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Federal Reserve Bank of Chicago

The Age of Reason:
Financial Decisions Over the Lifecycle
Sumit Agarwal, John C. Driscoll,
Xavier Gabaix, and David Laibson

WP 2007-05

The Age of Reason: Financial Decisions Over the Lifecycle
Sumit Agarwal, John C. Driscoll, 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 to both younger and older adults. We document this
pattern in ten financial markets. The measured eﬀects cannot be explained by observed risk
characteristics. The sophistication of financial choices peaks around age 53 in our cross-sectional
data. Our results are consistent with the hypothesis that financial sophistication rises and then
falls with age, although the patterns that we observe represent a mix of age eﬀects and cohort
eﬀects. (JEL: D1, D8, G2, J14).

Keywords: Household finance, behavioral finance, behavioral industrial organization,
aging, shrouding, auto loans, credit cards, fees, home equity, mortgages.

∗

Agarwal: Federal Reserve Bank of Chicago, sagarwal@frbchi.org. Driscoll: Federal Reserve Board,
john.c.driscoll@frb.gov. 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 (R01-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
System or the Federal Reserve Bank of Chicago. For their comments we thank Marco Basetto, Stephane
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
conference.

Introduction
Performance tends to rise and then fall with age.

Baseball players peak in their late 20s

(James 2003). Mathematicians, theoretical physicists, and lyric poets make their most important
contributions around age 30 (Simonton 1988). Chess players achieve their highest ranking in their
mid-30s (Charness and Bosnian 1990). Autocratic rulers are maximally eﬀective in their early 40s
(Simonton 1988). Authors write their most influential novels around age 50 (Simonton 1988).1
The present paper studies an activity that is less august, though it is relevant to the entire adult
population: personal financial decision making. Many financial products are complex and diﬃcult
to understand. Fees are sometimes shrouded and the true costs of financial services are not always
easily calculated. Making the best financial choices takes knowledge, intelligence, and skill.
This paper documents cross-sectional variation in the prices that people pay for financial services. We find that younger adults and older adults borrow at higher interest rates and pay more
fees than middle-aged adults controlling for all observable characteristics, including measures of
risk.
The hump-shaped pattern of financial sophistication is present in many markets.

We study

interest rates in six diﬀerent markets: mortgages, home equity loans, home equity credit lines, auto
loans, personal credit cards, and small business credit cards.

We study the failure to optimally

exploit balance transfer credit card oﬀers. Finally, we study three kinds of credit card fees: late
payment fees, cash advance fees, and over limit fees. All of the evidence available to us implies a
hump-shaped pattern of financial sophistication, with a peak in the early 50s.
Age eﬀects provide one parsimonious explanation for the hump-shaped pattern of financial
sophistication. We hypothesize that financial sophistication depends on a combination of analytic
ability and experiential knowledge. Research on cognitive aging implies that analytic ability follows
a declining (weakly) concave trajectory after age 20. We hypothesize that experiential knowledge
follows an increasing concave trajectory due to diminishing returns.

Adding together these two

factors implies that financial sophistication should rise and then fall with age.
Cohort eﬀects may also explain some of the eﬀects that we observe. Diﬀerences in educational
levels may explain why older adults are less financially sophisticated than middle-aged adults.
Naturally, such education eﬀects will not explain why young adults (around age 30) are less sophisticated than middle-aged adults. Additional work needs to be done to identify the relative
contributions of age eﬀects and cohort eﬀects.
The paper has 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 that economists’ output in top publications declines
sharply with age. This may simply reflect lower motivation with age. More optimistic data are reported in Weinberg
and Galenson (2005)’s study of Nobel (Memorial) Prize winners. They find that “conceptual” laureates peak at age
43, and “experimental” ones at age 61.

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. Section
15.1 discusses other findings on the eﬀects of aging and the diﬃculty in separately identifying age
eﬀects and cohort eﬀects. Section 16 concludes.

Motivating Evidence on Aging and Cognitive Performance from
Medical and Psychological Research
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. Analytic
performance is strongly negatively correlated with age in adult populations (Salthouse, 2005 and
Salthouse, forthcoming). On average analytic performance falls by two to three percent of one
standard deviation2 with every incremental year of age after age 20. This decline is remarkably
steady from age 20 to age 90 (see Figure 2).
The measured age-related decline in analytic performance results from both age eﬀects and
cohort eﬀects, but the available panel data implies that the decline is primarily driven by age
eﬀects (Salthouse, Schroeder and Ferrer, 2004).3

Medical pathologies represent one important

pathway for age eﬀects. For instance, dementia is primarily attributable to Alzheimer’s Disease
(60%) and vascular disease (25%). The prevalence of dementia doubles with every five additional
years of lifecycle age (Fratiglioni, De Ronchi, Agüero-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 oﬀset by age-driven increases in experience. Most day-to-day tasks rely on both analytic and experiential human capital — e.g. buying
a car. For such tasks, we hypothesize that task performance is hump-shaped with respect to age.4
Figure 3 illustrates this case.
The current paper tests the prediction that general task performance follows a hump-shaped
pattern with age. We focus on financial decision-making. Because our financial market data span
2

This is a standard deviation calculated from the entire population of individuals.
See Flynn (1984) for a discussion of cohort eﬀects.
4
This happens for instance under the following set of suﬃcient conditions: (i) general task performance is determined 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

Reasoning

Study the following words and then write as
many as you can remember

Select the best completion of the missing cell in
the matrix

Goat
Door
Fish
Desk
Rope
Lake
Boot
Frog
Soup
Mule

Spatial Visualization

Perceptual Speed

Select the object on the right that corresponds to
the pattern on the left

Classify the pairs as same (S) or different (D) as
quickly as possible

Figure 1: Four IQ tests used to measure cognitive performance. Source: Salthouse (forthcoming).
a small number of years, we are unable to decompose the relative contributions of age and cohort
eﬀects, and leave that analysis to future research with diﬀerent data sets.
The main contribution of the paper is to document a robust empirical regularity in all of our
cross-sectional datasets: a hump-shaped relationship between age and financial sophistication. We
note that this hump-shaped pattern is consistent with the aging evidence described above, but we
do not have any direct evidence for this cognitive/aging 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 human capital. The young and
the old might calculate that it is less valuable to acquire relevant human capital, perhaps because
the stakes are smaller for them. Another channel might be social networks. It is plausible that
middle-aged adults are generally in social 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
1.5
84

0.5

0.0

-0.5

Z-Score

Percentile

1.0

-1.0

16
Word Recall (N = 2,230)
Matrix Reasoning (N = 2,440)
Spatial Relations (N = 1,618)
Pattern Comparison (N = 6,547)

-1.5

-2.0
20

Chronological Age

Figure 2: Age-normed results from four diﬀerent cognitive tests. The Z-score represents the agecontingent mean, measured in units of standard deviation relative to the population mean. More
precisely, the Z-score is (age—contingent mean minus population mean) / (population standard
deviation). Source: Salthouse (forthcoming).

Cognitive
capital

Experiential
capital

Task
Performance

Performance
Analytic
capital
Age
Figure 3: Hypothesized relation between general task performance and age. Analytical capital
declines with age 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.
5

Overview
In the body of the paper, we document a U-shaped age-related curve in financial “mistakes.”

Such mistakes reflect the hump-shaped sophistication pattern discussed in the previous section.
We study ten separate contexts:

home equity loans and lines of credit; auto loans; credit card

interest rates; mortgages; small business credit cards; credit card late payment fees; credit card
over limit fees; credit card cash advance fees; and use of credit card balance transfer oﬀers.
We diagnose mistakes in three forms:

higher APRs (Annual Percentage Rates, i.e., interest

rates); higher fee payments; and suboptimal use of balance transfer oﬀers.
For each application, we conduct a regression analysis that identifies age eﬀects and controls
for observable factors that might explain patterns of fee payments or APRs by age. Thus, unless
otherwise noted, in each context we estimate a regression of the type:
(1)

F = α + β × Spline(Age) + γ × Controls + .

Here F is the level of the APR paid by the borrower (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 risk), and Spline(Age) is a piecewise linear function that takes consumer age as
its argument (with knot points at ages 30, 40, 50, 60 and 70).5 We then plot the fitted values for
the spline on age. Regressions are either pooled panel or cross-sectional, depending on the context.
Each section discusses the nature of the mistake, briefly documents the datasets used, and
presents the regression results and graphs by age. We provide summary statistics for the data sets
in the Appendix.

Home Equity Loans

4.1

Data Summary

We use a proprietary panel dataset constructed with records from a national financial institution
that has issued home equity loans and home equity lines of credit. The lender has not specialized in
subprime loans or other market segments. Between March and December 2002, the lender oﬀered
a menu of standardized contracts for home equity credits. Consumers chose between a credit loan
and line; between a first and second lien; and could choose to pledge diﬀerent amounts of collateral,
with the amount of collateral implying a loan-to-value (LTV) ratio of less than 80 percent, between
80 and 90 percent, and between 90 an 100 percent. In eﬀect, the lender oﬀered twelve diﬀerent
5

For instance, in Table 1, the “Age 30-40” spline is: max (30, min (40, Age)), the “Age < 30 ” spline is min (30, Age),
and the “Age > 70 ” spline is max (70, Age).

contract choices.6 For 75,000 such contracts, we observe the contract terms, borrower demographic
information (age, years at current job, home tenure), financial information (income and debt-toincome ratio), and risk characteristics (credit (FICO) score, and LTV). 7 We also observe borrower
estimates of their house values and the loan amount requested.

4.2

Results

Table 1 reports the results of estimating regressions of APRs (interest rates) on home equity
loans on a spline for age and control variables. As controls, we use all variables observed by the
financial institution that might aﬀect loan pricing, including credit risk measures, house and loan
characteristics, and borrower financial and demographic characteristics. The control variables all
have the expected sign, and most are statistically significant, although some of them lack economic
significance, surprisingly so in some cases.
The measure of credit risk, the log of the FICO score (lagged three months because it is only
updated quarterly), is statistically significant but with a negligible magnitude. Discussions with
people who work in the industry reveal that financial institutions generally use the FICO score
to determine whether a loan oﬀer is made, but conditional on the oﬀer being made, do not use
the score to do risk-based pricing. The results here, and for the other consumer credit products
discussed below, are consistent with this hypothesis.
Loan APRs do depend strongly on the absence of a first mortgage (reducing the APR) and
whether the property is a second home or a condominium. The absence of a first mortgage reduces
the probability of default and raises the amount that might be recovered conditional on a default.
Second homes and condominiums are perceived as riskier properties.

Log income and log years

on the job also have large and negative eﬀects on APRs, as expected, since they indicate more
resources available to pay oﬀ the loan and perhaps less risk in the latter case. The largest eﬀects
on APRs come from dummy variables for LTV ratios between 80 and 90 percent and for ratios
greater than 90 percent.
contract

This is consistent with diﬀerent LTV ratios corresponding to diﬀerent

choices.8

Even after controlling for these variables, we find that the age splines have statistically and
6
We interpret a high APR as the sign of a mistake for four reasons. First, contracts do not diﬀer in points charged
or in other charges to the borrower. Second, even conditioning on contract choice some borrowers pay higher APRs
than others. Third, we control for borrower risk characteristics. Fourth, in section 5.3, we show that the residual
variation in APRs is explained by the propensity to make an identifiable mistake in the loan acquisition process.
7
We do 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.
8
We estimate three variants as a specification check. First, we allow the FICO scores, income, and LTV ratios
to have quadratic and cubic terms. This allows us to make sure that the nonlinear eﬀects with age that we see are
not a consequence of omission of potential nonlinear eﬀects of other control variables. Second and third, we allow
the splines to have knot points at every five years, and have a dummy for each age, to ensure that the smoothing
caused by the use of ten-year splines does not artificially create a U-shape. In all three cases, our results are not
qualitatively or quantitatively changed.

Home Equity Loan APR
Intercept
Log(FICO Score)
Loan Purpose—Home Improvement
Loan Purpose—Rate Refinance
No First Mortgage
Log(Months at Address)
Second Home
Condominium
Log(Income)
Debt/Income
Log(Years on the Job)
Self Employed
Home Maker
Retired
Age < 30
Age 30-40
Age 40-50
Age 50-60
Age 60-70
Age > 70
LTV 80-90
LTV 90+
State Dummies
Number of Observations
Adjusted R-squared

Coeﬃcient
8.1736
-0.0021
0.0164
-0.0081
-0.1916
0.0021
0.3880
0.4181
-0.0651
0.0034
-0.0246
0.0106
-0.0333
0.0355
-0.0551
-0.0336
-0.0127
0.0102
0.0174
0.0239
0.7693
1.7357
YES
16,683
0.7373

Std. Error
0.1069
0.0001
0.0138
0.0113
0.0097
0.0039
0.0259
0.0165
0.0077
0.0002
0.0039
0.0161
0.0421
0.0225
0.0083
0.0043
0.0048
0.0039
0.0076
0.0103
0.0099
0.0111

Table 1: The first column gives coeﬃcient estimates for a regression of the APR of a home equity
loan on a spline with age as its argument, financial control variables (Log(FICO) credit risk score,
income, and the debt-to-income-ratio), and other controls (state dummies, a dummy for loans made
for home improvements, a dummy for loans made for refinancing, a dummy for no first mortgage
on the property, months at the address, years worked on the job, dummies for self-emplyed, retiree,
or homemaker status, and a dummy if the property is a condominium).

Home Equity Loan APR by Borrower Age
6.50

APR (Percent)

6.25

6.00

5.75

5.50

5.25

5.00

Borrower Age (Years)

Figure 4: Home equity loan 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.
economically significant eﬀects.

Figure 4 plots the fitted values on the spline for age for home

equity loans. The line has a pronounced U-shape.9 For this and the nine other studies, we present
in section 14.2 a 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 Equity Lines of Credit

5.1

Data Summary

The dataset described in the previous section is used here.

5.2

Results

Table 2 reports a regression of the APRs from home equity lines on a spline for age and the
same control variables used for the home equity loans regression. The control variables have similar
9
Mortgage and other long-term interest rates were generally falling during this period. Thus, another possible
explanation for the observed pattern is that younger and older adults disproportionately borrowed at the beginning
of the sample period. However, we found no time-variation in the age distribution of borrowers over the sample
period.

Home Equity Credit Line APR by Borrower Age
5.50

APR (Percent)

5.25

5.00

4.75

4.50

4.25

4.00

Borrower Age (Years)

Figure 5: Home equity credit line 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.
eﬀects on home equity line APRs as they did on home equity loan APRs. APRs.
Fitted values on the age splines, plotted in Figure 5, continue to reveal a pronounced U-shape.

5.3

One Mechanism: Borrower Misestimation of Home Values
The amount of collateral oﬀered by the borrower, as measured by the loan-to-value (LTV)

ratio, is an important determinant of loan APRs.

Higher LTVs imply higher APRs, since the

fraction of collateral is lower. At the financial institution that provided our data, borrowers first
estimate their home values, and ask for a credit loan or credit line falling into one of three categories
depending on the implied borrower-generated LTV estimate. The categories correspond to LTVs
of 80 percent or less; LTVs of between 80 and 90 percent; and LTVs of 90 percent or greater.
The financial institution then independently verifies the house value using an industry-standard
methodology. The bank then constructs a bank-generated LTV based on the bank’s independent
verification process. The bank-LTV can therefore diﬀer from the borrower-LTV.10
Loan pricing depends on the LTV category that the borrower falls into and not on the specific
LTV value within that category; for example, a loan with an LTV of 60 has the same interest
10

Bucks and Pence (2006) present evidence that borrowers do not generally have accurate estimates of their house
values.

Home Equity Line APR
Intercept
Log(FICO Score)
Loan Purpose—Home Improvement
Loan Purpose—Rate Refinance
No First Mortgage
Log(Months at Address)
Second Home
Condominium
Log(Income)
Debt/Income
Log(Years on the Job)
Self Employed
Home Maker
Retired
Age < 30
Age 30-40
Age 40-50
Age 50-60
Age 60-70
Age > 70
LTV 80-90
LTV 90+
State Dummies
Number of Observations
Adjusted R-squared

Coeﬃcient
7.9287
-0.0011
0.0551
-0.0386
-0.1512
-0.0160
0.3336
0.4025
-0.1474
0.0044
-0.0164
0.0135
-0.0818
0.0139
-0.0529
-0.0248
-0.0175
0.0152
0.0214
0.0290
0.6071
1.8722
YES
66,278
0.5890

Std. Error
0.0570
0.0000
0.0051
0.0047
0.0054
0.0019
0.0132
0.0079
0.0037
0.0001
0.0020
0.0073
0.0215
0.0109
0.0050
0.0023
0.0022
0.0035
0.0064
0.0154
0.0050
0.0079

Table 2: The first column gives coeﬃcient estimates for a regression of the APR of a home equity
lines of credit on a spline with age as its argument, financial control variables (Log(FICO) credit
risk score, income, and the debt-to-income-ratio), and other controls (state dummies, a dummy
for loans made for home improvements, a dummy for loans made for refinancing, a dummy for
no first mortgage on the property, months at the address, years worked on the job, dummies for
self-employed, retiree, or homemaker status, and a dummy if the property is a condominium).

rate as a loan with an LTV of 70, holding borrower characteristics fixed, since the LTVs of both
loans are less than 80.11

If the borrower has overestimated the value of the house, so that the

bank-LTV is higher than borrower-LTV, the financial institution will direct the buyer to a diﬀerent
loan with a higher interest rate corresponding to the higher bank-LTV. In such circumstances, the
loan oﬃcer is also given 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 who had
correctly estimated her LTV. If 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
to the bank-LTV (which is lower in this case than the borrower-LTV); the loan oﬃcer may simply
choose to oﬀer the higher interest rate associated with the borrower-LTV, instead of lowering the
rate to reflect the lower bank-LTV.12
Since the APR paid depends on the LTV category and not the LTV, home value misestimation
leads to higher interest rate payments if the category of the bank-LTV diﬀers from the category
of the borrower-LTV. If, in contrast, the borrower’s estimated LTV was 60, but the true LTV
was 70, the borrower would still qualify for the highest quality loan category (LTV<80) and would
not suﬀer an eﬀective interest rate penalty. We define a Rate-Changing Mistake (RCM) to have
occurred when the borrower-LTV category diﬀers from the bank-LTV category — for instance, when
the borrower estimates an LTV of 85 but the bank calculates an LTV of 75 (or vice versa).13 We
find that, on average, making a RCM increases the APR by 125 basis points for loans and 150 basis
points for lines (controlling for other variables, but not age).
To highlight the importance of RCMs, we first study the APR for consumers who do not make a
Rate-Changing Mistake. Figures 6 and 7 plot the fitted values from re-estimating the regressions in
Table 1 and 2, but now conditioning on borrowers who do not make a RCM. The plots show only
slight diﬀerences in APR paid by age. The APR diﬀerence for a home equity loan for a borrower
at age 70 over a borrower at age 50 has shrunk from 36 basis points to 8 basis points; for a home
equity line of credit, it has shrunk from 28 basis points to 4 basis points. For a borrower at age 20,
the APR diﬀerence over a borrower at age 50 has shrunk to 3 basis points for home equity loans
and 3 basis points for home equity lines of credit. We conclude that, conditional on not making a
RCM, the APR is essentially flat with age. So the U-shape of the APR is primarily driven by the
Rate-Changing Mistakes.
We next study who makes a RCM. Figures 8 and 9 plot the probability of making a ratechanging mistake by age for home equity loans and home equity lines, respectively. The figures
11

We have verified this practice in our dataset by regressing the APR on both the level of the bank-LTV and
dummy variables for whether the bank-LTV falls into one of the three categories. Only the coeﬃcients on the
dummy variables were statistically and economically significant.
12
Even if the financial institution’s estimate of the true house value is inaccurate, that misestimation will not
matter for the borrower as long as other institutions use the same methodology.
13
Recall that the categories are less than 80, 80 to 90, and greater than 90.

Home Equity Loan APRs for Borrowers Who Do Not Make a
Rate-Changing Mistake
6.50

APR (Percent)

6.25

6.00

5.75

5.50

5.25

5.00

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 APRs for Borrowers Who Do Not
Make a Rate-Changing Mistake
5.50

APR (Percent)

5.25

5.00

4.75

4.50

4.25

4.00

Borrower Age (Years)

Figure 7: Home equity credit line 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.
13

Propensity of Making a Rate-Changing Mistake on Home
Equity Loans by Borrower Age
100%
90%
80%

Percent

70%
60%
50%
40%
30%
20%
10%

Borrower Age (Years)

Figure 8: Propensity of making a Rate Changing Mistake on home equity loans by borrower age.
We define a 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 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.

Propensity of Making a Rate-Changing Mistake on Home
Equity Credit Lines by Borrower Age
100%
90%
80%

Percent

70%
60%
50%
40%
30%
20%
10%

Borrower Age (Years)

Figure 9: Propensity of making a Rate Changing Mistake on home equity credit lines by borrower
age. We define a 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
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.

show U-shapes for both. Borrowers at age 70 have a 16 (19) percentage point greater chance of
making a mistake than borrowers at age 50 for home equity loans (lines); borrowers at age 20 have
a 35 (41) percentage point greater chance of making a mistake than borrowers at age 50.

The

unconditional average probability of making a rate-changing mistake is 24 percent for loans and 18
percent for lines.
This age eﬀect is consistent with the cost of a RCM calculated above and the additional probability of making a RCM by age. For example, a 70-year old has a 16 and 19 percent additional
chance of making a RCM for loans and lines, respectively. Multiplying this by the average APR
cost of a RCM for home equity lines and loans of about 150 and 125 basis points, respectively, gives
an expected incremental APR paid of about 26 and 23 basis points.

These diﬀerences are very

close to the estimated diﬀerences of about 23 basis points for loans (reported in Figure 4) and of
about 28 basis points for lines (reported in Figure 5).
We conclude that in the example of home equity lines and loans, we have identified the channel
for the U-shape of the APR as a function of age (as always, controlling for other characteristics).
Younger and older consumers have a greater tendency to misestimate the value of their house,
which leads to a Rate-Changing Mistake, which leads them to borrow at an increased APR. On
the other hand, for consumers who do not make a Rate-Changing Mistake, the APR is essentially
independent of age. Hence, this channel explains quantitatively the higher APR paid by younger
and older adults.
Given the large costs associated with a Rate-Changing Mistake, one might ask why borrowers
do not make greater eﬀort to more accurately estimate their house values. One possibility is that
potential borrowers may not be aware that credit terms will diﬀer by LTV category; or, even if they
are aware of this fact, they may not know how much the terms diﬀer by category. This particular
aspect of loan pricing may thus be a shrouded attribute.

“Eureka” Moments: Balance Transfer Credit Card Usage

6.1

Overview

Credit card holders frequently receive oﬀers to transfer account balances on their current cards
to a new card. Borrowers pay substantially lower APRs on the balances transferred to the new
card for a six-to-nine-month period (a ‘teaser’ rate).

However, new purchases on the new card

have high APRs. The catch is that payments on the new card first pay down the (low interest)
transferred balances, and only subsequently pay down the (high interest) debt accumulated from
new purchases.
The optimal strategy during the teaser-rate period, is for the borrower to make all new purchases
on her old credit card and to make all payments to her old card.

The optimal 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
making any purchases with the new card. Some borrowers will never identify the optimal strategy.
Some borrowers may not initially identify the optimal strategy, but will discover it after one or more
pay cycles after observing their (surprisingly) high interest charges.

Those borrowers will make

purchases for one or more months, then have a “eureka” moment, after which they will implement
the optimal strategy.14

6.2

Data Summary

We use a proprietary panel data set from several large financial institutions, later acquired by
a single financial institution, that made balance transfer oﬀers nationally. The data set contains
14,798 individuals who accepted such balance transfer oﬀers over the period January 2000 through
December 2002.

The bulk 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, 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 transfer, and the end date of the balance transfer APR oﬀer. At a quarterly
frequency, we observe each customer’s credit bureau rating (FICO) and a proprietary (internal)
credit ‘behavior’ score. We have credit bureau data about the number of other credit cards held
by the account holder, total credit card balances, and mortgage balances. We have data on the
age, gender, and income 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.

6.3

Results

About one third of all customers who make a balance transfer do no spending on the new card,
thus implementing the optimal strategy immediately. Slightly more than one third of customers
who make a balance transfer spend every month during the promotional period, thus never experiencing a “Eureka” moment. The remaining nearly one-third of customers experience “Eureka”
moments between the first and sixth months.
Figure 10 plots the frequency of Eureka moments for each age group. The plot of those who
never experience a “Eureka” moment — that is, who never implement the optimal strategy — is a
pronounced U-shape by age. The plot of those who implement the optimal strategy immediately
(the "Month One" line) is a pronounced inverted U-shape by age.
14

Plots for Eureka moments

We thank Robert Barro for drawing our attention to this type of potentially tricky financial product.

Fraction of Borrowers in Each Age Group Experiencing a
Eureka Moment, by Month
60%

Percent of Borrowers

50%

Month One

Month Two

Month Three

Month Five

Month Six

No Eureka

Month Four

40%

30%

20%

10%

18 to 24

25 to 34

35 to 44

45 to 64

Over 65

Borrower Age Category

Figure 10: Fraction of borrowers in each age group experiencing specific delays. For example,
the dashed line plots the fraction of borrowers experiencing no delay to a Eureka moment. These
sophisticated borrowers represent a large fraction of middle-aged households and a much smaller
fraction of younger and older households.
in the interior of the time space (that is Eureka moments that occur strictly after Month One)
are flat.15

The No Eureka line implies that the groups with the greatest frequency of maximal

confusion are younger adults and older adults. The group with the greatest frequency of optimality
is middle-aged adults.
Table 3 reports the results of a regression of a dummy variable for ever having a Eureka moment
on a spline for age and controls for credit risk (log(FICO)), education, gender, and log(income).16 .
Credit risk is included because higher scores may be associated with greater financial sophistication.
Similarly, we would expect borrowers with higher levels of education to be more likely to experience
Eureka moments The coeﬃcients on the age spline imply that young adults and older adults are
less likely to 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
to make mistakes. Consistent with the evidence so far, we observe a performance peak in middle
15

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.
16
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.

Propensity of ever experiencing a “Eureka” Moment
Intercept
Age < 30
Age 30-40
Age 40-50
Age 50-60
Age 60-70
Age > 70
Some High School
High School Graduate
Some College
Associate’s Degree
Bachelor’s Degree
Graduate Degree
Log(FICO)
Log(Limit)
Log(Income)
Number of Observations
Adjusted R-squared

Coeﬃcient
0.2587
0.0134
0.0019
-0.0001
-0.0029
-0.0035
-0.0083
-1.6428
-0.6896
-0.4341
-0.2439
0.3280
0.6574
0.0102
0.0120
-0.0044
3,622
0.1429

Std. Error
0.0809
0.0026
0.0005
0.0000
0.0009
0.0008
0.0072
0.9570
0.8528
0.8944
0.4537
0.5585
0.3541
0.0019
0.0022
0.0067

Table 3: 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 spline
with age as its argument and other control variables.
age.

Credit Cards

7.1

Data Summary

We use a proprietary panel dataset from several large financial institutions that oﬀered credit
cards nationally, later acquired by a larger financial institution. The dataset contains a representative random sample of about 128,000 credit card accounts followed monthly over a 36 month period
(from January 2002 through December 2004). The bulk 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. At
a quarterly frequency, we observe each customer’s credit bureau rating (FICO) and a proprietary
(internal) credit ‘behavior’ score. We have credit bureau data about the number of other credit
cards held by the account holder, total credit card balances, and mortgage balances. We have data
on the age, gender and income of the account holder, collected at the time of account opening.
Further details on the data, including summary statistics and variable definitions, are available in
18

Propensity of Ever Experiencing a "Eureka" Moment by
Borrower Age
90%
85%
80%

Percent

75%
70%
65%
60%
55%
50%
45%

40%

Borrower Age (Years)

Figure 11: Propensity of ever experiencing a “Eureka” moment by borrower age. The figure plots
the residual eﬀect of age, after controlling for other observable characteristics, such as log(income),
education, and credit-worthiness.
the data Appendix.

7.2

Results

Table 4 reports the results of regressing credit card APRs on a spline with age as its argument
and other control variables.

As controls, we again use information observed by the financial

institution that may influence pricing. As before, we find that credit scores have little impact on
credit card APRs. APRs rise with the total number of cards, though the eﬀect is not statistically
significant.

Other controls, including the total card balance, log income, and balances on other

debt, do not have economically or statistically significant eﬀects on credit card APRs.
Figure 12 plots the fitted values on the spline for age. A U-shape is present, though it is much
weaker than the age-based patterns that we document for other financial products.

Auto Loans

8.1

Data Summary

We use a proprietary data set of auto loans originated at several large financial institutions
that were later acquired by another institution.

The data set comprises observations on 6,996

loans originated for the purchase of new and used automobiles. We observe loan characteristics
19

Credit Card APR
Coeﬃcient
14.2743
-0.0127
-0.0075
-0.0041
0.0023
0.0016
0.0016
-0.0558
-0.0183
0.0003
-0.0000
92,278
0.0826

Intercept
Age < 30
Age 30-40
Age 40-50
Age 50-60
Age 60-70
Age > 70
Log(Income)
Log(FICO)
Home Equity Balance
Mortgage Balance
Number of Observations
Adjusted R-squared

Std. Error
3.0335
0.0065
0.0045
0.0045
0.0060
0.0184
0.0364
0.0803
0.0015
0.0022
0.0000

Table 4: This table gives coeﬃcient estimates for a regression of the APR of a credit card on a
spline with age as its argument, financial control variables (Log(FICO) credit risk score, income,
total number of cards, total card balance, home equity debt balance and mortgage balance).

Credit Card APR by Borrower Age
18.50

APR (Percent)

18.25

18.00

17.75

17.50

17.25

17.00

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.

Auto Loan APR
Intercept
Age < 30
Age 30-40
Age 40-50
Age 50-60
Age 60-70
Age > 70
Log(Income)
Log(FICO)
Debt/Income
Japanese Car
European Car
Loan Age
Car Age
State Dummies
Quarter Dummies
Number of Observations
Adjusted R-squared

Coeﬃcient
11.4979
-0.0231
-0.0036
-0.0054
0.0046
0.0031
0.0091
-0.3486
-0.0952
0.0207
-0.0615
-0.0127
0.0105
0.1234
YES
YES
6,996
0.0928

Std. Error
1.3184
0.0045
0.0005
0.0005
0.0007
0.0017
0.0042
0.0176
0.0059
0.0020
0.0270
0.0038
0.0005
0.0031

Table 5: This table gives coeﬃcient estimates from a regression of the APR of an auto loan on a
spline with age as its argument, financial control variables (Log(FICO) credit risk score, income,
and the debt-to-income-ratio), and other controls (state dummies, dummies for whether the car is
Japanese or European, loan age and car age).
including the automobile value and age, the loan amount and LTV, the monthly payment, the
contract rate, and the time of origination.

We also observe borrower characteristics including

credit score, monthly disposable income, and borrower age.

8.2

Results

Table 5 reports the results of regressing the APR paid for auto loans on an age-based spline
and control variables. FICO credit risk scores again have little eﬀect on the loan terms. Higher
incomes lower APRs and higher debt-to-income ratios raise them, though the magnitudes of the
eﬀects are small. We also include car characteristics, such as type and age, as one of us has
found those variables to matter for APRs in other 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. The graph shows a pronounced U-shape.

Auto Loan APR by Borrower Age
9.50

APR (Percent)

9.25

9.00

8.75

8.50

8.25

8.00

Borrower Age (Years)

Figure 13: Auto loan 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.

Mortgages

9.1

Data Summary

We use a proprietary data set from a large financial institution that originates first mortgages in
Argentina. Using data from one other country provides suggestive evidence about the international
applicability of our findings. The data set covers 4,867 owner-occupied, fixed rate, first mortgage
loans originated between June 1998 and March 2000 and observed through March 2004.

observe the original loan amount, the LTV and appraised house value at origination, and the APR.
We also observe borrower financial characteristics (including income, second income, years on the
job, wealth measures such as second house ownership, car ownership and value), borrower risk
characteristics (Veraz score, a credit score similar to the U.S. FICO score, and mortgage payments
as a percentage of after-tax income), and borrower demographic characteristics (age, gender, and
marital status).

9.2

Results

Table 6 reports results of regressing the mortgage APR on an age-based spline and control
variables. As controls, we again use variables observed by the financial institution that may aﬀect
loan pricing, including risk measures (credit score, income, mortgage payment as a fraction of

Mortgage APR by Borrower Age
13.00

APR (Percent)

12.75

12.50

12.25

12.00

11.75

11.50

Borrower Age (Years)

Figure 14: APR for Argentine mortgages by borrower age. The figure plots the residual eﬀect of
age, after controlling for other observable characteristics, such as log(income) and 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
space). The coeﬃcients on the controls are again of the expected sign and generally statistically
significant, though of small magnitude.
The coeﬃcients on the age spline are positive below age 30, then negative through age 60 and
positive thereafter. Figure 14 plots the fitted values on the spline for age. The figure provides
only partial support for the U-shape hypothesis.

Small Business Credit Cards

10.1

Data Summary

We use a proprietary data set of small business credit card accounts originated at several large
institutions that issued such cards nationally.

The institutions were later acquired by a single

institution. The panel data set covers 11,254 accounts originated between May 200 and May 2002.
Most of the business are very small, owned by a single family, and have no formal financial records.
The data set has all 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 APR
Intercept
Age < 30
Age 30-40
Age 40-50
Age 50-60
Age 60-70
Age > 70
Log(Income)
Log(Credit Score)
Debt/Income
Loan Term
Loan Term Squared
Loan Amount
Loan to Value
Years on the Job
Second Home
Auto
Auto Value
Gender (1=Female)
Married
Two Incomes
Married with Two Incomes
Employment: Professional
Employment:Non-Professional
Merchant
Bank Relationship
Number of Observations
Adjusted R-squared

Coeﬃcient
12.4366
0.0027
-0.0023
-0.0057
0.0127
0.0155
0.0234
-0.2843
-0.1240
0.0859
-0.0114
-0.0000
-0.0000
0.1845
-0.0108
0.1002
0.1174
0.0000
0.0213
-0.0585
-0.1351
-0.0116
-0.0438
0.0853
-0.1709
-0.2184
4,867
0.1004

Std. Error
4.9231
0.0046
0.0047
0.0045
0.0093
0.0434
0.0881
0.1303
0.0217
0.2869
0.0037
0.0000
0.0000
0.0187
0.0046
0.1014
0.0807
0.0000
0.0706
0.0831
0.1799
0.1957
0.1174
0.1041
0.1124
0.1041

Table 6: This table reports the estimated coeﬃcients from a regression of mortgage APR on a
spline with age as its argument and financial and demographic control variables.

Small Business Credit Card APR
Intercept
Age < 30
Age 30-40
Age 40-50
Age 50-60
Age 60-70
Age > 70
Years in Business 1-2
Years in Business 2-3
Years in Business 3-4
Years in Business 4-5
Years in Business 5-6
Log(FICO)
Number of Cards
Log(Total Card Balance)
Log(Total Card Limit)
Number of Observations
Adjusted R-squared

Coeﬃcient
16.0601
-0.0295
-0.0068
-0.0047
-0.0017
0.0060
0.0193
-0.5620
-0.7463
-0.2158
-0.5100
-0.4983
-0.0151
0.1379
<0.0001
<0.0001
11,254
0.0933

Std. Error
0.6075
0.0081
0.0040
0.0038
0.0055
0.0209
0.0330
0.1885
0.1937
0.1031
0.0937
0.0931
0.0008
0.0153
<0.0001
<0.0001

Table 7: This table reports the estimated coeﬃcients from a regression of the APR for small business
credit cards on a spline with the business owner’s age as its argument and other control variables
(dummies for years in business, log(FICO) credit risk score, number of cards, total card balance,
and total card limit).

10.2

Results

Table 7 reports the results of regressing the APR for small business credit cards on an agebased spline and control variables.

As with individual credit card accounts, we control for the

FICO score of the business owner, the total number of cards, card balance, and card limit. We
also include dummy variables for the number of years the small business has been operating —
we expect APRs to fall for businesses with longer operating histories.

All control variables are

statistically significant and have the expected sign, though only the dummies for years in business
have substantial magnitudes.

APRs are decreasing in the age of the borrower through age 60 and increasing thereafter. Figure
15 plots the fitted values on the spline for age. The graph shows a pronounced U-shape.

Small Business Credit Card APR by Borrower Age
16.00

APR (Percent)

15.75

15.50

15.25

15.00

14.75

14.50

Borrower Age (Years)

Figure 15: Small business 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.

Credit Card Fee Payments: Late Fees

11.1

Overview

Certain credit card uses involve the payment of a fee. Some kinds of fees are assessed when
terms of the credit card agreement are violated. Other fees are assessed for use of services.
In the next three sections, we focus on three important types of fees: late fees, over limit fees,
and cash advance fees.17 We describe the fee structure for our data set below.
1. Late Fee: A late fee of between $30 and $35 is assessed if the borrower makes a payment
beyond the due date on the credit card statement. If the borrower is late by more than 60
days once or by more than 30 days twice within a year, the bank may also impose ‘penalty
pricing’ by raising the APR to over 24 percent.

The bank may also choose to report late

payments to credit bureaus, adversely aﬀecting consumers’ FICO scores.

If the borrower

does not make a late payment during the six months after the last late payment, the APR
17

Other types of fees include annual, balance transfer, foreign transactions, and pay by phone. All of these fees
are relatively less important to both the 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.

will revert to its normal (though not promotional) level.
2. Over Limit Fee: An over limit fee — also between $30 and $35 — is assessed the first time
the borrower exceeds his or her credit limit. Over limit violations generate penalty pricing
that is analogous to the penalty pricing that is imposed as a result of late fees.
3. Cash Advance Fee: A cash advance fee — which is the greater of 3 percent of the amount
advanced, or $5 — is levied for each cash advance on the credit card.
fees, this fee can be assessed many times per month.

Unlike the first two

It does not cause the imposition of

penalty pricing. However, the APR on cash advances is typically greater than the APR on
purchases, and is usually 16 percent or more.
Payment of these fees is not generally a mistake. For example, if a card holder is vacationing in
Tibet, it may not be optimal to arrange a credit card payment for that month. However, payments
of fees are sometimes mistakes, since the fee payment can often be avoided by small and relatively
costless changes in behavior.

For instance, late fees are sometimes due to memory lapses that

could be avoided by putting a reminder in one’s calendar.
We use the same data set as that used for the credit card APR case study discussed above.

11.2

Results

Table 8 presents panel regressions for each type of fee.

In each of the three regressions, we

regress a dummy variable equal to one if a fee is paid that month on an age-based spline and control
variables. Hence the coeﬃcients give the conditional eﬀects of the independent variables on the
propensity to pay fees.
The control variables diﬀer from those of the preceding six examples. Now we control for factors
that might aﬀect the propensity to pay a fee, which are not necessarily the same as factors that might
lead borrowers to default or otherwise aﬀect their borrowing terms. “Bill Existence” is a dummy
variable equal to one if a bill was issued last month; borrowers will only be eligible to pay a late
fee if a bill was issued. “Bill Activity” is a dummy variable equal to one if purchases or payments
were made on the card; borrowers will only be eligible to pay over limit or cash advance fees if the
card was used. “Log(Purchases)” is the log of the amount purchased on the card, in dollars; we
would expect that the propensity to pay over limit and cash advance fees would be increasing with
the amount of purchases. “Log(FICO)” is the credit risk score, and “Log(Behavior)” is an internal
risk score created by the bank to predict late and delinquent payment beyond that predicted by
the FICO score.

Higher scores mean less risky behavior.

because they are only updated quarterly.

The scores are lagged three months

We would expect the underlying behavior leading to

lower credit risk scores would lead to higher fee payment. “Debt/Limit” is the ratio of the balance

Late Fee
Intercept
Age < 30
Age 30-40
Age 40-50
Age 50-60
Age 60-70
Age > 70
Bill Existence
Bill Activity
Log(Purchases)
Log(Behavior)
Log(FICO)
Debt/Limit
Acct. Fixed Eﬀ.
Time Fixed Eﬀ.
Number of Obs.
Adj. R-squared

Coeﬀ.
0.2964
-0.0021
-0.0061
-0.0001
-0.0002
0.0004
0.0025
0.0153
0.0073
0.0181
-0.0017
-0.0016
-0.0066
YES
YES
3.9 Mill.

0.0378

Std. Err.
0.0446
0.0004
0.0003
0.0000
0.0000
0.0002
0.0013
0.0076
0.0034
0.0056
0.0000
0.0007
0.0033

Over Limit Fee

Cash Adv. Fee

Coeﬀ.
0.1870
-0.0013
-0.0003
-0.0002
-0.0002
0.0003
0.0003
0.0104
0.0088
0.0113
-0.0031
-0.0012
0.0035
YES
YES
3.9 Mill.

Coeﬀ.
0.3431
-0.0026
-0.0004
-0.0002
-0.0003
0.0004
0.0004
0.0055
0.0055
0.0179
-0.0075
-0.0015
0.0038
YES
YES
3.9 Mill.

Std. Err.
0.0802
0.0006
0.0001
0.0000
0.0000
0.0001
0.0001
0.0031
0.0030
0.0023
0.0012
0.0003
0.0013

0.0409

Std. Err.
0.0631
0.0011
0.0002
0.0000
0.0000
0.0000
0.0000
0.0021
0.0021
0.0079
0.0036
0.0005
0.0012

0.0388

Table 8: This table reports coeﬃcients from a regression of dummy variables for credit card fee
payments on a spline for age, financial control variables (log(FICO) credit risk score, internal bank
behavior risk score, debt over limit) and other control variables (dummies for whether a bill existed
last month, for whether the card was used last month, dollar amount of purchases, account- and
time- fixed eﬀects).
of credit card debt to the credit limit; we would expect that having less available credit would raise
the propensity to pay over limit fees, and possibly other fees.
For late fee payments — column one of the table —all control variables have the expected signs
and are statistically significant, though they are also small in magnitude. Note that some control
variables may partly capture the eﬀects of age-related cognitive decline on fees. For example, if
increasing age makes borrowers more likely to forget to pay fees on time, that would both increase
the propensity to pay late fees and decrease credit and behavior scores.

Hence the estimated

coeﬃcients on the age splines may understate some age-related eﬀects.
Coeﬃcients on the age splines are uniformly negative for splines through age 50, negative or
weakly positive for the spline between age 50 and 60, and positive with increasing slope for splines
above age 50.
The top line in Figure 16 plots fitted values for the age splines for the late fee payment regression.18
18

In Agarwal, Driscoll, Gabaix and Laibson (2006), we study this propensity of paying fees as the interaction of
learning from the payment of past fees, and forgetting.

Frequency of Fee Payment by Borrower Age
0.35
Late Fee

Fee Frequency (per month)

0.33

Over Limit Fee

Cash Advance Fee

0.31
0.29
0.27
0.25
0.23
0.21
0.19
0.17

0.15

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) and credit-worthiness.

Credit Card Fee Payments: Over Limit Fees
The second column of Table 8 presents regression results for the over limit fee, on the same

controls and age splines that were used for the late fee. 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.

Credit Card Fee Payments: Cash Advance Fees
The second column of Table 8 presents regression results for the cash advance fee, on the same

controls and age splines that were used for the late fee. Results are similar to those generated in
analysis of the late fee and the over limit fee.
The middle line in Figure 16 plots fitted values of the age splines for the cash advance fee
payment regression.

The Peak of Performance

14.1

Locating the Peak of Performance

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 and 50 and 60 with a single spline running
from 40 to 60, and the square of that spline. This enables us to more precisely estimate the local
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

(2)

= α + β × Spline(Age)Age∈[40,60]
+ γ × Controls +
/

+a × Spline (Age)Age∈[40,60] + b · Spline (Age)2Age∈[40,60] .

Here Spline(Age) is a piecewise linear function that takes consumer age as its argument (with
represents the splines outside of the
knot points at ages 30, 40, 60 and 70). Spline(Age)Age∈[40,60]
/

[40, 60] age range, while Spline (Age)Age∈[40,60] is the linear spline with knot points at 40 and 60.
Hence, for age between 40 and 60, the above formulation is implicitly quadratic in age:
F = Controls + a × Age + b × Age2 .
The peak of performance is defined as the value that minimizes the above function:
(3)

P eak = −a/ (2b) .

We calculate the asymptotic standard errors on P eak using the delta method, so that the standard
error of P eak is the standard error associated with the linear combination: −1/(2b)·(Coeﬃcient on
age) + a/(2b2 )·(Coeﬃcient on age2 ).

In Table 9, we report the location of the ‘age of reason’: the point at which financial mistakes
are minimized.

The mean age of reason appears to be at 53.3 years. The standard deviation

calculated by treating each study as a single data point is 4.3 years.
Formal hypothesis testing (H0 : a + 2b × 53 = 0) shows that only the location of the Eureka

moment is statistically diﬀerent from 53 years. Interestingly, the Eureka task is arguable the most
most dependent on analytic capacity and least dependent on experience (since the kinds of balance
transfer oﬀers that we study were new 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 “diﬃculty” of a task, the
interpretation of the Eureka case remains speculative.
30

Age of Peak Performance

Standard Error

55.9
53.3
45.8
50.3
49.6
56.0
61.8
51.9
54.0
54.8
53.3

4.2
5.2
7.9
6.0
5.0
8.0
7.9
4.9
5.0
4.9

Home Equity Loans—APR
Home Equity Lines—APR
Eureka Moment
Credit Card—APR
Auto Loans—APR
Mortgage—APR
Small Business Credit Card—APR
Credit Card Late Fee
Credit Card Over Limit Fee
Credit Card Cash Advance Fee
Average over the 10 Studies

Table 9: Age at which financial mistakes are minimized, for each case study

14.2

Formal Test of a Peak of Performance Eﬀect

Table 9 allows us do a formal test for a peak eﬀect. In regression (2), the null hypothesis of a
peak eﬀect is: (i) b > 0, and (ii) P eak = −a/ (2b) ∈ [40, 60]. Together these conditions imply that
mistakes follow a U-shape, with a peak that is between 40 and 60 years of age.

For criterion (i), we note that the b coeﬃcients are positive for all 10 studies.

For 9 of the

10 studies, b is significantly diﬀerent from zero (the credit card APR study is the exception).19
For criterion (ii), Table 9 shows that a peak in the 40-60 age range can not be rejected for all ten
studies.

14.3

A Possible Interpretation of the Location of the Performance Peak

What determines the age of peak performance? If peak performance reflects a trade-oﬀ between experience (that is accumulated with diminishing returns) and analytic ability (that declines
linearly after age 20), the sooner people start experimenting with the product, the earlier peak
of performance should be. For instance, take the simple functional forms presented in section 2.
Suppose Analytic Capital declines linearly with age, so that Analytic Capital = α − age/β. Sup-

pose that Experiential Capital is accumulated with diminishing returns — for instance, Experiential
Capital = ln(age − γ age0 ), where age0 is the actual age at which people start using the product,

and γ age0 < age0 is the eﬀective age at which people start using the product (so γ < 1). The

eﬀective age is less than the actual age since consumers get indirect experience (observation and
advice) as a result of their interactions with slightly older individuals who use the product. The
19

To save space, we only report the t−statistics associated with the b coeﬃcients. Following the order of Table 9,
they are: 2.20, 4.55, 7.80, 8.77, 17.05, 1.61, 4.57, 2.91, 3.08, 2.67.

model implies that peak performance occurs at P eak = β + γ age0 . Hence, peak performance is
later when people start using the product later in life.
To evaluate this hypothesis for 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 call “age10% ”. It is a crude proxy for the age at which people start using
the product. We then regress the location of the peak of performance on age10% . We find: Peak=
33 + 0.71×age10% , (R2 = 0.62, n = 10; the s.e. on the coeﬃcients are respectively 5.7 and 0.19).20
We reject the null hypothesis of no relationship between P eak and age10% . Products that are first
used later in life tend to have a later performance peak.
This minimal analysis only provides suggestive evidence. It would be desirable to explore this
correlation and the hypothesized mechanism with other data sets.

Discussion and Related Work

15.1

Alternative Explanations

Age eﬀects oﬀer a parsimonious explanation for our findings.

However, our cross-sectional

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 in default risk. For instance,
the U-shape of APRs could be due to a U-shape of default by age. We test this alternative hypothesis
by regressing default rates on age splines for credit cards, auto loans, and home equity loans and
credit lines. We plot fitted values in Figure 17. None of the graphs is U-shaped. On the contrary,
home 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 eﬀects could be generated by age-variation in the
opportunity cost of time (Aguiar and Hurst, forthcoming). However, such opportunity-cost eﬀects
would predict that retirees make fewer mistakes, which is not what we observe in our data. Nevertheless, our findings and those of Aguiar and Hurst do not contradict one another.

Shopping

for a familiar commodity, like a gallon of milk, is less analytically demanding than shopping for
a complicated and somewhat unfamiliar product that can diﬀer across many dimensions, like a
20

The eﬀect is robust to the choice of the 10th percentile. For instance, the correlation between Peak age and
Median age (of users for the product, in our data set) is 0.83.

Percent Defaulting by Borrower Age
9.00%

Credit Cards
HE-Lines

8.00%

Auto Loans
Argentina Mortgage

HE-Loans
Small Business

Percent Defaulting

7.00%

6.00%

5.00%

4.00%

3.00%

2.00%

1.00%

0.00%

Borrower Age (Years)

Figure 17: Default frequency by borrower age. The figure plots the residual eﬀect of age, after
controlling for other observable characteristics, such as log(income) and credit-worthiness.
mortgage.

Hence, we should expect to see older adults sustain or even improve their ability to

shop for food at the same time that they lose ground in the domain of financial decision-making.
In addition, shopping at stores and supermarkets may be a more pleasant activity than shopping
at banks and other lenders, leading consumers to do more comparison shopping for food than for
loans.
Medical Expenses: Older consumers may need to borrow to meet higher medical expenses.
This increased demand for borrowing may worsen their borrowing terms; it may also lead them to
be less attentive to terms and fee payments.
Using individual credit card transactions data, we look at the average fraction of monthly
spending on medical categories. The fraction is 1.18 percent for borrowers between ages 20 and 39;
1.19 percent for borrowers between ages 40 and 59; and 1.06 percent for borrowers between ages
60 and 79. Thus, it does not appear that older consumers are disproportionately using credit card
borrowing to finance medical expenditures.
Discrimination: The presence of age eﬀects might also be interpreted as evidence for some
kind of age discrimination. We believe this to be unlikely, for two reasons. First the 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 all card holders face the same rules). Second,

firms avoid age discrimination for legal reasons.

Penalties for age discrimination from the Fair

Lending Act are substantial (as would be the resulting negative publicity).
Sample Selection:

Measured age eﬀects could also be attributable to diﬀerences in the

pool of borrowers by age group: a selection eﬀect.

Older consumers using home equity loans

and lines of credit may, on average, be a less financially savvy group that the pools of 40-to-50year-old borrowers, since more savvy borrowers may instead choose to use their savings to finance
expenditures.21
Three reasons lead us to doubt that this eﬀect is quantitatively large. First, the pool of borrowers
in their 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 one of the financial products we study. Yet that
group does worse in all ten domains than 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.

Figure

18 shows that credit risk (FICO) scores on home equity loans and lines decline by about 5 points
over the age distribution – an amount too small to either change lending terms or represent a
substantial change in riskiness.

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 home equity loans
and lines of credit, but dropping data on all borrowers over the age of 60.

There is less reason

to believe that the pool of borrowers below 60 are subject to the sample selection issues discussed
above. The results still show a U-shape, albeit a somewhat less pronounced one.22
Cohort Eﬀects: Older borrowers in the cross-section may make less sophisticated financial
choices not because they are older, but because they belong to a cohort that is less familiar with
current financial products. Although we cannot eliminate the possibility that cohort eﬀects are
driving the patterns that we observe, several facts make us skeptical of this explanation.
First, one leading cohort story would imply that borrowers currently in their 20s, 30s and 40s
would be best positioned to understand new financial products. However, we find that younger
borrowers are prone to make less 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
21

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 is likely
not responsible for the results.
22

FICO Score By Home Equity Borrower Age
740
735
730
FICO

725
720
715
710

Lines

Loans

705
80

700
Borrow er Age

Figure 18: This figure plots the FICO (creditworthiness) scores of home equity loan and line of
credit borrowers by age. A high FICO score means a high creditworthiness.

LTV Ratio by Home Equity Borrower Age
70.00
65.00

LTV

60.00
55.00
50.00

Loans

45.00

Lines

40.00
Borrow er Age

Figure 19: This figure plots the loan-to-value (LTV) ratio of home equity loan and line of credit
borrowers by borrower age.

APR by Home Equity Borrower Age, Removing Borrowers
above Age 60
7.00
6.50

APR

6.00
5.50
5.00
4.50

Lines

Loans
60

4.00
Borrow er Age

Figure 20: This figure plots the residual eﬀect of age on home equity loan and line APRs, after
controlling for other observable characteristics, such as log(income) and credit-worthiness. Observations on borrowers over age 60 have been dropped.
to be less involved in financial decision making than their male contemporaries. Figures 21 and 22
plot the residual eﬀects of age on home equity line and loan APR for female and male borrowers,
respectively. Both show a U-shaped pattern by age, with no substantive diﬀerence between the
two groups.
Finally, for two products—auto loans and credit cards—we have data from 1992, ten years earlier
than the data used for our other studies. Figures 23 and 24 replicate the plots of the fitted values of
the eﬀects of age on APR for this earlier dataset. Both plots show the same pronounced U-shape,
with the minimum in the early 50’s (like our results using later cross-sections). If our findings were
driven by cohort eﬀects, the U-shape should not reproduce itself in cross-sections from diﬀerent
years.

15.2

Market Equilibrium

The markets we describe may seem paradoxical. First, they look competitive, since there are
many competing firms selling commodity credit products. However, consumers with identical risk
characteristics fare diﬀerently, implying that somehow the good being sold is being de-commodified.
Markets like this have been described in the industrial organization literature. A first generation
of models (e.g. Salop and Stiglitz 1977, Ellison 2005, and the citations therein) emphasizes diﬀerent

Home Equity Line and Loan APR by Borrower Age - Women
7.00
6.50

Lines

Loans

6.00

APR

5.50
5.00
4.50
4.00
3.50

3.00
Borrow er Age

Figure 21: This figure plots the residual eﬀect of age on home equity loan and line APRs for women,
after controlling for other observable characteristics, such as log(income) and credit-worthiness.

Home Equity Line and Loan APR by Borrower Age - Men
8.00
7.50

Lines

7.00

Loans

6.50
APR

6.00
5.50
5.00
4.50
4.00
3.50
80

3.00
Borrow er Age

Figure 22: This figure plots the residual eﬀect of age on home equity loan and line APRs for men,
after controlling for other observable characteristics, such as log(income) and credit-worthiness.

Auto Loans APR by Borrower Age, 1992 Data
9.90
9.70

APR (Percent)

9.50
9.30
9.10
8.90
8.70

8.50
Borrow er Age

Figure 23: Auto loan 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. Data
is from 1992.

Credit Card APR by Borrower Age, 1992 Data
18.90

APR (Percent)

18.70
18.50
18.30
18.10
17.90
17.70

17.50
Borrow er 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) and credit-worthiness. Data
is from 1992.
38

“search costs,” which are costs of discovering the products of diﬀerent firms. A second generation
(sometimes under the name of “behavioral industrial organization”, e.g. 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 some consumers are smart enough to
exploit. Some consumers unravel the shrouded attribute — the “catch” that they should transfer
balances to the card but make no purchases with it — and some consumers never get it. In the
market equilibrium (with competition and free entry), the naive consumers end up paying above
marginal cost, subsidizing the sophisticated consumers, who pay below marginal cost. From an ex
ante point of view, the market is fully competitive, since expected profits of the firm are zero.23
Most of the other markets work in similar ways. In equilibrium, sophisticated consumers get
subsidies from the unsophisticated consumers.

Since the markets are competitive, the financial

institutions themselves break even.

15.3

On the Economic Magnitude of the Eﬀects

The eﬀects we find are sometimes large and sometimes small. For instance, for a home-equity
line of $60,000 (the mean value, see Table A1), and a duration of 5 years, a diﬀerence in the
loan interest rate of 1 percentage point means a diﬀerence in total payments of $3000. For other
quantities, say credit card fees, the implied age diﬀerentials are much smaller — roughly $10-$20
per year for each kind of fee.24 We do not claim that each of the economic decisions that we
study is of significant economic relevance on its own, but rather that there is a U-shape pattern
of mistakes that may merit economists’ attention become it points to a phenomenon that applies
to all decision domains (large and small). We have studied credit decisions in the current paper.
An important question is whether the U-shape of mistakes translates into other decision domains,
including savings choices, asset allocation choices and health care choices.

15.4

Related 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 use census data to impute education levels and data from the Survey of Health, Aging
23

One may ask how such a potentially ineﬃcient equilibrium can persist in a competitive environment. An answer
is proposed in 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 are robust even when the equilibria
are ineﬃcient.
24
A diﬀerence in fee probabilty of 3% per month, and and a fee amount $35, leads to a total extra yearly expense
of $12. Note, however, that some of these fees, if paid too often, can trigger “penalty pricing,” in which interest
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.

and Retirement in Europe to estimate a model of cognitive abilities. They find that investors with
cognitive declines earn annual returns between 3-5 percentage points lower on a risk adjusted basis.
In their work on financial literacy, Lusardi and Mitchell find evidence consistent with an inverseU shape of financial proficiency. Lusardi and Mitchell (2006) find a decline in financial knowledge
after age 50. 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
cards shows a U-shaped pattern of credit card APR terms by age (Dunn, personal communication).
Fiona Scott Morton has reported that in her data set of indirect auto loans (made by banks and
finance companies using the dealer as an intermediary; see Scott Morton et al., 2003), loan markups
show a U-shaped pattern (Scott Morton, personal communication). 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 mortgage APRs 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 for everyday items by spending more time shopping around. In contrast, we find that older adults seem to
make more mistakes in personal financial decision-making. We reconcile these findings by noting
that financial products require more analytic ability than everyday items (like food or clothing).
Moreover, financial products may generate a less pleasurable shopping experience.
Turning to purely noneconomic domains, there is a literature on estimating performance peaks
in professional athletics and other competitive areas. Fair (1994, 2007) estimates the eﬀects of age
declines in baseball and chess, among other sports. Simonton (1988) is a useful survey.
A new literature in psychology and economics reports systematic diﬀerences in “rationality”
between groups of people. Benjamin, Brown and Shapiro (2006) find that subjects with higher test
scores, or less cognitive load, display fewer behavioral biases. Frederick (2005) identifies a measure
of “analytical IQ”: people with higher scores on cognitive ability tasks tend to exhibit fewer/weaker
psychological biases. While this literature is motivated by experimental data (where it is easier to
control for unobservables), we rely on field 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
rates (‘teaser’ rates) and at the persistence of otherwise high interest rates. Shui and Ausubel
(2004) show that consumers prefer credit card contracts with low initial rates for a short period
of time to ones with somewhat higher rates for a longer period of time, even when the latter is
ex post more beneficial. Consumers also appear ‘reluctant’ to switch contracts. DellaVigna and
Malmendier (2004) theorize that financial institutions set the terms of credit card contracts to
reflect 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 Shleifer (2005), Oster and Scott Morton (2005),
Spiegler (2006). In some of those papers, it is important to have both naive and sophisticated
consumers (Campbell 2006). The present paper suggests than those naive consumers will disproportionately be younger or older adults.
Bertrand et al. (2006) find that randomized changes in the “psychological features” of consumer
credit oﬀers aﬀect adoption rates as much as variation in the interest rate terms. Ausubel (1991)
hypothesizes that consumers may be over-optimistic, repeatedly underestimating the probability
that they will borrow, thus possibly explaining the stickiness of credit card interest rates. Calem
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 to
argue that such costs continue to be important. Kerr and Dunn (2002) use data from the 1998 SCF
to argue that having large credit card balances raises consumers’ propensity to search for lower
credit card interest rates. Kerr, Cosslett and Dunn (2004) use SCF data to argue that banks oﬀer
better lending terms to consumers who are also bank depositors and about whom 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 number
of sometimes inappropriate heuristics. Our 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 about consumer credit card use. Our work most closely
overlaps with that of Agarwal et al. (2005), who use another large random sample 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 of borrowers initially choose suboptimal contracts.
While some borrowers incur hundreds of dollars of such costs, most borrowers subsequently switch
41

to cost-minimizing contracts. The results of our paper complement those of Agarwal et al. (2007),
since we 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

rates rose in the mid-1990s due to declining default costs, rather than a deterioration in the creditworthiness of borrowers. Gross and Souleles (2002b) find that increases in credit limits and declines
in interest rates lead to large increases in consumer debt. Ravina (2005) estimates consumption
Euler equations for credit card holders and finds evidence for habit persistence.
Finally, from a methodological perspective our work is related to recent research that studies
age variation along other dimensions. For example, Blanchflower and Oswald (2007) report that
well-being is U-shaped over the lifecycle controlling for observable demographic characteristics.
The trough occurs in the 40s.

15.5

Some Open Questions for Future Research

Our findings suggest several directions for future research.
First, it would be useful to study age eﬀects in other decision domains. We have described a
simple procedure for this: (1) identify the general shape of age eﬀects, as in (1), using controls and
age splines; (2) estimate a linear-quadratic form to localize the peak of performance, as in (2)-(3).
Second, it may be possible to develop models that predict the location of peak performance.
There is a growing consensus that analytically intensive problems — like mathematics — are associated with younger peak ages (see Simonton, 1988, Galenson, 2005, and Weinberg and Galenson,
2005). Analogously, problems that require more experiential training have older peak ages. For
instance, Jones (2006) finds that the peak age for scientists has drifted higher in the twentieth
century. More knowledge now needs to be accumulated to reach the cutting edge of the field.
In our last case study, we found that what is arguably the most analytically demanding task —
deducing the best way to exploit “interest-free” balance transfers — is associated with the youngest
age of peak performance. It would be useful to assess the generality of this association between
analytically demanding problems and young peak ages.
Third, it would be desirable to identify cost-eﬀective regulations that would help improve financial decisions. Forced disclosure is not itself suﬃcient, since disclosing costs in the fine print will
have little impact on distracted and boundedly rational consumers.25 Good disclosure rules will
need to be eﬀective even for consumers who do not take the time to read the fine print or who have
limited financial education.

We conjecture that eﬀective regulations would produce comparable

See Gabaix, Laibson, Moloche, and Weinberg (2006) and Kamenica (2007) for recent models of economic behavior
under information overload.

and transparent products. On the other hand, such homogenization has the dynamic cost that it
may create a hurdle to innovation.
Fourth, studying cognitive lifecycle patterns should encourage economists to pay more attention
to the market 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 who are now required to
make their own financial decisions.

Conclusion
We find that middle-age adults borrow at lower interest rates and pay lower fees in ten financial

markets. Our analysis suggests that this fact is not explained by age-dependent risk factors. For
example, FICO scores show no pattern of age variation. Moreover, age variation in default actually
predicts the opposite pattern from the one that we measure.
Age eﬀects parsimoniously explain the patterns that we observe, but, other eﬀects may also
play a role — for instance, cohort eﬀects or endogenous human capital accumulation.

Whatever

the mechanism, there appears to be a robust relationship between age and financial sophistication
in cross-sectional data. Future research should untangle the diﬀerent forces that give rise to these
eﬀects. If age eﬀects are important, economists should analyze the eﬃciency of modern financial
institutions — like defined contribution pension plans — that require retirees to make most of their
own saving, dissaving, and asset allocation decisions.

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Appendix: Data Summary Statistics
Table A1: Home Equity Loans and Credit Lines
Loans
Description (Units)
APR(%)

Mean

Credit Lines

Std. Dev.

Mean

Std. Dev.

7.96

1.16

4.60

0.88

78,791

99,761

90,293

215,057

Debt/Income (%)

FICO (Credit Bureau Risk) Score

713

733

Customer LTV (%)

Appraisal LTV (%)

Borrower Home Value Estimate ($)

196,467

144,085

346,065

250,355

Bank Home Value Estimate ($)

186,509

123,031

335,797

214,766

Loan Requested by Borrower ($)

43,981

35,161

61,347

50,025

Loan Approved by Bank ($)

42,871

33,188

60,725

51,230

First Mortgage Balance ($)

79,496

83,560

154,444

112,991

Months at Address

122

129

No First Mortgage (%)

Second Home (%)

Condo (%)

Refinancing (%)

Home Improvement (%)

Consumption (%)

Self Employed (%)

7.9

7.8

Retired (%)

9.5

7.7

Homemaker (%)

1.4

1.3

Years on the Last Job

6.3

8.1

7.6

9.1

Borrower Age (Years)
Income ($, Annual)

Table A2: Credit Cards
Account Characteristics

Frequency

Purchase APR

Monthly

14.40

2.44

Interest Rate on Cash Advances (%)

Monthly

16.16

2.22

Credit Limit ($)

Monthly

8,205

3,385

Current Cash Advance ($)

Monthly

148

648

Payment ($)

Monthly

317

952

New Purchases ($)

Monthly

303

531

Debt on Last Statement ($)

Monthly

1,735

1,978

Minimum Payment Due ($)

Monthly

Debt/Limit (%)

Monthly

Total Fees ($)

Monthly

10.10

14.82

Cash Advance Fee ($)

Monthly

5.09

11.29

Late Payment Fee ($)

Monthly

4.07

3.22

Over Limit Fee ($)

Monthly

1.23

1.57

Extra Interest Due to Over Limit or Late Fee ($)

Monthly

15.58

23.66

Extra Interest Due to Cash Advances ($)

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

FICO (Credit Bureau Risk) Score

Quarterly

731

Behavior Score

Quarterly

727

Number of Credit Cards

At Origination

4.84

3.56

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

Age (Years)

At Origination

42.40

15.04

Income ($)

At Origination

57,121

114,375

Mean

Std. Dev.

Fee Payment

Borrower Characteristics

Notes: The “Credit Bureau Risk Score” is provided by Fair, Isaac and Company. The greater the score,
the less risky the consumer is. The “Behavior Score” is a proprietary score based on the consumer’s past
payment history and debt burden, among other variables, created by the bank to capture consumer payment
behavior not accounted for by the FICO score.

Table A3: Auto Loan APRs
Description (Units)

Mean

APR(%)

Std. Dev.

8.99

0.90

3416

772

FICO (Credit Bureau Risk) Score

723

Monthly Loan Payment ($)

229

11,875

4,625

4172

1427

Borrower Age (Years)
Income ($, Monthly)
LTV(%)

Blue Book Car Value ($)
Loan Amount ($)
Car Age (Years)
Loan Age (Months)

Table A4: Mortgage Loans
Loans
Description (Units)

Mean

Std. Dev.

APR(%)

12.64

2.17

Borrower Age (Years)

40.54

9.98

Income ($)

2,624

2,102

Monthly Mortgage Payment/Income (%)

22.84

12.12

686

253

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=1)

30.96

46.24

Second Income (%)

20.44

40.33

Married (%)

71.32

45.23

Married with Two Incomes (%)

16.75

37.34

Self Employed (%)

13.87

34.57

Professional Employment (%)

15.78

36.46

Nonprofessional Employment (%)

52.78

49.93

Relationship with Bank (%)

10.40

30.52

Veraz (Credit Bureau Risk) Score
LTV (%)
Loan Amount ($)
Years at Current Job

Table A5: Small Business Credit Cards APRs
Description (Units)

Mean

Std. Dev.

APR(%)

13.03

5.36

Borrower Age (Years)

47.24

13.35

9,623.95

6,057.66

12,627.45

17,760.24

715.86

55.03

102,684.70

160,799.57

Line Amount ($)
Total Unsecured Debt
FICO (Credit Bureau Risk) Score
Mortgage Debt ($)

Table A6: Age Distribution by Product
Product

Age Percentile
10%

25%

50%

75%

90%

Home Equity Loans

Home Equity Lines

“Eureka”

Credit Card

Auto Loans

Mortgage

Small Business Credit Card

Credit Card Late Fee

Credit Card Over Limit Fee

Credit Card Cash Advance Fee

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Full text of Working Papers (Federal Reserve Bank of Chicago) : The Age of Reason : Financial Decisions Over the Lifecycle, Working Paper 2007-05

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