Fuzzy Math and Red Ink

"Fuzzy Math and Red Ink"

Victor Stango, Tuck School of Business, Dartmouth College

Jonathan Zinman, Department of Economics, Dartmouth College

Introduction

Research at the intersection of economics and psychology is expanding on traditional views about how people make financial decisions. There is an emerging consensus that individuals often have self-control problems, overly optimistic expectations, and heuristics that do not square well with traditional concepts of rationality. These “behavioral” aspects of financial decision-making have been shown to have important real-world effects.

Our research sets out in a new direction. We first document that people’s intuitive assessments about complex mathematical problems are biased in ways that encourage borrowing and discourage saving. These biases - what we call "fuzzy math" in household financial decisions - have a clear foundation in cognitive psychology.

We then ask how fuzzy math affects short- and long-run financial decisions, the financial outcomes that result, the strategies that firms selling loans and investments use, and the design of public policy related to household finance (such as Truth in Lending legislation).

Click here to read a recent Wall Street Journal Article about our research.

What is Fuzzy Math?

Consider these two scenarios, which are representative of those commonly faced by households:

1. How much would you end up with if you invested $10,000 in a mutual fund that earns a 7% average annual return, withdrawing the money after 30 years?

2. If you were borrowing $10,000 to buy a car and had quotes from two lenders, one for an interest rate of 8% and one for 48 monthly payments of $299, which would you prefer?

While many people use calculators or other aids in such situations, many others do not. Instead they rely on their best “educated guess.” In principle this is not a problem, as long as a substantial share of people are close to correct, or if people’s mistakes are not biased in particular directions.

But our research shows that for the questions above and a host of others, people don’t just make mistakes: they are biased toward mistakes that lead to borrowing too much and saving too little.

Take the first example: the “future value” of the initial $10,000 investment described above ends up being roughly $76,000. But most people estimate a future value that is far below that. In general, individuals tend to systematically underestimate the returns to long-term saving and investing.

Take the second example: the second loan offer described above, with the $299 monthly payment, implies an APR of about 20%. But most people guess that the APR on the offer is much lower. In general, most people tend to systematically underestimate the interest rate when they try to infer it from information on (“low”) monthly payments.

Our "fuzzy math" research agenda sets out to do the following:

1. Develop a theory can can tie these biases together;

2. Estimate the real-world economic importance of fuzzy math across a range of household decisions and outcomes;

3. Apply what we learn to the development of sound public policy.

Click here for a more detailed summary of our research and some other suggested reading.

Jon's web page has a variety of other plain language summaries of our research, including his recent webinar "What To Do About Fuzzy Math and Red Ink," presented to the Behavioral Finance Forum. That presentation also includes some more technical details regarding the biases above.

Research to Date

We have two working papers exploring these issues:

"The Price is Not Right: Exponential Growth Bias, Present-Biased Perceptions and Household Finance." (with Jon Zinman). April 2008. Revise and resubmit, Journal of Finance.

We show that many consumers have present-biased perceptions about relative prices for borrowing and saving: they systematically underestimate the cost of short-term borrowing and the return to long-term saving. These misperceptions can be explained by exponential growth bias, a cognitive tendency to linearize exponential functions when assessing them intuitively. Misperceptions matter: conditional on a rich set of characteristics, a household-level metric of present-bias is strongly correlated with borrowing, savings, portfolio choice, wealth and delegation. There is only weak evidence that our measure of bias is a proxy for broader financial sophistication. We conclude that exponential growth bias should be added to the list of psychological biases that might affect household finance.

A previous version of the paper was circulated with the title "Fuzzy Math and Household Finance" (November 2007)

"Fuzzy Math, Disclosure Regulation and Credit Market Outcomes" (November 2007)

This paper documents that most consumers have "payment/interest bias": a tendency to substantially underestimate a loan interest rate when inferring it from a principal, maturity and monthly payment. This bias provides lenders with an incentive to shroud interest rates and market "low monthly payments" when not constrained by regulation. More important, we find that an individual-level measure of payment/interest bias is correlated with rates on actual installment loans, but only on loans from lenders facing relatively lax Truth-in-Lending enforcement. Our results hold even when we control for unobserved heterogeneity at the household level by examining households with multiple loans from lenders facing different enforcement. Our results provide a clear microfoundation for the mandated disclosure of Annual Percentage Rates (APRs) in loan marketing and contracts. They also suggest that when properly enforced, mandated interest rate disclosure can prevent lenders from catering to a cognitive bias in how consumers perceive interest rates.

Future Work

In current work not yet completed, we are extending the analysis in several directions. Because the studies above use data from the early 1980s, we are collecting updated data on the biases we have documented. We are also collecting more information on how firms (lenders and retail money managers) can or do provide "frames" that either exploit or mitigate bias. Finally, we are extending our theoretical work to ask whether the exponential growth bias that underpins our theory can explain a broader set of anomalies in household finance.