?^
=
0.62,
n
reject the null hypothesis of
used later in
life
It is
.
a crude proxy for the age at which people start using
—
10; tlie s.e.
on the
coefficients are respectively 5.7
and
0.19).^°
no relationship between Peak and ageiQ%. Products that are
It
and the hypothesized mechanism with other data
Discussion and Related
15
Peak=
find:
first
tend to have a later performance peak.
This minimal analysis only provides suggestive evidence.
correlation
We
then regress the location of the peak of performance on ageio%-
would be desirable to explore
this
sets.
Work
Alternative Explanations
15.1
Age
However, our cross-sectional
a parsimonious explanation for our findings.
effects offer
evidence does not definitively support this interpretation.
In the current section,
we review some
alternative explanations.
Risk: Some of our results could be driven by unobserved variation
the U-shape of
APRs
could be due to a U-shape of default by age.
by regressing default rates on age splines
credit lines.
home
We
for credit cards,
None
plot fitted values in Figure 17.
in default risk.
For instance,
We test this alternative hypothesis
auto loans, and
of the graphs
is
home
U-shaped.
equity loans and
On
the contrary,
equity loans and lines show a pronounced inverted U-shape, implying that the young and
old have lower default rates.
Credit cards and auto loans also show a slight inverted U-shape.
Hence, Figure 17 contradicts the hypothesis that our results are driven by an unmeasured default
risk.
Also, note that age-dependent default risk could not explain the observed patterns in credit
card fee payments or suboptimal use of balance transfers.
Opportunity Cost of Time: Some age
be generated by age-variation
in the
opportunity cost of time (Aguiar and Hurst, forthcoming). However, such opportunity-cost
effects
would predict that
retirees
ertheless, our findings
for
The
effect
Median age
is
mistakes, which
is
not what we observe in our data. Nev-
and those of Aguiar and Hurst do not contradict one another.
a familiar commodity,
a complicated and
make fewer
effects could
like
a gallon of milk,
is
less analytically
somewhat unfamiliar product that can
robust to the choice of the 10th percentile.
(of users for the product, in our
data
set)
is
0.83.
.32
Shopping
demanding than shopping
differ across
many
dimensions,
for
like
a
For instance, the correlation between Peak age and
Percent Defaulting by Borrower
HE-Loans
-Auto Loans
-Arger^tina Mortgage
Credit Cards
HE-Lines
Age
""''-Small Business
Borrower Age (Years)
Figure
17:
The
Default frequency by borrower age.
figure plots the residual effect of age, after
controlling for other observable characteristics, such as log(income)
mortgage.
shop
for
credit- worthiness.
Hence, we should expect to see older adults sustain or even improve their ability to
food at the same time that they lose ground in the domain of financial decision-making.
In addition, shopping at stores and supermarkets
at
and
may be
a more pleasant activity than shopping
banks and other lenders, leading consumers to do more comparison shopping
for food
than
for
loans.
Medical Expenses:
This increased
be
demand
less attentive to
Older consumers
for
borrowing
terms and
fee
may need
may worsen
to
their
borrow to meet higher medical expenses.
borrowing terms;
it
may
also lead
them
to
payments.
Using individual credit card transactions data, we look at the average fraction of monthly
spending on medical categories.
The
fraction
1.19 percent for borrowers between ages 40
60 and 79.
Thus,
it
is
1.18 percent for borrowers between ages 20
and
59;
and 1.06 percent
for
and
39;
borrowers between ages
does not appear that older consumers are disproportionately using credit card
borrowing to finance medical expenditures.
Discrimination:
The presence
kind of age discrimination.
We
of -age effects might also be interpreted as evidence for
believe this to be unlikely, for
two reasons.
First the
some
U-shaped
pattern shows up in contexts such as fee payments and failures to optimally use balance transfer
offers in
which discrimination
is
not relevant (since
33
all
card holders face the same rules).
Second,
Penalties for age discrimination from the Fair
firms avoid age discrimination for legal reasons.
Lending Act are substantial
Sample
(as
would be the resulting negative
Measured age
Selection:
pool of borrowers by age group:
and
lines of credit
a selection
may, on average, be
year-old borrowers, since
effects
publicity).
could also be attributable to differences in the
effect.
home
Older consumers using
equity loans
group that the pools of 40-to-50-
a less financially savvy
more savvy borrowers may instead choose
to use their savings to finance
expenditures.^^
Three reasons lead us to doubt that
in their
this effect
is
quantitatively large. First, the pool of borrowers
20s through 40s should not be on average financially less savvy than other groups, since
most people
in these age groups will use at least
group does worse
in all ten
domains than
one of the financial products we study.
Yet that
slightly older individuals.
Second, measurable financial characteristics do not show a pattern consistent with a worsening
pool by age.
Figure 17 above showed that default rates are lower for older borrowers.
18 shows that credit risk
(FICO) scores on home equity loans and
over the age distribution
— an
substantial change in riskiness.
amount too small
lines decline
Figure
by about 5 points
to either change lending terms or represent a
Figure 19 shows that loan to value ratios decline substantially
with age, indicating that borrowers are devoting a smaller fraction of their assets to servicing this
particular kind of debt.
Third, Figure 20 below shows the results of re-estimating the regressions for
and
lines of credit,
but dropping data on
to believe that the pool of borrowers
above.
The
Cohort
results
still
Effects:
all
borrowers over the age of 60.
show a U-shape,
albeit a
somewhat
less
First,
Although we cannot eliminate the
we observe,
several facts
make
less sophisticated financial
familiar with
possibility that cohort effects are
one leading cohort story would imply that borrowers currently
less
is less
us skeptical of this explanation.
would be best positioned to understand new financial products.
borrowers are prone to make
reason
pronounced one.^^
may make
choices not because they are older, but because they belong to a cohort that
driving the patterns that
equity loans
is less
below 60 are subject to the sample selection issues discussed
Older borrowers in the cross-section
current financial products.
home
There
in their 20s, 30s
and 40s
However, we find that younger
sophisticated financial choices than borrowers in middle- age.
Second, we observe the U-shaped pattern over a broad range of products; while some of these
products, such as mortgages, have seen substantial changes in their institutional characteristics
over time, others, such as auto loans, have not.
Third,
if
cohort effects were dominant, we might expect to see differences in
APRs between
male
and female borrowers on the grounds that the current cohort of older female borrowers has tended
"'While they may in principle also be riskier, we have discussed that possibility above.
"^This graph also reinforces the arguments above that potential higher riskiness of borrowers above age 60
not responsible for the results.
34
'
is
likely
RCO Score By Home
Equity Borrower
Age
715
710
Loans
Lines
705
Borrower Age
Figure 18: This figure plots the
credit borrowers
by age.
A
high
FICO (creditworthiness)
FICO score means a high
scores of
home
equity loan and line of
creditworthiness.
LTV Ratio by Home Equity Borrower Age
70.00
65.00
60.00
40.00
J
00
CM
in
(D
IT)
<0
CD
CO
tD
CNI
CD
Borrower Age
Figure 19: This figure plots the loan- to- value (LTV) ratio of
borrowers by borrower age.
35
home
equity loan and line of credit
APR
by
Home
Removing Borrowers
Equity Borrower Age,
above Age 60
^
6.50
^
<
6.00
-
5.50
-
5.00
-
4.50
-
4.00
-
__^
^^^—^__^
___
Loans
Lines
CO
<-M-i--orotDa)c>jmcD
CNCNjrvjnconrO"*^^
•r-
m
rt
m
o
1-^
in
CD
Borrower Age
Figure 20: This figure plots the residual effect of age on
home
equity loan and line
controlling for other observable characteristics, such as log(income)
APRs,
and credit-worthiness.
after
Obser-
vations on borrowers over age 60 have been dropped.
to be less involved in financial decision
plot the residual effects of age
making than
on home equity
line
Both show a U-shaped pattern by
respectively.
their
male contemporaries.
and loan
age, with
APR
for
Figures 21 and 22
female and male borrowers,
no substantive difference between the
two groups.
Finally, for
two products-auto loans and credit cards~we have data from 1992, ten years
than the data used
for
the effects of age on
with the
minimum
APR
earlier
Figures 23 and 24 replicate the plots of the fitted values of
our other studies.
for this earlier dataset.
Both
plots
show the same pronounced U-shape,
in the early 50's (like our results using later cross-sections).
driven by cohort effects, the U-shape should not reproduce
itself in
If
our findings were
cross-sections from different
years.
15.2
Market Equilibrium
The markets we
many competing
describe
firms selling
may seem
paradoxical.
commodity
characteristics fare differently, implying that
Markets
of
models
like this
(e.g.
have been described
First, they look competitive, since there are
credit products.
However, consumers with identical risk
somehow the good being sold
is
being de-commodified.
in the industrial organization literature.
A first generation
Salop and Stiglitz 1977, Ellison 2005, and the citations therein) emphasizes different
36
Home
Equity Line and Loan
APR
by Borrower Age
-Women
7.00
6.50
-
6.00
-
5,50
5.00
4.50
4.00
3.50
3.00
in
CD
(D
ID
Borrower Age
Figure 21: This figure plots the residual
eflPect
of age
on home equity loan and
after controlling for other observable characteristics,
Home
Equity Line and Loan
APR
line
APRs
for
women,
such as log(income) and credit-worthiness.
by Borrower Age
-
IWen
8.00
7.50
7.00
6.50
6.00
5.50
5.00
4.50
4.00
3.50
3.00
Figure 22: This figure plots the residual effect of age on
home
equity loan and line
after controlhng for other observable characteristics, such as log(income)
37
and
APRs
for
men,
credit- worthiness.
Auto Loans
APR by Borrower Age,
1992 Data
9,90
9.70
\^^^
9.50
^^
\^
c
e
^-~,^^^
^~~^-^^_^
9.30
a.
£
<
'''^
—
—--
9.10
^__^-
_
~__
8.90
8.70
8.50
-
sssssKS5?^sssssss;;
'^
r^
o
t^
CO
r-^
Borrower Age
Figure 23:
controUing
is
Auto loan
for other
APR
by borrower age.
The
figure, plots the residual effect of age,
observable characteristics, such as log(inconie) and credit-worthiness.
after
Data
from 1992.
Credit Card
18.90
APR by Borrower Age, 1992 Data
-
18.70
„
18.50
c
%
18.30
t
£
<
^
18.10
17.90
^^^---^.^^
17.70
17.50
--^
^--^
^_^,_^
ococDoicMiDcoT-'d-h-oirjuDajcMio.a:
Th-
"^
N-
r^
h-
o
CO
Borrower Age
Figure 24: Credit card
APR
by borrower
age.
The
figure plots the residual effect of age, after
controlling for other observable characteristics, such as log(income)
is
from 1992.
38
and
credit- worthiness.
Data
"search costs," which are costs of discovering the products of different firms.
name
(sometimes under the
of "behavioral industrial organization", e.g.
A
second generation
Gabaix and Laibson
2006, Ellison 2005) emphasizes different levels of rationality and farsightedness by consumers. For
instance, a balance transfer offer provides a rent that only
balances to the card but
make no purchases with
market equilibrium (with competition and
it
are smart
- and some consumers never get
free entry), the naive
marginal cost, subsidizing the sophisticated consumers,
ante point of view, the market
Most
some consumers
enough
to
unravel the shrouded attribute - the "catch" that they should transfer
Some consumers
exploit.
is
work
of the other markets
who pay below marginal
fully competitive, since
in similar ways.
it.
In the
consumers end up paying above
cost.
Prom an ex
expected profits of the firm are zero.^^
In equilibrium, sophisticated consumers get
Since the markets are competitive, the financial
subsidies from the unsophisticated consumers.
institutions themselves break even.
On
15.3
The
line of
the Economic Magnitude of the Effects
effects
we
find are
mean
$60,000 (the
loan interest rate of
1
sometimes large and sometimes small. For instance,
per year for each kind of
is
to
may
imphed age
We
home-equity
differentials are
important question
is
and
much
smaller - roughly $10-$20
do not claim that each of the economic decisions that we
its
own, but rather that there
merit economists' attention
decision domains (large
all
An
fee.""*
of significant economic relevance on
of mistakes that
for a
5 years, a difference in the
percentage point means a difference in total payments of $3000. For other
quantities, say credit card fees, the
study
and a duration of
value, see Table Al),
small).
We
become
it
points to a
is
a U-shape pattern
phenomenon
that applies
have studied credit decisions in the current paper.
whether the U-shape of mistakes translates into other decision domains,
including savings choices, asset allocation choices and health care choices.
Related
15.4
Work
Other authors have studied the
effects of
aging on the use of financial instruments.
Korniotis
and Kumar (2007) examine the performance of investors from a major U.S. discount brokerage
house.
They
may
use census data to impute education levels and data from the Survey of Health, Aging
how such a potentially inefficient equilibrium can persist in a competitive environment. An answer
Gabaix and Laibson (2006): the cross-subsidy from naives to sophisticates makes the market more
"sticky." The sophisticates may not have an incentive to switch from the firms with shrouded attributes (at which
they are getting cross-subsidies). Such stickiness explains why these equilibria arc robust even when the equilibria
"''One
is
proposed
ask
in
are inefficient.
"*
A
3% per month, and and a fee amount $35, leads to a total extra yearly expense
Note, however, that some of these fees, if paid too often, can trigger "penalty pricing," in which interest
difference in fee probabilty of
of $12.
rates ten percentage points or higher are levied on card balances, thus greatly increasing the cost of fee payment.
See Agarwal
et.
al.
(2006) for further discussion.
39
and Retirement
in
Europe
to estimate a
model of cognitive
They
abilities.
cognitive declines earn annual returns between 3-5 percentage points lower
In their
U
work on
and Mitchell
financial literacy, Lusardi
find that investors with
on a
shape of financial proficiency. Lusardi and Mitchell (2006) find a dechne
after age 50.
risk adjusted basis.
find evidence consistent
with an inverse-
in financial
knowledge
Lusardi and Mitchell (2007) also find an inverse U-shape in the mastery of basic
financial concepts,
such as the
ability to calculate percentages or simple divisions.
After some of our presentations other researchers have offered to look for age patterns of financial
mistakes in their
own data sets. Lucia Dunn has reported
to us that the
Ohio State Survey on
credit
caids shows a U-shaped pattern of credit card
APR terms by
Fiona Scott Morton has reported that
data set of indirect auto loans (made by banks and
in her
age (Dunn, personal communication).
finance companies using the dealer as an intermediary; see Scott
Morton
show a U-shaped pattern (Scott Morton, personal communication).
markups
et al., 2003), loan
Luigi Guiso finds that,
when
picking stocks, consumers achieve their best Sharpe ratios at about age 43, and this effect appears to
be entirely driven by the participation margin (Guiso, personal communication). Ernesto Villanueva
finds that
APRs
mortgage
in
Spanish survey data (comparable to the U.S. Survey of Consumer
Finances) are U-shaped by age (Villanueva, personal communication).
A relationship between earning and performance has been noted
in
many
non-financial contexts.
Survey data suggests that labor earnings peak around age 50 (Gourinchas and Parker, 2002) or
after
about 30 years of experience (Murphy and Welch, 1990). Shue and Luttmer (2006) find that
older and younger voters disproportionately
make more
errors in voting.
Aguiar and Hurst (2007, forthcoming) demonstrate that older adults find lower prices
day items by spending more time shopping around.
make more mistakes
In contrast,
in personal financial decision-making.
We
we
reconcile these findings
that financial products require more analytic ability than everyday items
Moreover, financial products
may
declines in baseball
A new
and
and other competitive
chess,
(like
among
literature in psychology
is
areas.
food or clothing).
Fair (1994, 2007) estimates the effects of age
other sports. Simonton (1988)
is
a useful survey.
and economics reports systematic differences
find that subjects
in "rationality"
with higher test
scores, or less cognitive load, display fewer behavioral biases. Frederick (2005) identifies a
:
to
a hterature on estimating performance peaks
between groups of people. Benjamin, Brown and Shapiro (2006)
of "analytical IQ"
seem
by noting
generate a less pleasurable shopping experience.
Turning to purely noneconomic domains, there
in professional athletics
for every-
find that older adults
measure
people with higher scores on cognitive ability tasks tend to exhibit fewer/weaker
psychological biases. While this literature
control for unobservables),
we
rely
on
is
field
motivated by experimental data (where
it is
easier to
data in our paper. Similarly, Massoud, Saunders and
Schnolnick (2006) find that more educated people
make fewer mistakes on
their credit cards,
and
Stango and Zinman (2007) find evidence that more naive consumers make mistakes across a range
of financial decisions.
40
Several researchers have looked at the response of consumers to low, introductory credit card
and
rates ('teaser' rates)
at the persistence of otherwise high interest rates.
of time to ones with
ex post
more
somewhat higher
beneficial.
Consumers
rates for a longer period of time, even
when
also appear 'reluctant' to switch contracts.
the latter
is
DellaVigna and
financial institutions set the terms of credit card contracts to
Malmendier (2004) theorize that
reflect
Shui and Ausubel
prefer credit card contracts with low initial rates for a short period
(2004) show that consumers
consumers' poor forecasting ability over their future consumption.
Many
of those effects are discussed in "behavioral industrial organization," a literature that
documents and studies markets with behavioral consumers and rational
firms:
DellaVigna and
Malmendier (2004), Gabaix and Laibson (2006), Heidhues and Koszegi (2006), Malmendier and
Devin Shanthikumar (2005), Mullainathan and
Spiegler (2006).
In
some
of those papers,
it
is
Shleifer (2005), Oster
and Scott Morton
(2005),
important to have both naive and sophisticated
consumers (Campbell 2006). The present paper suggests than those naive consumers
will dispro-
portionately be younger or older adults.
Bertrand
et al. (2006) find that
randomized changes
credit offers affect adoption rates as
hypothesizes that consumers
much
may be
in the "psychological features" of
as variation in the interest rate terms.
consumer
Ausubel (1991)
over-optimistic, repeatedly underestimating the probability
Calem
that they will borrow, thus possibly explaining the stickiness of credit card interest rates.
and Mester (1995) use the 1989 Survey
of
Consumer Finances (SCF)
to argue that information
barriers create high switching costs for high-balance credit card customers, leading to persistence
of credit card interest rates,
and Calem, Gordy, and Mester (2005) use the 1998 and 2001 SCFs
argue that such costs continue to be important. Kerr and
Dunn
(2002) use data from the 1998
to
SCF
to argue that having large credit card balances raises consumers' propensity to search for lower
credit card interest rates.
Dunn
Kerr, Cosslett and
better lending terms to consumers
who
are also
(2004) use
SCF
data to argue that banks
bank depositors and about
whom
offer
the bank would
thus have more information.
A
literature analyzes heuristics
and biases
in financial decision
making. For instance, Benartzi
and Thaler (2002) show that investors prefer the portfolios chosen by other people rather than
the ones chosen by themselves, a pattern which suggests that task difficulty prevents people from
reaching an optimal decision. Benartzi and Thaler (forthcoming) also document the use of a
of sometimes inappropriate heuristics.
Our
number
findings imply that the U-shape pattern of financial
mistakes should also be found in the examples that Bernatzi and Thaler document.
A number
of researchers have written
overlaps with that of Agarwal et
al.
about consumer credit card
(2005),
who
use another large
use.
Our work most
random sample
closely
of credit card
accounts to show that, on average, borrowers choose credit card contracts that minimize their total
interest costs net of fees paid.
About 40 percent
While some borrowers incur hundreds of
of borrowers initially choose suboptimal contracts.
dollars of such costs,
41
.
most borrowers subsequently switch
to cost-miniinizing contracts.
we
since
The
paper complement those of Agarwal
results of our
et
al.
(2007),
find evidence of learning to avoid fees and interest costs given a particular card contract.
Other authors have used credit card data to evaluate more general hypotheses about consumption.
Agarwal, Liu, and Souleles (2004) use credit card data to examine the response of consumers to
the 2001 tax rebates.
Gross and Souleles (2002a) use credit card data to argue that default
due to declining default
rates rose in the mid-1990s
worthiness of borrowers.
in interest rates lead to large increases in
Euler equations
for credit
well-being
U-shaped over the
is
The trough
it
is
related to recent research that studies
For example, Blanchflower and Oswald (2007) report that
lifecycle controlling for observable
for
age splines;
(2)
Second,
it
this:
domains.
effects in other decision
have described a
be possible to develop models that predict the location of peak performance.
a growing consensus that analytically intensive problems -
like
mathematics - are
asso-
and Weinberg and Galenson,
Analogously, problems that require more experiential training have older peak ages.
More knowledge now needs
In our last case study,
peak age
to be
for scientists
accumulated to reach the cutting edge of the
we found that what
is
age of peak performance.
analytically
Third,
it
little
would be
is
not
is
associated with the youngest
useful to assess the generality of this association between
would be desirable to identify
Forced disclosure
ages.
cost-effective regulations that
even for consumers
limited financial education.
We
would help improve
itself sufficient, since disclosing costs in
impact on distracted and boundedly rational consumers. '^^
effective
field.
arguably the most analytically demanding task -
demanding problems and young peak
cial decisions.
need to be
It
For
has drifted higher in the twentieth
deducing the best way to exploit "interest-free" balance transfers -
have
We
estimate a linear-quadratic form to localize the peak of performance, as in (2)-(3).
may
instance, Jones (2006) finds that the
century.
characteristics.
(1) identify the general shape of age effects, as in (1), using controls and
ciated with younger peak ages (see Simonton, 1988, Galenson, 2005,
2005).
demographic
Future Research
would be useful to study age
simple procedure for
is
Ravina (2005) estimates consumption
findings suggest several directions for future research.
First,
There
in the credit-
occurs in the 40s.
Some Open Questions
Our
consumer debt.
from a methodological perspective our work
Finally,
than a deterioration
card holders and finds evidence for habit persistence.
age variation along other dimensions.
15.5
costs, rather
Gross and Souleles (2002b) find that increases in credit limits and declines
who do
Good
finan-
the fine print will
disclosure rules will
not take the time to read the fine print or
who have
conjecture that effective regulations would produce comparable
'^See Gabaix, Laibson, Moloche, and Weinberg (2006) and Kamenica (2007)
under information overload.
42
for recent
models
of
economic behavior
-
and transparent products.
may
On
the other hand, such homogenization has the
dynamic
cost that
it
create a hurdle to innovation.
Fourth, studying cognitive hfecycle patterns should encourage economists to pay more attention
market
to the
for advice.
Advice markets
may
not function efficiently because of information
asymmetries between the recipients and the providers of advice (Dulleck and Kerschbamer, 2006).
It is
particularly important to study the advice market for older adults
make
their
own
who
are
now
required to
financial decisions.
Conclusion
16
We
find that middle-age adults
markets.
Our
example,
FICO
borrow at lower
analysis suggests that this fact
scores
show no pattern
is
of age variation.
predicts the opposite pattern from the one that
Age
effects
interest rates
and pay lower
fees in ten financial
not explained by age-dependent risk factors.
For
Moreover, age variation in default actually
we measure.
may
parsimoniously explain the patterns that we observe, but, other effects
play a role - for instance, cohort effects or endogenous
human
also
Whatever
capital accumulation.
the mechanism, there appears to be a robust relationship between age and financial sophistication
in cross-sectional data.
effects.
If
Future research should untangle the different forces that give
age effects are important, economists should analyze the efficiency of
institutions - like defined contribution pension plans - that require retirees to
own
saving, dissaving,
and
rise to these
modern
financial
make most
of their
asset allocation decisions.
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Appendix: Data Summary
Statistics
Home
Table Al:
Equity Loans and Credit Lines
Loans
Mean
Description (Units)
APR(%)
Annual)
(S,
Std. Dev.
1.16
4.60
43
14
46
12
78,791
99,761
90,293
215,057
Debt/Income (%)
FICO
Mean
7.96
Borrower Age (Years)
Income
Credit Lines
Std. Dcv.
(Credit Bureau Risk) Score
0.88
40
18
41
19
713
55
733
49
24
Customer
LTV
(%)
66
26
62
Appraisal
LTV
(%)
69
29
64
23
196,467
144,085
346,065
250,355
186,509
123,031
335,797
214,766
43,981
35,161
61,347
50,025
42,871
33,188
60,725
51,230
79,496
83,560
154,444
112,991
92
122
99
129
29
45
15
42
3
14
3
12
8
18
6
17
66
47
39
49
18
39
25
44
16
39
35
35
7.9
27
7.8
27
Retired (%)
9.5
29
7.7
27
Homemaker (%)
1.4
12
1.3
11
6.3
8.1
7.6
9.1
Borrower
Home
Value Estimate
Bank Home Value Estimate
Loan Requested by Borrower
Loan Approved by Bank
Mortgage Balance
First
Months
No
First
at
($)
($)
($)
($)
($)
Address
Mortgage (%)
Second
Home
(%)
Condo (%)
Refinancing (%)
Home Improvement
(%)
Consumption (%)
Self
Employed (%)
Years on
tlie
Last Job
.48
Table A2:
Credit Cards
Account Characteristics
Purchase
Interest
Frequency
APR
Rate on Cash Advances (%)
Credit Limit ($)
Current Cash Advance
Payment
New
($)
(S)
Purchases
($)
Mean
Std. Dev.
Monthly
14.40
2.44
Monthly
16.16
2.22
Monthly
8,205
3,385
Monthly
148
648
Monthly
317
952
Monthly
303
531
1,978
Debt on Last Statement
($)
Monthly
1,735
Minimum Payment Due
($)
Monthly
35
52
Monthly
29
36
Monthly
10.10
14.82
Monthly
5.09
11.29
3.22
Debt/Limit (%)
Fee Payment
Total Fees ($)
Cash Advance Fee
($)
Late Payment Fee
($)
Over Limit Fee
($)
Extra Interest Due to Over Limit or Late Fee
Extra Interest Due to Cash Advances
($)
Monthly
4.07
Monthly
1.23
1.57
Monthly
15.58
23.66
Monthly
3.25
3.92
Cash Advance Fee Payments/Month
Monthly
0.38
0.28
Late Fee Payments/Month
Monthly
0.14
0.21
Over Limit Fee Payments/Month
Monthly
0.08
0.10
($)
Borrower Characteristics
FICO
(Credit Bureau Risk) Score
Behavior Score
Quarterly
731
76
Quarterly
727
81
3.56
Number
of Credit Cards
At Origination
4.84
Number
of Active
Cards
At Origination
2.69
2.34
Total Credit Card Balance ($)
At Origination
15,110
13,043
Mortgage Balance
At Origination
47,968
84,617
At Origination
42.40
15.04
At Origination
57,121
114,375
Age
Income
Notes:
($)
(Years)
The
($)
"Credit Bureau Risk Score"
the less risky the consumer
is.
is
provided by Fair, Isaac and Company.
The "Behavior
payment history and debt burden, among other
behavior not accounted for by the
FICO
Score"
is
variables, created
score.
49
The
greater the score,
a proprietary score based on the consumer's past
by the bank to capture consumer payment
Auto Loan APRs
Table A3:
Mean
Description (Units)
APR(%)
8.99
Borrower Age (Years)
Income
($,
Monthly)
LTV(%)
FICO
Std. Dev.
(Credit Bureau Risk) Score
Montirly Loan Payment
Blue Book Car Value
Loan Amount
772
44
10
723
64
229
95
4,625
4172
1427
{$)
Car Age (Years)
Loan Age (Months)
Table A4:
21
3416
11,875
($)
($)
0.90
40
2
1
12
8
Mortgage Loans
Loans
Mean
Description (Units)
Std. Dev.
APR(%)
12.64
Borrower Age (Years)
40.54
9.98
Income
2,624
2,102
22.84
12.12
686
253
($)
Monthly Mortgage Payment/Income (%)
Veraz (Credit Bureau Risk) Score
LTV
(%)
Loan Amount
($)
Years at Current Job
2.17
61
17
44,711
27,048
9.43
8.01
Second House (%)
15.54
5.18
Car Ownership (%)
73.56
44.11
Car Value
5,664
13,959
Gender (Female=l)
30.96
46.24
Second Income (%)
20.44
40.33
Married (%)
71.32
45.23
16.75
37.34
13.87
34.57
($)
Married with
Self
Two Incomes
(%)
Employed (%)
Professional
Employment (%)
Nonprofessional Employment (%)
Relationship with
Bank (%)
50
15.78
36.46
52.78
49.93
10.40
30.52
Table A5:
Small Business Credit Cards
Mean
Description (Units)
Std. Dev.
APR(%)
13.03
5.36
Borrower Age (Years)
47.24
13.35
Line
Amount
($)
Total Unsecured Debt
FICO
(Credit Bureau Risk) Score
Mortgage Debt
($)
Table A6:
Age
9,623.95
6,057.66
12,627.45
17,760.24
715.86
55.03
102,684.70
160,799.57
Distribution by Product
Age
Product
600-^
APRs
Percentile
50%
75%
90%
Home
Equity Loans
34
40
48
59
71
Home
Equity Lines
32
40
47
58
70
"Eureka"
24
34
44
53
63
Credit Card
25
34
44
57
68
Auto Loans
27
35
45
57
67
Mortgage
34
42
49
60
69
Small Business Credit Card
37
43
53
62
72
Credit Card Late Fee
25
35
45
58
67
Credit Card Over Limit Fee
26
34
43
56
65
Credit Card Cash Advance Fee
25
36
46
58
68
10%
25%
'-1
51
,
MIT LIBRARIES
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