View original document

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

Designing Monetary Policy Rules in an
Uncertain Economic Environment*

A

by Michael Dotsey and Charles I. Plosser

well-designed monetary policy can help the
economy respond efficiently to economic
disturbances by limiting the deviation of
economic activity from its potential while
keeping inflation close to its desired rate. But successful
implementation of such strategies must confront
significant challenges arising from various forms of
economic uncertainty. In this article, Michael Dotsey
and Charles Plosser discuss the design of monetary
policy rules in an environment in which policymakers
face two distinct forms of uncertainty: the uncertainty
surrounding the precise values of key policy variables that
often appear as determinants in such rules, and learning
uncertainty, which arises when people have only an
incomplete knowledge of the economy itself.

A well-designed monetary policy
can help the economy respond efficiently to economic disturbances by
limiting the deviation of economic
activity from its potential while keeping inflation close to its desired rate.
But successful implementation of such
strategies must confront significant
challenges arising from various forms
of economic uncertainty. This article
Michael Dotsey
is a vice
president and
senior economic
policy advisor
in the Research
Department of
the Philadelphia
Fed. This article
is available free
of charge at www.
philadelphiafed.
org/research-and-data/publications.
www.philadelphiafed.org

discusses the design of monetary policy
rules in an environment in which
policymakers face two distinct forms
of uncertainty. The first involves the
uncertainty surrounding the precise
values of key policy variables that often
appear as determinants in such rules.
These variables are typically measures
of resource utilization relative to some
concept of potential. This data uncertainty can arise because the relevant
conceptual definition of potential may
be uncertain and even if it is clearly
defined, it may not be observable and
thus measurement error becomes an
important consideration. The sec-

ond form of uncertainty we refer to
is learning uncertainty, which arises
when people have only an incomplete
knowledge of the economy itself.
Regarding the first source of uncertainty, it is well documented that
the key policy variables mentioned
above are measured with considerable error. Thus, the true value of
these variables is uncertain at the
time policy is made. With respect to
the second source of uncertainty, we
believe that most people do not possess
complete knowledge of the economy
and that their behavior is characterized by a continual learning process in
which their views about the economy
evolve over time. Policymakers must
recognize these uncertainties when
designing policy. Throughout our
discussion, we take as given the desirability of rule-like behavior for policy.1
It is widely accepted in the economics
profession that rule-like behavior is
preferable to discretion because more
desirable economic outcomes can be
obtained with commitment.2 We will
1
For example, see the following: Michael Dotsey
and Charles Plosser (2007), Michael Dotsey
(2008), and Charles Plosser (2007).

In the monetary setting, this has been made
abundantly clear by, among others, Richard
Clarida, Jordi Gali, and Mark Gertler, and
Michael Woodford.

2

Charles Plosser
is the president
and chief
executive
officer of the
Philadelphia Fed.

*The views expressed here are those of the authors and do not necessarily represent the views
of the Federal Reserve Bank of Philadelphia or
the Federal Reserve System.
Business Review Q1 2012 1

also concentrate on the conduct of
monetary policy in normal times and
will, therefore, not address the special
problems brought about by the zero
lower bound on nominal interest rates.3
The basic conclusion from the
literature is that when policymakers are
trying to achieve the best outcomes in
terms of economic welfare, these types
of uncertainty make it desirable for the
central bank to respond relatively aggressively to deviations of inflation from
target and to rely less on measured deviations of either output or unemployment from their natural or potential
values. Rather, the central bank should
also respond to economic growth irrespective of where economic activity is
with regard to potential or trend.4

ficient economic performance. Simple
interest-rate rules tend to perform well
in many different economic models, a
fact that suggests they can be useful in
practice. Thus, it is no accident that
the behavior of most central banks in
developed economies can be reasonably approximated by a simple interestrate rule.5
However, the formulation of
monetary policy rules must take into
account the uncertainty that policymakers face, since rules designed under
the assumption of no uncertainty are
often disastrous when one explicitly
considers uncertainty. In particular, a
rule may, in theory, perform quite well
when data are measured accurately but
be quite bad when data are subject to

It is no accident that the behavior of most
central banks in developed economies can be
reasonably approximated by a simple interestrate rule.
USEFULNESS OF
INTEREST-RATE RULES
In analyzing the design of beneficial ways in which to conduct monetary policy under uncertainty, we will
concentrate on the use of an interestrate rule. The types of rules we will
discuss are fairly simple ones and ones
that have been shown to be useful for
policymaking. These rules are generally designed to stabilize some measure
of economic activity and inflation,
because doing so leads to more ef-

For a discussion of the problems the zero lower
bound presents for monetary policy, see Dotsey’s
2010 article.
	
4
Potential output is the output that could be
produced with the labor, capital, and technology available in the absence of economic distortions arising from stickiness in prices and wages.
A more complete description of potential can
be found in the Business Review article by Roc
Armenter. Trend is the long-term growth path
of an economic variable.
3

2 Q1 2012 Business Review

severe measurement errors. Also, rules
that work well under the assumption
that individuals fully understand their
economic environment may not do so
well when individuals are constantly
learning about economic circumstances.
AN OVERVIEW OF
UNCERTAINTY
Many of the variables that a
central bank reacts to in the course of
setting its interest-rate instrument are
in fact poorly measured. In particular, statistical measures of potential
output or natural rates of unemployment are measured with great impreci-

sion.6 Thus, relying on these types of
measures can potentially lead policy
astray. By a statistical measure we
mean an estimate of potential output
or unemployment that is based solely
on data and, therefore, is independent
of any particular theoretical model.
For example, a common measure of
potential output involves extracting a
trend rate of output growth or some
other relatively smooth measure of output growth that removes much of the
short-run variation in output.7
There is also a concern that statistical measures are not likely to correspond to the conceptual metrics most
relevant for monetary policy. Indeed,
it is difficult to assign any theoretical
justification for the use of these purely
statistical constructs.8 Thus, when deciding on which measure of economic
activity is important for formulating
monetary policy, central banks operate
under a large degree of uncertainty.
Much recent research has shown that
ignoring this uncertainty can create
problems.
We will first discuss the problems that data uncertainty poses for
designing monetary policy. A strong
conclusion from the literature on data

The natural rate of unemployment is the rate
of unemployment that would arise if there were
no stickiness in the setting of wages and prices.
That is, it is the rate of unemployment that
would occur if prices and wages were completely
flexible. It is also the rate of unemployment that
the economy would converge to in the long run
after all price and wage rates had time to fully
adjust to economic disturbances. The concept
is thus tightly related to potential output (see
footnote 4).

6

Common statistical methods involve the use
of band-pass filters, Hodrick-Prescott filters, or
fitting polynomials of time to the data.

7

See the 2010 speech by Charles Plosser and
Roc Armenter’s and Keith Sill’s Business Review
articles. All three point out that there is no
agreed-upon way of measuring potential and
that various measures may differ. In addition,
Sill emphasizes that in setting prices, firms are
most concerned with the evolution of their marginal cost and that marginal cost is not highly
correlated with unemployment rates.

8

5
For a review of simple interest-rate rules, see
the article by John Taylor and John Williams.
See also the article by Marc Giannoni and
Michael Woodford and the one by Stephanie
Schmitt-Grohe and Martin Uribe for a discussion of their optimality.

www.philadelphiafed.org

uncertainty is that “gap-type measures,” especially statistical measures
of gaps, are not reliable enough to base
policy on, a conclusion that is shared
by the literature on learning.
Most of our attention will be focused on the topic of data uncertainty
for two reasons. First, the effects of
data uncertainty on policy design have
been more fully studied, and second,
the work done by the Philadelphia
Fed’s Real-Time Data Research Center
underscores the importance of measurement issues.
We then turn to some issues associated with the likely possibility that
people may not possess a fully articulated understanding of the economy.
Concept Uncertainty
In most modern macroeconomic
models used to study monetary policy,
minimizing the theoretical gap between actual output and potential output improves economic welfare. Thus,
the notion of potential output plays
a key role in setting monetary policy.
However, theory-based concepts of
potential often differ from the statistical concepts that many people believe
belong in policy rules. We refer to the
lack of coherence between statistical
and theoretical measures of gaps as
“concept uncertainty.”
The theoretical gaps are also specific to the particular theory or model
being used to study the economy. Because each model is different, the gaps
in each model are different. For example, the way that one models firms’
pricing decisions can theoretically affect the value of an output gap.9 This

9
In fact, as things stand theoretically, the situation is even a bit more muddled. It turns out
that it may not be the level of the gap that is
most relevant for policy; it may be the change in
the gap that should influence monetary policy.
For example, Woodford’s model shows that
changes in the theoretical gap, not the gap’s
level, are the relevant variable for welfare and
hence the relevant variable that the interest
rate should respond to.

www.philadelphiafed.org

lack of an agreed-upon macroeconomic
model indicates that designing monetary policy rules that help achieve reasonably good economic performance
is a challenging undertaking. How one
goes about doing this represents an
ongoing part of economists’ research

This occurs because when output
increases in response to an increase in
productivity, only part of that increase
is initially attributed to a change in
trend, and thus, statistically constructed potential output is always smoother
than actual output. Therefore, the two

Levels of statistical gaps may not be good
indicators of inflationary pressures in the
economy.
agenda and is beyond the scope of this
paper. What we will try to do here is to
emphasize certain lessons that appear
to be consistent across many economic
models and for which there is a growing consensus regarding their implications for policy.
One lesson from the literature is
that the statistical gaps often prescribe
policies opposite to those obtained
from the theory-based gap.10 For example, an unanticipated improvement
in productivity often leads potential
output to increase by more than actual
output and hence generates a negative
theoretical output gap. This outcome
occurs because various inflexibilities
built into operational models of the
U.S. economy imply that economic
variables move more slowly than they
would if they could adjust without cost
and with complete flexibility and potential output is the output that would
arise if there were, in fact, no inflexibilities.
In contrast, potential output
based on some statistical trend does
not increase as much as actual output
in response to a positive productivity
shock, leading to a positive output gap
(see the article by Roc Armenter).11

We wish to point out that there is also no
agreed-upon model of the macro economy and
that theoretical gaps differ across models. Our
discussion, however, pertains to results that
are consistent across a wide range of economic
models.
10

different measures would lead to opposite monetary policy responses, and the
response based on the statistical measure would be in the wrong direction.
Furthermore, levels of statistical
gaps may not be good indicators of
inflationary pressures in the economy. Empirically, they do not help to
forecast inflation and that has been
especially true over the last 25 years.12
Keith Sill analyzes some of the reasons
for this failure, namely, that measures
of various gaps are not very correlated
with the costs of producing goods, and
it is the underlying behavior of costs
that governs firms’ pricing decisions in
most modern macroeconomic models.
These conceptual problems
call into question the usefulness of
statistically based gaps in designing
monetary policy. Furthermore, it is far
from evident that monetary policy has
always been conducted with regard to
statistically based measures, and when
it has, the results have at times been
disastrous. We will return to this point
after discussing the measurement issues more fully, but the 2002 study by
Athanasios Orphanides has made a
compelling argument that part of the

11
A positive output gap occurs when actual
output is greater than potential output. A negative output gap occurs when actual output is less
than potential output.

For a detailed description of this failure, see
the studies by James Stock and Mark Watson.

12

Business Review Q1 2012 3

Great Inflation of the 1970s was due to
misperceptions about the unemployment gap.
UNCERTAINTY SURROUNDING
STATISTICAL MEASURES
Even though statistical output
gaps have not universally guided U.S.
monetary policy, it does appear that
they have periodically played a role
in influencing U.S. monetary policy.
Thus, it is worth looking into the measurement issues and the implications
that these measurement issues have for
using statistical gaps.
Essentially, constructing an output
or unemployment gap requires breaking down output or unemployment
into a trend component and a cyclical
component. From a policy perspective,
we are interested in how much current
output or unemployment is deviating
from the current measure of trend.
There are two primary reasons
why both statistical output gaps and
unemployment gaps may be poorly
measured from the perspective of implementing monetary policy. The first
is that the data from which they are
constructed are significantly revised,
and the second is that future data also
significantly affect our estimates of
the current and past measures of trend
and hence potential. That is, it helps
to know the entire path of output or
unemployment, both past and future,
when figuring out what part of their
current values reflect a general trend.
For example, consider a simple exercise that estimates trend unemployment and the deviation of unemployment from trend. The figure shows the
difference between estimates of trend
unemployment using all of the available data, which we denote as the final
estimate, and its estimate when only
data available at each point in time are
used to construct the trend. We will
refer to this as a real-time estimate.13
(See Constructing the Figure.)
Although we have used a very
4 Q1 2012 Business Review

simple statistical technique to calculate trend unemployment, the basic
thrust of our results would carry over if
more sophisticated statistical techniques were used.14 In addition, we
have performed the analysis using the
latest estimates of unemployment and
13
A true real-time estimate would use only
the data as they were reported at the time.
Therefore, we ignore measurement error issues
associated with initial data that are subsequently revised, but it turns out that estimation errors
associated with data revisions are a relatively
small problem.
14
For a detailed comparison of different statistical measures of trend unemployment, see the
2002 study by Athanasios Orphanides and John
Williams.

so have ignored the effects of data revisions. In general, although revisions
do contribute to measurement error in
estimating the unemployment gap in
real time, this channel is less important than the inability to see future
unemployment rates when estimating
trend unemployment.
The evidence regarding the statistical uncertainty in measuring unemployment gaps is also present when
one examines output gaps. A detailed
examination of the measurement
problems in calculating output gaps
is provided in a paper by Athanasios
Orphanides and Simon van Norden.
Their basic findings are similar to what

FIGURE
Potential and Actual Unemployment

Source: Estimates constructed by authors using data from the Bureau of Labor Statistics.
www.philadelphiafed.org

we have just shown for the unemployment gap. Using various statistical
estimates that are more sophisticated
than the one used in our example
(there are many ways to estimate a
trend), Orphanides and van Norden
arrive at very different estimates of
the gap, especially the real-time gap.
The different estimates in real time
can vary by more than 6 percentage
points and by more than 3 percentage points when final data are used.
Furthermore, for various measures the
revisions between real-time and final

estimates are frequently larger than 4
percentage points in absolute value.
Thus, the revisions are often nearly the
same size as the output gap measures
themselves. Also, the revisions are
persistent, implying that measurement
errors are long-lived.15 Finally, the
estimated gaps in real time are often of

15
Autocorrelation coefficients range from 0.80
to 0.96. Autocorrelations show the correlation between two values of the same variable
at different times, rather than the correlation
between two different variables.

Constructing the Figure
In this example, the trend is constructed using a common statistical technique of fitting the unemployment rate to an equation based on
time.* For the final estimate, the equation is estimated on data from the
first quarter of 1948 to the fourth quarter of 2010, and the orange line in
the top panel represents the fitted curve. The real-time estimates are constructed by estimating the same equation using data only up to the period
in question and calculating the trend value at that time. We start in 1963
so that our initial real-time estimate is made using 15 years of data. In
particular, for the estimate of the trend in the first quarter of 1963, we use
data from the first quarter of 1948 to the first quarter of 1963 and calculate the trend for the first quarter of 1963. We then update our estimation
of the trend by using an additional quarter of data and make the analogous calculation of the trend for the second quarter of 1963. We continue
this procedure until the fourth quarter of 2010. As we approach the end of
the sample period, the two trend measures begin to converge. They do so
because the data used in constructing each measure become similar as the
end of the sample is approached, and they are exactly the same for the last
data point. This happens not because the real-time estimates are getting
better but because the final-time estimates no longer have the advantage
of information contained in unemployment rates that have yet to occur.
The actual unemployment rate is shown by the black line in the top
panel of the figure, and estimates of the real-time trend are displayed by
the grey line. The final-time estimates are depicted by the orange line. It
is obvious that the real-time and final-time estimates are very different. In
the middle panel, we plot the unemployment gaps, which are the difference between the unemployment rate and the estimated trends. The average absolute values of the gaps are 0.83 for the real-time gap and 0.93 for
the final-time gap. The differences between the two gaps are large, with
an absolute average value of 0.95. Thus, the differences in the gap measures are bigger than the estimates of the gaps themselves. Furthermore,
the gaps are often of opposite sign and the differences in their values are
persistent.
*
In particular, we postulate that the unemployment rate is a particular function of time. In
particular we estimate u = a0+ a1t + a2t2 + a3t3 + a4t4 + a5t5 + e using data from 1948Q1
to 2010Q4, where t is the number of periods from the beginning of our data sample. We use
the estimate of this function to calculate the trend.

www.philadelphiafed.org

the opposite sign when compared with
the final estimates.
In general, data revisions also contribute a small share to the difference
in the real-time and final estimates of
the output gap. Most of the revision is
due to the fact that the final estimates
use all of the data over the full sample
and that data are useful in establishing
the estimated trend.
We should mention that there
are also data revisions of many inflation series and that inflation, therefore, suffers from measurement issues.
However, because the data uncertainty
surrounding inflation is affected only
by data revisions to inflation itself
and not by imprecise estimates of an
inflation gap, the data uncertainty surrounding inflation is generally minor
when compared to the uncertainty
surrounding the unemployment or
output gap. Therefore, we ignore the
uncertainty associated with inflation
and treat inflation as an accurately
measured variable in real time.16
After reviewing the measurement
problems, we conclude they are severe.
The question then is what role these
measurement problems should play in
the way we design monetary policy.
IMPLICATIONS OF DATA
UNCERTAINTY FOR
MONETARY POLICY DESIGN
The general message from the
literature is that basing policy on gaptype concepts is problematic and that
it pays to respond fairly aggressively to
movements in inflation from target.
It also appears that responding to
economic activity itself, as opposed to
“gaps,” is quite helpful when designHowever, there have been episodes in which
core personal consumption expenditures (PCE)
have been substantially revised. One particularly large episode occurred in 2001 when inflation, as measured by the core PCE, was revised
up by approximately 1 percent and what was
initially observed as declining inflation actually
became a period of rising inflation. For more
details, see the study by Dean Croushore.
16

Business Review Q1 2012 5

ing policy under data uncertainty.
Basically, one should not base policy
on poorly estimated measures, and
economic activity is much better measured than gaps.
A useful paper that articulates
this message is the 2002 study by Orphanides and Williams that investigates the effects of mismeasurement
of the natural rate of unemployment,
which is also easy to translate into a
similar message regarding the use of
statistically based output gaps.
Orphanides and Williams calibrate misperceptions of these natural
rates using U.S. data from the first
quarter of 1970 to the second quarter
of 2002. As in our analysis above, they
measure misperceptions by the difference between potential measured in
real time and potential when measured using the data over the entire
sample. For these authors as well, the
additional data provided by the full
sample turn out to be very important
for breaking down unemployment into
its true trend and cyclical movements.
Hence, the limitation of not observing the future potentially creates a
lot of uncertainty about the trend in
unemployment. As in the study by Orphanides and van Norden, the authors
show that the misperceptions about
the natural rate of unemployment are
large and highly persistent.
Given this uncertainty, Orphanides and Williams analyze what
types of monetary policy rules work
in their fairly simple environment.
Although it is natural to question
whether results in such a simple setting
can be generalized to more realistic
and complex models of the economy,
we believe that qualitatively, at least,
the lessons learned from their exercise
are informative for designing policy.
The basic result is that under data
uncertainty, the monetary authority
wants to minimize the degree to which
that uncertainty affects policy. That
conclusion seems quite intuitive. Fur6 Q1 2012 Business Review

thermore, the more uncertain the central bank is at any given point in time,
the more it should reduce the potential
effect that misperceptions may have on
policy. This is certainly a message that
should resonate with policymakers in
the current economic environment.
The central bank minimizes
uncertainty’s effect on monetary policy
by moderating its response to the
gap compared to what it would do if
it knew the gap with certainty. The
central bank also increases its response
to inflation and is somewhat inertial,
changing interest rates gradually. This
inertial behavior reduces the effects
of uncertainty. The results go further
and indicate that central bank policy is
improved when it responds to changes
in unemployment (or output growth)
rather than only responding to gaps.17
Furthermore, the optimal policy
derived under uncertainty does not
perform badly in a world that hypothetically has no uncertainty, while
policies formulated as if there were no
uncertainty can be quite disastrous
when, in fact, there are measurement
issues. In part, that feature, as Janet
Yellen has pointed out, is due to the
fact that rules based on natural rate
concepts tolerate significant departures
of inflation from target when natural
rates are badly measured. For example,
if the monetary authority incorrectly
thought that current output was well
below potential, it would ease monetary policy and tolerate additional inflation. The rules that instead respond
to changes in economic activity are
not as forgiving because economic activity is much more precisely measured,
and inflation is, therefore, less likely to
drift from target.

The substitution of responding to changes in
economic activity rather than responding to the
level of some gap is also reminiscent of the study
by Bennett McCallum and Edward Nelson, who
reach this conclusion using a model that is different from that of Orphanides and Williams.

The 2003 study by Orphanides
provides additional intuition as to why
gap-type rules perform badly when
both inflation and gaps are mismeasured in real time. With mismeasurement, these types of rules essentially
introduce a policy error into monetary
policy. The interest rate set by the central bank responds to measurement error because the interest rate is not only
responding to the true gap but also to
the error in measuring that gap. The
induced policy error, in turn, affects
the economy, increasing the variance
of both output and inflation.
The exercises in the 2002 study
by Orphanides and Williams and the
2003 study by Orphanides are, to
our minds, not just mere theoretical
curiosities but are indicative of actual
problems that have occurred when policy has been based on gaps and when
these gaps have been badly measured.
A particularly powerful example is given in the 2002 study by Orphanides, in
which he discusses the Great Inflation
of the 1970s. While we don’t believe
that mismeasurement is the sole reason
for the stagflation of that era, we do
believe it was a contributing factor.18
The economic experience of the
1970s was indeed a disaster, and monetary policy played a role in the decade’s dismal economic performance.
Part of the problem appears to have its
foundation in basing monetary policy
on unemployment gaps. Persistent errors in measurement lead to persistent
errors in policy.
Over much of the 1970s realtime estimates of the natural rate of
unemployment indicated that the
economy was operating below its fullemployment potential when in fact
the opposite was true. This mispercep-

17

Another potentially important aspect was
that individuals began to believe that the Fed
had raised its inflation target. We will return
to this feature when we discuss the role of
learning.

18

www.philadelphiafed.org

tion lent an inflationary bias to policy
over that period. Thus, had the Fed
been responding to inflation and the
unemployment gap by following a classic Taylor rule over this period, the
misperceptions about both potential
unemployment and forecasts of current
inflation would have led to funds rate
settings that were very close to what
actually occurred.19 Thus, the FOMC
might have believed it was operating
according to a well-designed policy
rule, when in fact the errors induced
by misperceptions about key variables
implied a policy that acted as if the
inflation target was increasing.
On the other hand, the 2002
study by Orphanides and Williams
also indicates that during the strong
growth of the late 1990s, the Fed
was not responding to gaps but was
following policy rules that incorporated economic growth. By adhering
to this alternative type of rule, which
responds aggressively to deviations
of inflation from target and to economic growth, the Fed averted a large
deflation that would have occurred if
it had, in fact, been paying attention
to unemployment gaps. According to
the book by Robert Hetzel, former Fed
Chairman Alan Greenspan’s dismissal
of the relevance of gaps as a basis for
setting monetary policy had its precursor under the regime of William
McChesney Martin. During most of
Martin’s tenure as Chairman, the Fed
raised interest rates early on in recoveries, responding to economic growth
rather than gaps.20
To summarize, the lessons from

Stanford economist John Taylor developed a
formula to suggest how a central bank should
set short-term interest rates as economic conditions change to achieve both its short-run goal
for stabilizing the economy and its long-run goal
for inflation.
19

William McChesney Martin served as Chairman of the Federal Reserve from April 1951 to
January 1970.

20

www.philadelphiafed.org

this literature for policymakers when
responding to statistical measures of
a gap are (1) statistical gaps should
not be a major contributing factor in
implementing policy, (2) policy should
aggressively respond to inflation when
it moves away from target, (3) it is appropriate to take measures of economic
growth into account when deciding on
the level of short-term interest rates,
and (4) there is a role for gradualism or
inertia in policy.
UNCERTAINTY DUE TO
LEARNING
Another type of uncertainty arises
because individuals may not be fully
aware of the underlying theoretical
model that explains the economy, even
when such a model exists. In this case,
individuals may look at actual data
and try to infer from the data what will
happen in the future. That is, their
economic forecasts will depend on
statistical inference based on histori-

best policy designed under the assumption that individuals know the true
model of the economy performs very
poorly when, in reality, individuals
don’t know the model and forecast the
future based solely on historical data.
To set the stage more precisely, we
examine their analysis in a bit more
depth. Their model, like most models
used for policy analysis, is one in which
there is a trade-off between stabilizing
inflation and stabilizing unemployment. One cannot fully stabilize both
inflation and unemployment. The
central bank can stabilize inflation to
a greater extent, but doing so leads to
more economic volatility. The reverse
is also true, so the central bank tries to
stabilize both variables as best it can.
Doing so requires the central bank
to react to deviations of inflation from
target and unemployment from its natural rate, raising the interest rate when
inflation is too high and lowering the
interest rate if unemployment is above

To understand how policy design is affected
by learning when individuals have an imperfect
understanding of the economy, we need to
first understand how the presence of learning
affects economic outcomes.
cal data and not on a deep theoretical
understanding of the economy. In this
case, the central bank’s own actions
affect what individuals believe about
the actions the central bank will take
in the future and cause individuals to
update their beliefs about the future.
It turns out that in such a situation, the best monetary policy will be
substantially different from the best
policy that would arise if everyone
knew how the economy operated. The
effects of this type of uncertainty are
dealt with in the 2006 and 2007 papers
by Orphanides and Williams. A striking feature of their results is that the

its natural rate. Thus, their economic
model embeds important real-world
characteristics.
To understand how policy design
is affected by learning when individuals have an imperfect understanding of
the economy, we need to first understand how the presence of learning
affects economic outcomes. Basically,
learning gives rise to more volatility and persistence in the economy.
Relative to knowing exactly how the
economy works, individuals are less informed and, therefore, make mistakes.
Thus, economic activity is influenced
not only by fundamental shocks to
Business Review Q1 2012 7

the economy but also by misperceptions due to learning. The effect of
economic disturbances becomes more
prolonged because it takes time for
individuals to learn.
For example, if inflation goes up
in response to some economic disturbance, inflation will be higher than
individuals originally thought. This
higher inflation will lead them to make
a forecasting error: They will forecast
higher inflation in the future, and importantly, they may reassess the value
of the central bank’s inflation target.
Their misperceptions will, to some extent, be realized. Firms, whose expectations of future inflation rise, raise their
prices and inflation does, in fact, rise.
As the effect of the economic disturbance wears off, individuals’ forecasts
of inflation will become more closely
aligned with what they would have
forecast if they had perfect knowledge
of the economy. However, the deviation of the forecast under imperfect
knowledge from that under perfect
knowledge persists for a while, and that
deviation leads to more persistence in
unemployment and inflation.
The effects of learning on the
actual behavior of inflation can be
even more dramatic and more harmful
if changes in inflation lead individuals
to reassess the central bank’s inflation target. In those circumstances,
individual expectations of inflation
and the goals of the central bank can
become unhinged. The result can be
economic instability.
Understanding that individuals
are learning, the monetary authority
can improve economic performance
by taking these features into account
when designing policy. For example,
the central bank should be more aggressive when reacting to deviations
of inflation from target. By doing so, it
reduces the persistence of inflation and
reduces the consequences that arise
when individuals gradually learn about
the economy. It also reduces the prob8 Q1 2012 Business Review

ability that individuals will reassess
the underlying goal for inflation. For
example, if the monetary authority reacted so vigorously to changes in inflation that inflation never changed, then
individuals would have no problem
forecasting inflation. It would always
be at the target. Individuals would
make no forecasting mistakes with
respect to inflation, and there would
be no deleterious effects from learning
on economic activity – at least with
regard to inflation.
Perfectly targeting inflation,
however, is not desirable because it
would create too much volatility in
unemployment. Recall the trade-off.
However, there is now an added cost of
inflation volatility in an environment
where individuals learn. Volatility in
inflation makes it harder to learn and
hence to forecast future inflation. It
is now beneficial for the central bank
to react more strongly to changes in
inflation. Also, as in the previous
discussion, it is worthwhile to react to
changes in unemployment and to not
rely solely on output gaps when conducting policy.
Not reacting aggressively to inflation and responding vigorously to
output gaps may have played a significant role in the rising inflation and
stagflation of the 1970s. This thesis is
persuasively argued in a 2005 paper by
Orphanides and Williams and serves
to validate the thesis set forth in Orphanides’ 2002 paper. In their study,
Orphanides and Williams postulate
that during the large oil-price shocks
in the 1970s, it is reasonable to assume
that individuals were constantly learning and updating their beliefs about
the economy. In addition, the authors
re-document the extreme real-time
mismeasurement of the natural rate of
unemployment in official estimates. In
particular, real-time measures of the
natural rate greatly underestimated
the true natural rate. Further, the
FOMC at the time was aggressively

responding to unemployment gaps in
an effort to stabilize the economy. The
misperception of the unemployment
gap led to persistent, overly expansionary monetary policy to the extent that
public perceptions of the Fed’s desired
inflation rate began to rise and inflation expectations became unhinged. In
other words, the Fed lost credibility for
maintaining price stability. The result
was stagflation: rising inflation and a
severe economic contraction.
Orphanides and Williams then
analyze two interesting hypothetical
situations in a model economy similar
to the one alluded to above. The first
hypothetical question is: What if the
FOMC had responded to the economy more like the subsequent policy
instituted by Paul Volcker, where
less weight was placed on stabilizing
unemployment or, more generally,
economic activity? The answer is that
both unemployment and inflation
would have been considerably lower.
The second hypothetical question is:
What if the FOMC had paid no attention at all to the unemployment
gap? In that case, both inflation and
unemployment would have been even
lower still. Thus, an overemphasis on
economic stabilization can in practice
have serious economic consequences,
which, in theory, can be avoided by responding aggressively to deviations of
inflation from target and placing less
emphasis on economic stabilization in
the policy rule.
SUMMARY
In this article, we have examined how two types of uncertainty
— uncertainty from badly measured
variables and uncertainty that arises
because individuals do not fully understand how the economy operates
— affect the design of monetary policy.
The message from both examples is
qualitatively the same. The central
bank should acknowledge the existence of the uncertainty and formulate
www.philadelphiafed.org

its response to the economy accordingly. Ignoring the uncertainty generally
leads to policies that do rather poorly
and can be significantly improved.
Taking account of the types of
uncertainty that we describe in this
article and which we think are signifi-

cant sources of uncertainty in reality
leads to monetary policies that aggressively respond to inflation and that
also respond to economic growth. Of
interest is that policy should downplay
the role of output and unemployment
gaps and that policy should be very in-

ertial, reacting gradually to economic
disturbances. In the current economic
environment, we believe the overriding message for future policy is that an
overreliance on the magnitude of any
particular gap is likely to yield results
that could be greatly improved. BR

Armenter, Roc. “Output Gaps: Uses and
Limitations,” Federal Reserve Bank of
Philadelphia Business Review (First Quarter
2011).

Orphanides, Athanasios. “Monetary
Policy Rules Based on Real-Time Data,”
American Economic Review, 91:4 (September 2001), pp. 964-85.

Plosser, Charles I. “Credibility and Commitment,” speech delivered to the New
York Association for Business Economics,
New York, March 6, 2007.

Clarida, Richard, Jordi Gali, and Mark
Gertler. “The Science of Monetary Policy:
A New Keynesian Perspective,” Journal of
Economic Literature, 37 (December 1999),
pp. 1661-1707.

Orphanides, Athanasios. “Monetary
Policy and the Great Inflation,” American
Economic Review Papers and Proceedings,
92:2 (May 2002), pp. 115-20.

Plosser, Charles I. “Output Gaps and Robust Policy Rules,” speech delivered to the
2010 European Banking & Financial Forum, Prague, The Czech Republic, March
23, 2010.

REFERENCES

Croushore, Dean. “Revisions to PCE Inflation Measures: Implications for Monetary
Policy,” Federal Reserve Bank of Philadelphia Working Paper No. 08-8.
Dotsey, Michael. “Commitment Versus
Discretion in Monetary Policy,” Federal
Reserve Bank of Philadelphia Business Review (Fourth Quarter 2008), pp. 1-8.
Dotsey, Michael. “Monetary Policy in a
Liquidity Trap,” Federal Reserve Bank
of Philadelphia Business Review (Second
Quarter 2010), pp. 9-15.
Dotsey, Michael, and Charles I. Plosser.
“Commitment Versus Discretion in
Monetary Policy,” Federal Reserve Bank
of Philadelphia 2007 Annual Report, pp.
4-17.
Giannoni, Marc P., and Michael M. Woodford. “Optimal Interest Rate Rules: II. Applications,” National Bureau of Economic
Research Working Paper 9420 (January
2003).
Hetzel, Robert L. The Monetary Policy of
the Federal Reserve: A History. Cambridge:
Cambridge University Press, 2008.
McCallum, Bennett T. “Should Monetary
Policy Respond Strongly to Output Gaps?”
American Economic Review Papers and Proceedings, 92:2 (May 2001), pp. 258-62.
McCallum, Bennett T., and Edward Nelson. “Performance of Operational Policy
Rules in an Estimated Semi-Classical
Structural Model,” in John B. Taylor, ed.,
Monetary Policy Rules. Chicago: University
of Chicago Press, 1999.
www.philadelphiafed.org

Orphanides, Athanasios. “Monetary
Policy Evaluation with Noisy Information,”
Journal of Monetary Economics, 50:3 (April
2003), pp. 605-31.
Orphanides, Athanasios, and Simon van
Norden. “The Unreliability of Output
Gap Measures in Real Time,” Review of
Economics and Statistics, 84:4 (November
2002), pp. 569-83.
Orphanides, Athanasios, and John C.
Williams. “Robust Monetary Policy Rules
with Unknown Natural Rates,” Brooking
Papers on Economic Activity (2002), pp.
63-118.
Orphanides, Athanasios, and John C.
Williams, “The Decline of Activist Stabilization Policy: Natural Rate Misperceptions, Learning, and Expectations,” Journal
of Economic Dynamics and Control, 29
(2005), pp. 1927-50.
Orphanides, Athanasios, and John C.
Williams. “Monetary Policy with Imperfect
Knowledge,” Journal of the European Economic Association, 4:2-3 (April-May 2006),
pp. 366-75.
Orphanides, Athanasios, and John C.
Williams. “Inflation Targeting Under
Imperfect Knowledge,” in F. Mishkin and
K. Hebbel-Schmidt, eds., Monetary Policy
Under Inflation Targeting. Santiago: Central
Bank of Chile, 2007, pp. 77-123.
Orphanides, Athanasios, and John C.
Williams. “Learning, Expectations Formation, and the Pitfalls of Optimal Control
Monetary Policy,” Journal of Monetary Economics, 55 (2008), pp. S80-S96.

Schmitt-Grohe, Stephanie, and Martin Uribe. “Optimal Simple and Implementable Monetary and Fiscal Rules,”
Journal of Monetary Economics, 54:6 (September 2007), pp 1702-25.
Sill, Keith. “Inflation Dynamics and the
New Keynesian Phillips Curve,” Federal
Reserve Bank of Philadelphia Business Review (First Quarter 2011).
Stock, James H., and Mark W. Watson.
“Why Has U.S. Inflation Become Harder
to Forecast?” Journal of Money, Credit and
Banking, Supplement to 39:1 (February
2007), pp. 3-33.
Stock, James H., and Mark W. Watson.
“Phillips Curve Inflation Forecasts,” in
Understanding Inflation and the Implications
for Monetary Policy: A Phillips Curve Retrospective, proceedings of the Federal Reserve
Bank of Boston’s 2008 annual economic
conference, Cambridge, MA: MIT Press,
2009.
Taylor, John B., and John C. Williams.
“Simple and Robust Rules for Monetary
Policy,” Federal Reserve Bank of San Francisco Working Paper 2010-10 (April 2010).
Woodford, Michael M. “Optimal Monetary
Policy Inertia,” manuscript (May 1999).
Yellen, Janet L. “Comments and Discussion,” Brooking Papers on Economic Activity
(2002), pp. 126-35.

Business Review Q1 2012 9

Risk and Uncertainty*

M

by Pablo A. Guerron-Quintana

any news reports and economic experts talk
about uncertainty. But what does the word
mean in an economic context? Specifically,
what do economists have in mind when they
talk about it? In this article, Pablo Guerron-Quintana
discusses the concepts of risk and uncertainty, what
the difference is between the two terms, and why their
presence in the economy may have widespread effects. He
also talks about measuring risk at the aggregate level —
that is, risk that affects all participants in the economy
— and he reviews the various types of risk measures that
economists have proposed.

Many news reports and economic experts talk about uncertainty.
Take, for example, the recent discussion about the U.S. budget situation.
Although several proposals have been
offered that aim to achieve a fiscally
sustainable budget, we do not know
with certainty which measures will
ultimately be adopted or their timeline.
According to some economists, this
uncertainty seems to have contributed
to a slowdown in investment, hiring,
and economic activity and has the
potential to affect our standard of liv-

Pablo GuerronQuintana is an
economic advisor
and economist
in the Research
Department of
the Philadelphia
Fed. This article
is available free
of charge at www.philadelphiafed.org/
research-and-data/publications.
10 Q1 2012 Business Review

ing. But what does uncertainty mean?
More important, what do economists
have in mind when they talk about it?
This article will discuss the concepts of risk and uncertainty and why
their presence in the economy may
have widespread effects. We will also
talk about measuring risk at the aggregate level, that is, risk that affects
all participants in the economy. Different measures of this aggregate risk
have been proposed: (1) disagreement
among forecasters, (2) stock market
volatility, (3) interest rate volatility,
and (4) tax rate volatility. Each of
these measures has its pros and cons.
Over the years, the concepts of
risk and uncertainty have often been
used interchangeably in the popular
press, but economists have long distin-

*The views expressed here are those of the
author and do not necessarily represent
the views of the Federal Reserve Bank of
Philadelphia or the Federal Reserve System.

guished between the two. Indeed, the
concept of uncertainty was probably
first introduced to economics by Frank
Knight in his 1921 treatise Risk, Uncertainty, and Profit.1 Knight drew the
distinction between risk – unknown
outcomes whose odds of happening
can be measured or at least learned
about – and uncertainty – uncertain
events that we do not even know how
to describe. Economists often label
these ideas Knightian risk and Knightian
uncertainty, although sometimes they
are called objective uncertainty and subjective uncertainty. (See Uncertainty Is
Different from Risk.)
Risk can affect us at an individual
level. In our daily lives, we get hit by
unanticipated events such as accidents
or diseases or being hired for a dream
job or even winning the lottery. While
the last two examples are pleasant
surprises, the first two events involve
physical and mental strain and potential monetary losses. Since most of us
dislike facing stressful situations, we
modify our behavior when bad luck
knocks on our door. For instance, we
buy insurance to protect us from the
monetary loss we could sustain from
car accidents or the cancellation of a
vacation trip. Furthermore, the knowledge that we may lose our job can be
strong enough to deter us from taking
that well-deserved vacation. All of
these examples provide powerful reasons why we may want to learn more
about risk.

1
The interest in uncertainty in economics seems to coincide with a broader wave of
interest in the topic in science, as reflected
by Heisenberg’s 1927 work on uncertainty in
physics.

www.philadelphiafed.org

Uncertainty Is Different from Risk

T

o understand the difference between
risk and uncertainty, let’s consider the
experiment of flipping a fair coin (Case
A). In this experiment, the unknown is
whether the coin will land heads or tails.
Since we are dealing with a fair coin,
we know that the odds of heads after each flip are 50-50.
That is, if we were to flip the coin let’s say 100 times,
the coin would land, on average, 50 times heads and 50
times tails. The crucial insight from this experiment is
the observation that we know exactly the odds of each of
the possible events: 50 percent heads and 50 percent tails.
Furthermore, we have this knowledge before starting the
experiment. This is precisely the essence of risk: We can
describe the odds of the unknowns.
Now let’s consider an alternative experiment (Case
B). As before, we are interested in learning the result of
flipping a coin. The key difference is that we know the
coin is no longer fair, but we do not know the odds of obtaining heads. Furthermore, the coin is replaced by a new
(and unfair) coin after each flip.a Under this scenario, the
only thing we know is that the coin will land either heads
or tails. If we were thinking about flipping the coin 100
times, we could not (before we start the experiment) tell
how many times the coin will land on heads. This is an
example of Knight’s uncertainty.
Another way to see the difference between risk and
uncertainty is as follows. Suppose 100 people are asked to
place odds on the coin landing on heads in experiments
A and B. In Case A, people would agree that the odds are
50-50, but in Case B, their assessment would range from
0 to 100 percent. Furthermore, those people would prefer
to bet on getting heads in experiment A than on getting
heads in experiment B.b
The concept of uncertainty goes beyond those situations in which we cannot establish the likelihood of
events. It also includes cases when we do not even know

the outcomes. An extreme example is as follows. Imagine that a person from the Midwest decides to vacation
in Volcanoland, a fictitious country buffeted by constant volcanic and seismic activity. If a sudden volcanic
eruption surprises our friendly Midwesterner, his lack of
knowledge and experience with volcanoes makes his immediate future quite uncertain. How long is the eruption
going to last? Does he have enough food and water? Is his
shelter safe? Our friend is asking himself these questions
because he is uncertain about the possible outcomes from
an eruption. In this example, we are aware that something has happened (an eruption), but we do not know its
potential consequences.
Assessing the impact of uncertainty is trickier. The
reason, as explained in the introduction, is that one cannot assign probabilities to the possible outcomes or one
does not know all the possible outcomes. This lack of
knowledge means that the consequences of uncertainty
can range from nothing to vast monetary losses.c To see
this point, let’s reconsider the case of tossing an unfair
coin 100 times. Suppose that we get $1 each time the
coin lands on heads and pay $1 otherwise. What we know
before flipping the coin is that we may make as much as
$100 (all trials land on heads) or we may lose $100 (all trials land on tails). Furthermore, any payment in between is
possible. The unfair nature of the coin makes it impossible for us to determine the expected payoff from entering
into this contest.
Now consider the case of the Midwesterner facing a
volcanic eruption in Volcanoland. What are the potential
consequences for this person? On the one hand, the only
annoyance our friend may face is ashes falling from the sky.
The uniqueness of this event also implies that if the eruption turns out to be violent, our friend may be risking a lot
more than a spoiled vacation. As with the case of the coin
tossing exercise, we cannot determine beforehand the potential losses from being exposed to a geologic contingency.

This assumption is needed to ensure that we cannot learn the odds of getting heads by repeatedly flipping the coin. If this were the case, after
the learning stage, we would be in a case essentially the same as that of flipping a fair coin, whose odds of landing on heads are a known constant,
although different from 50-50.

a

b

This preference to act on known rather than unknown probabilities is called the Ellsberg paradox (Ellsberg, 1961).

c

Larry Epstein and Tan Wang provide a comprehensive analysis of uncertainty.

The idea that risk can affect not
only our daily lives but also the overall
economy is not new. Indeed, in the
1930s, the English economist John
Maynard Keynes indicated that investors’ mood could lead to economic
www.philadelphiafed.org

downturns. He reasoned that investment was in part driven by investors’
view of the economy. If they are uncertain about the economy’s prospects,
they reduce investment, triggering a
downturn.

ASSESSING THE IMPACT OF
RISK
Risk can affect the economy in
at least two ways: through investment
and/or through savings. The current
“risky” scenario about where house
Business Review Q1 2012 11

prices are heading (up, down, or stable)
and whether interest rates are going up
makes the investment decision nontrivial. The optimal response to risky situations may be to wait and see. In other
words, households choose to delay investment (buying a house) until things
calm down. The reason is that individuals may face an adverse scenario
with high interest rates and a contraction in house prices. This possibility
makes investment quite risky, inducing
households to wait for better times.
Put differently, when facing uncertain
scenarios, investors must decide on the
timing of their investment decisions.2
But risk can affect savings as
well. Imagine that you owe credit card
debt and that your monthly payment
is $200. Suddenly, your credit card
company announces that interest rates
may go up next month. Moreover, the
company announces that if interest
rates go up, interest payments will
most likely double for some customers. Under these circumstances, you
may find it desirable to consume less
today and use that extra cash to repay
part of your debt. The additional cash
should be used to repay part or all of
your debt. If you choose otherwise, you
may face credit card payments as high
as $400 next month. Even more worrisome, because of those large payments,
you may have to cut your consumption
by a large amount tomorrow.
The previous example can be
extended to the case of countries.
Imagine that a country issues debt to
cover part of its investment and other
expenses. If the country’s creditors
disclose that interest rates may change
next month, the country may want to
repay part of its debt to reduce the future burden of interest rate payments.
In order to pay more today, the country needs to produce more. But inCommitting to early investment brings in extra returns, while waiting is beneficial because
of access to additional information. See the
article by Ben Bernanke.

2

12 Q1 2012 Business Review

creasing production takes time (hiring
more workers, building factories, and
so on). This means that the only way
the country can repay its obligations is
by cutting its expenses, that is, reducing consumption and investment. In
other words, the country needs to sell
more goods abroad (increase exports)
and buy fewer goods from abroad
(decrease imports). Since not all goods
can be exported (for example, haircuts, legal and medical services, and
houses), some industries will be forced
to produce less. This decline in production will result in higher unemployment for a segment of the population.
Obviously, how our decisions
change when we face risky situations
depends on our attitudes toward risk.
For instance, a gambler (a person who
loves taking additional risk) may well
opt to purchase a home with the hope
that prices will eventually recover.
The gambler understands there is a
big chance that prices may not recover
for a while. Yet the mere fact of taking
a chance gives him satisfaction and
hence drives him to bet on the housing
market. In contrast, a cautious person
may choose not to gamble on the
housing market and may refrain from
buying a house these days. For the
cautious person, the potential losses far
outweigh the benefits from buying a
house in a depressed market and hoping it will recover.3

In the context of an economic model, whereas
a gambler would correspond to a person whose
preferences are described by a linear utility
function, a risk-averse person — a cautious
person — has a concave utility function. If the
two persons were to invest in a risky project,
such as buying stocks, the gambler would
care only about the project’s payoff, since he
considers only his total consumption. He would
take on whatever project offers large rewards,
even though it may also entail large losses. In
contrast, the cautious person would also factor
in the odds that the project could fail. Even if
the promised payoff is large, a risk-averse person
may opt out of the project because the odds that
it will fail are too big. In other words, he would
rather have fewer swings in his income even if
that means a lower average income.

3

Since the presence of risk can
entail monetary losses, people try to
protect themselves by buying insurance. In simple terms, an insurance
contract transfers the risk of loss from
the policy holder to the insurer, usually
a large company. The contract typically sets a small and regular payment
to be made by the insured person. In

How our decisions
change when we
face risky situations
depends on our
attitudes toward risk.
exchange, the insurer promises to pay
the policy holder a given monetary
amount if certain events happen, as
defined in the contract. Some examples include having a car accident,
having a vacation trip cancelled, or being laid off from a job. In this last case,
the insured person is a worker and the
insurer is the federal government and/
or the state.
But accidents happen; people get
sick; workers get laid off. More important, these unpleasant events happen
more frequently than we would like.
So why do insurance companies exist?
One reason is that the insurer and the
policy holder may have different views
about the odds that an event will occur. To illustrate my point, imagine
a person who is afraid of flying. His
pessimistic view about air transportation leads him to look for insurance.
In contrast, an insurance company
knows that flying is the safest medium
of transportation. The odds of an incident are very small, so the insurer is
more than willing to extend a policy to
the concerned flyer.4
Even if the insurer and the policy
holder have the same assessment of
Indeed, the odds of dying in a plane crash for
the average American is about 1 in 11 million.

4

www.philadelphiafed.org

the odds that an event will occur, the
insurer may still be willing to extend a
policy to the insured person. For example, this is the case with car insurance.
For instance, a car owner who lives in
a crowded city has a greater probability of being involved in an accident,
a situation that requires payments
from the insurer to the policy holder.5
To reduce their exposure to this type
of event, insurance companies offer
policies to a large number of drivers.
Since car accidents tend to be isolated
events, the likelihood of an insurance
company facing accident claims from
all its insured customers at the same
time is very low. Hence, although the
insurer may need to make frequent
payments, the insurer is also receiving
payments (premiums) from those policy holders who have not been involved
in an accident or the deductibles from
those who have been. In this way, the
insurance company has enough funds
to pay its insured customers who have
car accidents.
MEASURING RISK:
SOME BASICS
From the discussion in the previous sections, it should be clear that risk
can influence our lives. Obviously, the
influence of risk depends on the circumstances under which it affects us.
For example, consider the risk associated with the weather. Under normal
circumstances, a day with bad weather
means that we may be late getting
to work; that is, the expected loss —
the risk — is low. But in some cases,
the risk can be high. Imagine if you
missed an interview for your dream job
because of bad weather. The stakes are
even higher when we think of the risk
associated with buying a house or a
government that is considering issuing
bonds. In the first case, risk arises from
Eric Smith and Randall Wright analyze the
interesting issue of why car insurance is so
expensive in certain metropolitan areas.
5

www.philadelphiafed.org

fluctuations in the price of houses, and
in the second case, the variability of
interest rates (and hence the cost of issuing bonds) matters. The bottom line
in these examples is that understanding the consequences of risk requires
measuring it. Once we have a measurement, we can then take actions such as
postponing the purchase of a house or
buying insurance.
Economists have proposed different measures of risk: (1) disagreement
among forecasters, (2) stock market
volatility, (3) fluctuations in interest
rates, and (4) fluctuations in tax rates.6
Disagreement Among Forecasters. Imagine that today is a bright
and sunny day. If you were asked to
forecast the weather for the afternoon,
assuming that you don’t have access to
a weather forecast service, you would
most likely answer “a sunny afternoon.” In fact, everyone would agree
with you. Now imagine that today is
sunny, but a few clouds lurk on the
horizon. The presence of those clouds
makes forecasting the weather for this
afternoon more difficult. Some people
may forecast a sunny afternoon; others
may guess a cloudy but dry afternoon,
while a third group may forecast a
rainy afternoon.
The idea behind the last example
is that periods of elevated risk are associated with very imprecise forecasts
about future events. In other words, the
more risky the event, the harder it is to
forecast and, therefore, the larger the
disagreement among forecasters. In our
example, the risky situation arises from
those clouds on the horizon. Rather
than the weather, economists are frequently interested in the total number
of goods that an economy produces,
that is, a country’s gross domestic product (GDP). Hence, our first measure

6
Economists have proposed other ways to
measure risk. The interested reader is invited
to consult the article by Nicholas Bloom, Max
Floetotto, and Nir Jaimovich.

of risk comes from the forecasters’ disagreement about what the growth rate
of GDP is going to be a year from now.
This measure is published quarterly by
the Federal Reserve Bank of Philadelphia in the Survey of Professional
Forecasters. It is the percent difference
between the 75th and 25th percentiles
of the one-year-ahead projections for
U.S. real gross domestic product.
Figure 1 shows that the degree of
riskiness (measured by forecast dispersion) was large in the 1970s, in particular, during the oil embargo of 1974 and
at the beginning of the Fed’s disinflationary era around 1979. The figure
also suggests that disagreement has
diminished during the 1990s and the
first half of the 2000s. This decline coincides with what economists call the
Great Moderation, that is, the period
between 1984 and 2007 characterized
by two relatively mild recessions and,
in general, moderate fluctuations in
the economy. During this period, the
increasing agreement among forecasters resulted from the more stable, and
thus more predictable, economy. This
reasoning has led some observers to
argue that the prolonged boom prior
to the recent crisis arose from a stable
economy.7 This stability stimulated
consumption and investment. To meet
higher demand, firms increased their
production by expanding their facilities
(additional investment) and increasing
employment.
Another look at Figure 1 reveals a
rise in risk since the start of the 2007
financial crisis. The highest level of
risk happens by the end of 2008, which
coincides with the collapse of Lehman
Brothers. What makes the 2007-2010
episode different from other periods over the last 20 years is that risk
remained heightened for more than a
year. With so much risk around, it is
not surprising that firms and house7
See the study by James Stock and Mark
Watson.

Business Review Q1 2012 13

holds postponed their purchasing and
investing decisions. Interestingly, the
improvement in the economy of recent
months seems to coincide with a decline in risk. Note how the measure at
the end of 2010 is getting close to its
pre-crisis levels. 8
A simple way to make sense of
the numbers in Figure 1 is as follows.
You and I own an apple tree, and we
are interested in forecasting our tree’s
annual production. Furthermore, let’s
suppose that our disagreement over
the years is represented by Figure 1. In
the first quarter of 1980, our forecast
disagreement reached an all-time high
of almost three. This means that at
that moment, if I had forecasted that
our tree would produce 100 apples in
1981, your forecast would have been
103.9 Now, let us move forward to
March 2007 when our disagreement
was the lowest (0.4). At that point, if
my forecast was 100 apples, you would
have forecasted 100.4 apples. We were
essentially making the same forecast.
After the turbulent financial events
of 2008, our disagreement rose to 1.5
apples and remained at that level for
most of 2009.
Stock Market Fluctuations. During times of high risk, new information about the state of a company
(for instance, its profits and prospects
for future projects) tends to arrive
frequently. In response to the arrival
of information, investors buy and sell
stocks in the company quite frequently.
As a result, the stock price of the
company fluctuates substantially in the
short run. The more uncertain inves-

8
Of course, the causality could go the other
way around: Periods of high growth promote
tranquil times and hence low risk. In a recent
paper, Scott Baker and Nicholas Bloom use
stock market information from several countries
to argue that the causality runs from risk to
economic growth.
9
For simplicity, I assume in this example that
I am the person making the conservative
forecast.

14 Q1 2012 Business Review

FIGURE 1
U.S. Real GDP Growth Forecast Dispersion

Source: Survey of Professional Forecasters from the Federal Reserve Bank of Philadelphia,
quarterly data 1970:Q1 - 2010:Q3

tors are about a company, the more
they bet up or down on that company’s
stock. Hence, our second measure of
risk comes from the variability (volatility) in the stock prices of companies
publicly traded on the New York stock
exchange. This indicator (displayed in
Figure 2) is closely tracked by financial
practitioners, since it is considered a
measure of investor sentiment: The
higher stock market volatility is, the
more pessimistic investors are, that is,
the greater the expectation that the
market will fall. But recall that worried
investors tend to wait and see. Hence,
a sudden and persistent increase in
stock market volatility may be signaling weak demand down the road and
a potential contraction in the overall
economy. It is this linkage between
stock market volatility and economic
activity that has made our second
measure of risk popular both in academia and in policy circles. (See the
studies by Nicholas Bloom.)
Based on Figure 2, it is clear that
periods of economic and financial

turmoil are associated with strong
fluctuations in the stock market.10
For example, the market was more
volatile during the oil embargo of 1974
or the Asian financial crisis and the
collapse of dot-com companies in the
late 1990s. Similarly, the stock market
crash of October 1987 resulted in a
large spike, albeit temporary, of our
measure of risk.11 Figure 2 also shows
that the U.S. economy enjoyed a
period of tranquility and low risk starting around 1988 and extending into
1997. More recently, the onset of the
mortgage crisis (2007) and the demise
of Bear Stearns (March 2008) and
The U.S. stock market volatility is taken from
the article by Nicholas Bloom. The measure
corresponds to the Chicago Board of Options
Exchange VXO index of implied volatility from
1986 onward. Prior to 1986, actual volatility in
monthly returns is calculated as the monthly
standard deviation of the daily S&P 500 index.

10

Some economic observers attributed this
quick reversal in risk to the Federal Reserve System’s (and its then-Chairman Alan
Greenspan’s) swift actions to support financial
markets. See the paper by Mark Carlson.

11

www.philadelphiafed.org

FIGURE 2
Stock Market Volatility: 1963 - 2011

Source: Nicholas Bloom. Monthly data 1963:M1 - 2011:M1

Lehman Brothers (September 2008)
shook financial markets. Figure 2
reveals that our measure of risk rose in
response to those events. In fact, risk
reached its all-time high in October
2008 and remained elevated for most
of 2009.
An advantage of the stock market volatility measure is that it goes
back to the 1960s and therefore allows us to illustrate how risk responds
to political events. For example, the
spike in risk at the beginning of 1964
coincides with President Kennedy’s
assassination. Moving forward, the
Cambodian campaign and the Kent
State shooting in 1970 pushed risk
up.12 Finally, the attacks on the World
The shooting at Kent State University (Kent,
Ohio) resulted in four people being killed and
nine others wounded. Students were protesting the Vietnam War. The shooting happened
just days after President Nixon announced
the launch of the Cambodian incursion. This
military action was intended to defeat North
Vietnam’s troops using the eastern part of Cambodia to stage attacks on South Vietnam.

12

www.philadelphiafed.org

Trade Center and the Pentagon in
September 2001 are also associated
with more risk in the market.
To make sense of the numbers
in Figure 2, let’s consider the following example. You own stock in a large
group of leading companies in diverse
industries in the U.S.13 You are interested in learning the odds that the
return on your portfolio will move up
or down by 10 percent next month. If
you were wondering this in October
2008 and asking about your return in
November 2008, the results in Figure 2
imply that the odds are roughly 50 percent that the return on your portfolio
will move up or down by 10 percent. In
contrast, if you were asking the same
question in December 2006, you would
conclude that the chances that your
returns would go up or down by 10
percent is practically 100 percent. This
More precisely, you own stock in each of the
500 companies that are part of the S&P 500
index.

13

means that you are almost certain that
the returns to your portfolio would
not exceed +/–10 percent in January
2007.14 This is because stock market
volatility was so low in December 2006
that sudden changes in stock prices
and hence abrupt movements in stock
returns were very unlikely.
I must stress that when stock
market volatility is high, it does not
necessarily mean that the market expects a sharp decline in stock prices.
It only means that the market expects
that sudden price movements in either
direction (up or down) are more likely.
Since most people tend to be concerned
about losses, investors seem to dislike
high stock market volatility (high risk)
because it signals that a sharp collapse
in stock prices is more likely.
Interest Rate Volatility. An alternative description of risk results from
direct measures of fluctuations in interest rates. Such measures have been
used recently in papers that try to assess the impact of risk on the economy.
(See my paper with Jesus FernandezVillaverde, Juan Rubio-Ramirez, and
Martin Uribe.)
The idea behind the measure of
interest-rate volatility is that people
tend to trade (sell or buy) bonds very
frequently during periods of high
risk. This frequent exchange of bonds
makes their price fluctuate substantially, which results in large swings in
interest rates.15 Hence, periods of large

These numbers were computed following the
interpretation outlined in the study by Robert
Whaley. Succinctly, the probability is computed
by asking ourselves what is the probability that a
random normal variable falls within σ standard
deviations from 0. Here, σ =
, Er is the
anticipated movement in the asset return, and
VIX is the stock market volatility in Figure 2. In
our first example, the values are Er = 10 percent
and VIX = 50 percent, which implies σ = 0.69
or a probability of 50 percent. If the VIX drops
to 10 percent, then σ = 3.46, which, based on a
normal distribution, implies a probability of 1.
14

The price and interest rate of a bond are inversely related, so any movement in prices translates directly to fluctuations in interest rates.

15

Business Review Q1 2012 15

fluctuations (volatility) in interest rates
are interpreted as episodes in which
risk is high. As an example, Figure 3
illustrates the evolution of our interestrate risk measure for Argentina. A
quick look at this figure reveals that
risk in Argentina was high in early
1998 and again during the period 2001
to 2004.16
To understand these changes in
risk, some background information
about Argentina is necessary. The
1990s were mostly a boom period for
Argentineans (presumably due to
economic reforms introduced early
in that decade). The country experienced sustained economic growth and
stable prices. In the eyes of investors,
Argentina was an example for other
countries to follow. However, this
stability started to collapse around
1998 when several East Asian countries experienced financial difficulties,
forcing them to stop payments on their
debt obligations to international lenders. Although Argentina was in better
economic health than the defaulting
countries, nervous lenders worldwide
feared that Argentina (and other
countries in South America) would
follow suit. Investors could not assess
how much the Argentinean economy
would be affected by the collapse of
Asian economies. Ultimately, Argentinean debt was heavily traded during
this period, which resulted in sudden
fluctuations in interest rates and hence
a spike in risk.17 As time went by, it was
clear that Argentina would be able to

The Argentinean interest rate is the sum of
the real rate on the three-month U.S. Treasury
bill plus Argentina’s Emerging Markets Bond
Index+ (EMBI+). The T-bill rate is taken from
the St. Louis Fed’s FRED database. The EMBI+
index is published monthly by J.P. Morgan. The
risk measure in Figure 3 is constructed using the
econometric approach described in my paper
with Jesus Fernandez-Villaverde, Juan RubioRamirez, and Martin Uribe.

16

Interestingly, risk in the U.S. was also elevated
in the late 1990s, as shown in Figure 2.
17

16 Q1 2012 Business Review

FIGURE 3
Interest Rate Volatility in Argentina

Source: Jesus Fernandez-Villaverde et al. (2011). Monthly data 1997:M12 - 2004:M9

meet its obligations, so the country became less risky. This is reflected by the
drop in our measure of risk between
1999 and 2000.
After almost a decade of boom,
the Argentinean economy slowed
down in 2000 and contracted in
2001. At the same time, the Argentinean currency (the peso) was greatly
overvalued, which made Argentina’s
products more expensive than those
imported from abroad and hence reduced its exports. This decline in production and lack of exports meant that
fewer resources were available to repay
debt. In response, investors demanded
higher interest rates for loans extended
to Argentina. These tough economic
conditions led the country to default
(stop paying principal and interest on
its debt), which triggered the spike in
our measure of risk by the end of 2001.
Risk remained heightened for the next
two years as the country continued to
miss payments on its obligations.
Figure 3 shows that risk started to
decline around 2003. This improve-

ment seems to coincide with the beginning of Nestor Kirchner’s presidency. To some observers, the economic
policies implemented by Kirchner and
his predecessor (Eduardo Duhalde)
paved the way to an orderly recovery.
By the end of our sample period (August 2004), risk had reached its lowest
level in three years, since international
investors anticipated that Argentina
would eventually try to meet or renegotiate its debt obligations. Indeed,
in 2005, the country restructured its
obligations with roughly 75 percent of
its debt holders.18
A simple way to make sense of
the numbers in Figure 3 is as follows.
Imagine that you are living in Argentina in August 2000. You just bought a
new car with an adjustable interest rate
loan. The prevailing annual interest
rate at that point was about 8 percent.

Old bonds were replaced by new debt with
longer maturity and nominal value of between
25 and 35 percent of the original debt.

18

www.philadelphiafed.org

FIGURE 4
Capital Tax Rate Volatility

Source: Jesus Fernandez-Villaverde et al. (2012). Quarterly data 1970:Q1 - 2010:Q1

By construction, Figure 3 tells us that
there was a 68 percent chance that
the interest rate would go up or down
by 2 percentage points. This means
that in August 2000 you believed that
your interest rate could be as high as
10 percent or as low as 6 percent in
September 2000. Let’s move forward
to December 2001. Our risk measure
indicates that with a probability of 68
percent, your interest rate could jump
up or down by 7 percentage points!
This means that, all other things
equal, you could have faced interest
rates as high as 15 percent on your
car loan. For a principal of $10,000,
these numbers imply that whereas your
monthly payment in September 2001
could have been as high as $800, your
payment in December 2001 could have
been $1,170.19 Clearly, there is a non-

An annual interest rate of 10 percent is
roughly equivalent to 0.8 percent on a monthly
basis. Similarly, a 15 percent annual interest rate translates into a monthly rate of 11.7
percent.

19

www.philadelphiafed.org

trivial increase in your payments when
the economy gets riskier.
The Argentinean example teaches
us two important lessons about risk.
First, risk can be contagious. Even
though Argentina was a well-positioned economy in the late 1990s, it
suffered from substantial fluctuations
in its risk index. In this case, risk
was imported from financial turmoil
abroad. The second lesson is that risk
can arise from domestic factors. The
economic instability of Argentina and
its subsequent inability to meet its obligations at the end of 2001 resulted in
the massive spike in Argentina’s risk.
Here, there were no foreign elements
triggering the sudden change in interest rate fluctuations.
Tax Rate Volatility. A final
description of risk comes from fluctuations in tax rates. This notion was recently proposed in my paper with Jesus
Fernandez-Villaverde, Keith Kuester,
and Juan Rubio-Ramirez. The idea is
that governments tend to overhaul tax
systems during periods of fiscal strain

(such as the current one), which results
in substantial fluctuations in tax rates.
The worse the fiscal situation, the
more volatile the taxes are.
Figure 4 presents our new risk
measure based on the volatility of the
capital tax rate in the United States.20
The measure shows that risk associated with fiscal policy was high during
President Clinton’s first term. Indeed,
the Omnibus Budget Reconciliation
Act, which was signed into law in
1993, raised tax rates, affecting both
individuals and businesses. Similarly,
our risk measure rises during President
George W. Bush’s tax cuts in the early
2000s.
It is also apparent from Figure
4 that the recent financial crisis has
heightened the fiscal-related risk. Risk
was high between 2007 and 2009; only
in early 2010 does risk linked to fiscal
policy go back to pre-crisis levels.
In our paper we show that risk
associated with fiscal policy can slow
down the economy. The reason is that
volatility makes it difficult to forecast future tax rates on capital. As a
consequence, investors considering
investing in new projects may opt to
wait or completely skip those projects.
This is because investors fear that large
volatility may ultimately translate into
large future taxes, thus reducing the
profitability of their investments. If the
capital tax rate volatility is sufficiently
high, the decline in investment can
induce a general contraction in economic activity (lower production and
higher unemployment).
Imagine that you are back in the
fourth quarter of 1995. You just invested in a new project whose payoffs
are taxed at 35 percent. By construc-

The tax rate on capital corresponds to aggregate effective rates on capital income. The
risk measure in Figure 4 is constructed using
the econometric approach described in my
paper with Fernandez-Villaverde, Kuester, and
Rubio-Ramirez.

20

Business Review Q1 2012 17

tion, Figure 4 tells us that there was
a 68 percent chance that the capital
tax rate would go up or down by 0.5
percentage point. This means that in
December 1995, you believed that the
tax rate on capital income could be as
high as 35.5 percent or as low as 34.5
percent in March 1996. Let’s move forward to December 2001. Our risk measure indicates that with a probability
of 68 percent, your tax rate could jump
up or down by 1.4 percentage points!
This means that, all other things
equal, you could have faced a tax rate
on capital as high as 36.4 percent.

This sudden change in the tax rate is
sufficient to deter investment, at least
temporarily, and induce a contraction
in economic activity.
SUMMARY
This article introduced the economic concepts of risk and uncertainty. It provides clear and simple
definitions and examples of risk and
uncertainty. Furthermore, this article
shows that risk can have important
consequences for economic activity.
For example, an increase in the volatility of interest rates at which countries

borrow can induce a contraction in
consumption and investment.
Economists have proposed alternative measures of risk: (1) disagreement
among forecasters, (2) stock market
volatility, (3) interest rate volatility,
and (4) tax rate volatility. All of these
measures indicate that risk increases
during periods of political and economic turmoil, such as President Kennedy’s
assassination, the 1987 stock market
crash, and the recent financial crisis.
Furthermore, these measures show that
risk in the U.S. was low during the late
1980s and the first half of the 1990s. BR

Epstein, Larry, and Tan Wang. “Intertemporal Asset Pricing under Knightian
Uncertainty,” Econometrica, 63 (1994).

LeRoy, Stephen, and Larry Singell. “Knight
on Risk and Uncertainty,” Journal of Political Economy 95:2 (1987), pp. 394-406.

Fernandez-Villaverde, Jesus, Pablo Guerron-Quintana, Juan Rubio-Ramirez, and
Martin Uribe. “Risk Matters: The Real
Effects of Volatility Shocks,” American
Economic Review, 10:6 (2011), pp. 2530-61.

Santomero, Anthony. “Monetary Policy
in the Post 9/11 Environment: Stability
Through Change,” speech for the Global
Interdependence Center’s 22nd Annual
International and Monetary Trade Conference, held at the Federal Reserve Bank of
Philadelphia, October 2, 2003.

REFERENCES

Baker, Scott, and Nicholas Bloom. “Does
Uncertainty Drive Business Cycles? Using Disasters as a Natural Experiment,”
mimeo, Stanford University.
Bernanke, Ben. “Irreversibility, Uncertainty, and Cyclical Investment,” Quarterly
Journal of Economics 97:1 (1983).
Bloom, Nicholas. “The Impact of Uncertainty Shocks,” Econometrica, 77:3 (May
2009), pp. 623-85.
Bloom, Nicholas, Max Floetotto, and Nir
Jaimovich. “Really Uncertain Business Cycles,” mimeo, Stanford University (2009).
Carlson, Mark. “A Brief History of the
1987 Stock Market Crash,” Board of
Governors of the Federal Reserve System,
Finance and Economics Discussion Series
2007-13 (2007).
Ellsberg, Daniel. “Risk, Ambiguity, and
the Savage Axioms,” Quarterly Journal of
Economics 75:4 (1961).

18 Q1 2012 Business Review

Fernandez-Villaverde, Jesus, Pablo Guerron-Quintana, Keith Kuester, and Juan
Rubio-Ramirez. “Fiscal Volatility Shocks
and Economic Activity,” Federal Reserve
Bank of Philadelphia Working Paper 1132/R (January 2012).

Smith, Eric, and Randall Wright. “Why
Is Automobile Insurance in Philadelphia
So Damn Expensive?” American Economic
Review, 82 (1992), pp. 756-72.

Heisenberg, Werner. “Quantum Theory
and Measurement,” Zeitschrift für Physik 43
(1927), pp. 172–98.

Stock, James and Mark Watson. “Has
the Business Cycle Changed and Why?,”
NBER Macroeconomics Annual (2002).

Knight, Frank H. Risk, Uncertainty, and
Profit. Boston: Houghton Mifflin, 1921.

Whaley, Robert. “Understanding the VIX,”
Journal of Portfolio Management, 35 (Spring
2009), pp. 98-105.

www.philadelphiafed.org

Everything You Always Wanted to Know About
Reverse Mortgages but Were Afraid to Ask*
by Makoto Nakajima

M

ost people have probably heard of reverse
mortgage loans. But even though these loans
have been getting more attention lately, it’s
possible that many people still aren’t sure
about what reverse mortgages really are. This is not
surprising, since reverse mortgages are a relatively new
type of mortgage loan. Although reverse mortgages are
currently used by only a small fraction of people, their
popularity has been growing in recent years. In this
article, Makoto Nakajima discusses reverse mortgage
loans, particularly the most popular type, which is
administered by the government. He discusses who
uses reverse mortgage loans and how they are used and
compares the pros and cons of these mortgages.

You’ve probably heard of reverse
mortgage loans. But even though these
loans have been getting more attention in the media and in academia, it’s
possible that you’re still not sure about
what reverse mortgages really are.1

This is not surprising, since reverse
mortgages are a relatively new type of
mortgage loan — and very different
from the conventional type of mortgage — and they are used only by older
homeowners.

1
For media reports, see, for example, “Pros and
Cons of Reverse Mortgages” (Time, July 20,
2009); “Pimping Up Your Reverse Mortgage”
(Businessweek, February 5, 2007). Various
transgressions associated with reverse mortgages
made the list of “Six Problems the Consumer

Financial Protection Bureau Should Tackle
First” (Time, July 6, 2010). In particular, Time
and the Wall Street Journal (“Debate on ReverseMortgage Risks Heats Up,” December 14, 2010)
report that some banks and brokers push older
households into taking out reverse mortgages
in ways that are not necessarily beneficial for
the borrowers but ways in which banks and
brokers can earn large fees or other profits.
However, both also report that improved federal
guidelines regarding fees associated with reverse
mortgages have helped to lower the incidence of
such transgressions.

Makoto Nakajima
is a senior economist
in the Research
Department of
the Philadelphia
Fed. This article
is available free
of charge at www.
philadelphiafed.org/
research-and-data/
publications.
www.philadelphiafed.org

*The views expressed here are those of the
author and do not necessarily represent
the views of the Federal Reserve Bank of
Philadelphia or the Federal Reserve System.

Although reverse mortages are
currently used by only a small fraction
of people, their popularity has been
growing in recent years. Surprisingly,
their popularity continued to grow into
2009, but the growth of reverse mortgage loans may have started to decline
in 2010.2
This article discusses reverse
mortgage loans, particularly the most
popular type, which is administered
by the government. One feature that
makes government-administered
reverse mortgage loans attractive to
borrowers in an economic downturn
accompanied by a house price decline
is that this type of mortgage loan has
a built-in insurance against declines in
house prices. I will explain this feature
and other features of reverse mortgage
loans below.
ABCs of REVERSE MORTGAGE
LOANS
Nowadays, the most popular type
of reverse mortgage loan is administered by the government, while the private market for reverse mortgages has
been relatively shrinking. The government-administered reverse mortgage
is called a home equity conversion
mortgage (HECM). These mortgage
loans are administered by the Federal Housing Administration (FHA),
which is part of the U.S. Department
of Housing and Urban Development
(HUD). HECM loans represent over
In 2011, the two biggest lenders of reverse
mortgage loans, Bank of America and Wells
Fargo, decided to leave the reverse mortgage
market. Reasons given include the decline in
house prices and the inability to assess borrowers’ financial health, such as income (New York
Times, “2 Big Banks Exit Reverse Mortgage
Business,” June 17, 2011).

2

Business Review Q1 2012 19

90 percent of all reverse mortgages
originated in the U.S. market (see Hui
Shan’s article).3
When buying a house, especially a
first house, most people in the U.S. use
a conventional mortgage loan. With a
conventional mortgage, people make
a down payment, which is typically
around 20 percent of the house value,
and borrow the remaining value of the
house (around 80 percent).4 The borrower repays the principal and makes
interest payments on the outstanding
loan balance. As the borrower repays
the principal, he accumulates home equity. The typical repayment period is 30
years. When the borrower finishes repaying the loan, he owns 100 percent of
the equity in his house, free and clear.
How are reverse mortgages different from the conventional mortgages
described above? Below are the six
distinctive features of the governmentadministered HECM loans. First, as
the name suggests, a reverse mortgage
loan works in the reverse way from a
conventional mortgage loan. With a
reverse mortgage, instead of paying
interest and principal and accumulating home equity, reverse mortgages allow homeowners to borrow against the
home equity they have accumulated.
Second, reverse mortgage loans
have different requirements than conventional mortgage loans. These mortgages are available only to borrowers
age 62 or older. Also, borrowers must
be homeowners and must live in the
house. Properties eligible for HECM
loans are (1) single-family homes, (2)
one unit of a one- to four-unit home,
and (3) a condominium approved by
3
Many other reverse mortgage products, such as
Home Keeper mortgages, which were offered by
Fannie Mae, or the Cash Account Plan offered
by Financial Freedom, were recently discontinued, in parallel with the expansion of the
HECM market. See the article by Bruce Foote.
4
Mortgages with lower (or zero) down payments
were also used, especially during the period
leading to the recent downturn.

20 Q1 2012 Business Review

HUD. Finally, borrowers must have
repaid all or almost all of their other
mortgage loan at the time they take
out a reverse mortgage. Home equity
lines of credit (HELOCs) are similar
to reverse mortgage loans in that they
allow households to borrow flexibly
against accumulated home equity.
However, while the repayment of
HELOCs is based partially on the borrower’s income, repayment of reverse
mortgages is based solely on the value
of the house. This difference makes
reverse mortgages more readily avail-

to live in the same house, there is no
need to repay any of the loan amount.
There is no gradual repayment with a
fixed schedule, as with a conventional
mortgage loan or a HELOC; repayment is made in a lump sum from the
proceeds from the sale of the house.
Naturally, borrowers who manage to
live in the same house for a long time
benefit most from reverse mortgages.
Fifth, borrowers are insured
against substantial drops in house
prices. Borrowers (or their heirs) can
repay the loan either by letting the

When buying a house, especially a first house,
most people in the U.S. use a conventional
mortgage loan.
able for use than HELOCs, especially
for those with limited income after
retirement. According to Andrew
Caplin, many older homeowners fail
to qualify for conventional mortgage
loans because of income requirements.
In short, reverse mortgages are more
suitable for older homeowners who
own the house they live in and whose
income is relatively low.
Third, reverse mortgage borrowers
are required to seek counseling from a
HUD-approved counselor in order to
be eligible for a HECM loan. The goal
is to be certain that older borrowers
understand what kind of loan they are
getting and what the potential alternatives are before taking out a reverse
mortgage loan.
Fourth, repayment of the cash
received is due only when the house is
sold and all the borrowers move out or
when all the borrowers die.5 As long as
at least one of the borrowers continues

Other incidents may make reverse mortgage
loans come due, such as the failure to pay property taxes or to maintain the property. On the
other hand, borrowers can pre-pay regardless
of when the loan is due, typically without any
additional cost.

5

reverse mortgage lender sell the house
or by paying in cash. Most use the
first option. In the first case, a mortgage lender sells the house attached
to the reverse mortgage loan and uses
the proceeds of the sale to repay the
loan and to pay for various costs. If
the sale value of the house turns out
to be larger than the sum of the total
loan amount and the various costs of
the loan, the borrowers receive the
remaining value. In the opposite case,
where the house value cannot cover
the total costs of the loan, the borrowers do not need to pay anything extra.
The insurance covers the difference.
In fact, the mortgage lender does not
have to absorb the loss, either, because
the loss is covered by insurance, which
is a part of HECM loans. The FHA
imposes an insurance premium for
this benefit; the insurance premium is
included in the total costs of a HECM
loan. In a housing market downturn,
reverse mortgage loans can play a particularly important role by protecting
older households with reverse mortgages from being hit by large declines
in house prices.6
Finally, there are various ways to
receive cash (payment options) out of
www.philadelphiafed.org

home equity. Borrowers can choose according to their needs when they borrow against the value of their house.
Here are the five payment options
listed on the home page of HUD’s
website. Borrowers can change the
payment options during the life of a
reverse mortgage, at a small cost.
•	 Tenure: Borrowers continue to
receive a fixed amount of cash as
long as one of the borrowers continues to live in the same house.
•	 Term: Borrowers receive a fixed
amount of cash for a fixed length
of time.
•	 Line of credit: Borrowers can
flexibly draw cash, up to a limit,
during a pre-determined drawing
period.
•	 Modified tenure: Combination of
the tenure option and the line of
credit option.
•	 Modified term: Combination of
the term option and the line of
credit option.
The tenure option is similar to
Social Security in the sense that the
borrowers can keep receiving cash as
long as they are alive (and stay in the
same house). The term option is similar to the tenure option, but borrowers
receive cash only during a fixed period.
If borrowers live and stay in the house
beyond the fixed period, borrowers
can no longer receive cash out of the
reverse mortgage.7 Under the tenure

Of course, the government and, ultimately,
taxpayers pay for the insurance benefit in cases
in which reverse mortgage borrowers are hit by
a large decline in house prices. Therefore, in
assessing the value of reverse mortgage loans for
society, we must compare the benefits enjoyed
by reverse mortgage borrowers on those occasions against the costs borne by taxpayers. I will
discuss this issue in the conclusion.
6

The borrowers might die or move out before
receiving all of the scheduled payments. In that
case, the debt under the term option is determined according to the amount the borrowers
have received up to that point.

7

www.philadelphiafed.org

option, the time span for receiving
cash is basically the remaining lifetime
of the borrowers. So the time span under the term option tends to be shorter
than under the tenure option. When
the total loan amount is the same,
the borrowers can receive higher cash
payments per period if they receive
them over a shorter time span under
the term option. The line-of-credit option is similar to a HELOC in that it is
flexible in terms of the timing and the
amount withdrawn.
How much can one borrow using
a reverse mortgage? Let’s start with
the case in which borrowers receive a
one-time cash payment under a reverse
mortgage. The starting point is the
appraised value of the house, but there
is a federal limit for a government-administered HECM loan. Currently, the
limit is $625,500 for most states. The
limit was raised in 2009 from $417,000
as part of the Housing and Economic
Recovery Act of 2008. If the appraised home value exceeds this limit,
the home value is assumed to be the
HECM limit when the loan amount
is calculated. Private mortgage lenders offer jumbo reverse mortgage loans,
which allow borrowers to cash out
more than the federal limit. However,
borrowers have used jumbo reverse
mortgages less and less often as the
federal limit has been raised.
Reverse mortgage borrowers cannot receive the full amount of the
house value (or the HECM limit if the
house value exceeds it) because there
are various costs that have to be paid
from the house value as well. There are
two types of costs: noninterest costs
and interest costs. Moreover, if borrowers have outstanding mortgages, part
of the new mortgage loan will be used
to pay off the outstanding balance of
other mortgages. Noninterest costs include an origination fee, closing costs,
an insurance premium, and a loan
servicing fee. The insurance premium
depends on the value of the house and

how long the borrowers live and stay
in the same house. More specifically,
the insurance premium is 2 percent
of the appraised value of the house
(or the limit if the value is above the
limit) initially and 1.25 percent of the
loan balance annually.8 Interest costs
depend on the interest rate, the loan
amount, and how long the borrowers
live and stay in the house. The interest
rate can be either fixed or adjustable.
In the case of an adjustable interest
rate, there is typically a ceiling on how
much the interest rate can go up per
year or during the life of the loan.
In sum, the amount that homeowners can borrow, which is called
the initial principal limit, is larger if (1)
the house value is larger, (2) there is
a lower (or zero) outstanding balance on other mortgage loans, (3) the
borrower is older,9 and (4) the interest rate is lower. Figure 1 shows the
distribution of the initial principal
limit among government-administered
HECM loans between 2003 and 2007,
expressed as a percentage of the house
value against which mortgage loans
are borrowed. You can see that many
homeowners can borrow around 60
to 70 percent of the appraised house
value using reverse mortgages. If the
term option is chosen, the total loan
amount is divided depending on the
number of times the borrowers receive
cash.10 With the tenure option, the

In October 2010, the annual insurance
premium was increased from 0.5 percent to 1.25
percent of the appraised value of the house, in
response to the decline in house prices.

8

9
As long as all of the borrowers live in the
same house, there can be multiple borrowers
for a reverse mortgage loan. In this case, “age of
the borrower” refers to the age of the youngest
borrower.

To be more precise, the total amount of
cash received will be adjusted because the
total amount of interest and noninterest costs
changes as the withdrawal schedule changes.
Typically, borrowers receive the same cash
amount each period.

10

Business Review Q1 2012 21

amount of cash payment per period is
determined by the number of times the
borrowers are expected to receive cash.
REVERSE MORTGAGE LOANS
BY THE NUMBERS
Since reverse mortgage loans
first appeared in 1987, the number of
households with reverse mortgages
has grown. Figure 2 shows the proportion of home-owning households age
65 or older that had reverse mortgages
between 1997 and 2009. Both government-sponsored and private mortgage
loans are included. As you can see in
the figure, the use of reverse mortgages was limited until around 2000.
In 2001, the proportion of older (65
years old or above) homeowners who
have reverse mortgages was about 0.2
percent. The proportion of households
using reverse mortgages has increased
rapidly since then, reaching 1.4 percent
in 2009. Although the level (1.4 percent) is still low, the growth is all the
more impressive if one considers that
the popularity of reverse mortgages
continued to rise even though the
housing market and mortgage markets
in general have been stagnating.11
For comparison, Figure 3 shows
how the popularity of HELOCs has
changed over time. The popularity of
HELOCs, as measured by the proportion of households with HELOCs, has
moved with house prices (Figure 4
shows the average U.S. house price),
rising from 1999 to 2005 but falling
since 2007. The difference in the dynamics suggests that the popularity of
reverse mortgages is driven not only by
the growth in house prices but also by
other elements. I will discuss some of
these elements below.
Why did the use of reverse mortgages continue to rise even during
the recession with the disappointing
Later in this article I will discuss why the
popularity of reverse mortgage loans remains
so low.
11

22 Q1 2012 Business Review

FIGURE 1
Distribution of Initial Principal Limit
of HECM Loans, 2003 - 2007

Source: Article by Hui Shan
Note: Only the government-administered HECM loans during 2003-2007 are included.

FIGURE 2
Percentage of Older Households with RMLs

Data Source: American Housing Survey, various years
Note: Both public and private reverse mortgage loans are included.
www.philadelphiafed.org

FIGURE 3
Precentage of Households with HELOCs

Data Source: American Housing Survey, various years

FIGURE 4
House Price Index for the U.S. (1997 = 100)

Data Source: Federal Housing Finance Agency

www.philadelphiafed.org

performance of the housing market?
There are five possible explanations.
First, the recession lowered the value
of retirees’ financial assets, especially
their stock market investments, and
these retirees had to tap home equity
in the form of reverse mortgages. Second, the maximum amount that older
households can take out using a government-administered reverse mortgage loan was increased in 2009. This
change might have attracted more potential borrowers. Third, the continued
increase in medical expenditures and
other health-care costs after retirement
has been pushing up the demand for
financial instruments, such as reverse
mortgages, that allow homeowners to
cash out home equity. Fourth, more
and more baby boomers have been
retiring with relatively insufficient savings. Finally, more and more people
have learned about reverse mortgages
or got to know people who use reverse
mortgage loans, both of which have
made people more familiar with these
financial products.
Whether the strong growth in the
reverse mortgage market will continue
depends on what lies behind its strong
growth so far. If the last three reasons
are the main ones, we should expect
reverse mortgages to continue to grow
in the near future. In addition, the fact
that people live longer and that the
proportion of older people in the total
population continues to get larger with
the aging of the baby boomers also
implies that it is likely that the reverse
mortgage market will continue to grow,
although the potential market size of
reverse mortgage loans is still being
debated. (See Estimating the Market
Potential of Reverse Mortgage Loans.)
So now we have seen that the use
of reverse mortgages has been increasing. But who is actually taking out
reverse mortgages? Hui Shan looked at
the characteristics of areas with more
reverse mortgage borrowers and then
investigated how those characteristics
Business Review Q1 2012 23

Estimating the Market Potential of Reverse Mortgage Loans

S

ince the inception of reverse mortgage
loans as a financial product, there has
been a discussion of how large the
potential market for reverse mortgages
is. The question has been of interest to
many people especially because the use
of reverse mortgage loans has been more limited than
expected.* An intuitive way to estimate the potential
market size of reverse mortgage loans is to count the
number of households in the data that might be better
off if they had access to reverse mortgages. One of
the first such calculations was conducted by David
Rasmusssen, Issac Megbolugbe, and Barbara Morgan.
Using 1990 U.S. census data, they argue that more
than 6.7 million households age 69 or above (almost 80
percent of home-owning households age 69 and above)
or 11.1 million of households age 62 or above could
benefit from access to reverse mortgages. They compute
this by counting households age 69 (or 62) or above with

home equity exceeding $30,000 and without mortgage
loans. Sally Merrill, Meryl Finkel, and Nandinee Kutty
implemented a similar exercise with a more conservative
set of assumptions. They counted the number of
households age 69 or above with housing equity between
$100,000 and $200,000, relatively low incomes of less
than $30,000 per year, and a strong commitment to stay
in their current house (specifically, those who have not
moved for the last 10 years), and that own their house
free and clear. Merrill, Finkel, and Kutty concluded that
the potential market size of reverse mortgage loans is
rather limited, at about 0.8 million households, or about
9 percent of all homeowners over age 69.
The two estimates are very different. But even the
lower estimate suggests that there might be a large potential for growth of the reverse mortgage market, considering that only 1.4 percent of home-owning households age
65 or above were using reverse mortgage loans in 2009.

* For example, until 1994, HUD had issued only 7,994 HECM loans, even though it was authorized to make 25,000 HECM loans, according to a
HUD report published in 1995.

changed over time.12 She found that
areas with more reverse mortgage borrowers tend to have lower household
income, higher house value, and relatively higher homeowner costs. These
characteristics are consistent with
the types of households that benefit
most from taking out reverse mortgage
loans. She also found that areas with
more reverse mortgage borrowers tend
to have lower credit scores. There are
two possible explanations for this finding. First, as mentioned earlier, reverse
mortgage loans do not require good
credit scores. Relatively younger households that want to borrow against
home equity but cannot qualify for
HELOCs because of low credit scores

12
Marvin M. Smith provides a nontechnical
summary of Shan’s work in the Federal Reserve
Bank of Philadelphia’s Cascade (Spring/Summer
2010).

24 Q1 2012 Business Review

might end up using reverse mortgage
loans. Second, borrowers with lower
credit scores tend to have lower overall wealth and thus need to borrow
against home equity. In terms of the
demographic characteristics of reverse
mortgage borrowers, Shan found that
more singles (both male and female)
are using reverse mortgages, compared
with couples, and reverse mortgage
borrowers tend to own houses of
higher value. The median house value
among reverse mortgage borrowers was
$222,000 in 2007, which was about
25 percent higher than the median
house value of all older homeowners
($175,000).
Shan also found that there have
been some notable changes in terms of
the characteristics of reverse mortgage
borrowers over the past 20 years. In
particular, reverse mortgage borrowers have always been older than those

who did not take out reverse mortgage
loans, but the gap has been closing
as average reverse mortgage borrowers have been getting younger. For
example, the average age of older
homeowners in 1989 was 70, while the
average age among reverse mortgage
borrowers was 75. In 2007 the average
age of reverse mortgage borrowers was
72, which was just one year above the
average age of older homeowners (71).
Figure 5 shows the age distribution of
reverse mortgage borrowers who took
out reverse mortgage loans in earlier
periods (1989-2002) and in more recent periods (2003-2007). You can see
that the distribution is shifting to the
left, meaning more and more relatively
younger households are taking out
reverse mortgage loans. An interesting observation is that there is a spike
at age 62 (the earliest age at which
the federally administered reverse
www.philadelphiafed.org

FIGURE 5
Age Distribution of Reverse Mortgage
Borrowers
Early Loans (1989 - 2002)

Recent Loans (2003 - 2007)

Source: Article by Hui Shan
Note: Only the government-administered HECM loans are included.

mortgage becomes available) in both
figures, and the spike has become more
dramatic in recent years. This suggests
that more and more households are
“waiting” to reach age 62 so that they
can take out reverse mortgage loans.
Remember the earlier discussion
of the various ways to receive cash
under a reverse mortgage. Which payment options are most popular? The
line of credit option has been the most
www.philadelphiafed.org

popular by far. HUD reports that the
line of credit plan is chosen either
alone (68 percent) or in combination
with the tenure or term plan (20 percent). In total, close to 90 percent of
borrowers use the line of credit plan.13

Using data from 2007, Shan also reports that
82 percent of borrowers choose the line of credit
plan. In Shan’s sample, only 10 percent choose
the tenure or modified tenure plan.

13

It seems that older homeowners use
reverse mortgages mainly to flexibly
withdraw cash out of accumulated
home equity.
THREE POTENTIAL BENEFITS
OF REVERSE MORTGAGE
LOANS
Now let’s analyze the benefits and
costs of reverse mortgage loans using economic intuition, starting with
benefits. First, when other, more conventional mortgage loans are not easy
to obtain, reverse mortgages provide
a way for older homeowners to cash
out home equity without leaving their
home. Alternatively, older homeowners can cash out their home equity by
either selling their home and downsizing (moving to a smaller and cheaper
house) or becoming renters. However,
research shows that is not what most
older homeowners want. The study by
Steven Venti and David Wise shows
that most older households do not
move unless some catastrophic event
occurs (such as the death of a spouse
or a sharp deterioration in health) and
they are forced to move out. Another study by the AARP (formerly,
the American Association of Retired
Persons) found that 89 percent of surveyed Americans over 55 years of age
reported that they want to remain in
their current residence as long as possible. Figure A in the box on page 26
shows the homeownership rate among
older households, taken from my working paper with Irina Telyukova (2011a).
(For more details, see Financial Situations of Older Households.) You can see
that the homeownership rate declines
as households age, but slowly. Considering this evidence, cashing out
home equity using reverse mortgages
while staying in the same house offers
substantial benefits over the alternatives of moving to a smaller house or
becoming a renter.
Second, reverse mortgages provide
insurance against a decline in house
Business Review Q1 2012 25

Financial Situations of Older Households

I

holds, especially in the later part of life, reduce their
n a working paper (2011a), Irina Telyuholdings of financial assets. The figure also shows that
kova and I organized the facts about the
younger households seem to have experienced some
financial situations of older U.S. houseincrease in their financial assets. This could be due to
holds, using a rich data set called the
booms in stock and housing prices during the period
Health and Retirement Study (HRS). To
1996-2006. While households in retirement tend to
keep track of the same households over
reduce their holdings of financial assets, the gains from
time, we looked at six groups of households — those age
strong markets overwhelmed the gradual reduction of
65, 70, 75, 80, 85, and 92 in 1996 — and kept track of
these households’ financial assets.
the financial situations of these six groups between 1996
Figure E looks at the median housing asset holdand 2006. Below is a summary of our findings.
ings. Median housing assets increased for most groups,
About 90 percent of households at age 65 are
but a large part of the increase was due to rising house
homeowners (Figure A). The proportion declines as
values during the period we are looking at.
households age, but it remains at around 50 percent for
households at age 90. A large fraction of the decline is
caused by two-adult households
becoming one-adult households,
possibly because of the death of
FIGURE A
a spouse. About 80 percent of
Homeownership Rate
two-adult households remain
homeowners even at age 90.
Older households also
consistently reduce borrowing as they age. Figure B shows
the proportion of households
with secured debt, mainly home
mortgages and other types of
borrowing against home equity. The proportion declines
with age; for example, among
households that are age 90, only
See legend below.
about 3 percent hold a positive balance of unsecured debt.
FIGURE B
If they cannot borrow even
though they want to, reverse
Proportion of Households with Secured Credit
mortgage loans can potentially
be beneficial for those households.
Figure C shows the proportion of households with
unsecured debt, mainly credit
card debt. The proportion also
decreases consistently with age.
About 5 percent of homeowners
hold a positive balance of credit
card loans.
Figure D exhibits how
financial asset holdings among
older households change as
the households age. The figure
shows that median older houseData Source: Health and Retirement Study, various years

26 Q1 2012 Business Review

www.philadelphiafed.org

FIGURE C
Proportion of Households with Unsecured
Credit

FIGURE D
Median Financial Asset Holdings

See legend below.

FIGURE E
Median Housing Asset Holdings

Data Source: Health and Retirement Study, various years

www.philadelphiafed.org

value, at the cost of an insurance
premium. The insurance does not
cover a small decline in house value
in the sense that reverse mortgage
borrowers do not benefit from the
insurance as long as the selling
price of the house when the loan
is due still covers the loan amount
and all the costs; in that case, the
borrowers just receive less cash
when the loan is due. However, in
a case where the selling price turns
out to be so low that it is insufficient to cover the loan amount and
the costs, the reverse mortgage borrower is not obliged to pay the gap.
The gap is paid by the insurance
that is a part of HECM loans. Currently in the U.S., because of the
recent sharp drop in house prices,
many homeowners are caught
in a situation where the value of
their house is lower than the total
amount of mortgage debt or the
HELOC borrowed against the
house (this situation is called negative home equity). They cannot sell
their house without paying the difference between the amount of debt
and the house value with cash or
by foreclosing. Under these circumstances, reverse mortgage borrowers
benefit from the insurance feature
because reverse mortgage borrowers
are protected from negative home
equity.
Third, reverse mortgage loans
provide insurance against longevity
risk when the tenure option is used.
Under the tenure option, reverse
mortgage borrowers do not need to
worry about outliving the loan because borrowers can keep receiving
payments no matter how long they
live. In this sense, the tenure option
is similar to the Social Security system with defined benefits, providing
an annuity and relieving borrowers
from the concerns of outliving their
savings. Since not many reverse
mortgage borrowers actually use
Business Review Q1 2012 27

this option, this benefit might not be
that important. Is the limited use of
the tenure option due to low demand
by reverse mortgage borrowers or due
to the high costs associated with it?
This is an open question.
THREE POTENTIAL
DISADVANTAGES OF REVERSE
MORTGAGE LOANS
Of course, reverse mortgages are
not without problems. First, reverse
mortgages might discourage saving
and thus hurt older homeowners who
discover that they did not save enough.
If households can always save exactly
the amount they need in the future,
there is no such problem. But can all
households do so? Research by David
Laibson says no. Laibson argues that
people tend to have self-control problems and cannot save as much as they
need. An illustrative example of such
a problem is quitting smoking. People
might think they can smoke today
but they will quit tomorrow. But when
tomorrow comes, they tend to think in
the same way: They can smoke today
and quit tomorrow. In the current
context, households think they can
spend today but start saving tomorrow.
But when tomorrow comes, they might
think in the same way: Spend today
and postpone saving one more day,
and so on. In such a situation, Laibson
argues, illiquid assets (in the sense that
they are costly to sell or withdraw) such
as housing or retirement plans (individual retirement accounts [IRAs],
401(K), etc.) give people a way to commit to saving. They are like a piggy
bank: Once you put cash into it, it is
not easy to get the cash out. Basically,
people can force their future selves not
to withdraw money and thus save.
However, under these circumstances, flexible mortgage instruments
such as reverse mortgage loans work
to undo the piggy bank role of housing and thus could hurt people. People
could commit to saving by purchasing
28 Q1 2012 Business Review

a house because it is not easy to sell
the house. However, this commitment
to saving is not effective if it is easy
to cash out one’s home equity using
reverse mortgages. It is still costly to
sell the house to get cash, but by using a reverse mortgage loan, one can
cash out flexibly without selling the
house. So reverse mortgages are like

mortgage loans come with another
kind of risk for borrowers: moving out
of the house too soon. Since reverse
mortgage loans require relatively large
upfront costs, borrowers suffer if they
have to move out of their house shortly
after taking out a reverse mortgage
and before fully enjoying its benefits.
In a sense, when taking out a reverse

Reverse mortgages help borrowers reduce
various kinds of risks, such as the risk of a
decline in house prices, but at the same time,
reverse mortgage loans come with another
kind of risk for borrowers: moving out of the
house too soon.
a big hole in the piggy bank. In this
sense, reverse mortgage loans could
hurt (relatively young) older homeowners by making it easy for them to cash
out home equity. (Relatively old) older
homeowners might end up having
insufficient savings because it was easy
for them to cash out home equity using reverse mortgages when they were
(relatively) younger.14 The age limit
for government-administered reverse
mortgage loans (62) and the requirement that to be eligible for reverse
mortgage loans households must own
their house with little or no outstanding mortgage balance can prevent such
dissaving through reverse mortgage
loans to some extent, but as people
live longer and longer, the problem
becomes more and more serious.
Second, reverse mortgages help
borrowers reduce various kinds of risks,
such as the risk of a decline in house
prices, but at the same time, reverse

At the same time, people might be discouraged from saving as much as they would like
because it is costly to sell a house or cash out
home equity. In this case, reverse mortgages
play a positive role in reducing such costs and
encouraging saving.

14

mortgage, borrowers are betting that
they will live in the same house long
enough to benefit from the reverse
mortgage, and naturally, some borrowers end up losing the bet. In her recent
working paper, Valentina Michelangeli
argues that this is the main reason,
regardless of all of the benefits of reverse mortgage loans listed earlier, only
a small number of eligible households
are actually using reverse mortgages;
the risk of moving out too soon is too
large even with all the benefits reverse
mortgages offer to borrowers.
Third, reverse mortgage loans
could exacerbate moral hazard problems, as analyzed by Thomas Davidoff
and Gerd Welke. Moral hazard, in
general, refers to a situation in which
a person insulated from risk does not
take responsibility for the consequences of his actions and, therefore, has a
tendency to act less carefully than he
otherwise would. A typical example
is an insured driver who drives carelessly because he is insured in case of
an accident. With reverse mortgages,
since borrowers are insured against
the risk of a decline in house prices,
the sale price of the house does not
affect reverse mortgage borrowers if it
www.philadelphiafed.org

is not enough to cover the total loan
amount and all the costs of the reverse
mortgage loan. In this case, how well
reverse mortgage borrowers maintain
a house will not affect how much they
gain, which is zero anyway. At the
end of the day, borrowers might not
maintain the house (and therefore
the house’s value). However, the poor
maintenance is not a direct problem
from the perspective of reverse mortgage borrowers (because they don’t
suffer from it), but this problem might
hurt reverse mortgage borrowers indirectly, since poor maintenance yields
a lower selling price, and the government, in response, has to raise the
cost of reverse mortgage loans to cover
the lower price. In addition, the poor
maintenance of the house might be a
cost to society as well.
WHY ARE SO FEW PEOPLE
USING REVERSE MORTGAGES?
One important question surrounding reverse mortgages is: why are only
1.4 percent of households using them,
when even a conservative estimate of
the proportion of older households that
could benefit from access to reverse
mortgage loans is 9 percent? (See Estimating the Market Potential of Reverse
Mortgage Loans.) One possible answer
is that the problems with reverse mortgages, especially the fear of moving out
of one’s house too soon after taking
out a reverse mortgage and the high
costs, outweigh their benefits, and thus
not many households actually want
reverse mortgage loans.15 Another possible answer is that many households
that could benefit from reverse mortgages don’t know about them. Let me
introduce three more explanations for
the limited use of reverse mortgages.

A self-control problem might actually work
to increase the popularity of reverse mortgage
loans because households cannot resist the
urge to use reverse mortgages according to the
hypothesis.

15

www.philadelphiafed.org

First, older households may want
to leave wealth — of which housing is a large part — as a bequest.
Older households may not use reverse
mortgages possibly because having a
reverse mortgage may make it harder
to include a house as part of a bequest.
However, there are studies, including
the one by Michael Hurd, that have
found that people’s desire to leave a
bequest is not strong, except for very
wealthy households.16
Second, households may be worried about large medical expenditures
and may want to keep their housing
to pay for such expenditures in the
future. Mariacristina De Nardi, Eric
French, and John Jones found that
older households want to keep wealth
(and thus do not want to use reverse
mortgages) because they expect to
incur large medical expenditures, es-

Therefore, medical expenditures could
increase or reduce the popularity of
reverse mortgages.
Third, Andrew Caplin emphasizes
psychological elements. According to
him, many older households might
simply be reluctant to take on debt. Or
some households may fear that a medical problem will keep them away from
home for a lengthy period of time, in
which case the reverse mortgage may
become due and they have to vacate
their house. The genuine risk of losing their house under these circumstances scares older households away
from reverse mortgages, no matter
how large the benefits are.18 Moreover,
news stories such as those that involve
an older household being tricked into
taking out a reverse mortgage to pay
hefty costs for home repairs also play a
role in strengthening older households’

News stories such as those that involve an
older household being tricked into taking out a
reverse mortgage to pay hefty costs for home
repairs also play a role in strengthening older
households’ aversion to reverse mortgage loans.
pecially toward the end of life.17 This
implies that when households actually
need to cash out their home equity,
they will not use reverse mortgages
because they need immediate cash
and probably do not expect to stay in
their current house very long. On the
other hand, reverse mortgages could
help households that need to pay large
medical bills by allowing them to pay
the bills and still remain in their home.

16
In my working paper with Irina Telyukova
(2011b), we investigate the importance of this
and other hypotheses of why the take-up rate of
reverse mortgage loans is so low.
17
Naturally, they focus on out-of-pocket medical
expenditures, which are the uninsured portion
of medical expenditures.

aversion to reverse mortgage loans.
In my working paper with Irina
Telyukova (2011a), we show that between the 1990s and the 2000s, during
which time the reverse mortgage market was expanding, older households
did not reduce their wealth much as
they aged. (See Financial Situations of
Older Households for more details.) At
first sight, this evidence suggests that
they do not need to extract home equity using reverse mortgage loans. How-

18
Remember that borrowers have to live in the
house, pay property taxes in a timely fashion,
and maintain the house properly in order to
keep using a reverse mortgage. If borrowers are
out of the house for an extended period, this
could make the reverse mortgage become due
and force the borrowers to vacate the house.

Business Review Q1 2012 29

ever, we argue that it might be partly
because the housing and stock markets
were both in good shape during that
period, which reduced the need to tap
in home equity. If that is the case, the
demand for reverse mortgage loans will
keep growing if the housing market
stagnates further and the stock market
cannot compensate for the lackluster
performance of the housing market.19
CONCLUSION
In this article, I described reverse
mortgage loans and shed some light on
their economic benefits and costs. An
important question surrounding reverse mortgages is how large the market for them will become. Since the
take-up rate of reverse mortgage loans
increased between 2000 and 2009,
coinciding with the housing boom, and
since there are signs that the growth
in reverse mortgage loans may be slowing down, it is hard to answer questions about the long-term potential
On the other hand, if house prices are not
consistently increasing, reverse mortgage loans
become riskier for mortgage lenders. In that
case, mortgage lenders either need to increase
the costs of reverse mortgages to cover the risk
or eventually get out of the business.
19

30 Q1 2012 Business Review

of reverse mortgages. In this article,
I have argued that reverse mortgage
loans have the potential to be beneficial for older households in the long
run. As reverse mortgage loans become
a standard tool for older households to
extract home equity, it becomes even
more important to understand the pros
and cons of this financial instrument,
not only for making sound decisions
in terms of personal finances but also
for understanding why public resources
are used for the market. As I discussed,
the government-administered reverse
mortgage loans (HECM loans) have
more than 90 percent of the market
share, according to a recent study.
The government regulates the terms
of HECMs and subsidizes the loans.
Moreover, the government insures
against the risk of substantial drops
in house prices for reverse mortgage
borrowers by imposing an insurance
premium.
Do we really need such extensive
government involvement in the reverse
mortgage market? This question is
important, since the government’s
support for reverse mortgage loans
is ultimately financed by taxpayers.
There are two ways to look at the role

of reverse mortgages from a policy
perspective. One way is to understand
the government’s involvement in the
reverse mortgage market as part of the
public support for homeownership.20
Although the government has been
supporting homeownership through
various measures, this support is being
re-examined in the wake of the financial crisis, which was partially triggered
by the decline in house prices and the
subsequent slow economic recovery.
The government’s role in the reverse
mortgage market will naturally be reexamined in the same context.
Another way to understand government’s support of reverse mortgage
loans is to consider it as part of the
support for life after retirement, similar
to Social Security payments; taxpayers
are supporting older households indirectly through reverse mortgage loans.
Ultimately, whether and how the government should remain a key player in
the reverse mortgage market is an open
question. BR

The Business Review article by Wenli Li and
Fang Yang discusses a variety of government
programs to promote homeownership.

20

www.philadelphiafed.org

REFERENCES
Caplin, Andrew. “The Reverse Mortgage
Market: Problems and Prospects,” in Olivia
S. Mitchell, Zvi Bodie, Brett Hammond,
and Steve Zeldes, eds., Innovations in
Retirement Financing, Philadelphia:
University of Pennsylvania Press, 2002,
pp. 234-53.
Davidoff, Thomas, and Gerd Welke.
“Selection and Moral Hazard in the
Reverse Mortgage Market,” unpublished
manuscript, University of British Columbia
(2007).
De Nardi, Mariacristina, Eric French, and
John B. Jones. “Why Do the Elderly Save?
The Role of Medical Expenses,” Journal of
Political Economy, 118:1 (2010), pp. 39-75.
Foote, Bruce E. “Reverse Mortgages:
Background and Issues,” Congressional
Research Service Report (2010).
Hurd, Michael D. “Mortality Risk and
Bequests,” Econometrica, 57:4 (1989), pp.
779-813.
Laibson, David. “Golden Eggs and Hyperbolic Discounting,” Quarterly Journal of
Economics, 112:2 (1997), pp. 443-77.

www.philadelphiafed.org

Li, Wenli, and Fang Yang. “American
Dream or American Obsession? The Economic Benefits and Costs of Homeownership,” Federal Reserve Bank of Philadelphia Business Review (Third Quarter 2010),
pp. 20-30.
Merrill, Sally R., Meryl Finkel, and Nandinee Kutty. “Potential Beneficiaries from
Reverse Mortgage Products for Elderly
Homeowners: An Analysis of American
Housing Survey Data,” Real Estate Economics, 22:2 (1994), pp. 257-99.
Michelangeli, Valentina. “Does It Pay to
Get a Reverse Mortgage?” unpublished
manuscript, Boston University (2008).
Nakajima, Makoto, and Irina A. Telyukova. “Home Equity Withdrawal in Retirement,” Federal Reserve Bank of Philadelphia Working Paper 11-15 (2011a).
Nakajima, Makoto, and Irina A. Telyukova. “Reverse Mortgage Loans: A Quantitative Analysis,” unpublished manuscript, University of California, San Diego
(2011b).

Redfoot, Donald L., Ken Scholen, and S.
Kathi Brown. “Reverse Mortgages: Niche
Product or Mainstream Solution? Report
on the 2006 AARP National Survey of Reverse Mortgage Shoppers,” AARP Public
Policy Institute Research Report, No. 22
(2007).
Shan, Hui. “Reversing the Trend: The
Recent Expansion of the Reverse Mortgage
Market,” Federal Reserve Board Finance
and Economics Discussion Series, No. 41
(2009).
Smith, Marvin M. “Spotlight on Research:
Is a Reverse Mortgage in Your Retirement
Plans?” Federal Reserve Bank of Philadelphia Cascade (Spring/Summer 2010).
U.S. Department of Housing and Urban
Development. “Evaluation of the Home
Equity Conversion Mortgage Insurance
Demonstration,” Washington, D.C. (1995).
Venti, Steven F., and David A. Wise. “Aging and Housing Equity: Another Look,”
in David A. Wise, ed., Perspectives on the
Economics of Aging. Chicago: University of
Chicago Press, 2004, pp. 127-75.

Rasmussen, David W., Issac F. Megbolugbe, and Barbara A. Morgan. “Using
the 1990 Public Use Microdata Sample to
Estimate Potential Demand for Reverse
Mortgage Products,” Journal of Housing
Research, 6:1 (1995).

Business Review Q1 2012 31

Recent Developments
in Consumer Credit and Payments*

O

by Mitchell Berlin

n September 22-23, 2011, the Research
Department and the Payment Cards Center
of the Federal Reserve Bank of Philadelphia
held their sixth joint conference to present
and discuss the latest research on consumer credit
and payments. Eighty-four participants attended the
conference, which included seven research papers on
the role of home equity in the decision to move to a new
job; credit supply and house prices; legally mandated
removal of credit remarks; policies to prevent mortgage
default; adoption and use of payment instruments by
U.S. consumers; liquidity constraints and consumer
bankruptcy; and credit supply to bankrupt consumers.
In this article, Mitchell Berlin summarizes the papers
presented at the conference.

In her welcoming remarks, Loretta
Mester, executive vice president and
director of research at the Philadelphia
Fed, noted that the recent financial
crisis has uncovered a range of new
issues related to household finance and
payments and, further, that the Federal

Mitchell Berlin is
a vice president
and economist
in the Research
Department of
the Philadelphia
Fed and head
of the Banking
and Financial
Markets section. This article is available
free of charge at www.philadelphiafed.org/
research-and-data/publications/.
32 Q1 2012 Business Review

Reserve System has taken on a menu
of new responsibilities. She stressed
that the long-term research typified by
the papers presented at the conference
is an essential input into good regulatory policy.
Mester highlighted the variety of
research approaches represented in the
conference program and stressed the
possibilities for integrating the various approaches. In particular, she said
*The views expressed here are those of the
author and do not necessarily represent
the views of the Federal Reserve Bank of
Philadelphia or the Federal Reserve System.
Links to most of the papers presented can
be found on the Philadelphia Fed’s website
at: http://www.philadelphiafed.org/researchand-data/events/2011/consumer-credit-andpayments/agenda.cfm.

that the program included macroeconomic structural models that bring
new perspectives that complement the
findings of microeconomic studies of
consumer credit. Mester argued that,
in exchange, the microeconomic studies enrich the macro structural models,
which rely on the parameter estimates
for their calibration exercises.
Furthermore, she found the extensive use of large micro data sets in
a number of the papers striking. The
Philadelphia Fed has taken a leading
role in managing these large data sets.
In particular, the Philadelphia Fed administers RADAR,1 a data warehouse
that serves the Federal Reserve System.
HOUSE PRICES AND JOB
SEARCH
In the first paper of the day, Yuliya
Demyanyk, of the Federal Reserve
Bank of Cleveland, reported on a study
(with Dmytro Hryshko, Maria Jose
Luengo-Prado, and Bent Sorensen) of
the relationship between the decline in
house prices and individuals’ willingness or ability to move to seek employment. She emphasized that the results
were very preliminary and that the
audience should view them as provisional. During the recent recession,
the record decline in housing prices
was cited as one of the reasons for
stubbornly high unemployment rates,
a view that has generated conflicting
reactions in the economic literature.
Some economists have argued that
households with negative equity have
been unable to search for work in more
distant labor markets because they are

1
Risk Assessment, Data Analysis, and Research.

www.philadelphiafed.org

unable to sell their houses without defaulting. Demyanyk and coauthors did
not find much evidence for this view.
The authors presented results using two methodologies. The first used
regression techniques and anonymized
data sets from credit bureaus. The second used a calibrated macroeconomic
model.
Demyanyk and coauthors’ empirical approach was to use regression
methods to estimate how the probability of moving was affected by local
unemployment rates and households’
home equity. Specifically, Demyanyk
argued that if the likelihood of moving from a poorly performing local
labor market was lower for households
with lower home equity, this would
be evidence of a lock-in effect. The
researchers estimated the probability of
two different types of moves separately:
moves to a different county within the
same state and moves to a different
state. Although either type of move
might be associated with changing jobs
— the actual employment outcome
cannot be directly observed — Demyanyk argued that moves to a different
state were more likely to involve movement to a different labor market.
The researchers performed regressions using two different data sets,
each with its own advantages and disadvantages.2 The first data set merged
information from one of the credit reporting agencies (TransUnion) with a
separate source of mortgage-loan-level
data. The disadvantage of this merged
data set is that it is not fully representative; the sample is dominated by
subprime homeowners, and as result,
prime borrowers are underrepresented
and renters aren’t included at all. The
advantage, however, is that this data
set permits the authors to estimate
households’ home equity with some

precision. Demyanyk presented results
from a 10 percent subsample of the
whole data set at this conference.
The second data set that Demyanyk and coauthors used is from the
New York Fed’s Consumer Credit
Panel, a 5 percent sample of all consumers in the Equifax credit files from
1999-2011. The authors selected a
random subset of those consumers and

The long-term research typified by the papers
presented at the conference is an essential
input into good regulatory policy.
included in their data members of the
same household as those consumers.3
This data set included both prime and
subprime homeowners and renters and
was thus more nearly representative
of households in the nation. But the
authors could not directly estimate a
household’s home equity using this
data set. Instead, they used whether local housing prices were rising or falling
as a proxy for high or low home equity.
The authors’ preliminary conclusion was that there is not much
evidence for lock-in effects on the
basis of their regression results. For
the TransUnion data set, the authors
found that in weak local labor markets
(negative employment growth), moves
to another county were less likely for
households with negative equity than
for households with positive equity,
but moves out of state were more likely
for households with negative equity.
If the authors’ argument that out-ofstate moves are more likely to require
moving to change jobs is correct, this
result is inconsistent with the view
that households are locked-in by negative equity. Somewhat more ambigu-

In this data set, household members are
defined as consumers ages 25-66 with the
same address as an individual included in the 5
percent sample.

3

Note that all the data used by the authors were
anonymized. The data sets contain no personally identifiable information.
2

www.philadelphiafed.org

ously, the researchers found that in
somewhat stronger local labor markets
(positive employment growth), moves
both to another county or to another
state were less likely for households
with negative equity than for households with positive equity.
For the Equifax data set, the
authors found no significant effect for
rising or falling house prices on the

probability of moving either outside
the county or outside the state. While
Demyanyk said that this offers no
evidence for lock-in, she recognized
that rising or falling housing prices in
a locality are a very noisy indicator of a
household’s home equity.
Demyanyk also offered some very
preliminary findings from the study of
a calibrated macroeconomic model,
which she viewed as a way of providing more insight into the precise
mechanisms through which housing
shocks might affect moving to find a
job. The model explicitly included the
possibility of unpredictable declines
in regional wage income and declines
in house prices and also included the
possibility of moving to seek a new job
in response to both local and distant
job offers. The authors conducted an
experiment in which some regions experience a housing price decline, some
a housing price increase, and some
experience no change.
The model generated results
broadly consistent with Demyanyk and
coauthors’ regression findings. They
found that unemployed households
moved whether or not housing prices
had appreciated or fallen and that
households with negative equity were
more likely than other borrowers to
take a distant job.
Business Review Q1 2012 33

EASY CREDIT AND HOUSE
PRICES
Manuel Adelino, of Dartmouth
College, reported the results of a study
(with Antoinette Schoar and Felipe
Severino) that provided evidence that
easy credit led to higher home prices
during the housing boom. Adelino
explained that it is difficult to establish the direction of causality when we
observe easier credit terms and rising
housing prices. While the rise in
house prices might have been caused
by easier credit, rising prices may create expectations that house prices will
continue to rise, thus making larger
mortgage loans appear less risky to
lenders.
From the researcher’s standpoint,
the difficulty is to find some factor that
affects credit terms without directly
affecting house prices. Then if changes
in this factor are associated with
changes in house prices, the channel
arguably flows through its effect on
the availability of credit. The authors’
approach was to examine the effects of
changes in conforming loan limits during the period of rapidly rising home
prices.4 The authors argue that while
the conforming limit was relaxed to reflect rising average home prices in the
nation, there is substantial variation
in both the level and rate of growth
in house prices across local markets.
Thus, changes in the conforming loan
limit were unlikely to be driven by
conditions in any one local market. In
formal terms, Adelino and coauthors
argue that the loan limits are plausibly
exogenous with respect to local housing markets.
Adelino explained that the underlying assumption of their research
design is that borrowing is significantly
4
Only loan sizes above the conforming loan
limit can receive guarantees from the GSEs. In
addition to the value of the guarantee against
default, the market for mortgage-backed securities composed of conforming loans is much
deeper than for nonconforming loans.

34 Q1 2012 Business Review

less costly for loan-to-value ratios below 80 percent. That is, a house whose
price is just above 125 percent of the
conforming loan limit is significantly
more costly to finance than an essentially identical house that is just below
125 percent of the conforming loan
limit.
The authors used data from home
sales for 10 MSAs over an 11-year period (1998-2008), which includes the
housing boom years. In addition to the
date of sale, the address of the property, and the sale price, the data set
included a number of characteristics
that affect the quality — and, potentially, the price — of the house, e.g.,
the number of rooms, the number of
bathrooms, and the age of the house,
among other characteristics.
Adelino described the logic of
the authors’ research design as follows. Imagine a home that was sold
for slightly less than 125 percent of the
conforming loan limit in 1999. Now,
imagine that a very similar home in

the only material difference between
those two homes is that the second
one could be purchased with lowercost financing due to the increase in
the conforming loan limit.
Using a difference-in-difference
approach, the authors compared the
difference between the sale prices of
the first two homes described above
to the difference in the sale prices of
the second two homes. They hypothesized that since more potential
borrowers would qualify to buy the
more expensive home in 2000 than in
1999, demand for such homes would
increase. Thus, the sale price of those
homes would tend to rise; in particular, it should rise more than the sale
price of homes that were initially (and
that remained) less expensive than the
conforming limit.
Indeed, this is what they found in
their main regression: If two houses
were sold in subsequent years in the
same zip code, the value per square
foot was $1.10 lower for the house with

From the researcher’s standpoint, the difficulty
is to find some factor that affects credit terms
without directly affecting house prices.
the same neighborhood sold in 2000
and that the conforming loan limit
had risen during the year. Although
other factors may explain the difference between the prices of these two
very similar homes, the change in the
conforming limit would not, since it
was not binding for either home in
either year.
Now, imagine another pair of very
similar homes in the same neighborhood. The first was sold for slightly
more than 125 percent of the conforming loan limit in 1999. The second
was sold in 2000, again for more than
125 percent of the 1999 conforming
loan limit, but for less than the actual
conforming loan limit in 2000. Thus,

a price above the cutoff in the earlier year. Furthermore, the effect was
stronger in the earlier part of the period (1998-2001). According to the authors, this finding was consistent with
their hypothesis, because the conforming loan limit became less important as
households’ access to second liens and
to jumbo loans in the latter part of the
sample period lowered financing costs.
In addition to their main regressions, in which the researchers
controlled only for house size and
neighborhood, they also ran regressions taking into account other factors
that might affect the house’s price. In
particular they estimated hedonic regressions, in which the house price (or,
www.philadelphiafed.org

alternatively, house value per square
foot) was broken down into two parts:
one part that can be explained by a
host of observable characteristics, e.g.,
the number of rooms and bathrooms,
among other factors, and another
part that can’t be explained by these
characteristics, the residual. Using
this residual as an alternative measure
of home value, they found that value
per square foot was $0.65 lower if the
house price was above the cutoff. In
light of this finding, Adelino argued
that unmeasured quality differences
among houses were not likely to be the
explanation for their main results.
The authors also found that the
effect of being above the cutoff was
stronger in those zip codes in which
household income growth was negative. They argue that in such localities,
households are more likely to be credit
constrained, strengthening the argument that it is changes in the cost of
credit that drive their results.
SHOULD CREDIT REMARKS
BE FORGOTTEN?
Marieke Bos, of the Swedish Institute for Social Research, discussed the
results of her study (with Leonard Nakamura) of the effect of legal mandates
to drop credit remarks from individuals’ credit files after a specified period
of time. The study’s main conclusion
was that creditworthiness and access
to credit increased when credit remarks were removed and that, for most
consumers, the effects were long-lasting. Bos emphasized that her results
were preliminary. She explained that
while 90 percent of the 113 countries
with credit bureaus do expunge credit
remarks after some period of time, the
amount of time varies significantly. In
Sweden, credit remarks are removed
after three years.5
In the U.S., reported delinquencies are expunged after seven years and bankruptcy filings
after 10 years.

5

www.philadelphiafed.org

To help motivate her empirical
work, Bos cited Ronel Elul and Piero
Gottardi’s (2011) model of the optimal
policy for “forgetting” a default. In that
model, expunging credit remarks increases the likelihood that an individual will make risky decisions prior to

and that both applications for credit
and access to credit increased. The
improvements in credit scores were
most striking for those individuals with
credit scores in the middle range before the derogatory credit remark was
removed. Loan applications increased

The study’s main conclusion was that
creditworthiness and access to credit
increased when credit remarks were removed
and that, for most consumers, the effects were
long-lasting.
defaulting, but once an individual has
actually defaulted, forgetting improves
his or her subsequent incentive to
make prudent decisions. The optimal
time to forgetting balances these two
forces.
Prior empirical research by David
Musto on the effects of removing a
bankruptcy flag from credit files in
the U.S. yields pessimistic results. In
Musto’s sample, individuals’ access to
credit improves when the bankruptcy
flag is removed but most of those
consumers subsequently experience declines in creditworthiness. In contrast
to Musto’s focus on removing bankruptcy flags, Bos and Nakamura focus
on removing credit remarks, which,
Bos argued, could easily arise from an
oversight, a legal dispute, or more generally, from temporary factors outside
the individual’s control.
Bos and Nakamura’s data set
includes the credit files for individuals
in Sweden for a six-year period, from
February 2000 to October 2005. First,
the authors examine the outcomes for
individuals who had a remark removed
(the removal group) compared with all
individuals without a credit remark
during the sample period.
Focusing first on the short-term
effects of removing the credit remark,
the authors found that individuals’
credit scores improved significantly

just prior to removal of the remark
for many borrowers — which, Bos
suggested, might reflect individuals’
uncertainty about the precise timing of
removal — and remained high.
The authors then turned to
longer-run outcomes. Bos noted that
in contrast to Musto’s findings, the
initial improvement in credit scores for
most consumers was not reversed in
the longer term. She and Nakamura
also found that removal led to a longterm increase in both applications for
credit and access to credit. Furthermore, while the likelihood of delinquency was substantially higher for this
group than for other individuals, the
delinquency rate was not very high.
The results described so far are
based on a comparison of outcome
variables for consumers before and
after a derogatory credit remark is removed. Bos noted that such a comparison is not a natural experiment that
might isolate the effects of removing
the derogatory credit remark from
other time-varying factors that might
affect individuals’ outcomes. Nor can a
true natural experiment be constructed. Instead, the authors compared the
outcomes of the removal group with
the outcomes for a control group of individuals, similar to the removal group.
Specifically, the authors used the propensity score matching technique to
Business Review Q1 2012 35

identify individuals who were similar
to the removal group at the time the
remark was removed.
Bos and Nakamura compared the
change in various measures of creditworthiness and credit availability at
different time horizons for the removal
group and the control group. Relative
to the pattern for the control group,
they found that among members of the
removal group, credit scores improved
immediately after the removal of the
derogatory remark and that the boost
in creditworthiness lasted up to two
years. Loan applications increased immediately prior to removal, and there
was a differential effect of up to three
and a half years. They also found that
various measures of access to credit
increased with removal. Following an
initial decline, which the authors argue
reflects a lag between applications for
credit and the receipt of funds, the
number of loans increased, as did credit limits and outstanding balances, for
up to 30 months. The average increase
in outstanding credits was SEK 21,000
(about $3,100), a large increase.
The authors then considered default behavior over time. They found
that the removal group had a significantly higher probability of delinquency than other individuals; up to
24 percent of the removal group was
delinquent after 36 months, compared
with 9 percent among the individuals
with no remark and 11 percent among
the matched sample. Nonetheless, the
likelihood of subsequent delinquency
was significantly lower than that found
in Musto’s sample.
HOUSING PRICES AND
DEFAULT
Leonardo Martinez, of the International Monetary Fund, explained
the results of a macroeconomic
modeling exercise (with Juan Carolos
Hatchondo and Juan Sanchez) that
focused on the implications of housing price risk for household behavior.
36 Q1 2012 Business Review

Among other things, they used the
model to examine the effects of minimum down payment restrictions and
laws that permit lenders to garnish the
income of defaulting homeowners.
Martinez explained that in their
model, households have limited opportunities to hedge against declines
in their labor income or to sudden

sions about how big a house to buy,
how much money to put down, etc.
That is, households can self-insure.
The authors used calibration techniques to fix the model’s parameters.
They chose a number of the model’s
parameters, for example, households’
aversion to risk and the correlation
between house prices and personal

The main innovations of this paper were to
include a realistic long-term mortgage contract
and to allow the major contract terms, e.g.,
interest rates and down payments, to arise
endogenously through supply and demand in a
competitive market.
declines in housing prices. Although
other researchers have examined similar models with and without explicit
housing decisions, the main innovations of this paper were to include a
realistic long-term mortgage contract
and to allow the major contract terms,
e.g., interest rates and down payments,
to arise endogenously through supply
and demand in a competitive market.
In their model, households can
decide to either buy or rent — by assumption, renting is intrinsically less
attractive than buying for all households — and households take out longterm fixed-rate mortgages to finance
their home purchases. Mortgages can
be refinanced and households may
default. In the model, households make
all decisions knowing that their future
wage income or house prices might rise
or fall in any period. Households know
how income and house prices move
together on average, but they can’t predict precisely what will happen in any
particular period. Even though the
authors assume that households can’t
purchase explicit insurance against declines in labor income or house prices,
they can protect themselves through
prudent savings decisions, their deci-

income, from the existing literature.
Then authors chose values for the
remaining model parameters with the
goal of matching three targeted factors
that can be measured from published
data: the average house-price to income ratio, the median net-worth to
income ratio, and the homeownership
rate from the 2004 Survey of Consumer Finances.
The authors then simulated the
fully calibrated model to see how
closely it could match certain empirical
features of housing markets. Martinez
reported that the model was relatively
successful in matching the distribution
of down payments across the population of homeowners, as well as the
homeownership rates for households
of different age groups. The model’s
ability to match these factors with
some accuracy provides a rationale for
viewing the model as a useful representation of the real world.
Next, the authors examined
how successfully households could
self-insure in a world where income
might fall without warning precisely
when house prices are also falling, a
potential disaster in a world in which
households prefer to avoid risk. Despite
www.philadelphiafed.org

households’ lack of explicit insurance
opportunities in the model, the authors found that households were able
to self-insure just as well in a model
economy with housing risk as they
were in an otherwise identical model
economy without housing.
Martinez and his coauthors then
used their model economy to analyze
the effects of two policy experiments.
In the first, they examined the effect
of imposing a 20 percent down payment requirement for all mortgages.
They found that this policy had only a
modest effect on homeownership rates
and led to a reduction in default rates
and interest rates. While higher down
payments reduced the well-being of
renters and younger households, who
were forced to wait longer to purchase
a home, the authors argue that most
households would gain from such a
policy.
The second policy allowed lenders
to garnish defaulting households’ income above some predetermined floor.
They modeled garnishment in a stylized way: Households can make binding pledges of future income to service
debts without imposing large collection
costs on lenders. This policy increased
homeownership rates, reduced default
rates, and lowered mortgage rates.
Martinez suggested that this policy
would be welfare-enhancing for nearly
all households. Unlike a policy of
minimum down payments, this policy
increased the availability of mortgage
credit for younger households who
might not have sizable enough savings
to make a down payment.
THE ADOPTION AND USE OF
PAYMENTS INSTRUMENTS
Scott Schuh, of the Federal Reserve Bank of Boston, presented results
from a study (with Sergei Koulayev,
Marc Rysman, and Joanna Stavins)
of the adoption and usage patterns of
payments instruments — e.g., cash,
check, and debit, among others — by
www.philadelphiafed.org

U.S. consumers. Schuh emphasized
that the results were preliminary. He
explained that payments systems are
changing rapidly and that we know
relatively little about what an optimal payments system might look
like. Nonetheless, policymakers are
making regulatory decisions that have
an impact on the payment choices of
consumers.
The authors estimated a structural
model of consumer decision-making
that explicitly separates adoption
decisions (“Do I open a credit card
account?”) and usage decisions (“Do
I use credit or debit to buy this TV?”).
This permitted the authors to analyze how households might respond to
market-driven or regulatory changes
that affect the cost or usefulness of
various payment instruments. In
particular, Schuh explained that they
can use this model to examine some
of the potential effects of regulatory
ceilings on debit card interchange fees
paid by merchants mandated under
the Durbin Amendment of the DoddFrank Act of 2010.6 Schuh noted that
some banks had increased debit card

Survey of Consumer Payment Choice,
jointly constructed by the Federal
Reserve Bank of Boston and the Rand
Corporation. To construct this data
set, the Boston Fed and Rand asked
1,500 households to fill out a detailed
survey that asked which payment instruments the consumers used and for
what types of purchases. Respondents
also answered questions about their attitudes toward the various instruments,
for example, the ease of adoption, the
speed with which transactions could
be completed, and the relative security
of using an instrument. The data set
also includes demographic information about the household, e.g., income,
marital status, and education, among
other factors. This is a continuing survey; the authors estimated the model
using information from the 2008 survey. For this study, the authors limited
their attention to households with a
checking account, yielding a sample of
997 households.
In their modeling approach,
Schuh and coauthors viewed households as making a two-stage decision.
In the adoption phase, they choose to

Payments systems are changing rapidly and
we know relatively little about what an optimal
payments system might look like. Nonetheless,
policymakers are making regulatory decisions
that have an impact on the payment choices of
consumers.
fees or reduced rewards for consumers
in response to the regulatory change
and that this model could be used to
see how customers might respond and
to measure how the change might affect their well-being.
The researchers estimated the
model using a data set, called the

6

Section 1075 of Pub. L. 111-203.

adopt a bundle of payments instruments, i.e., a checking account plus
any or all of the following: cash,
debit card, credit card, stored-value
card, online bill payment, direct bank
deduction, and income deduction.
Households make the initial adoption
decision knowing the various types
of purchases they are going to make
in the future and, thus, their future
choice of payment instruments, the
Business Review Q1 2012 37

usage stage. The authors estimated
two separate equations jointly: One
equation represented the household’s
usage among the payment instruments
from the bundle initially chosen, and
a second represented the household’s
adoption decision, that is, the initial
choice among bundles.
Schuh explained that their modeling approach was flexible, in the
sense that it permitted a wide range
of interactions among usage patterns
by different households. A possibly
significant limitation of their approach
was the assumption that the adoption
of one instrument does not affect the
cost of adopting another instrument.
While this may be an unrealistic assumption — made for technical reasons — the researchers’ approach does
permit the adoption of one instrument
to affect the consumer’s cost or value
of using another instrument. So, in
their model, adopting a credit card
doesn’t make it cheaper to also adopt a
debit card, but it could make it easier
to use the debit card.
Schuh then highlighted some of
the insights from the model. Focusing first on the usage equation, Schuh
and coauthors found that consumers’
income was strongly positively related
to usage of all payment instruments
except for stored-value (prepaid) cards.
Consumer ratings were also important
determinants of usage, with ease of use
and cost of use being particularly important, while security was a relatively
unimportant concern for households.
Schuh argued that this was an unexpected result, evidence of the value of
the researchers’ structural modeling
approach.
Turning to the adoption equation,
the authors found that credit cards
were the least costly to adopt, followed
by debit cards. The authors also found
that adoption costs were negatively
related to income for all instruments,
but the negative relationship between
income and credit card adoption costs
38 Q1 2012 Business Review

was particularly strong. Schuh suggested that this may reflect the role of
underwriting in the supply of unsecured credit.
Schuh then discussed the effects
of the Durbin Amendment, which
placed a ceiling on debt card interchange fees paid by merchants.7 First,
the authors estimated the usage benefits and adoption costs for debit cards.
Schuh showed that usage benefits
were roughly the same for consumers
with different incomes, while adoption costs were significantly lower for
higher-income consumers. Schuh and
coauthors concluded that policies that
increase debit adoption costs are likely
to have a disproportionate effect on
low-income households, at least those
with checking accounts.
Next, the authors used their
model to simulate how consumers might respond to an increase in
adoption costs or an increase in usage
costs that reduced the market share of
debit cards by 1 percent. The authors
considered both short- and long-term

similar. The authors also found that
low-income customers with checking
accounts would suffer larger declines in
well-being compared with the declines
experienced by consumers with higher
incomes. That is because households
with higher incomes tend to use more
payment instruments, thereby incurring lower costs of adjusting to the new
environment.
LIQUIDITY CONSTRAINTS
AND BANKRUPTCY
Tal Gross, of Columbia University, reported the results of an empirical study (with Matthew Notowidigdo
and Jialan Wang) of the effects of tax
rebates on bankruptcy filings. Their
main finding was that tax rebates
increased Chapter 7 filings, evidence
that many households without ready
cash were unable to file bankruptcy
unless they could pay the required
court costs and lawyers’ fees.
Gross noted first that a number of
other empirical studies had found that
liquidity constraints have significant

Schuh and coauthors concluded that policies
that increase debit adoption costs are likely to
have a disproportionate effect on low-income
households, at least those with checking
accounts.
effects of such changes. In the short
run, in which consumers cannot immediately adjust their bundles of payment instruments, they shift a significant portion of their transactions to
cash, with a somewhat smaller shift to
checks and credit cards. The results
for the long run, in which consumers can choose a different bundle, are

7
Note that in all simulations in this paper, it
is assumed that merchants would continue to
accept the forms of payment they accepted prior
to the policy experiment.

effects on consumption decisions. He
and his coauthors explored whether
liquidity constraints might also limit
households’ access to social insurance programs — programs designed
to protect households against catastrophic declines in consumption levels
— when these programs require a
household to pay a fee. Bankruptcy is a
particular type of social insurance program designed to reduce a household’s
debt payments when they become too
large relative to income, but court
fees are $300 and Chapter 7 lawyers’
www.philadelphiafed.org

fees fall between $500 and $1500.
Gross suggested that these fees might
represent a significant barrier to using
bankruptcy for households in financial
distress and without cash on hand.
The authors’ approach was to
use a natural experiment to examine
the effects of the tax rebates of 2001
and 2008 on bankruptcy filings. They
found that bankruptcy filings increased
after households received the rebates
for both episodes. But this increase
occurred only for Chapter 7 filings and
not for filings under Chapter 13.
The authors’ approach exploited
a feature of the tax rebates that make
them an ideal natural experiment; the
timing of the rebates was based solely
on the last two digits of the recipient’s
Social Security number. The key is
that the last two digits of a recipient’s
Social Security number are essentially
random; it is a characteristic that is
unrelated to any other factor that
might plausibly affect the recipient’s
economic behavior, such as income,
marital status, age, etc. The authors
used court records to identify the
Social Security number of households
that entered bankruptcy in 2001 and
2008 from 72 of the 90 bankruptcy
courts in the U.S., a sample that included 74 percent of the bankruptcy
filings and 95 percent of the U.S.
population.
The authors then used a difference-in-difference framework to
determine whether tax rebates affected
the number of households filing for
bankruptcy. Specifically, in any twoweek period, the authors added up
the number of filings for those individuals whose Social Security numbers indicated that they might have
received tax rebates in that two-week
period and compared this with the
number of households that could not
have received tax rebates during that
period. The authors found that for the
2001 rebate, the number of Chapter 7
bankruptcy filings was nearly 4 percent
www.philadelphiafed.org

higher for Social Security number
groups that had received rebates. For
the 2008 rebate, the comparable figure
was even higher, nearly 5 percent.
Gross noted that this was interesting because the 2005 bankruptcy act
had been explicitly designed to make
it more difficult for households with
above-average incomes to qualify for
Chapter 7.

easier. The authors’ results suggest that
fees are ordeal mechanisms; that is,
they pose a hurdle that makes it harder
for liquidity-constrained households
to file for bankruptcy. In principle,
this might be justified if it improves
households’ financial incentives to act
prudently and to make decisions that
lower the probability of bankruptcy.
Nonetheless, if policymakers do not

The authors’ results suggest that fees are
ordeal mechanisms; that is, they pose a hurdle
that makes it harder for liquidity-constrained
households to file for bankruptcy.
In contrast, the authors found
only a small negative effect on Chapter
13 filings in 2001 and no effect in
2008. Gross argued that this finding was consistent with the view that
relaxed liquidity constraints were the
true cause of the rise in bankruptcy filings, because only Chapter 7 filers are
required to pay the filing fee immediately. Chapter 13 filers are permitted
to pay fees over time as part of their
repayment program.
The authors conducted a simple
falsification test to ensure that their
results could not have arisen by chance
or because of some factor other than
the tax rebates. They conducted
identical experiments for each of the
other years between 1998 and 2008
and found that there was no evidence
of a similar timing effect in those years
when tax rebates were not sent out.
Furthermore, Gross noted that their
empirical estimates of the effects of the
rebates were probably conservative, because not all individuals with the same
last two digits of their Social Security
numbers actually received rebates.
Gross concluded by drawing out
the policy implications of his research.
He noted that one could not automatically conclude that policymakers
should seek to make bankruptcy filings

want to penalize liquidity-constrained
households by limiting access to the
bankruptcy courts, the researchers’ results suggest that simplified procedures
that require lower out-of-pocket costs
for filers might be desirable.
THE SUPPLY OF CREDIT TO
BANKRUPT HOUSEHOLDS
Song Han, of the Federal Reserve Board, reported on the results
of a study (with Benjamin Keys and
Geng Li) of the supply of credit to
bankrupt individuals. Using a data set
that monitors credit card mailings to
a sample of households to measure the
supply of credit, their main results were
that bankrupt individuals (filers) continued to receive offers of credit; the
terms of the credit card offers were less
favorable for filers than those offered
to individuals who had not gone bankrupt (nonfilers); and recent filers were
more likely to receive an offer of credit
than filers who were about to have the
bankruptcy flag in their credit files
removed.
Han explained that it is typically
difficult to empirically disentangle
the effects of changes in the supply of
credit from changes in the demand for
credit simply by observing credit terms.
Theoretically, the supply of credit to a
Business Review Q1 2012 39

filer might decrease if the bankruptcy
flag reveals higher credit risk. But it
could also increase because bankruptcy eliminates existing debt and places
legal limits on future filings. Han argued that it is essential to understand
how the supply of credit is affected by
bankruptcy to understand the bankruptcy decision.
To conduct their study, the authors used a data set that includes a
more direct measure of the supply of
credit. A sample of 3,000 households
from July 2009 to August 2010 sent the
data provider all credit card mailings
they had received within the previous
month. The information about the
number and the terms of the offers
was then linked to data from individuals’ credit bureau files, which include
the date on which some individuals filed for bankruptcy, as well as a
range of other information about the
individual’s finances.8 The bankruptcy
flag in the data set file did not distinguish whether the individual entered
Chapter 7 proceedings — in which all
debts are written off — or Chapter 13
proceedings — in which the individual
agrees to a repayment plan.
Han first presented anecdotal
evidence that bankrupt individuals
received credit card offers targeted
specifically to households that had just
exited bankruptcy proceedings. He
then presented summary statistics indicating that the percentage of filers who
had opened an account was nearly the
same as for nonfilers, while, on average, offered interest rates were substantially higher, credit limits substantially
lower, and accounts substantially more
likely to bear annual fees for filers.9 He
said that these offers were typically of
the “credit building” variety; that is,
the offer had annual fees but without

8
Note that the data used by the authors were
anonymized. No personally identifiable information is contained in the data set.

40 Q1 2012 Business Review

the rewards typical of “premium rewards” offers.
The researchers then examined
how the supply of credit evolved over
time after a bankruptcy filing. One
factor that might affect the supply
of credit is the restriction that filers can’t file for bankruptcy for eight
years (while bankruptcy markers are
dropped from credit files after 10
years). Unsecured lenders might view
recent filers as a relatively lower risk,
everything else equal, given the restrictions on filing again. Consistent with
this view, Han and coauthors found
that, over time, the probability of
getting a card offer declined following bankruptcy. But among filers who
did receive offers, interest rates and
some other credit terms in those offers
improved modestly as the time elapsed
since the bankruptcy increased.
Han and coauthors then carried out a formal regression analysis,
estimating the effects of filing on the
probability of receiving an offer and
on the credit terms received by filers. These regressions also took into
account the individual’s credit score,

In their analyses of differences in interest
rates offered to filers and nonfilers, the authors
focus on the “go to” rate, that is, the interest
rate charged on revolving balances after any
promotional interest rates have expired. This
is a conservative approach, since nonfilers are
much more likely than filers to receive generous
promotional rate offers.

9

demographic information, and information about the individual’s balance
sheet. Broadly consistent with the
summary statistics reported above, the
authors found that filers were only 7
percentage points less likely than nonfilers to receive an offer in any given
month and individuals who had filed
in the previous two years were as likely
to receive an offer as a nonfiler.
Conditional on receiving an offer,
the probability that the offer required
an annual fee was 13 percentage points
higher — a large difference, since only
26 percent of nonfilers’ offers contained an annual fee. In addition, filers
were offered interest rates that were 77
basis points higher than rates offered
to comparable nonfilers. Filers were
offered a minimum credit limit that
was $470 (29 percent) lower than that
offered to comparable nonfilers.
Finally, the authors examined the
possibility that card issuers included
less generous terms in the fine print of
the mailing — where they were presumably less likely to be noticed — a
practice known as shrouding in the economic literature. Indeed, they found
that offers to filers were more likely to
include higher fees or interest rates on
balance transfers and higher minimum
payments. Additional fees and other
more onerous contract features were
more commonly included in the fine
print of the offers made to filers than
to nonfilers. BR

REFERENCES
Elul, Ronel, and Piero Gottardi. “Is
It Enough to Forgive, or Must We
Also Forget?” Federal Reserve Bank
of Philadelphia Working Paper 11-14
(April 2011).

Musto, David. “What Happens When
Information Leaves a Market? Evidence from Post-bankruptcy Consumers,” Journal of Business, 77 (2004), pp.
725-48.

www.philadelphiafed.org


Federal Reserve Bank of St. Louis, One Federal Reserve Bank Plaza, St. Louis, MO 63102