THE JOURNAL OF FINANCE • VOL. LXIV, NO. 6 • DECEMBER 2009
Exponential Growth Bias and Household Finance
VICTOR STANGO and JONATHAN ZINMAN∗
ABSTRACT
Exponential growth bias is the pervasive tendency to linearize exponential functions
when assessing them intuitively. We show that exponential growth bias can explain
two stylized facts in household finance: the tendency to underestimate an interest
rate given other loan terms, and the tendency to underestimate a future value given
other investment terms. Bias matters empirically: More-biased households borrow
more, save less, favor shorter maturities, and use and benefit more from financial
advice, conditional on a rich set of household characteristics. There is little evidence
that our measure of exponential growth bias merely proxies for broader financial
sophistication.
WHAT DRIVES HOUSEHOLD financial decisions? The canonical economic model as-
sumes that consumers choose to consume, borrow, or save based on their prefer-
ences, their expectations, and the costs and benefits of borrowing and saving. A
growing body of work applies insights from psychology to enrich specifications of
three of the model’s key pieces: preferences, expectations, and problem-solving
conditional on parameter values.1 In this paper, we bring psychological evi-
dence to bear on a fourth specification issue: How consumers perceive the costs
and benefits of borrowing and saving.
We begin by tying together existing and new evidence on these cost percep-
tions to show that most consumers err systematically when given information
commonly available in the market. On the saving side, consumers display fu-
ture value bias: a systematic tendency to underestimate a future value given
∗University of California-Davis, Dartmouth College. Thanks to Jonathan Bauchet for research
assistance and to Bob Avery and Art Kennickell for discussions on the 1983 Survey of Consumer Fi-
nances. Thanks to Dan Benjamin; Andy Bernard; James Choi; Xavier Gabaix; Al Gustman; David
Laibson; Anna Lusardi; Ted O’Donoghue; Jesse Shapiro; Jon Skinner; Doug Staiger; and semi-
nar/conference participants at the Yale SOM Behavioral Science Conference; Kellogg; Cornell; UC
Davis; Georgetown; IZA; SITE; the AEA Annual Meetings; the Federal Reserve Banks of Boston,
Chicago, and Philadelphia; the Federal Reserve Board; the Federal Trade Commission; the Uni-
versity of Michigan Retirement Research Center; the Dartmouth Economics Department; and the
Dartmouth Social Psychology Research Interest Group for comments. Special thanks to Chris Sny-
der for help with the math of exponential growth bias. Previous versions of this paper circulated
under the titles “Fuzzy Math and Household Finance: Theory and Evidence,” and “The Price Is Not
Right. . . .”
1 We borrow this three-pronged taxonomy from DellaVigna’s (2009) review of field evidence on
psychology and economics. For a review focused on behavioral finance, see Barberis and Thaler
(2003).
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2808 The Journal of Finance R©
a present value, time horizon, and rate of return.2 On the borrowing side, we
present new evidence that consumers display payment/interest bias: a system-
atic tendency to underestimate a loan interest rate given a principal, monthly
payment, and maturity. The biases vary asymmetrically with maturity: Fu-
ture value bias increases with the time horizon, whereas payment/interest bias
declines with maturity.
The striking thing about these perceptions of costs and benefits is not that
consumers make mistakes, but that the mistakes are biased in particular ways.
The “wisdom of crowds” fails here, and fails to a greater or lesser degree depend-
ing on the side of the balance sheet and maturity. What explains this particular
pattern? And is the pattern indicative of biases that affect actual decisions?
We show that future value bias and payment/interest bias are potentially
linked by a single cognitive micro-foundation: exponential growth bias, the ten-
dency to linearize functions containing exponential terms when assessing them
intuitively. A literature in cognitive psychology documents that individuals dis-
play exponential growth bias in a variety of contexts, and that the degree of ex-
ponential growth bias varies substantially in the cross-section. But economics
has largely ignored the potential implications of exponential growth bias for
household finance.3
The intuition for how exponential growth bias drives future value bias is
straightforward: Consumers underestimate how quickly a given yield com-
pounds, so they underestimate the expected future value for any given future
date. Future value bias becomes more pronounced as the periodic return rises
and the compounding horizon lengthens. On the borrowing side, exponential
growth bias is mathematically equivalent to failing to account for the declining
principal balance on an installment loan. So consumers overestimate how long
they actually get to borrow the principal, thereby underestimating the true cost
of borrowing. Payment/interest bias is more severe on short-term loans because
principal balances on those loans decline faster than on long-term loans.4
We next examine the following critical question for household finance: Does
exponential growth bias affect household balance sheets in the real world? We
are not aware of any prior work on this question. To answer it we construct a
2 Future value bias is our term for the tendency documented most directly in Eisenstein and
Hoch (2005).
3 The cognitive psychology literature began with Wagenaar and Sagaria (1975); we provide
a brief review in Internet Appendix A (please find all Internet Appendices at http://www.
afajof.org/supplements.asp). Economic applications of exponential growth bias to date have been
limited to perceptions about savings (Eisenstein and Hoch (2005)) and inflation (Jones (1984),
Kemp (1984), and Keren (1983)). Exponential growth bias does not appear in any of the many
reviews of psychological evidence for economists; see, for example, Rabin (1998), Gilovich, Griffin,
and Kahneman (2002), and Kahneman (2003).
4 We treat the link between exponential growth bias and borrowing cost perceptions formally in
Internet Appendix B, but for intuition the limiting case in the other direction is instructive. The
formula for the interest rate on an infinite maturity (interest-only) loan is i = p/L, the periodic
payment divided by the principal; it does not involve any exponentiation and the principal balance
never declines, so exponential growth bias (or failure to account for declining principal balances)
is not an issue.
Exponential Growth Bias and Household Finance 2809
household-level measure of payment/interest bias, and correlate it with a wide
range of household financial outcomes. The results suggest that bias matters:
Payment/interest bias is strongly correlated with more borrowing, less sav-
ing, portfolios tilted toward short-term installment debt and short-term assets,
and lower net worth.5 All of these results are conditional on controls for de-
mographic and life-cycle factors, available resources, preferences, expectations,
and other decision inputs.6 While our data lack a direct measure of future value
bias, the pattern of results suggests that payment/interest bias captures future
value bias as well; in particular, payment/interest bias is correlated with asset
allocation conditional on the level of assets.
The above findings motivate four follow-on questions. First, why doesn’t con-
sumer adaptation (learning, calculators, heuristics, etc.) render bias irrelevant?
We find that many consumers do in fact effectively debias themselves by relying
on outside financial advice. More-biased households get more outside advice,
all else equal, suggesting that many consumers are aware of their bias and/or
its effects. Further, more-biased households who get outside advice are just as
wealthy as the least-biased households. Yet our results also suggest that many
biased households do not delegate, learn rapidly enough, or otherwise undo the
effects of bias. Psychology again offers an explanation: Cognitive biases tend
to persist and decision-making heuristics tend to fail when decisions are ab-
stract and made infrequently (Stanovich (2003)). Many borrowing, saving, and
portfolio decisions in household finance seem to fit that description.
A second question is why supply-side factors or regulation fail to eliminate
the effects of bias. We do find that credit constraints play a mitigating role,
by preventing some biased households from borrowing as much as they would
like. Existing Truth-in-Lending laws could make payment/interest bias irrel-
evant by forcing lenders to disclose an annual percentage rate (APR), but the
APR disclosure mandated by Truth-in-Lending is imperfectly enforced. Many
lenders use “monthly payment” marketing that shrouds or misrepresents in-
terest rates, itself prima facie evidence that bias matters in the market given
that violating Truth-in-Lending is costly.7 Our related work examines this is-
sue in further detail, and shows that consumers with greater payment/interest
5 Methodologically speaking, empirical work testing relationships between an individual-level
measure of a potentially biased decision input and household/consumer financial choices is rare.
Ashraf, Karlan, and Yin (2006) and Meier and Sprenger (2008) use survey questions to construct
measures of time-inconsistent preferences and then examine relationships between preferences
and saving or borrowing decisions. Puri and Robinson (2007) examine relationships between a
measure of optimism based on life expectancy and financial decisions in the 1995 to 2001 Surveys
of Consumer Finances. Graham, Harvey, and Puri (2008) summarize and extend the corporate
finance literature on links between managerial attitudes (e.g., preferences and beliefs) and firm
behavior.
6 Our Internet Appendix C details the full set of controls. We use the 1983 Survey of Consumer
Finances because no more recent data set has data on biased interest rate perceptions. In Section
VI, the Conclusion, we note that the expansion and increased sophistication of retail financial
markets may make biased perceptions even more relevant today (despite the growth of low-cost
decision aids).
7 See Gabaix and Laibson (2006) for a model of a shrouding equilibrium.
2810 The Journal of Finance R©
bias pay higher loan interest rates (Stango and Zinman (2009)).8 On the saving
side, firms selling saving and investment products have incentives to debias
consumers, but regulation may hinder them from highlighting returns over
long horizons, where future value bias is most severe.9
A third question is whether our results reflect the specific effects of expo-
nential growth bias, or whether bias is a measure of low financial sophistica-
tion defined more broadly.10 On the asset side of the balance sheet, we con-
duct additional tests by estimating conditional correlations between our bias
and standard indicators of sophistication, focusing on outcomes that would
not necessarily be driven by exponential growth bias in its narrow form. The
most-biased households are less likely to hold bonds, but the correlation is eco-
nomically small. There is also some evidence of a relationship between bias
and poor diversification. On two other indicators—holdings of own-company
stock and frequent stock trading—we find no correlations with bias. On the
liability side of the balance sheet, a standard hypothesis is that sophistication
reduces the participation cost of borrowing. Hence, under this hypothesis one
might expect our more-biased households to hold less debt if unmeasured so-
phistication were driving our results.11 We find little evidence of this pattern;
short-term borrowing increases with bias, and long-term borrowing is uncorre-
lated. Overall, then, there seems to be a weak relationship between bias and
lack of financial sophistication more broadly. Nevertheless, the results do not
rule out a link between bias and financial sophistication, and we hope that they
will provoke further inquiry. Perhaps, for example, being aware of one’s bias is
a component of financial literacy.
Fourth and finally, it is possible that our measure of bias is correlated with
unobserved elements of preferences or expectations. Our controls do include
measures of time preference, risk aversion, and income expectations, making
it unlikely that they are omitted variables driving the results. However, we
lack measures of “behavioral” biases such as time inconsistency, loss aversion,
8 More specifically, we find that biased consumers pay higher interest rates on short-term in-
stallment loans, but only when borrowing from lenders facing relatively weak Truth-in-Lending
enforcement. Imperfectly enforced Truth-in-Lending may also have the perverse consequence of
creating folk wisdom that using interest rates is the “right” way to make decisions and thereby
nudging some biased consumers away from an effective decision rule: “Never try to infer an interest
rate. Rather, make borrowing decisions based on other loan terms.”
9 For example, SEC rule 230.482 requires mutual funds that advertise performance data to
present 1-, 5-, and 10-year returns with equal prominence. A mutual fund that wishes to present
returns earned over a longer horizon can do so, but only in addition to the 1-, 5-, and 10-year
horizons, and with equal prominence. Our findings may also explain why mutual funds would
highlight arithmetic rather than geometric mean fund returns. See Welch (2000) for a discussion
of the difference.
10 Several papers have found positive correlations between broader measures of financial sophis-
tication (or planning, or cognitive ability) and stock market participation or wealth, for example:
Ameriks, Caplin, and Leahy (2003), Lusardi and Mitchell (2007), Benjamin, Brown, and Shapiro
(2006), Christelis, Jappelli, and Padula (2006), and van Rooij, Lusardi, and Alessie (2007).
11 Sophistication might instead push households to borrow less and save more; for instance, if
sophisticates recognize subtle future risks (long-term care costs, reductions in social insurance)
and others do not.
Exponential Growth Bias and Household Finance 2811
or optimism. It may therefore be the case that individuals with exponential
growth bias have biases in other dimensions as well, and that those other biases
drive our observed relationships between payment/interest bias and financial
decisions. This is a promising line of inquiry for future theoretical and empirical
work. One intriguing possibility is that exponential growth bias is a tractable
way to measure a portfolio of behavioral biases.
Taken together, the findings above offer a new class of psychological bi-
ases that might affect household finance. Previous work has incorporated
psychology-based specifications of preferences, expectations, and problem-
solving.12 But most work in household finance continues to assume that con-
sumers correctly perceive the decline (increase) in future consumption that
results from borrowing (saving) today. Our findings suggest that exponential
growth bias leads consumers to get these assessments wrong, and to err sys-
tematically in particular directions that tilt portfolios toward short-term debt
and away from long-term saving, increase borrowing and reduce saving, and
depress overall wealth accumulation.
The paper proceeds as follows. Section I presents evidence showing that con-
sumers display both future value bias and payment/interest bias. Section II
shows that exponential growth bias can explain both biases, and also discusses
some other explanations for the observed pattern of biases. Section III describes
our approach to estimating the link between payment/interest bias and house-
hold financial outcomes, and also reports summary data on our outcomes and
control variables. Section IV presents our results. Section V discusses comple-
mentary/alternative interpretations of the results. Section VI concludes.
I. Payment/Interest Bias and Future Value Bias: Evidence
In this section we discuss previous work showing empirical evidence of pay-
ment/interest bias and future value bias, present new empirical evidence of the
former, and summarize the stylized facts that one can draw from all of the work
to date.
A. Prior Work
Eisenstein and Hoch (2005) present lab data showing that most consumers
display future value bias. Their study asks Internet survey participants to es-
timate a future value given a present value, time horizon, and interest rate.
Eisenstein and Hoch show that future value bias is prevalent (over 90% of re-
spondents err on the low side), large on average, and increasing in the time
12 For heuristic alternatives to dynamic optimization see, for example, Lettau and Uhlig (1999),
Hurst (2006), and Benartzi and Thaler (2007). There is also a related literature on financial plan-
ning; see for example, Ameriks, Caplin, and Leahy (2003) and Lusardi (2003). For alternative
formulations of beliefs see, for example, Brunnermeier and Parker (2005) and Puri and Robin-
son (2007). For alternative formulations of preferences see, for example, Angeletos et al. (2001),
Barberis, Huang, and Santos (2001), and Gul and Pesendorfer (2004).
2812 The Journal of Finance R©
horizon.13 Respondents display a strong tendency to anchor on a linear forecast
of the future value, and to ignore the returns provided by compounding.
On the borrowing side, several previous studies contain empirical evidence
that consumers make mistakes when assessing interest rates.14 Most studies
establish this by asking respondents to estimate the interest rate implied by
a given loan principal, maturity, and repayment stream. This work includes
Juster and Shay (1964), National Commission on Consumer Finance (1972),
Day and Brandt (1974), Parker and Shay (1974), and Kinsey and McAlis-
ter (1981). More recently, Bernheim (1995, 1998) and Moore (2003) find evi-
dence consistent with limited understanding of loan terms, including interest
rates.
The focus of prior work on the borrowing side is noteworthy; it primarily
seeks to measure consumers’ mistakes in assessing interest rates, rather than
determine the extent to which mistakes are biased in particular directions.
The empirical implications of (presumably mean-zero) mistakes are different
from the implications of bias, a point we elaborate on below. However, despite
the focus of previous work on measuring mistakes, it is often easy to infer from
summary data provided in the papers that consumers display payment/interest
bias. Some papers do make more direct statements about bias; for instance,
Parker and Shay (1974, p. 217) note that consumers display “a strong ten-
dency to underestimate annual percentage rates of charge by about one-half or
more . . .”
B. New Evidence: Payment/Interest Bias on Hypothetical Loans
We build on the prior work above in several ways. We start by presenting
nationally representative empirical evidence on payment/interest bias from
two previously untapped sources: the 1983 and 1977 Surveys of Consumer
Finances.15 We use the 1983 SCF because it has the most recent (and, as far
as we know, the only) nationally representative data on both payment/interest
bias and household financial outcomes. We use the 1977 SCF because it con-
tains richer data on payment/interest bias than the 1983 survey; the downside
of the 1977 SCF is that it lacks comprehensive data on the household balance
sheet. More recent SCFs lack any questions that elicit payment/interest bias
and hence are not usable for our purposes.
13 Lusardi and Mitchell (2007) show that responses to a question on savings yields in the Health
and Retirement Study (HRS) are consistent with the underestimation of compound yields. We
note, however, that the HRS question does not necessarily capture a bias per s
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