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Best Guesses and Surprises
William Poole

I

have a simple message today—that anyone
interested in monetary policy should spend
less time on economic forecasts and more time
on implications of forecast surprises. If you are in
the forecasting business, it makes good sense to
write at length about the forecast and the analysis
behind it. For the rest of us, the forecast provides
the baseline for examining the most important
policy issues. The true art of good monetary policy
is in managing forecast surprises and not in doing
the obvious things implied by the baseline forecast.
I’ll proceed by outlining the consensus outlook
and then will discuss how I view the job of dealing
with surprises. I’ll emphasize that the key issue is
that monetary policy responses to surprises ought
not to be random, but as predictable as possible.
There are some principles of good responses that
make it easier for students of monetary policy to
predict what the Federal Reserve will do.
Before digging into the substance of my subject,
I want to emphasize that the views I express do not
necessarily reflect official positions of the Federal
Reserve System. I thank my colleagues at the Federal
Reserve Bank of St. Louis for their comments—
especially Bob Rasche, senior vice president and
Director of Research, who provided special assistance. However, I retain full responsibility for errors.

CONSENSUS OUTLOOK TODAY
What is the consensus outlook for the U.S. economy today? Numerous forecasts are in the public
domain, from government and private sources.1
1

A partial list includes Blue Chip Economic Indicators (published each
month); Survey of Professional Forecasters (compiled quarterly by the
Federal Reserve Bank of Philadelphia); Wall Street Journal Forecasting
Survey (published early January and July of each year); Congressional
Budget Office, Budget and Economic Outlook (published each February
and August); Council of Economic Advisers economic outlook

Direct comparison of these forecasts is not straightforward, as there are differences among the variables
for which the forecasts are presented, differences
in the forecasting time horizons, and differences in
averaging, with some forecasts presented on a fourthquarter to fourth-quarter basis and others presented
on an annual-average over annual-average basis.
Nevertheless, at present a remarkably uniform
picture from a perusal of these various sources
emerges for the major economic indicators. Real
gross domestic product (GDP) is forecast to grow in
the 4 to 41/2 percent range from the fourth quarter
of 2003 to the fourth quarter of 2004. Inflation as
measured by the consumer price index (CPI) is forecast in the 11/2 to 2 percent range and as measured
by the GDP chain price index is forecast in the 1 to
11/2 percent range over that horizon. The unemployment rate is forecast to be around 51/2 percent by
the fourth quarter of 2004.
My colleagues around the Federal Open Market
Committee (FOMC) table are on average slightly more
bullish than the above picture: The midpoint of the
range of forecasts of real GDP growth included in
the Monetary Policy Report to the Congress submitted
two weeks ago is 41/2 percent for the fourth quarter
of 2004 over the fourth quarter of 2003. The midpoint of the range of inflation forecasts (measured
by the chained price index for personal consumption
expenditures) in that report is 1.13 percent, and the
midpoint of the forecast for the unemployment rate
in the fourth quarter of 2004 is 5.38 percent. I’ll refer
to this forecast as the “FOMC members’ forecast.”
The forecast reflects a survey of FOMC members,
(published each February in the Economic Report of the President and
updated each July); and Federal Reserve System, Monetary Policy Report
to the Congress (published each February and July), containing the
economic projections of the Federal Reserve governors and Reserve
Bank presidents.

William Poole is the president of the Federal Reserve Bank of St. Louis. This article was adapted from a speech of the same title presented at the
Charlotte Economics Club, Charlotte, North Carolina, February 25, 2004. The author thanks colleagues at the Federal Reserve Bank of St. Louis.
Robert H. Rasche, senior vice president and Director of Research, provided special assistance. The views expressed do not necessarily reflect official
positions of the Federal Reserve System.
Federal Reserve Bank of St. Louis Review, January/February 2004, 86(3), pp. 1-7.
© 2003, The Federal Reserve Bank of St. Louis.

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Poole

but is not an FOMC forecast per se because the
Committee does not debate and vote on the forecast
to make it a Committee forecast as such. Nor is it the
Board of Governors staff forecast prepared for each
FOMC meeting and reproduced in the Greenbook;
the Greenbook is released with the FOMC meeting
transcript only after a five-year lag.
Those forecasters who risk interest rate forecasts
(the Wall Street Journal Forecasting Survey, the Blue
Chip Economic Indicators, and the Congressional
Budget Office Economic Outlook) expect Treasury
bill rates around 1.2 percent, and ten-year Treasury
bond rates around 4.6 percent either on an annual
average basis or at the middle of 2004. I should note
that FOMC members do not make public forecasts
of interest rates.

HOW RELIABLE IS THE CONSENSUS
OUTLOOK?
The small dispersion among forecasts today is
not unusual and should not be interpreted as a
measure of likely forecast accuracy. Over the years,
numerous studies have investigated the forecast
accuracy of private forecasters. More recently several
studies have compared the accuracy of both the
FOMC members’ forecasts and the Greenbook forecasts with those of private forecasters. One recent
analysis was produced by William Gavin and Rachel
Mandal in the Research Department at the Federal
Reserve Bank of St. Louis. Their paper was published
last year in the International Journal of Forecasting.2
Because of the lag in releasing the Greenbook, this
study analyzes the Greenbook forecasting record
up through 1996. The other comparisons include
forecasts through 2001.
The authors compared the Blue Chip forecasts,
the Greenbook forecasts, and the FOMC members’
forecasts against a naive, same-change forecast
beginning in 1980 for both real output growth and
inflation. Three different forecasting horizons were
examined: six, twelve, and eighteen months.3 Not
surprisingly, the accuracy of the forecasts deteriorates as the forecasting horizon is lengthened. For
a one-year-ahead forecast, the root-mean-squared
forecast error (a measure of the dispersion of the
forecasts around the realized value) for real output
growth is on the order of 1.4 percentage points for
2

William T. Gavin and Rachel J. Mandal, “Evaluating FOMC Forecasts,”
International Journal of Forecasting, 2003, 19(4), pp. 655-67.

3

Details can be found in Tables 4 and 5 of Gavin and Mandal.

2

M AY / J U N E 2 0 0 4

REVIEW
all the three sets of forecasts considered. The rootmean-squared forecast error for the naive forecast
is considerably larger, on the order of 2.2 percentage
points.
Clearly, the forecast accuracy of the forecasters
is substantially better than that of the naive forecast,
but still leaves a lot of room for surprises. To make
this point clear in today’s context, if for convenience
we say that the GDP growth forecast is 4 percent
over the four quarters ending 2004:Q4, then one
standard error leaves us with a forecast band of 3 to
6 percent growth over this period. If we were to have
a 3 percent outcome, everyone would fear that the
recovery is faltering; if we were to have a 6 percent
outcome, the most likely characterization would be
that we have a boom on our hands.
Moreover, keep in mind that one standard deviation on either side of the expected value does not
by any means exhaust the range of possible outcomes. As a rough approximation, one time out of
three, the one-year-ahead forecast of real output
growth will fall outside a range of plus or minus
1.4 percentage points of the stated forecast number.
Assuming a symmetrical distribution of forecast
errors, which seems reasonable, there is a probability of about 0.16 that real output growth over the
next four quarters will exceed 6 percent and a
probability of about 0.16 that output growth will
fall short of 3 percent.
Clearly the range of error associated with the
current state of the forecasting art fails to distinguish
between a really strong expansion—a boom—and
a faltering recovery. And the accuracy of inflation
forecasts is not much better. On a one-year-ahead
forecasting horizon, the root-mean-squared error
of inflation forecasts is in the range of 0.75 to 0.9
percentage points. This forecasting record is not
much better than would have been achieved with a
naive forecasting model. As with real GDP, there is
a significant probability that the outcome could fall
outside the one-standard-deviation band. And it is
also true that an inflation outcome outside the band
would create considerable concern.
Published forecasts are repeatedly updated on
ever shorter and shorter forecasting horizons. The
results reported by Gavin and Mandal indicate that
as the horizon becomes shorter the uncertainty
surrounding the forecast realization is reduced—
though, perhaps surprisingly, not by a particularly
large amount. Their analysis suggests that for real

FEDERAL R ESERVE BANK OF ST. LOUIS

GDP growth the root-mean-squared forecast error
on an eighteen-month horizon is between 1.5 and
1.9 percentage points while at a six-month horizon
it is reduced to only 1.3 percentage points. For inflation, the root-mean-squared forecast error at the
eighteen-month horizon is between 1.1 and 1.3
percentage points but is substantially reduced to
around 0.5 percentage points at a six-month horizon.
As we go through the year, the forecast for 2004
will be updated as results for each quarter come in.
An example of this process is provided by the
monthly Blue Chip consensus forecast for 2003.
The initial release of the Blue Chip forecast for last
year was in January 2002; thus, we have a record
of 24 successive Blue Chip forecasts for 2003. The
initial forecast was for a year-over-year growth rate
of 3.4 percent. Through the first half of 2002 the
consensus forecast was revised up slightly, reaching
a peak of 3.6 percent in June. Thereafter the consensus was fairly steadily revised downward over
the next year, reaching a trough of 2.3 percent in
August 2003. The final forecast, in December 2003,
was 3.1 percent, which is the currently published
number for real growth in 2003 over 2002. The
initial release of the consensus CPI inflation forecast
for 2003 over 2002 in January 2002 was 2.4 percent.
This forecast changed very little over the following
24 months, increasing to 2.5 percent in mid-2002
and then settling down at 2.3 percent, the CPI inflation rate that was realized for 2003 over 2002.
The relatively low variability of the consensus
forecast for 2003 masks the heterogeneity among
the individual survey respondents that reflects the
inherent uncertainty of economic forecasts. In early
2002, the range of forecasts for real growth in 2003
across the Blue Chip respondents was 2.0 to 6.0
percent. By the beginning of 2003 this range had
narrowed to about 2.5 to 4.5 percent. Only after the
middle of 2003, when data from six of the eight
quarters involved in the computation of a year-overyear growth rate were available, did the range of
individual forecasts drop below 1 percentage point.
A similar dispersion is observed among the
individual forecasts of CPI inflation for 2003. At the
beginning of 2002 the range of forecasts was from
less than 1.0 percent to almost 4.5 percent. By early
2003 this range had narrowed to less than 1.5 to
slightly more than 2.5 percent. It was only after
September 2003 that the range of forecasts shrunk
to less than 1 percentage point.

Poole

SOME EXAMPLES OF FORECAST
SURPRISES
Forecast surprises, or forecast errors, are a
standard part of the policy landscape. It is very
easy to criticize forecasts and extremely difficult to
come up with better forecasts. The fact is that good
forecasters produce state-of-the-art forecasts. Policymakers must deal with forecast surprises. What are
the sources of those surprises?
The difficulty of forecasting turning points in
economic activity is most significant. Whatever
creates a recession also creates a forecast surprise.
For example, the October 2000 Blue Chip consensus
for real growth over the five quarters ending 2001:Q4
was for a very steady quarter-to-quarter expansion
in real GDP in the range of 3.3 to 3.6 percent at an
annual rate. The business cycle dating committee
of the National Bureau of Economic Research later
dated a cycle peak in March 2001 and a trough in
November 2001. Actual quarter-to-quarter real
growth during this period ranged from –1.3 to 2.1
percent. Thus, five months before the onset of the
2001 recession, the Blue Chip consensus forecast
missed the recession completely!
My point here is not to pick on the Blue Chip
respondents. My colleagues on the FOMC had no
greater foresight. In the minutes of the FOMC meeting in October 2000 we can read that, “[l]ooking
ahead, they [FOMC members] generally anticipated
that the softening in equity prices and the rise in
interest rates that had occurred earlier in the year
would contribute to keeping growth in demand at
a more subdued but still relatively robust pace.”4
A second noteworthy example is October 2001.
In the immediate aftermath of the 9/11 attacks, forecasters turned extremely bearish on the near-term
prospects. The Blue Chip consensus for real growth
in 2001:Q4 in the October 10, 2001, survey was –1.3
percent, with a range of forecasts from –3.2 to 0.8
percent. The Blue Chip respondents were particularly
pessimistic about prospects for the manufacturing
sector; the consensus was for growth of –3.1 percent,
with a range from –7.4 to 0.6 percent. We now know
that in 2001:Q4 the economy rebounded to a 2.1
annual rate of growth in real GDP, led by an all-time
record rate of light vehicle sales. Keep in mind that
this GDP growth rate was above the forecast of every
single one of the 50 plus Blue Chip respondents at
the beginning of the quarter.
4

Minutes of the FOMC Meeting of October 3, 2000, Federal Reserve
Bulletin, January 2001, p. 23.

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Poole

A third example is the history of real growth and
inflation forecasts in the second half of the 1990s
after the now-apparent increase in trend productivity
growth. Consider the midpoint of the range of forecasts of real growth and inflation by FOMC members
prepared each February for the four quarters ending
in the fourth quarter of each year from 1996 through
1999. On average these forecasts underestimated
real growth by 2.1 percentage points for these four
years. The range of forecast errors was from 2.4 to
1.9 percentage points. The errors were all in the
same direction and all of significant size. During
the same four years the CPI inflation forecast error
averaged 0.0 percent—right on the button. However
the forecast errors for the individual years ranged
from –1.2 to 0.6 percentage points.
The reasons for forecast errors are many. Some
reflect incomplete understanding of how the economy works, such as the errors in projecting productivity growth, or consumer behavior right after the
9/11 terrorist attacks. Some reflect unpredictable
shocks, such as a sharp change in energy prices or
the 9/11 terrorist attacks themselves. Some reflect
financial disturbances, such as the 1987 stock
market crash. Whatever may be the reasons for
forecast errors, they are a fact of life.

THE POLICY SIGNIFICANCE OF
FORECAST UNCERTAINTY
What are the implications of the documented
uncertainty surrounding forecasts of future economic activity? Some dismiss forecasts altogether
and view them as irrelevant for policy because their
errors are so large. To me, that response is completely
wrong. Instead, policy needs to be informed by the
best guesses incorporated in forecasts and by knowledge of forecast errors. Forecast errors create risk,
and that risk needs to be managed as efficiently as
possible. And the surprises that create forecast
errors also create the need for policy changes that
cannot be anticipated in advance because the surprises cannot be anticipated.
Given the size of forecast errors, we will frequently observe the economy evolving along a
substantially different path from that portrayed by
consensus forecasts only a short time earlier. With
newly available information, forecasters will adjust
their prognostications, and policymakers, such as
the FOMC, will adjust their view of the appropriate
policy stance. If the revised view of the appropriate
policy stance is sufficiently changed, policymakers
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can and should implement the changes in policy
settings, such as the intended federal funds rate, that
they believe are consistent with the new information.
Such policy actions should be implemented
whether or not they will come as surprises to market
participants and the general public. Here it is important to be clear about the distinction between a policy
and a policy action. A policy should be viewed as a
rule or response regularity that links policy actions,
such as adjustments in the intended federal funds
rate, to the state of the world. A policy is like a decision to drive 65 miles per hour; given that policy, a
policy action is the adjustment of the accelerator to
maintain the target speed. If the effects of wind and
hills on speed cannot be anticipated, then neither
can the policy actions of accelerator adjustments.
A good policy requires clarity about policy objectives
and as much precision as possible as to how policy
actions will respond to new information to best
achieve the policy objectives.
In the monetary policy context, anticipated
policy actions are naturally tied closely to the forecast. To maintain the policy of achieving low and
stable inflation, unanticipated policy actions must
often accompany forecast surprises. Should an
inflationary shock hit the economy, for example,
that shock and an increase in the FOMC’s target
federal funds rate would both be surprises.
On numerous occasions I have stated my view
that the FOMC should communicate its intention
about monetary policy as precisely as possible to
get markets in “synch” with policy. My view should
not be interpreted to imply that the FOMC can only
act after it has “prepared” market participants for a
change in the intended federal funds rate. There will
be times when significant unforeseen economic
news will be revealed very suddenly—events that
can be appropriately described as “shocks.” If, in the
judgment of the FOMC, such news calls for policy
actions even though market participants could not
have been forewarned of such actions, the FOMC
would be derelict in its responsibilities if it failed to
act. Given the shock, the FOMC’s action ought not
to be a surprise. The real surprise would arise if the
FOMC were to do nothing in the face of a shock
calling for action.
A couple of examples are illustrative. Consider
the Asian debt crisis, the Russian default, and the
collapse of Long Term Capital Management (LTCM)
in August-September 1998. No one foresaw this
combination of events, nor was the impact of these
events on the liquidity of major financial markets

FEDERAL R ESERVE BANK OF ST. LOUIS

predictable. At the time of the FOMC meeting on
August 18, 1998, federal funds futures for contracts
as far out as December 1998 were trading within a
couple of basis points of the prevailing 4.50 percent
intended funds rate. Nevertheless, by the conclusion
of the FOMC meeting on November 17, 1998, the
intended funds rate had been reduced in three steps
by a total of 75 basis points, including a cut of 25
basis points at an unscheduled conference call
meeting on October 15.
These rate cuts in the fall of 1998 were a surprise
from the vantage point of early August. But the real
surprise would have been if the FOMC had totally
ignored the Russian default and collapse of LTCM.
Holding the intended funds rate constant given the
market turmoil would not have been consistent with
the Fed’s responsibility to contribute to financial
stability.
I could walk through numerous other examples
to drive home the point that a key feature of monetary policy is measured and appropriate responses
to the constant stream of surprises. In discussions
of monetary policy, I would like to see much more
emphasis on appropriate policy responses to surprises and potential surprises and much less emphasis on forecasts. An overemphasis on consensus
forecasts may lead market participants to a false
precision in their views about the federal funds
rate going forward. It is much more productive to
think through the sorts of things that might happen
and the appropriate response to such events. A careful analysis of risks helps to prepare the mind for
dealing with surprises when they occur. Market
participants and the FOMC should not focus on the
predictability of a particular path for the funds rate,
but instead on the predictability of the response of
the FOMC to new information about the economy.

PRINCIPLES OF FOMC RESPONSES
TO “SHOCKS”
For at least 40 years, economists have been trying to develop a quantitative characterization of
FOMC policy actions—a policy reaction function.5
A review published in 1990 analyzed 42 published
examples of attempts at characterizing FOMC
behavior.6 Since 1993, the prevalent framework to
5

6

An early analysis is William G. Dewald and Harry G. Johnson, “An
Objective Analysis of the Objectives of American Monetary Policy,
1952-61,” in Deane Carson (ed.), Banking and Monetary Studies,
Homewood, IL: Richard D. Irwin, 1963, pp. 171-89.
Salwa S. Khoury, “The Federal Reserve Reaction Function: A Specifi-

Poole

quantify FOMC action is the “Taylor rule.”7 None of
these efforts have achieved their objective.8 In my
judgment, it is not possible at the current state of
knowledge to define a precise reaction function of
the FOMC, and perhaps it never will be possible.
It is possible, however, to describe some general
principles that guide FOMC behavior and that can
be applied by market participants to form expectations about how the FOMC will respond to new and
unexpected information. I believe that these principles are fairly widely accepted, but different FOMC
members will apply them in different ways at different times. And the principles always involve a
degree of judgment.
The first principle is that the FOMC will not
respond to “shocks” that are seen as very transitory.
Policy should only react to “shocks” that are longer
lasting—highly persistent. The reason for this principle is quite straightforward—nothing that the
FOMC can do will offset the impact on the economy
of a “here today, gone tomorrow” event. While
economists continue to debate exactly how “long
and variable” the response of the economy is to a
policy action, there is a consensus of professional
opinion that it takes at least several months before
the economy responds. Of course, judgment is
always necessary to determine whether any particular shock is likely to be transitory.
Some transitory shocks occur because “news”
does not provide accurate information. Many data
releases are subject to several revisions, and often
the revised data reveal a different picture than that
portrayed by the initial release. Quarterly GDP data
are revised twice until the “final estimates,” and
these “final estimates” are subject to annual benchmark revisions and comprehensive revisions at
roughly five-year intervals. For a recent example of
significant data revisions, initial measurement of the
2001 recession suggested negative real GDP growth
in the second and third quarters of 2001, whereas
the currently available data measure negative real
growth as early as the third quarter of 2000 and for
the first three quarters of 2001.
cation Search,” in Thomas Meyer (ed.), The Political Economy of
American Monetary Policy, New York: Cambridge University Press,
1990, pp. 27-50.
7

John B. Taylor, “Discretion versus Policy Rules in Practice,” CarnegieRochester Conference Series on Public Policy, 1993, 39(0), pp. 195-214.

8

An illustration of the deviations of the predicted from actual funds rate
from a Taylor rule with a constant target inflation rate over the past
decade can be found in Federal Reserve Bank of St. Louis, Monetary
Trends, p. 10, available at http://research.stlouisfed.org/publications/mt/.

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The monthly payroll employment data are
revised in the two months following the initial release
and are revised again at the beginning of the following calendar year to incorporate benchmarks to the
unemployment insurance system records. With the
initial release of the payroll employment numbers
for October 2003 at the beginning of last November,
the measured monthly increase of 126,000 workers
generated the hope that the transition from the twoyear “jobless recovery” to a period of rapid employment growth was at hand. The October data as
currently revised indicate an increase in payroll
employment of only 88,000 workers. We now believe
that only in January 2004 did month-to-month payroll employment growth exceed 100,000 jobs—and
only an anemic 112,000 at that.
The presence of measurement error in individual economic data series, particularly in the initial
releases of such data, requires that analysts and
policymakers examine multiple data sources for a
consistent picture of the underlying trends in economic activity. There is no way to generalize about
this issue. Different series have different sources of
error and different frequencies of large revisions.
Some series are more subject to special disturbances,
such as bad weather, than others. The Federal
Reserve has tremendous staff expertise and access
to statistical agencies that permit it to form the best
judgments possible on these tricky issues.
As an aside, let me offer another observation.
Currently, the Federal Reserve enjoys very high
credibility. Among other benefits, that credibility
enables the Fed to react to its best judgment about
what incoming data mean. The Fed does not have
to act to maintain appearances. For example, my
impression is that there were times in the 1970s
when the Fed failed to react to accumulating evidence of economic weakness for fear that to react
before inflation declined could be interpreted as a
lack of inflation-fighting resolve. Policy actions
designed primarily to attempt to affect expectations,
even though contrary to the fundamentals, ultimately
increase uncertainty as it becomes clear that the
action did not fit the fundamentals. Success in bringing down inflation and keeping it down means that
the Fed can ignore a surge in price indices or any
other troubling information if its best judgment is
that the data reflect a statistical aberration or a
transitory event.
I’ve argued that the Federal Reserve must analyze
the data for potential statistical problems and that
6

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REVIEW
it must do its best to sort out transitory disturbances
from longer lasting ones. Another dimension of
the problem is that a central part of making such
judgments is to collate information from a variety
of sources. Employment data provide an excellent
example. The establishment and household surveys
are quite distinct statistically, as the surveys’ coverage
and methods do not overlap. Data on initial claims
for unemployment insurance supplement the
message from the two main surveys. In addition, the
Federal Reserve accumulates a wealth of anecdotal
information on the labor market from contacts
across the country; much of this information appears
in the Beige Book. When data from diverse sources
point in the same direction, confidence in the direction indicated is increased. Conversely, when the
signals are conflicting, there is often good reason
to reserve judgment and delay policy action. Analysis
of the strength of household demand, business
investment demand, inflationary pressures, and all
other key elements of the picture can and does proceed the same way.
Once FOMC members have reached a conclusion
on where the economy is and where it is heading,
there are situations where the decision on the
appropriate policy response is straightforward and
other cases where the appropriate response is problematic. Consider some examples of easy cases first.
Suppose the economy has shown robust growth
with low inflation for a period of time, and information accumulates that leads to a reasonable interpretation that both real growth and inflation pressures
are increasing, or both decreasing. Faced with such
information, central bankers with a dual mandate
(such as the FOMC) are likely to respond by raising
or lowering, as appropriate, the nominal interest
rate target. When credibility is high, moreover, the
decision need not be a quick one. But when the
issue is clear, the central bank must act vigorously
enough to ensure maintenance of a non-inflationary
equilibrium.
Indeed, such responses are, qualitatively, exactly
those predicted by the Taylor rule. Under these
conditions, market participants and private agents
can likely accurately anticipate the direction, if not
the timing and magnitude, of FOMC actions. The
FOMC practice since February 1994 of generally
restricting changes in the intended federal funds
rate to regularly scheduled meetings and making
changes in multiples of 25 basis points has demonstratively improved the predictability of the timing

FEDERAL R ESERVE BANK OF ST. LOUIS

and magnitude of changes in the intended funds
rate in such cases.9
The appropriate policy response in other cases
is less clear. Suppose the economy has shown robust
growth with low inflation for a period of time and
information arrives that leads to a reasonable interpretation that real growth is decreasing and inflation
is increasing. A historical episode of this sort is the
“oil shock” in late 1973 and 1974. Here, one component of a “dual mandate” signals a policy action
in one direction and the other component in the
opposite direction. This is a dilemma case in which
the behavior of the economy is pulling the policymakers to be both easier and tighter. A weighting
of objectives and careful attention to long-run concerns is necessary. Even if a central bank were to
follow a Taylor rule approach to implementing policy
changes, in the absence of disclosure of the exact
reaction function, outside observers would be unable
to predict the policy action. It is unrealistic to believe
that a central bank can provide the transparency
required for outsiders to accurately predict policy
actions in all such circumstances.
Predictability in the dilemma cases can be
improved and the appropriate policy response
facilitated when a central bank has a credible commitment to maintaining low inflation in the long
run. In these circumstances, the central bank can
likely pursue short-run stabilization objectives without significant influence on expectations of longrun inflation. In current parlance, inflationary
expectations are “well anchored.” In such environments, policy actions aimed at short-run stabilization are likely to be more effective. Under conditions
of high credibility, policy actions are likely more
predictable.
The Federal Reserve has policy responsibilities
beyond a narrow interpretation of the “dual man-

9

Poole

date.” In particular, a fundamental responsibility
envisioned by the architects of the Federal Reserve
Act was that the new central banking structure avoid
recurrence of episodes of financial instability and
banking panics such as those that occurred regularly
in the late 19th and early 20th century. The Great
Depression was a Federal Reserve policy failure of
the first order. Recent episodes, such as the 1987
stock market crash, the financial market upset in
the fall of 1998, Y2K, and 9/11 provide evidence that
the Federal Reserve has learned lessons from the
1930s well and can deal effectively with systemic
threats to financial stability.
It is important to understand, however, that
concerns about financial stability require that the
Federal Reserve sort out shocks that raise such
concerns from those that do not. Not every large
event creates risks for the financial system as a
whole. The large stock market decline that started
in early 2001 did tend to depress economic activity
but, unlike the crash of 1987, never raised issues of
systemic stability.

CONCLUDING COMMENT
Forecast uncertainty is a fact of life. Forecasts
are like newspapers. Just as last week’s newspaper
is of little value in understanding today’s news, last
month’s forecast is of little value in determining
today’s policy stance. Old newspapers and old forecasts are primarily of historical interest.
The obvious fact that we insist on using the
most up-to-date forecast available indicates that
forecasts change, sometimes substantially, with new
information. Forecasts are valuable in formulating
monetary policy, but it is of critical importance
that we not allow today’s policy settings to become
entrenched in our minds.

William Poole, Robert H. Rasche, and Daniel L. Thornton, “Market
Anticipations of Monetary Policy Actions,” Federal Reserve Bank of
St. Louis Review, July/August 2002, 84(4), pp. 65-93; and William Poole
and Robert H. Rasche, “The Impact of Changes in FOMC Disclosure
Practices on the Transparency of Monetary Policy: Are Markets and
the FOMC Better ‘Synched’?” Federal Reserve Bank of St. Louis Review,
January/February 2003, 85(1), pp. 1-9.

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8

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Monetary Policy Actions, Macroeconomic
Data Releases, and Inflation Expectations
Kevin L. Kliesen and Frank A. Schmid

D

o surprises in macroeconomic data releases
and monetary policy actions of the Federal
Reserve lead economic agents to update
their beliefs about the rate of inflation? If so, which
macroeconomic data releases matter for inflation
expectations? Does Federal Reserve communication
(for example, speeches and testimonies by Fed
officials) affect the uncertainty surrounding the
rate of inflation that economic agents expect for
the following 10 years? These are some of the
questions we are trying to answer in this paper.
We gauge inflation expectations by two different
concepts of inflation compensation, both of which
are derived from the market valuation of the
expected cash flows of nominal Treasury securities
versus inflation-indexed Treasury securities (TIIS). We
look at 35 macroeconomic data series (for example,
the monthly change in nonfarm payroll employment) and determine whether daily changes in inflation compensation are associated with the surprise
component in these series. We define the surprise
component as the difference between the expected
and the actually released value of the series, normalized by the degree of uncertainty surrounding these
expectations. The time period of our analysis is
January 31, 1997, to June 30, 2003, for one concept
of inflation compensation and January 4, 1999, to
June 30, 2003, for the other. For the 35 macroeconomic data series, we find the following: for 17, the
surprise component in the announcement has no
bearing on inflation expectations; for 5, the surprise
component has an effect on one measure of inflation
expectations, but not on the other; for 13, the surprise component in the release consistently affects
inflation expectations, independent of the employed
concept of inflation compensation. Further, we show
that monetary policy actions that are tighter or easier
than expected by the federal funds futures market
have a statistically significant effect on the expected

rate of inflation, independent of the employed
concept of inflation compensation. Finally, we provide evidence that Federal Reserve communication
and surprises in monetary policy actions bear on
the uncertainty surrounding the expected rate of
inflation. For one concept of inflation expectations,
we find that Federal Reserve communication
reduces uncertainty about the future rate of inflation,
while surprises in monetary policy actions increase
this uncertainty. For the other concept of inflation
compensation, we find no such effects.

RELATED LITERATURE
The effect of macroeconomic announcements
on inflation compensation embedded in the market
valuation of expected cash flows of nominal Treasury
securities versus TIIS has been investigated before.
The studies most closely related to our work
are Sack (2000) and Gürkaynak, Sack, and Swanson
(2003). Using daily data, Sack (2000) analyzes how
surprises in the releases of six monthly macroeconomic data series affect the inflation compensation embedded in Treasury securities for the period
1997-99. These macroeconomic data series are the
consumer price index (CPI), the CPI excluding food
and energy (core CPI), the producer price index for
finished goods (PPI), nonfarm payroll employment,
retail sales, and the NAPM index.1 Sack matches the
on-the-run 10-year TIIS with a portfolio of nominal
Treasury STRIPS (Separate Trading of Interest and
Principal Securities) that replicates the pattern of
expected payments of the TIIS.2 The author finds a
1

The National Association for Purchasing Managers’ (NAPM) index is
now simply the Purchasing Managers Index; it is released by the
Institute for Supply Management.

2

The Treasury STRIPS program, which was introduced in January 1985,
“lets investors hold and trade the individual interest and principal
components of eligible Treasury notes and bonds as separate securities”
(www.publicdebt.treas.gov/of/ofstrips.htm).

Kevin L. Kliesen is an economist and Frank A. Schmid is a senior economist at the Federal Reserve Bank of St. Louis. Jason Higbee and Thomas
Pollmann provided research assistance.
Federal Reserve Bank of St. Louis Review, May/June 2004, 86(3), pp. 9-21.
© 2004, The Federal Reserve Bank of St. Louis.

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Kliesen and Schmid

statistically significant response of inflation expectations to surprises in the CPI, the core CPI, retail
sales, and the NAPM index.
Gürkaynak, Sack, and Swanson (2003) analyze
the response of inflation compensation embedded in
one-year nominal versus inflation-adjusted forward
interest rates to surprises in macroeconomic data
releases and Federal Reserve monetary policy
actions—that is, changes to the Federal Open Market
Committee’s (FOMC) federal funds target rate. The
forward rates are derived from the yields of 10-year
Treasury securities—the TIIS and nominal securities.
The pair of one-year forward rates that the authors
study is the one for the 12-month time window
between the maturity dates of the on-the-run 10year TIIS and the (off-the-run) TIIS issued 12 months
earlier. Prior to July 2002, and starting in 1997, 10year TIIS were issued only once per year, in January.
This implies that the authors analyze changes to
the inflation rate that is expected to prevail during
a 12-month time window that starts, on average, 8.5
years from the time of the data release. The sample
period runs from January 1997 through July 2002
and covers 39 macroeconomic data series. The
authors show that the rate of inflation expected to
prevail in about nine years’ time correlates positively
with surprises in consumer confidence, consumer
credit, the employment cost index (ECI), gross
domestic product (GDP, advance), new home sales,
and retail sales and negatively with surprises in the
federal funds target rate. The authors conclude (on
p. 2) that their “empirical findings suggest that private agents adjust their expectations of the longrun inflation rate in response to macroeconomic
and monetary policy surprises.”
Like Gürkaynak, Sack, and Swanson (2003), we
analyze Treasury securities with a 10-year maturity.
Unlike those authors, we study the average inflation
rate expected for the next 10 years rather than the
value expected for a 12-month window late in this
time period. In other words, we make no statement
about whether (and, if so, the degree to which) surprises in monetary policy actions and macroeconomic data releases affect the rate of inflation that
economic agents expect to prevail in 8 to 9 years.
Another study related to ours is by Kohn and
Sack (2003), who study the effect of Federal Reserve
communication on financial variables but make no
attempt to gauge the influence that Chairman
Greenspan’s speeches and testimonies have on the
level of Treasury yields. Rather, the authors measure
the effect of Fed communication on Treasury yield
10

M AY / J U N E 2 0 0 4

volatility. These authors investigate the effect that
Federal Reserve communication has on various
financial variables by using daily observations for
the period January 3, 1989, through April 7, 2003.
Federal Reserve communication comprises statements released by the FOMC and, since June 1996,
congressional testimonies and speeches delivered
by Chairman Greenspan. Among the financial variables Kohn and Sack analyze are the yields (to maturity) of the 2-year and 10-year Treasury notes. These
authors find that statements of the FOMC and testimonies of Chairman Greenspan have a statistically
significant impact on the variance of 2-year and
10-year Treasury note yields; no such effect was
found for Chairman Greenspan's speeches. We follow
Kohn and Sack (2003) and study the effect of Federal
Reserve communication on the (conditional) volatility of inflation compensation—that is, on the uncertainty that surrounds the future rate of inflation.

MEASURES OF INFLATION
COMPENSATION
In 1997, the U.S. Treasury introduced TIIS. These
securities are issued alongside traditional (nominal)
Treasury securities. Both types of securities are endowed
with a fixed coupon yield—that is, the coupon
payment per annum as a percent of the principal.
Unlike the principal of the nominal Treasury, which
is fixed for the lifetime of the security, the principal
of the TIIS is adjusted daily to past changes in the
rate of inflation, as measured by the (not seasonally
adjusted) CPI for all urban consumers. The coupon
payments of TIIS are made off of the inflationadjusted principal. If the rate of inflation turns negative, the principal is adjusted downward, possibly
dropping below the par amount at issue. At maturity,
TIIS are redeemed at their inflation-adjusted principal or par value at issue, whichever is greater.
It has become common practice to gauge inflation expectations—that is, expectations about the
future, average rate of change in the CPI—from the
inflation rate at which the market prices of comparable TIIS and nominal Treasury securities break
even. To illustrate the theoretical motivation of this
concept, consider, as an example, two default-free
securities with annual coupon payments, identical
coupon yield, an original principal of $1, and a time
to maturity of one year. One is a nominal Treasury
security and the other is a TIIS. For the two securities to deliver the same return to an investor who is
indifferent to inflation risk (but not to inflation, of

FEDERAL R ESERVE BANK OF ST. LOUIS

course), the following equation must hold:
1 + c (1 + π ) (1 + c )
,
=
pn
pi
•

(1)

where c is the coupon yield, π is the expected rate of
inflation, and p n and p i are the prices of the nominal
security and the TIIS, respectively. Solving equation
(1) for the expected rate of inflation delivers

(2)

1+ c
pn
yn − yi
π̂ =
− 1;
≈ yn − yi ,
1+ c
1 + yi
pi

where yn and yi are the yields to maturity of the
nominal security and the TIIS, respectively. Equation
(2) states that the break-even inflation rate, π̂ —that
is, the expected rate of inflation at which the two
securities trade at the same price—can be approximated by the difference in the yields to maturity
between a nominal and an inflation-indexed security.
For securities of more than one year to maturity,
matters are more complex but the same principle
applies.
Although the break-even rate of inflation makes
up the bulk of the inflation compensation embedded
in the market valuation of the expected cash flows
of nominal securities versus TIIS, there is also compensation for inflation risk. Hence, the embedded
inflation compensation exceeds the expected rate
of inflation. Further, for positive rates of inflation,
the payment stream on TIIS is back-loaded compared
with the cash flow of nominal Treasury securities.
This is because the TIIS principal and, hence, the
coupon payments grow with the price level. Because
the payment stream of TIIS is back-loaded, their
duration with respect to the real (that is, inflationadjusted) term structure of interest rates is longer
than the duration of nominal Treasury securities.
In other words, the two types of securities do not
have the same price sensitivity to real interest rates.
Hence, the real-interest-rate risk (and thus the
amount of compensation for this type of risk) might
differ between the two securities; this may distort
the measured inflation compensation. For technical
details on the differences between the two securities,
see Emmons (2000) and Sack (2000).
A simple and readily available concept of inflation compensation is the difference in yields to
maturity between the on-the-run nominal Treasury
security and the on-the-run TIIS of the same original
time to maturity. This concept of gauging inflation

Kliesen and Schmid

expectations has four major disadvantages. First,
and most importantly, the market for nominal
Treasury securities is more liquid than the market
for TIIS, which may cause the yield spread to understate the expected rate of inflation by a liquidity
premium (Sack, 2000). Second, nominal Treasury
securities and TIIS might not have the same duration
with respect to real interest rates, which might cause
the compensation for real-interest-rate risk in the
yields of the two securities to differ. Third, the two
types of securities might not be issued at the same
dates and with the same frequency. Hence, the two
on-the-run securities might not have the same
remaining time to maturity. For instance, whereas
nominal 10-year Treasuries are issued several times
per year, the corresponding inflation-indexed securities are issued only once (1997-2001) or twice (2002)
per year. Fourth, the remaining time to maturity of
on-the-run securities varies because new securities
are not issued every trading day.
To avoid some of the drawbacks that come with
the simple difference in yields between the on-therun nominal and inflation-indexed securities, we
derive inflation compensation from a smoothed
zero-coupon yield curve estimated from off-the-run
nominal Treasury coupon securities. We use two
different measures for the inflation-indexed yield.
The first measure uses the on-the-run TIIS—the OTR
measure. The other measure uses a smoothed zerocoupon yield curve estimated from TIIS, which allows
us to compare the nominal and inflation-indexed
yields at constant maturity—the CM measure.

THE DATA
Our analysis covers the period from January 31,
1997, to June 30, 2003, for the OTR measure, and
from January 5, 1999, to June 30, 2003, for the CM
measure. Each period begins on the starting date of
the respective daily data series, provided by the
Board of Governors of the Federal Reserve System.
Both series contain missing values (OTR: 53; CM:
16)—that is, have trading days for which no OTR or
CM observation is on record. The macroeconomic
data releases are from Money Market Services. The
dataset comprises median polled forecast values
for 38 macroeconomic data series, along with the
sample standard deviations of these forecast values.
The Money Market Services survey is conducted
every Friday morning among senior economists
and bond traders with major commercial banks,
brokerage houses, and some consulting firms mostly
in the greater New York, Chicago, and San Francisco
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Kliesen and Schmid

areas. Among these 38 series in the survey, there
are three items—CPI, PPI, and retail sales—for which
there also exists a “core” concept. Whereas the
comprehensive items of the CPI and the PPI include
food and energy items, the respective core measures
do not. For retail sales, the narrowly defined concept
excludes automotive sales. In the regression analysis,
we exclude the three “core” concepts, which leaves
us with 35 macroeconomic variables.3 Data that were
released on days when the markets were closed were
moved to the next trading day—the day on which
this information could be priced in the marketplace.
We try to relate daily changes in inflation compensation to the surprise component in macroeconomic data releases. We define the surprise
component as the difference between the actual
and the median forecast values, normalized by the
sample standard deviation of the individual forecasts.4 We also control for Federal Reserve communication and actions. Our concept of Federal Reserve
communication comprises (i) Chairman Greenspan’s
semi-annual testimony to Congress (formerly known
as Humphrey-Hawkins Testimony) and (ii) speeches
and other testimonies of Chairman Greenspan.
Consistent with the macroeconomic data releases,
we moved Federal Reserve communication to the
next trading day if this communication occurred
after-hours (that is, after the data input for the
inflation compensation measures were recorded)
or on days on which there was no trading. Finally,
we control for the surprise component in changes
(or the absence thereof) of the federal funds target
rate, which we measure as suggested by Kuttner
(2001) and discussed by Watson (2002). For each
scheduled and unscheduled FOMC meeting, we
scaled up by 30/(k+1) the change of the price of
the federal funds futures contract for the current
month on the day of the FOMC meeting, t, where
t+k denotes the last calendar day of the month.5
Note that this variable is not on the same scale as
3

As will be discussed, our exclusion of the “core” variables did not
materially change our empirical results.

4

Fleming and Remolona (1997, 1999) calculate the surprise component
by normalizing the difference between the actual and the forecast
values by the mean absolute difference observed for the respective
variable during the sample period. Balduzzi, Elton, and Green (2001)
normalize the difference between the actual and the forecast values
by the standard deviation of this difference during the sample period.
Gürkaynak, Sack, and Swanson (2002) do not normalize their variables.

5

Following Gürkaynak, Sack, and Swanson (2003), we use the (unscaled)
change in the price of the federal funds futures contract due to expire
in the following month if the FOMC meeting took place within the
last seven calendar days of the month.

12

M AY / J U N E 2 0 0 4

the surprise component in the macroeconomic
data releases. In a sensitivity analysis, we use an
alternative measure of the surprise component in
monetary policy actions. This alternative measure,
devised by Poole and Rasche (2000), rests on price
changes of federal funds futures contracts also.6
Table 1 shows the frequency with which releases
of the 38 macroeconomic data series match recorded
OTR and CM inflation compensation during the two
respective sample periods. The numbers of data
releases during the sample period are in parentheses,
and the differences in the two numbers are due to
missing values. We also report matches for scheduled
and unscheduled FOMC meetings—the federal funds
target variable, the surprise component of which
was calculated as outlined above—and the two
Federal Reserve communication variables defined
above—(i) semi-annual testimony to Congress and
(ii) Greenspan speeches, testimonies other than
semi-annual testimony to Congress. The only weekly
series in the dataset, initial jobless claims, has the
highest frequency. The next-to-highest frequency
is observed for testimonies other than semi-annual
testimony to Congress, followed by monthly data
releases, FOMC actions (federal funds target), quarterly data releases, and the Chairman’s semi-annual
testimonies to Congress. An exception is nonfarm
productivity, which entered the Money Market
Services dataset during the sample period; the first
surveyed number refers to the first quarter of 1999.
Table 2, center column, offers a frequency distribution for the coincidence of surprises in macroeconomic data releases (Money Market Services
survey) and monetary policy actions. For instance,
for the OTR measure of inflation expectations, 453
of the 1,555 trading days analyzed had no surprises
in data releases or monetary actions, possibly
because no data were released or no action taken;
615 trading days (40 percent) had more than one
surprise; and 270 (17 percent) had more than two
surprises. Table 2, right column, offers a frequency
distribution with Federal Reserve communication
included.

EMPIRICAL FINDINGS
Our empirical approach rests on the following
regression equation:
6

For a discussion of measures of market expectations concerning
monetary policy actions, see Gürkaynak, Sack, and Swanson (2002).

FEDERAL R ESERVE BANK OF ST. LOUIS

Kliesen and Schmid

Table 1
Number of Data Releases That Match Inflation Compensation Observations
Data series (FOMC communication and actions)

OTR measure

Auto sales
Business inventories
Capacity utilization
Civilian unemployment rate
Construction spending
Consumer confidence
Consumer credit
Consumer price index (CPI-U)
CPI excluding food and energy
Durable goods orders
Employment cost index (Q)
Existing home sales
Factory orders
Federal funds target: unscheduled FOMC meetings*
Federal funds target: scheduled FOMC meetings*
GDP price index (advance) (Q)
GDP price index (final) (Q)
GDP price index (preliminary) (Q)
Goods and services trade balance (surplus)
Greenspan speeches, testimonies other than semi-annual testimony to Congress*
Hourly earnings
Housing starts
Industrial production
Initial jobless claims (W)
Leading indicators
Purchasing Managers’ Index
New home sales
Nonfarm payrolls
Nonfarm productivity (preliminary)
Nonfarm Productivity (revised)
Personal consumption expenditures
Personal income
Producer price index (PPI)
PPI excluding food and energy
Real GDP (advance) (Q)
Real GDP (final) (Q)
Real GDP (preliminary) (Q)
Retail sales
Retail sales excluding autos
Semi-annual testimony to Congress*
Treasury budget (surplus)
Truck sales

75 (78)
76 (78)
77 (78)
75 (78)
75 (78)
76 (78)
77 (78)
75 (78)
75 (78)
75 (78)
25 (26)
76 (78)
75 (78)
4 (4)
51 (52)
25 (26)
25 (26)
25 (26)
76 (78)
130 (135)
75 (78)
76 (78)
77 (78)
323 (334)
75 (78)
75 (78)
75 (78)
75 (78)
16 (17)
17 (17)
75 (78)
75 (78)
76 (78)
76 (78)
25 (26)
25 (26)
25 (26)
76 (78)
76 (78)
12 (13)
74 (78)
75 (78)

CM measure
51 (54)
54 (54)
54 (54)
54 (54)
51 (54)
54 (54)
54 (54)
54 (54)
54 (54)
54 (54)
18 (18)
54 (54)
53 (54)
2 (3)
36 (36)
18 (18)
18 (18)
18 (18)
54 (54)
89 (90)
54 (54)
53 (54)
54 (54)
224 (234)
53 (54)
51 (54)
53 (54)
54 (54)
17 (17)
17 (17)
53 (54)
53 (54)
54 (54)
54 (54)
18 (18)
18 (18)
18 (18)
54 (54)
54 (54)
8 (9)
53 (54)
51 (54)

NOTE: Monthly series if not indicated otherwise (Q, quarterly; W, weekly). Numbers in parentheses indicate total number of observation, not all of which are used because of missing observations for the measures of inflation compensation.
*Variables not included in the dataset of macroeconomic data releases.

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Table 2
Frequency Distribution of Coincidence in Surprises
Number of observations
MMS survey,
federal funds target, and
Federal Reserve communication

MMS survey and
federal funds target
Number of surprises
per trading day

OTR

CM

OTR

CM

0

453

323

415

298

1

487

335

488

329

2

345

249

355

265

3

147

112

159

113

4

86

68

96

79

5

21

10

25

13

6

10

9

10

8

7

3

2

3

3

8

1

1

2

1

9
Total

2

1

2

1

1,555

1,110

1,555

1,110

35

(3)

πˆ t − πˆ t −1 = α + β D + ∑ δ k xtk + γ fft + ε t ,
•

•

•

k =1

where π̂ t – π̂ t–1 is change in the inflation compensation from trading day t –1 to trading day t, D is an
indicator variable that is equal to 1 if all explanatory
variables are equal to 0 (and is equal to 0 otherwise),
xtk is the surprise component in the macroeconomic
data release, fft is the surprise component in the
Federal Reserve action (the federal funds target variable), and ε t is an identically and independently
distributed error term with mean 0 and finite variance
σ 2.7 The dependent variable is, alternately, the OTR
and the CM measures of inflation compensation.8
We expect signs on the surprises in the macroeconomic data releases to be consistent with the
conventional macroeconomic theory as taught in
the classroom. Bernanke (2003) presents a brief
summary of this theory using the expectations7

The intercept indicator variable, D, eliminates the influence on the
observed mean of the dependent variable of those observations for
which none of the explanatory variables contains information pertinent
to the measured inflation compensation.

8

Using kernel estimation, we verified that the dependent variables
are close to normally distributed. Yet, there is mild (and statistically
significant) skewness (OTR: 0.402; CM: 0.409) and excess kurtosis
(OTR: 1.673; CM: 1.114).

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M AY / J U N E 2 0 0 4

augmented Phillips curve. In this model, inflation
depends on inflation expectations, the output gap,
and supply shocks. The most important determinant
of inflation is the expectation component. Anything
that causes people to expect more inflation is likely
to lead to behavior that causes higher inflation. Forecasting models and studies using surveys of inflation
expectations show that the most important variable
in predicting future inflation is past inflation.9 Therefore, we expect surprise increases in price indices
(such as the CPI or PPI) to lead to higher inflation
expectations.
We assume that real variables affect inflation
indirectly through the output gap, that potential
output is relatively stable (as measured by the
Congressional Budget Office, CBO), and that most
news about real activity is news about aggregate
demand. Therefore a surprise increase in any subset
of real economic activity may lead to expectations
of higher inflation. The Phillips curve model also
performs better if we account for supply shocks. A
surprise in real activity may be associated with a
supply shock rather than an aggregate demand
shock. The real variable included in this study that
9

See Stock and Watson (1999) for evidence about the role of past
inflation and real variables in predicting inflation.

FEDERAL R ESERVE BANK OF ST. LOUIS

is explicitly thought to measure changes in aggregate
supply is labor productivity.
The expected sign of the federal funds target
variable is negative. Remember that this variable
measures the surprise in the choice of the federal
funds target rate at scheduled and unscheduled
FOMC meetings. We predict economic agents to
revise down (up) their expected rate of inflation in
response to FOMC actions that are indicative of
monetary policy tighter (easier) than expected.
Tables 3 and 4 show the regression results for
the OTR and CM measures, respectively.10 The
regression coefficients of the federal funds target
variable have the expected sign and are statistically
significant. A surprise in the expected federal funds
target rate of 10 basis points reduces the expected
rate of inflation by 2.2 basis points (OTR measure)
and 1 basis point (CM measure), respectively. The
macroeconomic data series that prove statistically
significant are ranked in Table 5 by the magnitude
of their influence on each measure’s (OTR and CM)
inflation expectations. Remember that all macroeconomic data items are on the same scale (scaled
by their standard deviation). Data releases whose
surprise component proved statistically significant
in the Gürkaynak, Sack, and Swanson (2003, Table 3)
study, are noted with an asterisk. All statistically
significant regression coefficients have the expected
sign, except consumer credit and housing starts.11
Greater than expected numbers for consumer credit
and housing starts numbers might be thought of as
“bullish”; yet, the regression coefficient is negative.
The six common variables whose surprise components bear most heavily on both measures of inflation expectations are the employment cost index,
the Purchasing Managers’ Index, CPI, retail sales,
factory orders, and personal income. The capacity
utilization rate was the most significant mover of
inflation expectations using the CM measure, while
the ECI mattered the most in the OTR measure.
We repeat the regression analysis (3) for the
core measures of CPI, PPI, and retail sales. That is,
we replace the respective comprehensive (total)
10

The t-statistics and the F-statistics are based on Newey-West (1987)
corrected standard errors. We applied a standard lag length of
floor(4(T/100)2/9 ), where floor(.) indicates rounding down to the
nearest integer and T is the number of observations. This lag length
is also used for the Ljung-Box statistic shown in the tables.

11

Note that deficits in the Treasury budget and the trade balance are
recorded as negative numbers. In other words, a positive surprise
component in these variables indicates a deficit that is smaller than
expected in absolute value or a surplus that is greater than expected.

Kliesen and Schmid

numbers in model (3) by CPI excluding food and
energy, PPI excluding food and energy, and retail
sales excluding automotive. These regression results,
which are not shown, have less explanatory power
than the regression equations with the comprehensive numbers, as judged by the R2. Further, while
CPI retains its statistical significance, retail sales do
not; PPI remains statistically significant only for
the OTR measure. The results for the federal funds
target variable are nearly unchanged.
Poole, Rasche, and Thornton (2002) argue that
monetary policy surprises as gauged by the change
in federal funds futures prices are measured with
error. This is because federal funds futures prices
not only change in response to monetary policy
actions, but also respond to other information pertinent to the future path of the federal funds rate.
Because of the measurement error introduced by
such ambient price changes of federal funds futures
contracts, the regression coefficient of the federal
funds target variable is biased toward 0. We deal
with the error-in-variables problem by employing an
instrumental-variables approach. As an instrument
for the federal funds target, we use an indicator that
is equal to 1 if the federal funds target exceeds its
median positive value, equal to –1 if it falls short of
its median negative value, and 0 otherwise.12
Table 6 shows the regression results of the instrumental-variables approach applied to equation (3).
We use two different definitions of the surprise
component of monetary policy actions (the federal
funds target variable). First, we provide results for
the concept that we have used throughout the
paper—the measure suggested by Gürkaynak, Sack,
and Swanson (2003), which is denoted federal funds
target (GSS) in the table. Second, we present results
for the surprise measure devised by Poole and Rasche
(2000), which is denoted federal funds target (PR) in
the table. Unlike the GSS measure, which rests on
the scaled price change of the current month’s
federal funds futures contract (unless the monetary
policy surprise happens within the last seven days
of the month), the PR measure always uses the price
change of the next month's federal funds futures
contract. One of the regression coefficients for the
federal funds target (GSS) is indeed larger (in absolute
value) than without the error-in-variables correction
(Table 4, CM measure), while the other is smaller
(Table 3, OTR measure); also, both federal funds
12

For details on this error-in-variables approach, see Greene (2002).

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Table 3
Regression Results for the 10-year OTR Measure
Explanatory variable

Coefficient
–5

Auto sales
Business inventories
Capacity utilization
Civilian unemployment rate
Construction spending
Consumer confidence
Consumer credit
Consumer price index (CPI-U)
Durable goods orders
Employment cost index
Existing home sales
Factory orders
Federal funds target
GDP price index (advance)
GDP price index (final)
GDP price index (preliminary)
Goods and services trade balance (surplus)
Hourly earnings
Housing starts
Industrial production
Initial jobless claims
Leading indicators
Purchasing Managers’ Index
New home sales
Nonfarm payrolls
Nonfarm productivity (preliminary)
Nonfarm productivity (revised)
Personal consumption expenditures
Personal income
Producer price index (PPI)
Real GDP (advance)
Real GDP (preliminary)
Real GDP (final)
Retail sales
Treasury budget (surplus)
Truck sales
Intercept indicator variable (D)
Intercept

–3.250 · 10
2.928 · 10–3
3.395 · 10–3
–2.759 · 10–3
–1.604 · 10–3
3.643 · 10–3
–2.157 · 10–3
1.016 · 10–2
1.760 · 10–3
1.223 · 10–2
–5.957 · 10–7
8.538 · 10–3
–2.194 · 10–1
8.201 · 10–3
3.793 · 10–3
1.617 · 10–3
–4.242 · 10–3
4.269 · 10–3
–3.087 · 10–3
7.385 · 10–3
–1.840 · 10–3
2.114 · 10–3
1.045 · 10–2
4.375 · 10–3
4.099 · 10–3
–2.588 · 10–3
–2.398 · 10–3
–6.524 · 10–4
5.176 · 10–3
–1.634 · 10–3
1.010 · 10–3
–2.305 · 10–3
–7.614 · 10–3
1.015 · 10–2
–1.121 · 10–2
6.420 · 10–4
–1.434 · 10–3
–6.330 · 10–4

F-statistic (1)
F-statistic (2)
R2
R2 adj.
Ljung-Box statistic
Rao’s score test
Number of nonzero observations
Number of observations

3.621***
3.790***
0.081
0.059
18.02**
13.16***
1,100
1,555

t-statistic
–0.011
0.808
0.514
–1.612
–0.892
2.237**
–1.658*
2.109**
0.800
2.673***
–0.497
3.210***
–2.424**
1.602
1.900*
0.816
–2.764***
1.773*
–1.806*
1.297
–1.996**
0.526
4.757***
2.310**
2.673***
–0.545
–0.334
–0.211
1.730*
–0.954
0.185
–0.641
–1.042
2.748***
–2.117**
0.247
–0.587
–0.436

NOTE: ***/**/* Indicate significance at the 1/5/10 percent levels (t-tests are two-tailed). F-statistics and t-statistics are Newey and
West (1987) corrected. Federal funds target is not included in the MMS survey. F-statistic (1): all MMS survey variables and federal
funds target; F-statistic (2): all MMS survey variables. The number of nonzero observations indicates the number of trading days
where Federal Reserve communication or the surprise in a monetary policy action was priced.

16

M AY / J U N E 2 0 0 4

FEDERAL R ESERVE BANK OF ST. LOUIS

Kliesen and Schmid

Table 4
Regression Results for the 10-year CM Measure
Explanatory variable

Coefficient
–4

Auto sales
Business inventories
Capacity utilization
Civilian unemployment rate
Construction spending
Consumer confidence
Consumer credit
Consumer price index (CPI-U)
Durable goods orders
Employment cost index
Existing home sales
Factory orders
Federal funds target
GDP price index (advance)
GDP price index (final)
GDP price index (preliminary)
Goods and services trade balance (surplus)
Hourly earnings
Housing starts
Industrial production
Initial jobless claims
Leading indicators
Purchasing Managers’ Index
New home sales
Nonfarm payrolls
Nonfarm productivity (preliminary)
Nonfarm productivity (revised)
Personal consumption expenditures
Personal income
Producer price index (PPI)
Real GDP (advance)
Real GDP (preliminary)
Real GDP (final)
Retail sales
Treasury budget (surplus)
Truck sales
Intercept indicator variable (D)
Intercept

–4.363 · 10
2.325 · 10–3
1.241 · 10–2
–1.669 · 10–3
–2.740 · 10–3
3.046 · 10–3
–2.680 · 10–3
7.698 · 10–3
2.075 · 10–3
9.162 · 10–3
8.273 · 10–4
6.343 · 10–3
–9.907 · 10–2
1.466 · 10–2
4.147 · 10–3
3.469 · 10–3
–2.121 · 10–3
5.752 · 10–3
–4.455 · 10–3
2.740 · 10–3
–2.160 · 10–3
7.567 · 10–4
1.086 · 10–2
2.574 · 10–3
3.921 · 10–3
–6.456 · 10–3
–1.675 · 10–3
–1.184 · 10–5
6.184 · 10–3
–1.845 · 10–3
9.222 · 10–3
–2.707 · 10–3
–4.609 · 10–3
8.745 · 10–3
–6.082 · 10–3
–4.671 · 10–4
–2.896 · 10–4
1.676 · 10–3

F-statistic (1)
F-statistic (2)
R2
R2 adj.
Ljung-Box statistic
Rao’s score test
Number of nonzero observations
Number of observations

2.749***
2.867***
0.087
0.055
14.47**
1.352
785
1,110

t-statistic
–0.152
0.528
2.082**
–0.734
–1.441
2.012**
–1.896*
1.723*
0.743
2.038**
0.591
2.008**
–3.071***
1.193
2.350**
2.049**
–1.534
1.998*
–2.149**
0.681
–2.048**
0.210
5.221***
1.505
1.818*
–1.073
–0.246
–0.025
1.696*
–0.878
1.500
–0.668
–0.700
2.127**
–1.208
–0.153
–1.070
1.025

NOTE: ***/**/* Indicate significance at the 1/5/10 percent levels (t-tests are two-tailed). F-statistics and t-statistics are Newey and
West (1987) corrected. Federal funds target is not included in the MMS survey. F-statistic (1): all MMS survey variables and federal
funds target; F-statistic (2): all MMS survey variables. The number of nonzero observations indicates the number of trading days
where Federal Reserve communication or the surprise in a monetary policy action was priced.

M AY / J U N E 2 0 0 4

17

REVIEW

Kliesen and Schmid

Table 5
Ranking of Macroeconomic Data Releases by Impact on Inflation Expectations
Data release

OTR sign (+/–)

CM sign (+/–)

OTR rank

CM rank

Employment cost index*

+

+

1

4

Capacity utilization

0

+

N/A

1

Treasury budget (surplus)

–

0

2

N/A

Purchasing Managers’ Index

+

+

3

2

Consumer price index (CPI-U)

+

+

4

5

Retail sales*

+

+

5

3

Factory orders

+

+

6

6

Personal income

+

+

7

7

New home sales*

–

0

8

N/A

Hourly earnings

+

0

9

N/A

Goods and services trade balance (surplus)

+

+

10

8

Nonfarm payrolls

+

+

11

11

GDP price index (final)

+

+

12

10

Consumer confidence*

+

+

13

13

Housing starts

–

–

14

9

Consumer credit*

–

–

15

14

Initial jobless claims

–

–

16

15

GDP price index (preliminary)

0

+

N/A

10

NOTE: Variables in Tables 3 and 4 that are significant at the 10 percent level (based on two-tailed t-tests) are ranked above; 0 is not
significant.
*Five of the six variables that turned out statistically significant in Gürkaynak, Sack, and Swanson (2003, Table 3).

target (PR) coefficients are larger in magnitude when
corrected (original estimates not shown).
Finally, we turn to the influence of Federal
Reserve communication. As discussed above, the
surprise component in Federal Reserve communication is next to impossible to ascertain. Yet, following Kohn and Sack (2003), we can analyze the effect
of Federal Reserve communication on the (conditional) volatility of the dependent variable. Specifically, we are interested in whether Federal Reserve
communication and surprises in monetary policy
actions bear on inflation rate uncertainty. Intuitively,
one might expect Federal Reserve communication
to decrease the uncertainty surrounding the future
rate of inflation as the chairman of the Federal
Reserve offers guidance about the future path of
monetary policy. Also, one might expect that monetary policy actions that take the market by surprise
will increase uncertainty about future inflation.
Note that, if Federal Reserve communication and
18

M AY / J U N E 2 0 0 4

surprises in monetary policy actions bear on inflation
uncertainty, then the error term of the regression
equation (3) is heteroskedastic. Rao’s score test on
heteroskedasticity shows that the null hypothesis
of no heteroskedasticity is indeed rejected for the
OTR measure of inflation compensation (Table 3)
but not for the CM inflation compensation measure
(Table 4).13
To address the issue of inflation uncertainty,
we use the squared residuals from regression equation (3)—the regression results of which are shown
in Tables 3 and 4—in an estimation approach suggested by Amemiya (1977, 1978). We regress these
squared residuals on the federal funds target variable,
an indicator variable that is equal to 1 on days where
Federal Reserve communication was priced in the
market (and 0 otherwise), and the previously introduced intercept indicator variable (D). The regression
13

For Rao’s score test, see Amemiya (1985).

FEDERAL R ESERVE BANK OF ST. LOUIS

Kliesen and Schmid

Table 6
Instrumental-Variables Approach
Panel A: OTR measure
Explanatory variable

Federal funds target (GSS)
Federal funds target (PR)

Coefficient

t-statistic

–1

–2.710**

–1

–3.191***

–2.016 · 10
–2.659 · 10
Panel B: CM measure

Explanatory Variable

Coefficient
–1

t-statistic

Federal funds target (GSS)

–1.671 · 10

–2.975***

Federal funds target (PR)

–1.239 · 10–1

–2.575**

NOTE: ***/** Indicate significance at the 1/5 percent levels (t-tests are two-tailed; t-statistics are Newey and West (1987) corrected).
GSS and PR indicate the federal funds market measure for monetary policy surprises as suggested by Gürkaynak, Sack, and Swanson
(2002) and Poole and Rasche (2000), respectively.

Table 7
Inflation Uncertainty
Panel A: OTR measure
Explanatory variable

Coefficient

t-statistic

–8.632 · 10–3

–3.989***

1.547 · 10–3

4.009***

Intercept indicator variable (D)

–4

9.189 · 10

4.017***

Intercept

1.049 · 10–3

4.157***

Federal Reserve communication
Federal funds target

Number of nonzero observations
Number of observations

166
1,555
Panel B: CM measure

Explanatory variable

Coefficient

Federal Reserve communication

3.021 · 10–3

1.295

Federal funds target

5.160 · 10–4

1.107

–4

1.104

Intercept indicator variable (D)

4.173 · 10

Intercept

1.381 · 10–3

Number of nonzero observations
Number of observations

t-statistic

3.740***

117
1,110

NOTE: *** Indicates significance at the 1 percent level (t-tests are two-tailed). The variable Federal Reserve communication equals 1
on trading days on which Chairman Greenspan’s semi-annual testimony to Congress (formerly known as Humphrey-Hawkins testimony)
or speeches and other testimonies of Chairman Greenspan were priced in the market. The number of nonzero observations indicates
the number of trading days where Federal Reserve communication or the surprise in a monetary policy action was priced.

M AY / J U N E 2 0 0 4

19

Kliesen and Schmid

results, which are presented in Table 7, indicate that
neither Federal Reserve communication nor monetary policy surprises bear on the conditional variance
of the CM measure of inflation compensation. This
finding is not surprising, given that Rao's score test
does not suggest heteroskedasticity. Things are different with the OTR measure of inflation compensation.
Here, Rao's score test indicates heteroskedasticity,
and, indeed, the coefficients for the variables Federal
Reserve communication and federal fund target are
statistically significant and have the expected sign.
Hence, we conclude that, at least judged by one of
our two measures of inflation compensation, Federal
Reserve communication diminishes the uncertainty
surrounding the future rate of inflation, while surprises in monetary policy actions increase it.

CONCLUSION
Do monetary policy actions that are tighter or
easier than expected by the federal funds futures
market bear on the average rate of inflation that
economic agents expect to prevail over the next 10
years? Moreover, do surprises in macroeconomic
data releases lead economic agents to update their
beliefs about the average rate of inflation they expect
for the next 10 years; if so, which data series matter
the most? We gauged inflation expectations by two
different measures of inflation compensation, both
of which are derived from the market valuation of
the expected cash flows of nominal and inflationindexed Treasury securities.
We find that surprises in monetary policy actions
bear on both measures of inflation expectations.
Monetary policy actions that are viewed as tighter
(easier) than expected by the market lead economic
agents to revise down (up) their expected rate of
inflation. Further, one measure indicates that Federal
Reserve communication reduces uncertainty about
the future rate of inflation, while surprises in monetary policy actions increase uncertainty about the
path the rate of inflation is going to take. We also
show that surprises in macroeconomic data releases
matter. In particular, we show that the surprise components in data releases for the employment cost
index, the Purchasing Managers’ Index, CPI, retail
sales, factory orders, and personal income bear most
heavily on both measures of inflation expectations.

REFERENCES
Amemiya, Takeshi. “A Note on a Heteroscedastic Model.”
Journal of Econometrics, November 1977, 6(3), pp. 365-70.
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M AY / J U N E 2 0 0 4

REVIEW
Amemiya, Takeshi. “Corrigenda.” Journal of Econometrics,
October 1978, 8(2), p. 275.
Amemiya, Takeshi. Advanced Econometrics. Cambridge, MA:
Harvard University Press, 1985.
Balduzzi, Pierluigi; Elton, Edwin J. and Green, Clifton T.
“Economic News and Bond Prices: Evidence from the U.S.
Treasury Market.” Journal of Financial and Quantitative
Analysis, December 2001, 36(4), pp. 523-43.
Bernanke, Ben S. “An Unwelcome Fall in Inflation?“ Remarks
before the Economics Roundtable, University of California–
San Diego, La Jolla, California, July 23, 2003.
www.federalreserve.gov/boarddocs/speeches/2003/
20030723/default.htm.
Emmons, William R. “The Information Content of Treasury
Inflation-Indexed Securities.” Federal Reserve Bank of St.
Louis Review, November/December 2000, 82(6), pp. 25-37.
Fleming, Michael J. and Remolona, Eli M. “What Moves
Bond Prices?” Journal of Portfolio Management, Summer
1999, 25(4), pp. 28-38.
Fleming, Michael J. and Remolona, Eli M. “What Moves the
Bond Market?” Federal Reserve Bank of New York
Economic Policy Review, December 1997, 3(4), pp. 31-50.
Greene, William H. Econometric Analysis. 5th edition.
Upper Saddle River, NJ: Prentice-Hall, August 2002.
Gürkaynak, Refet S.; Sack, Brian P. and Swanson, Eric T.
“The Excess Sensitivity of Long-Term Interest Rates:
Evidence and Implications for Macroeconomic Models.”
Working paper, Division of Monetary Affairs, Board of
Governors of the Federal Reserve System, April 4, 2003.
www.clevelandfed.org/CentralBankInstitute/conf2003/
august/sensitivity_apr4.pdf.
Gürkaynak, Refet S.; Sack, Brian P. and Swanson, Eric T.
“Market-Based Measures of Monetary Policy Expectations.”
Working paper, Division of Monetary Affairs, Board of
Governors of the Federal Reserve System, August 1, 2002.
www.federalreserve.gov/pubs/feds/2002/200240/
200240pap.pdf.
Kohn, Donald L. and Sack, Brian P. “Central Bank Talk:
Does It Matter and Why?” Paper presented at the Macroeconomics, Monetary Policy, and Financial Stability
Conference in honor of Charles Freedman, Bank of
Canada, Ottawa, Canada, June 20, 2003.

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Kliesen and Schmid

www.federalreserve.gov/boarddocs/speeches/2003/
20030620/paper.pdf.
Kuttner, Kenneth N. “Monetary Policy Surprises and
Interest Rates: Evidence from the Fed Funds Futures
Market.” Journal of Monetary Economics, June 2001, 47(3),
pp. 523-44.
Newey, Whitney K. and West, Kenneth D. “A Simple, Positive
Semi-Definite, Heteroskedasticity and Autocorrelation
Consistent Covariance Matrix.” Econometrica, May 1987,
pp. 703-08.
Poole, William and Rasche, Robert H. “Perfecting the
Market’s Knowledge of Monetary Policy.” Journal of
Financial Services Research, December 2000, 18(2-3), pp.
255-98.
Poole, William; Rasche, Robert H. and Thornton, Daniel L.
“Market Anticipations of Monetary Policy Actions.”
Federal Reserve Bank of St. Louis Review, July/August
2002, 84(4), pp. 65-93.
Sack, Brian P. “Deriving Inflation Expectations from Nominal
and Inflation-Indexed Treasury Yields.” Journal of Fixed
Income, September 2000, 10(2), pp. 6-17.
Stock, James H. and Watson, Mark W. “Forecasting Inflation.”
Journal of Monetary Economics, October 1999, 44(2), pp.
293-335.
Watson, Mark W. Commentary. Federal Reserve Bank of St.
Louis Review, July/August 2002, 84(4), pp. 95-97.

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A Rational Pricing Explanation for the Failure
of the CAPM
Hui Guo

F

ama and French (2003), among many others,
show that the capital asset pricing model
(CAPM) does not explain stock returns. These
results should not be a surprise because the model
has some strong assumptions, and the failure of
any one of them may cause the model to fail. In
particular, the CAPM is a static model in which
expected stock returns are assumed to be constant.
However, if expected returns are time-varying,
Merton (1973) and Campbell (1993), among others,
show that the return on an asset is determined not
only by its covariance with stock market returns,
as in the CAPM, but also by its covariance with
variables that forecast stock market returns. In this
article, I estimate a variant of Campbell’s intertemporal CAPM (ICAPM), using forecasting variables
advocated in recent research. I find that the CAPM
fails to explain the predictability of stock market
returns because covariances with the forecasting
variables are also important determinants of stock
market returns. Therefore, consistent with some
recent authors, for example, Brennan, Wang, and
Xia (forthcoming) and Campbell and Vuolteenaho
(2002), the failure of the CAPM is related to timevarying expected returns.
The remainder of the article is organized as
follows. I first briefly summarize the recent developments of the asset pricing literature and then present
evidence that stock market returns and volatility are
predictable. For illustration, I discuss and estimate
a variant of Campbell’s ICAPM and show that changing investment opportunities have important effects
on stock prices.1

A BRIEF REVIEW OF THE LITERATURE
In the past two decades, financial economists
have documented many anomalies in financial
1

Stock market returns and volatility are measures of investment
opportunities.

markets. For example, contrary to the market efficiency hypothesis by Fama (1970), Fama and French
(1989) argue that stock market returns are predictable. There is also evidence of the predictability in
the cross section of stock returns, which casts doubt
on the widely accepted CAPM by Sharpe (1964) and
Lintner (1965). In particular, Fama and French (1992,
1993) report that value stocks, stocks of high
book-to-market value ratio, have much higher riskadjusted returns than growth stocks, stocks of low
book-to-market value ratio. Also, Jegadeesh and
Titman (1993) show that the momentum strategy
of buying the past winners and selling the past losers
is quite profitable.
The advocates of the market efficiency hypothesis argue quite convincingly that many of these
anomalies can be attributed to data snooping. For
example, if we experiment with a large number of
macro variables, it should not be a surprise that a
few of them might be correlated with future stock
market returns by chance. However, investors cannot
profit from such an ex post relation if it does not
persist in the future. Indeed, Bossaerts and Hillion
(1999), among others, find that, although the variables uncovered by the early authors forecast stock
returns in sample, their out-of-sample predictive
power is negligible. Similarly, Schwert (2002), among
others, finds that many trading strategies, which
have been found to generate abnormal returns, were
unprofitable in the past decade. Overall, Malkiel
(2003) asserts that there is no reliable evidence of
persistent stock return predictability and the U.S.
equity market is remarkably efficient in the sense
that abnormal returns disappear quickly after they
are discovered.
Some anomalies, however, cannot be easily
discarded as data snooping. Jegadeesh and Titman
(2001) and Schwert (2002) find that the momentum
strategy remained highly profitable in the 1990s,
one decade after it was published in academic jour-

Hui Guo is an economist at the Federal Reserve Bank of St. Louis. William Bock and Jason Higbee provided research assistance.
Federal Reserve Bank of St. Louis Review, May/June 2004, 86(3), pp. 23-33.
© 2004, The Federal Reserve Bank of St. Louis.

M AY / J U N E 2 0 0 4

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REVIEW

Guo

Table 1
Forecasting Quarterly Stock Market Returns and Volatility
Intercept

rm

σ 2m

cay

rrel

Adjusted R2

Return

–1.50
(–5.12)

0.02
(0.34)

2.42
(5.13)

7.19
(4.73)

–5.63
(–2.95)

0.20

0.39
(4.17)

0.68
(0.93)

0.24

Volatility

0.05
(3.49)

0.01
(1.32)

–0.09
(–3.37)

NOTE: White-corrected t-statistics are in parentheses.

nals. Also, recent authors, for example, Lettau and
Ludvigson (2001), show that the consumption-wealth
ratio, especially when combined with realized stock
market volatility, has statistically and economically
significant out-of-sample forecasting power for
stock market returns. It is reasonable to believe, as
argued by Campbell (2000), that stock returns have
some predictable variations. Moreover, the excess
stock volatility puzzle (Shiller, 1981), the equity
premium puzzle (Mehra and Prescott, 1985), and
large fluctuations of stock market volatility (Schwert,
1989) remain unexplained by conventional theories
(e.g., Lucas, 1978).
The failure of rational expectations theories
leads some researchers to be skeptical about the
assumption that individual investors are fully
rational. They try to incorporate various welldocumented cognitive biases into asset pricing
models and find that such combinations have some
success in explaining the anomalies mentioned
above. Behavioral finance has developed rapidly
since the 1990s, and Shiller (2003), among others,
has stressed its important role in rebuilding modern
finance. However, in my view, we should be at least
cautious about it. The main criticism is that a long
list of cognitive biases gives researchers so many
degrees of freedom that anything can be explained.
But financial economists are more interested in the
out-of-sample forecast than in explaining what has
happened. Also, it is difficult to believe that the
investors who frequently misinterpret fundamentals
can survive in an arbitrage-driven financial market.
Barberis and Thaler (2003) provide a comprehensive
survey of the behavioral finance literature and come
to this conclusion: “First, we will find that most of
our current theories, both rational and behavioral,
24

M AY / J U N E 2 0 0 4

are wrong. Second, substantially better theories
will emerge.”
In this article, I want to emphasize the promising
role of another alternative hypothesis—stock return
predictability does not necessarily contradict rational
expectations theories.2 In particular, Campbell and
Cochrane (1999) recently proposed a novel explanation using a habit-formation model that investors
are more risk tolerant and thus require a smaller
equity premium during economic expansions than
during economic recessions. Their model not only
replicates stock return predictability, but also resolves
many other outstanding issues, including the equity
premium puzzle and the excess volatility puzzle.
As mentioned, stock return predictability has
important implications for asset pricing. Fama (1991)
also conjectures that we should relate the crosssection properties of expected returns to the variation
of expected returns through time. Consistent with
these theories, some recent authors (e.g., Brennan,
Wang, and Xia, forthcoming; and Campbell and
Vuolteenaho, 2002) find that the predictability of
stock market returns and volatility indeed helps
explain the cross section of stock returns.

FORECASTING STOCK MARKET
RETURNS AND VOLATILITY
The early authors, for example, Campbell (1987)
and Fama and French (1989), find that the short2

This point has been well understood in theory; for example, Lucas
(1978) shows that predictable variations of stock returns should be
explained by predictable variations of consumption growth. Similarly,
in the CAPM, the equity premium is predictable because of predictable
variations of stock market volatility, a measure of stock market risk.
However, these models cannot generate sizable predictable variations
of stock returns as observed in the data.

FEDERAL R ESERVE BANK OF ST. LOUIS

Guo

Figure 1
Expected Excess Stock Market Returns
Rate of Return
0.2

0

–0.2
Mar-53

Mar-58

Mar-63

Mar-68

Mar-73

Mar-78

Mar-83

Mar-88

Mar-93

Mar-98

NOTE: Shaded bars indicate recessions as determined by the National Bureau of Economic Research.

term interest rate, the dividend yield, the default
premium, and the term premium forecast stock
market returns. Recently, Lettau and Ludvigson
(2001) report that the consumption-wealth ratio,
cay—the error term from the cointegration relation
among consumption, net worth, and labor income—
forecasts stock market returns in sample and out
of sample. Interestingly, I (Guo, 2003a) find that the
predictive power of cay improves substantially if
past stock market variance, σm2 , is also included in
the forecasting equation and the stochastically
detrended risk-free rate, rrel, provides additional
information about future returns.3
I replicate this result in the upper panel of
Table 1, with the White-corrected (White, 1980) tstatistics reported in parentheses. It shows that all
three variables are statistically significant in the
forecasting equation of real stock market return, rm,
and the adjusted R2 is about 20 percent; however,
the lagged dependent variable is insignificant.4
Moreover, these variables drive out the other commonly used forecasting variables, including the
dividend yield, the default premium, and the term
3

The stochastically detrended risk-free rate is the difference between
the nominal risk-free rate and its average in the previous 12 months.

4

See the appendix for data descriptions.

premium.5 Figure 1 plots the fitted value from the
forecasting regression of returns and shows that
expected returns tend to rise during recessions.
Schwert (1989), among many others, also finds
clustering in stock market volatility: When volatility
increases, it stays at its high level for an extended
period before it reverts to its average level. Research
shows that some macro variables predict stock volatility as well. Consistent with Lettau and Ludvigson
(2003), the lower panel of Table 1 shows that, while
past volatility is positively related to future volatility,
cay is negatively related to it. Figure 2 plots the fitted
value from the forecasting regression of stock
market volatility, which also tends to increase during
recessions.
I (Guo, 2003b) provide some theoretical insight
on these empirical results in a limited stock market
participation model. In particular, I argue that, in
addition to a market risk premium (as in the standard
consumption-based model), investors also require
a liquidity premium on stocks because investors
cannot use stocks to hedge income risk—due to
limited stock market participation. Therefore, stock
volatility and the consumption-wealth ratio forecast
5

To conserve space, I do not report the results here; but they are
available upon request.

M AY / J U N E 2 0 0 4

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Guo

Figure 2
Expected Stock Market Volatility
0.015

0.01

0.005

0
Mar-53

Mar-58

Mar-63

Mar-68

Mar-73

Mar-78

Mar-83

Mar-88

Mar-93

Mar-98

NOTE: Shaded bars indicate recessions as determined by the National Bureau of Economic Research.

stock market returns because they are proxies for
the risk and liquidity premiums, respectively.6
It should not be a surprise that stock market
volatility forecasts returns, which is an important
implication of the CAPM.7 Intuitively, risk-averse
investors tend to reduce their holding of equities relative to safe assets such as Treasury bills when volatility is expected to rise. To induce investors to hold a
broadly measured stock market index, the expected
stock market return has to rise as well. Given that
the level of volatility tends to persist over time, we
expect that past volatility should provide some indication of future volatility and hence stock market
returns. On the other hand, the consumption-wealth
ratio measures investors’ liquidity conditions. When
investors are borrowing constrained because of, for
example, a bad income shock, they require a high
liquidity premium on stocks and stock prices thus fall.
Conversely, the liquidity premium is low and stock
prices rise when investors have plenty of liquidity.
6

Patelis (1997) suggests that variables such as the stochastically
detrended risk-free rate forecast stock returns because these variables
reflect the stance of monetary policies, which have state-dependent
effects on real economic activities through a credit channel (e.g.,
Bernanke and Gertler, 1989).

7

However, it is puzzling that many authors (e.g., Campbell, 1987; Glosten,
Jagannathan, and Runkle, 1993; and Lettau and Ludvigson, 2003)
report a negative risk-return tradeoff in the stock market. As I will
discuss here, these results reflect the fact that the early authors fail to
control for the liquidity premium, which may be negatively related
to the risk premium.

26

M AY / J U N E 2 0 0 4

It is important to note that the risk and liquidity
premiums or their proxies, stock market volatility
and the consumption-wealth ratio, could be negatively related to one another in the limited stock
market participation model. Intuitively, when
investors have excess liquidity, they might be willing
to hold stocks when the expected return is low, even
though expected volatility is high. This implication
is particularly relevant for the stock market boom in
the late 1990s, during which investors accepted a
low expected return even though volatility rose to
a historically high level. Indeed, as shown in Table 1,
while volatility and the consumption-wealth ratio
are both positively related to future stock market
returns, they are negatively related to one another in
the post-World War II sample. This pattern explains
that, because of an omitted variable problem, the
predictive power of the consumption-wealth ratio
improves dramatically when past variance is also
included in the forecast equation. As shown in Guo
and Whitelaw (2003), it also explains why the early
authors fail to find conclusive evidence of a positive
risk-return relation, as stipulated by the CAPM.
There is an important conceptual issue of using
the consumption-wealth ratio as a forecasting variable, because consumption and labor income data
are subject to revision. In particular, Guo (2003c)
finds that the predictive power of the consumptionwealth ratio deteriorates substantially if we use information available at the time of the forecast. It is

FEDERAL R ESERVE BANK OF ST. LOUIS

important to note that the use of real-time data does
not call the predictive abilities of the consumptionwealth ratio into question. In fact, we expect the
consumption-wealth ratio to have better predictive
power in the current vintage data than in the realtime data because the latter is a noisier and potentially biased measure of its “true” value. Moreover,
investors may obtain similar information from
alternative sources; for example, Guo and Savickas
(2003a) show that a measure of the (value-weighted)
idiosyncratic volatility, which is available in real
time, has forecasting abilities that are very similar
to those of the consumption-wealth ratio. Therefore,
as stressed by Lettau and Ludvigson (2003), it is
appropriate to use the consumption-wealth ratio
estimated from the current vintage data in this paper
because I address the question of whether expected
excess returns are time-varying.8

CAMPBELL’S ICAPM
In this section, I briefly discuss how stock market
returns are determined in a rational expectations
model (i.e., Campbell’s, 1993, ICAPM) if stock market
returns and volatility are predictable. In particular,
Campbell argues that the expected return on any
asset is determined by its covariance with stock
market returns and variables that forecast stock
market returns. This simple exercise helps illustrate
why the CAPM fails to explain the cross section of
stock returns, as mentioned in the introduction.
Campbell’s ICAPM is quite intuitive. For example,
because the consumption-wealth ratio is positively
related to future stock market returns, a negative
innovation in the consumption-wealth ratio indicates a low future expected return or worsened
“future investment opportunities.” A stock is thus
risky if its return is low when future investment
opportunities deteriorate—that is, there is a negative
shock to the consumption-wealth ratio. As a result,
in addition to compensation for the market risk,
investors require additional compensation on this
stock because it provides a poor hedge for changing
investment opportunities. Below, I briefly discuss
the testable implications of Campbell’s ICAPM.
Interested readers may look to Campbell (1993,
1996) for details.
8

I focus on the consumption-wealth ratio in this article because, as
mentioned, it is a theoretically motivated variable. In contrast, the
idiosyncratic volatility forecasts stock returns because of its comovements with the consumption-wealth ratio, and such a link has
not been well understood. Also, the consumption-wealth ratio is
available in a longer sample than the idiosyncratic volatility.

Guo

Campbell’s ICAPM is a model of an infinite
horizon economy, in which a representative agent
maximizes an Epstein and Zin (1989) objective
function,
(1)
U t = {(1 − β}Ct1−(1/ σ ) + β ( EtU t1+−1γ )[1−(1/ σ )]/ (1−γ )}1/ [1−(1/ σ )]
= [(1 − β )Ct(1−γ )/ θ + β ( EtU t1+−1γ )1/ θ ]θ / (1−γ ),
subject to the intertemporal budget constraint
Wt +1 = Rm,t +1(Wt − Ct ) .

(2)

In the above equations, Ct is consumption, Wt is
aggregate wealth, Rm,t+1 is the return on aggregate
wealth, β is the time discount factor, γ is the relative
risk aversion coefficient, σ is the elasticity of intertemporal substitution, and θ is defined as θ=(1– γ ) /
[1– (1/σ )]. If we set θ equal to 1, we obtain the familiar
power utility function, in which the relative risk
aversion coefficient is equal to the reciprocal of the
elasticity of intertemporal substitution.
Suppose that there are (K–1) state variables,
xt+1=[x1,t+1,…,xK–1,t+1]′, lags of which forecast
stock market return, rm,t+1, and its volatility.9 Also,
rm,t+1 and xt+1 follow a first-order vector autoregressive (VAR) process:
(3)

 ε1,t +1 
rm,t  
rm,t +1

 x  − A0 − A  x  =  M  ,
 t  ε
 t +1 

 K, t +1

where A0 is a K-by-1 vector of intercepts, A is a K-by-K
matrix of slope coefficients, and [ε1,t+1, ε2,t+1,…,
ε K,t+1]′ is a K-by-1 vector of error terms, which are
orthogonal to the lagged state variables. Campbell
(1993) shows that, if stock market returns and
volatility are predictable, as shown in equation (3),
the expected return on any asset, e.g., ri,t+1, is
determined by its covariance with stock market
returns and variables that forecast stock market
returns:
(4)
Et ri ,t +1 − r f ,t +1 +

K
Vii ,t
θψ
= γ Vim,t + ∑ [(γ − 1 −
)]λhkVik,t ,
σ
2
k =1

where rf,t+1 is the risk-free rate, V is conditional
variance or covariance, Ψ is the coefficient relating
stock market return to volatility, and λ hk is a function
9

rm,t+1 is the log of return on aggregate wealth, Rm,t+1.

M AY / J U N E 2 0 0 4

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Guo

Table 2

p1 = γ + [(γ − 1 −

Model Specifications
Model

Restrictions on equation (5)

I

λhk = 0, k = 1, …, K

II

θψ
=0
σ

III

No restrictions

IV

Coefficients of εm,t+1εk,t+1, k = 1, …, K
are free parameters

(6)
pi = [(γ − 1 −

θψ
)]λh1
σ

θψ
)]λhi , i = 2, ..., K ,
σ

where εm,t+1 is the shock to the stock market
return, which I also denote as ε1,t+1 in equation (3).
Equation (5) indicates that stock market return is
predictable because its covariances with state variables—for example, stock market volatility, ε 2m,t+1—
are predictable.
Campbell’s ICAPM of equations (3) and (5) can
be estimated using the generalized method of
moments (GMM) by Hansen (1982). I use a quarterly
sample spanning from 1952:Q4 to 2000:Q4, with a
total of 193 observations. To mitigate the potential
small sample problem, I follow the advice of Ferson
and Foerster (1994) and use the iterative GMM unless
otherwise noted. I assume that the error terms in
equations (3) and (5) are orthogonal to the lagged
state variables and have zero means. Equation (3) is
exactly identified. In equation (5), there are two
θψ
parameters, γ and
, and K+1 orthogonality
σ
conditions. The equation system, therefore, is overidentified with K –1 degrees of freedom. Hansen’s
(1982) J-test can be used to test the null hypothesis
that the pricing error of equation (5), um,t+1, is
orthogonal to the lagged state variables and has a
zero mean. We can also back-out the price of risk
for each factor using the formula

where p1 is the risk price for stock market returns
and p i is the risk price for forecasting variable i.
If we impose the restriction that Ψ—the parameter for time-varying stock market volatility—is equal
to zero, we obtain the special case analyzed by
Campbell (1996), in which volatility changes have
no effects on asset prices. It should be noted that,
as discussed in footnote 10, equation (4) or (5) is a
special case of Campbell’s ICAPM with time-varying
volatility. Under general conditions (e.g., conditional
stock market volatility is a linear function of lagged
state variables), I (Guo, 2002) show that conditional
stock market return is still a linear function of its
covariances with state variables, but the risk prices
are complicated functions of the underlying structural parameters. For robustness, I also estimate
equation (5) by assuming that the risk prices are free
parameters. It should also be noted that equation
(5) reduces to the familiar CAPM if we drop the
covariances between stock market returns and the
forecasting variables. These four specifications are
nested, and the D-test proposed by Newey and West
(1987) can be used to test the restrictions across
these specifications.
Table 2 summarizes the specifications of the
four models investigated in this paper. Model I is
the CAPM, in which I assume that the covariances
with variables that forecast stock market returns
have no effects on the expected stock market return.
Model II is Campbell’s ICAPM with constant stock
θψ
market volatility, in which the parameter
is
σ
restricted to be zero. In Model III, I allow volatility
changes to affect the expected stock market return
θψ
and estimate
as a free parameter. Model IV is
σ
the general case of Campbell’s ICAPM, in which I
estimate the risk prices as free parameters. In models
II and III, I estimate the structural parameters γ
θψ
and/or
and use equation (6) to back-out the risk
σ
prices. The risk prices are estimated directly in
models I and IV.

10

EMPIRICAL RESULTS

of A.10 In particular, excess stock market return is
given by

ε 2 m,t +1
2
− γε m
,t +1
2
K
θψ
− ∑ [(γ − 1 −
)]λ hkε m,t +1ε k,t +1 = um,t +1,
σ
k =1

rm,t +1 − r f ,t +1 +
(5)

For example, Vi1,t=Et (ε1,t+1ε i,t+1) is the conditional covariance
between the shock to stock market return, ε1,t+1, and the shock to the
return on asset i, ε i,t+1. To derive equation (4), I also use a simplifying
assumption, Et rm,t+1=Ψ Vmm,t, as suggested by Campbell (1993).

28

M AY / J U N E 2 0 0 4

Before presenting the empirical results, I want
to emphasize that Campbell’s ICAPM is not a general

FEDERAL R ESERVE BANK OF ST. LOUIS

Guo

Table 3
Campbell’s ICAPM with Constant γ
Risk prices for
Model

γ

θψ
σ

rm

cay

2
σm

rrel

J-test (p-value)

χ 2(4) = 14.01
(0.01)

I

6.53
(5.12)

6.53
(5.12)

II*

32.82
(3.35)

9.50
(3.13)

441.67
(2.79)

405.79
(3.37)

–807.87
(–3.17)

χ 2(4) = 7.12
(0.13)

III

31.29
(2.31)

8.91
(2.02)

449.16
(2.10)

447.76
(2.40)

–719.24
(–2.58)

χ 2(3) = 0.73
(0.87)

9.32
(1.03)

71.44
(0.18)

387.39
(1.27)

–739.37
(–0.94)

χ 2(1) = 0.04
(0.85)

IV

–14.62
(–1.97)

D-test (p-value)
I vs. IV: χ 2(3) = 19.64 (0.00)
II vs. IV: χ 2(3) = 7.19 (0.07)
II vs. III: χ 2(1) = 5.60 (0.02)
III vs. IV: χ 2(2) = 1.01 (0.60)
NOTE: * I use the identity matrix as the initial weighting matrix and use five iterations; t-statistics are in parentheses unless otherwise
indicated.

equilibrium model, because it takes stock return
predictability as given. Therefore, the test of
Campbell’s ICAPM is a joint test of an equilibrium
model, which explains the choice of forecasting
variables. This explains, in contrast with my results,
that the early authors such as Campbell (1996), Li
(1997), and Chen (2002) find little support for
Campbell’s ICAPM because they use different sets
of forecasting variables.
Table 3 presents the empirical results. Consistent
with asset pricing theories, the relative risk aversion
coefficient, γ , is statistically positive with a point
estimate of about 6.5 in model I.11 However, the Jtest rejects the model at the 1 percent significance
level, indicating that the stock return predictability
cannot be explained solely by predictable variations
in volatility. This result, which is consistent with
Harvey (1989), should not be a surprise. Table 1
shows that other variables such as the consumptionwealth ratio and the stochastically detrended riskfree rate also forecast stock market returns. Their
covariances with stock market returns, therefore,
11

The price of the market risk is equal to the relative risk aversion
coefficient in the CAPM.

are also components of the expected stock market
return, as shown in equation (5).
In model II, the relative risk aversion coefficient
is also significantly positive, with a point estimate
of about 32.8. Moreover, the risk prices of all factors
are statistically significant with expected signs. In
particular, the covariance with the consumptionwealth ratio, cay, and realized stock market variance,
σm2 , is positively priced because these two variables
are positively related to future stock market returns,
as shown in Table 1. Similarly, the covariance with
the stochastically detrended risk-free rate, rrel, is
negatively priced because it is negatively related to
future stock market returns. The price of the market
risk, rm, is positive; its point estimate of 9.5, however,
is much smaller than that of the relative risk aversion coefficient. This result, as argued by Campbell
(1996), reflects the mean-reversion in stock market
returns. However, there is only weak support for
model II: It is not rejected at the 10 percent significance level by the J-test.
θψ
In model III, the coefficient
is negative and
σ
statistically significant. This should not be a surprise
given mounting evidence of large fluctuations in
M AY / J U N E 2 0 0 4

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Guo

Figure 3
A Decomposition of Stock Market Return
0.08
Premium on
Market Risk
0.04

Average
Return

Premium
on cay

Premium
on rrel

Pricing
Error

0

–0.04
Premium
on Volatility
–0.08

stock market volatility, e.g., Schwert (1989). Moreover,
model III fits the data pretty well: It is not rejected
at the 80 percent significance level, according to
the J-test. Nevertheless, the point estimates of the
relative risk aversion coefficient and the risk prices
are similar to those reported in model II. Finally, we
find that model IV, the most general specification,
also explains the dynamic of stock market returns
well.
The D-test reveals a similar pattern. Model I is
overwhelmingly rejected relative to model IV, indicating that the CAPM cannot explain the dynamic
of stock market returns. Model II is also rejected
relative to models III and IV, indicating that changes
in volatility have important effects on asset prices.12
However, we cannot reject model III relative to model
IV at the 60 percent significance level. Therefore,
equation (4) or (5) provides a good approximation
for the effect of return heteroskedasticity. One advantage of model III is that it allows us to estimate the
structural parameter of the relative risk aversion
coefficient, γ.
In Figure 3, I use the estimation results of model
III in Table 2 to decompose the average stock market
return into its covariances with the four risk factors
and the pricing error. It shows that, although the
market risk is an important determinant of the
average return, the risk premiums on cay, σm2 , and
rrel are also substantial. The pricing error, however,
is very small relative to the average return, which
confirms the J-test in Table 3.

Figure 3 sheds light on the failure of the CAPM,
as argued by Fama and French (2003), among others:
The market risk is not the only determinant of
stock returns when conditional stock market return
and volatility change over time. For example, as
mentioned in the introduction, value stocks earn
higher average returns than growth stocks, even
though their covariances with stock market returns
are similar. This is because value stocks have higher
covariances with cay than growth stocks; similarly,
the momentum profit is explained by the fact that
the past winners have higher covariances with σm2
than the past losers do (Guo, 2002). Brennan, Wang,
and Xia (forthcoming) and Campbell and Vuolteenaho
(2002) also find that a hedge for changing investment opportunities explains the value premium,
although they use different instrumental variables.
Lastly, I want to stress that, although many
financial economists agree that the CAPM does not
explain the cross section of stock returns, they disagree on the source of the deviation from the CAPM.
This is because the early authors test the CAPM
using portfolios formed according to various characteristics, such as book-to-market value ratios, and
the failure of the CAPM is consistent with a host of
alternative hypotheses. For example, while Fama
and French (2003) interpret the value premium as
being consistent with ICAPM, Lakonishok, Shleifer,
and Vishny (1994) and MacKinlay (1995) attribute
it to irrational pricing and data mining.13 Based on
13

12

Ang et al. (2003) also find that stock market volatility is a significantly
priced risk factor.

30

M AY / J U N E 2 0 0 4

The value premium is the return on a portfolio that is long in stocks
with high book-to-market value ratios and short in stocks with low
book-to-market value ratios.

FEDERAL R ESERVE BANK OF ST. LOUIS

Campbell’s ICAPM or equation (4), Guo and Savickas
(2003b) provide some new insight on this issue by
forming portfolios on conditionally expected returns.
In particular, they use the same variables used in
this paper to make out-of-sample forecasts for individual stocks and then sort the stocks into decile
portfolios based on the forecast. They show that
the decile portfolios, which are motivated directly
from the ICAPM and thus not vulnerable to the
criticism of data mining or irrational pricing, pose
a serious challenge to the CAPM. Their results provide direct support for ICAPM.

CONCLUSION
In this article, I provide a brief survey of rational
pricing explanations for stock return predictability.
For illustration purposes, I also estimate and test a
variant of Campbell’s ICAPM, which allows for timevarying conditional return and volatility. Consistent
with the recent authors, ICAPM appears to explain
the dynamic of stock market returns better than the
CAPM does. The results suggest that stock return
predictability is important for understanding asset
pricing.

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Method of Moments Estimators.” Econometrica, July 1982,
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Merton, Robert C. “An Intertemporal Capital Asset Pricing
Model.” Econometrica, September 1973, 41(5), pp. 867-87.

Harvey, Campbell R. “Time-Varying Conditional Covariances
in Tests of Asset Pricing Models.” Journal of Financial
Economics, October 1989, 24(2), pp. 289-317.

Merton, Robert C. “On Estimating the Expected Return on
the Market: An Exploratory Investigation.” Journal of
Financial Economics, December 1980, 8(4), pp. 323-61.

Jegadeesh, Narasimhan and Titman, Sheridan. “Returns to
Buying Winners and Selling Losers: Implications for
Stock Market Efficiency.” Journal of Finance, March 1993,
48(1), pp. 65-91.

Newey, Whitney K. and West, Kenneth D. “Hypothesis
Testing with Efficient Method of Moments Estimation.”
International Economic Review, October 1987, 28(3), pp.
777-87.

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FEDERAL R ESERVE BANK OF ST. LOUIS

Guo

Patelis, Alex D. “Stock Return Predictability and The Role
of Monetary Policy.” Journal of Finance, December 1997,
52(5), pp. 1951-72.

Shiller, Robert J. “Do Stock Prices Move Too Much to Be
Justified by Subsequent Changes in Dividends?”
American Economic Review, June 1981, 71(3), pp. 421-36.

Schwert, William G. “Why Does Stock Market Volatility
Change Over Time?” Journal of Finance, December 1989,
44(3), pp. 1115-53.

Shiller, Robert J. “From Efficient Markets Theory to
Behavioral Finance.” Journal of Economic Perspectives,
Winter 2003, 17(1), pp. 83-104.

Schwert, William G. “Anomalies and Market Efficiency.”
Handbook of the Economics of Finance, Chap. 15.
Amsterdam: North-Holland, 2002.

White, Halbert L. “A Heteroskedasticity-Consistent
Covariance Matrix Estimator and a Direct Test for
Heteroskedasticity.” Econometrica, May 1980, 48(4), pp.
817-38.

Sharpe, William F. “Capital Asset Prices: A Theory of
Market Equilibrium Under Conditions of Risk.” Journal
of Finance, September 1964, 19(3), pp. 425-42.

Appendix

DATA DESCRIPTIONS
Because the consumption-wealth ratio, cay, is
available on a quarterly basis, I analyze a quarterly
sample spanning from 1952:Q4 to 2000:Q4, with a
total of 193 observations. Following Merton (1980),
among many others, realized stock market variance,
σm2 , is the sum of the squared deviation of the daily
excess stock return from its quarterly average in a
given quarter. It should be noted that, as in Campbell
et al. (2001), I make a downward adjustment for the
realized stock market variance of 1987:Q4, on which
the 1987 stock market crash has a compounding
effect. The stochastically detrended risk-free rate,
rrel, is the difference between the risk-free rate and
its average over the previous four quarters, and the

quarterly risk-free rate is approximated by the
sum of the monthly risk-free rate in a quarter. The
consumption-wealth ratio data were obtained from
Martin Lettau at New York University. I obtain the
daily value-weighted stock market return from the
Center for Research in Security Prices (CRSP) at the
University of Chicago. The daily risk-free rate is not
directly available, but I assume that it is constant
within a given month. The monthly risk-free rate is
also obtained from the CRSP. The real stock market
return, rm, is the difference between the CRSP valueweighted market return and the inflation rate of
the consumer price index obtained from the Bureau
of Economic Analysis.

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How Costly Is Sustained Low Inflation for the
U.S. Economy?
James B. Bullard and Steven Russell

1. INTRODUCTION

I

n this paper we describe and analyze a
quantitative-theoretic general equilibrium
model in which permanent changes in monetary policy have important welfare consequences
for households. Our main findings are estimates
of the welfare cost of inflation that are an order of
magnitude larger than most estimates found in the
cost-of-inflation literature. In particular, we find
that a permanent, 10-percentage-point increase in
the inflation rate—a standard experiment in this
literature—imposes an annual welfare loss equivalent to 11.2 percent of output. Most estimates of
the cost of inflation place this loss at less than 1
percent of output. Thus, our analysis helps account
for the widely held view that the benefits of reducing the inflation rate from the double-digit levels
experienced during the 1970s were very large.
The model we employ belongs to a class of
models—the overlapping generations (OLG) or
general equilibrium life-cycle models—that have
rarely been used to study the cost of inflation and
have never been used to obtain practical estimates
of the magnitude of these costs. The distinctive
features of the model allow us to study a source of
welfare losses from inflation that has not been
described previously. Although our analysis is novel
in these respects, in most other ways it is entirely
conventional. We make standard assumptions about
preferences, production, and capital accumulation.
Households and firms have rational expectations,
and equilibria occur at prices and interest rates that
clear markets. Money demand is introduced through
a reserve requirement. Changes in monetary policy

take the form of permanent changes in the growth
rate of the base money stock that produce permanent
changes in the rate of inflation. We follow the bulk
of the inflation-cost literature by basing our cost estimates on comparisons of alternative steady states.
We follow the recent trend in applied macroeconomic theory by calibrating our model to increase
the empirical credibility of its predictions. The principal goal of our calibration procedure is to produce
a steady-state equilibrium that matches certain longrun-average features of U.S. postwar data. We have
given the model a variety of characteristics that
increase both its overall plausibility and its ability
to mimic these data. The characteristics include
households that live for a large but finite number
of periods, exogenous technological progress, exogenous population growth, costly financial intermediation, and endogenous labor-leisure decisions. The
model also includes a fairly elaborate government
sector, including real expenditures (government purchases), taxes on labor and capital income, seigniorage revenue, and government debt. The importance
of the role played by the government sector is a
distinctive feature of our analysis.
A characteristic of the observed public finance
system that plays a key role in driving our results is
that capital income taxes are levied on net nominal
income, so that increases in the inflation rate increase
effective capital income tax rates. In this respect,
our analysis is similar to recent work by Feldstein
(1997) and Abel (1997). However, their estimates of
the cost of inflation are based largely on the tendency of higher effective capital income tax rates
to increase the wedge between the before-tax and

James B. Bullard is a vice president and economist at the Federal Reserve Bank of St. Louis. Steven Russell is a professor of economics at Indiana
University–Purdue University at Indianapolis (IUPUI).
The authors thank Bruce Smith at the conference “Macroeconomic Theory and Monetary Policy,” sponsored by the University of Pennsylvania and
the Federal Reserve Bank of Philadelphia; Roger Farmer at the conference “Dynamic Models of Economic Policy,” sponsored by the University of
Rochester, University of California, Los Angeles, and the Federal Reserve Bank of Minneapolis; Wilbur John Coleman II at a Summer North American
Meeting of the Econometric Society; and Frank Gong at a meeting of the Federal Reserve System Committee on Macroeconomics for useful discussant
comments. They also thank seminar participants at the Bank of England, Cornell University, Indiana University, Midwest Macroeconomics, Rutgers
University, Simon Fraser University, University of Texas, and the University of Western Ontario for helpful feedback. Deborah Roisman provided
research assistance.
Federal Reserve Bank of St. Louis Review, May/June 2004, 86(3), pp. 35-67.
© 2004, The Federal Reserve Bank of St. Louis.

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Bullard and Russell

after-tax real rates of return on capital. We identify
an entirely new channel through which increased
effective capital income tax rates contribute to the
cost of inflation. Our inflation-cost estimates are
attributable mostly to this channel, which we discuss
at length below.
We can use our model to identify the portions
of our total welfare-cost estimates that are attributable to effects analogous to those studied by other
researchers. In particular, the “purely monetary”
component of our cost estimate—the portion that
is due to the fact that an increase in the inflation rate
is a decrease in the real rate of return on money—
accounts for somewhere between 1 and 5 percent
of our total cost estimate, which makes it roughly
as large as most inflation-cost estimates in the literature. The component of the cost that is due to the
effects emphasized by Feldstein accounts for roughly
15 percent of our total cost estimate. Thus, the new
inflation-cost-generating mechanism we describe
is responsible for about 80 percent of our estimate
of the total welfare cost of inflation.

1.1 Previous Research
Some of the previous research on the cost of
inflation has been conducted using partial equilibrium models. One recent contribution to this literature is Feldstein (1997), which is closely related to
our analysis. Much of the rest of the recent work
on the cost of inflation is based on general equilibrium models—almost invariably, the infinitehorizon representative agent (IHRA) model, which
has become the standard model in applied macroeconomic theory. Research of this type includes
Cooley and Hansen (1989),·Imrohoroğlu and Prescott
(1991), Gomme (1993), Lucas (2000), Haslag (1994),
Jones and Manuelli (1995), Dotsey and Ireland
(1996), and Lacker and Schreft (1996). Another
example is Abel (1997), who presents a general
equilibrium adaptation of Feldstein’s analysis. For
our purposes, Feldstein (1997) and Abel (1997) can
serve as the representatives of cost-of-inflation
research using partial equilibrium models and IHRA
models, respectively.
Feldstein follows most other partial equilibrium
investigations of the cost of inflation by assuming
that the before-tax real interest rate (or real rate of
return on capital) is invariant to policy-induced
changes in the inflation rate. According to Feldstein,
most of the cost of inflation grows out of the fact
that it increases the effective tax rate on capital
income and consequently reduces the after-tax real
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M AY / J U N E 2 0 0 4

rate of return facing savers. Feldstein also emphasizes
a closely related problem, which is that inflation
affects the after-tax rates of return on some assets
(notably, housing capital) more strongly than others,
causing capital to be misallocated.
Feldstein also discusses the effect of inflation
on the rate of return on money and the opportunity
cost of holding money. This effect has been the main
one emphasized by most other contributors to the
cost-of-inflation literature. The “monetary cost” of
inflation grows out of the fact that an increase in
the opportunity cost of holding money causes households to overeconomize on transactions balances,
while a reduction in the rate of return on money
distorts saving and/or labor-leisure decisions by
increasing the opportunity cost of future consumption. In Feldstein’s analysis the net monetary cost
of inflation is actually negative (i.e., a welfare benefit),
since an increase in the inflation rate produces an
increase in currency seigniorage revenues that
allows a reduction in other distorting taxes—a
reduction whose welfare benefits exceed the costs
just described.1 Although most other analyses of
the monetary cost of inflation produce positive
cost estimates, these estimates are uniformly small
relative to Feldstein’s estimates of the total cost of
inflation estimates or to the total cost estimates we
present in this paper.
Cost-of-inflation analyses using IHRA models
do not assume that the before-tax real interest rate
is constant. However, in the standard IHRA model
the steady-state value of the after-tax real interest
rate is essentially invariant to monetary or fiscal
policy: It is a function of the exogenous output
growth rate plus preference parameters such as
the rate of time preference and the intertemporal
elasticity of substitution in consumption.2 For this
reason, in Abel’s general equilibrium adaptation of
Feldstein’s analysis, an increase in the inflation rate
produces an increase in the before-tax real rate of
return on capital that is roughly equal to the decrease
1

Feldstein’s estimates of the monetary cost of inflation are based on
empirical evidence suggesting that money demand is not very sensitive
to changes in the rate of return on money. As a result, the distortions
caused by increasing the inflation tax on money balances are relatively
modest, and the resulting increases in the volume of currency
seigniorage revenue are relatively large.

2

In stochastic models, uncertainty about asset returns also plays a role
in the determination of real interest rates on both safe and risky assets.
In a formal model, changes in the average rate of inflation do not in
themselves affect the amount of uncertainty of this type. There is, however, a fairly extensive literature on the empirical relationship between
the average level of inflation and the variability of the inflation rate.

FEDERAL R ESERVE BANK OF ST. LOUIS

in the after-tax real rate of return predicted by
Feldstein. The increase in the pretax return rate on
capital causes a substantial decline in the capital
stock—a decline that reduces the marginal product
of capital and produces a lower wage rate. It is this
decline in household income, rather than a decrease
in the rate of return facing savers, that is responsible
for most of Abel’s estimate of the welfare cost of
inflation. Despite this rather profound difference
between the inflation-cost-generating mechanisms
postulated by Feldstein and Abel, their estimates of
the total cost of inflation are very close to one
another.

1.2 Our Approach
Although our analysis of the cost of inflation
shares a number of important features with the
analyses conducted by Feldstein and Abel, it differs
from these analyses in one centrally important way:
In the Feldstein and Abel models, the change in the
real rate of return to capital produced by an increase
in the inflation rate must be approximately equal
to the implied increase in the effective tax rate on
the real return to capital. The after-tax real rate falls
(Feldstein) or the before-tax real rate rises (Abel) by
this amount, leaving the other rate unchanged. In
our model, by contrast, an increase in the inflation
rate causes a decrease in both the after-tax real rate
of return to capital and the before-tax real rate of
return to capital, and it also widens the spread
between these two rates. The increase in the spread
is equal to the increase in the effective tax rate on
capital returns, but the total decline in the after-tax
real interest rate is considerably larger. For example,
in our baseline case, a 10-percentage-point increase
in the inflation rate causes the spread between the
before-tax real rate of return on capital and the aftertax real rate of return to increase by approximately
1.8 percentage points. However, the total decline in
the after-tax real rate of return is 3.6 percentage
points.
The large changes in real interest rates that
produce our relatively high inflation-cost estimates
are driven by a combination of two features of our
model. The first feature involves our assumptions
about the role of the government budget constraint—
more specifically, about the disposition of the substantial increase in capital income tax revenue that
an increase in the inflation rate produces (all else
held constant) when the government taxes on a
nominal basis. In the Feldstein and Abel analyses,
this revenue is used to finance proportional decreases

Bullard and Russell

in all direct tax rates. In our analysis, on the other
hand, the government uses the increase in capital
income tax revenue to reduce the amount it borrows
from the public. The resulting decrease in aggregate
demand for credit produces a substantial decline
in the before-tax real interest rate. This decline is
possible because of the second distinctive feature
of our analysis: In the general equilibrium model
we use, it is possible for the government to change
the amount it borrows without adjusting future taxes
in a way that produces offsetting shifts in the aggregate supply of credit. We discuss both of these features of our model in detail below.
One interesting result we obtain concerns the
implications of attempts to reduce the inflation rate
from its postwar-average level of approximately 4
percent to a level of 0 percent or lower. As we have
indicated, under normal conditions the government
can use debt policy to offset the loss of revenue
caused by declines in the inflation rate. However,
our analysis implies that once the inflation rate
reaches a threshold level, further increases in government borrowing no longer succeed in increasing net
government revenue. Additional progress in reducing the inflation rate then requires active cooperation from the fiscal authorities, who must be willing
to reduce government expenditures and/or increase
tax rates.3
Our results indicate that the threshold level of
the inflation rate is about 2.5 percent. They also indicate that once this threshold is reached, the welfare
benefits from further reductions in the inflation rate
are much smaller because of the corresponding
need to increase direct tax rates. Thus, our analysis
suggests that further reductions in the inflation rate
for the U.S. economy are likely to be both much
more difficult to achieve, and much less beneficial
if achieved, than the reductions that have taken
place since the early 1980s.
In the next section we present a more complete
description of our approach to analyzing the real
effects of changes in monetary policy and the welfare
costs of inflation. This section also includes a graphical depiction of our mechanism for generating high
inflation costs and a discussion of the empirical
plausibility of our approach. In section 3 we lay out
3

We view changes in government borrowing as constituting a passive
cooperation by the fiscal authorities. In the United States, the Treasury
Department can (and does) respond to most changes in borrowing
requirements without seeking authorization from Congress. Changes
in expenditures or tax rates, however, require Congressional action.

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the model that we use to obtain our welfare cost
estimates. Section 4 describes the procedure we use
to select values for the parameters of the model,
while section 5 describes the baseline steady state
associated with our parameter choices and discusses
some of its features. In section 6 we calculate the
welfare costs of changes in the inflation rate using
our baseline parameterization and some alternative
parameterizations. Section 7 discusses some qualifications of our results.

2. A NEW APPROACH TO THE WELFARE
COST OF INFLATION
2.1 Theoretical Principles
Our objective in this section is to explain in
general terms the principles behind the model, as
well as the mechanisms at work, and to defend the
empirical plausibility of our results before proceeding to the formal model in the next section.
For almost a generation, two-period versions of
the OLG model have been widely used for theoretical
analyses of the real effects of monetary policy. An
important reason for this is that in OLG models,
unlike the IHRA models that have been favored by
empirically oriented macroeconomists, permanent
changes in monetary policy can have large permanent effects on real interest rates and other real
variables. In our multi-period model, as in many of
its two-period predecessors, permanent changes in
monetary policy affect real interest rates by influencing the government’s demand for credit. This is
possible because the finite lives of OLG households
make it possible for government credit demand to
rise or fall without producing offsetting adjustments
in households’ supply of credit. In the case of particular interest to us, this can happen because the government’s debt is “unbacked”: It does not have to be
serviced by a stream of future surpluses. Government debt can be unbacked because OLG models,
unlike IHRA models, can have steady-state competitive equilibria in which the real interest rate is lower
than the output growth rate. These equilibria were
first studied by Samuelson (1958) and Diamond
(1965) and are sometimes described as “Samuelson
case” equilibria following Gale (1973). (Equilibria
with higher real interest rates are often called
“classical case” equilibria.4)
4

Stochastic versions of IHRA models can have stationary equilibria in
which the average real interest rate is lower than the average output
growth rate. However, these equilibria do not have most of the other
distinctive characteristics of low-real-rate steady states in nonstochastic
OLG models.

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Bullard and Russell (1999) use a calibrated multiperiod OLG model—a simpler version of the model
developed in this paper—to argue that it is empirically plausible to model the postwar U.S. economy
as a Samuelson-case steady state and to view the
postwar U.S. government debt as unbacked. Their
analysis is grounded on the fact that during the postwar period the average real interest rate on U.S.
government debt has been substantially lower than
the average U.S. output growth rate and the government’s average primary surplus has been approximately zero.5
If the government issues debt at a real interest
rate lower than the output growth rate, then it can
earn “bond seigniorage” revenue in a steady state
by extending the debt at the rate necessary to keep
its share of output constant.6 Across steady states
of this type, a permanent decrease in the debt stock
will shift the aggregate credit demand curve to the
left along an unchanged aggregate credit supply
curve, causing the steady-state real interest rate to
fall. The decline in the real interest rate will have
permanent effects on investment, output, and other
real variables, including the welfare of households.
2.1.1 The Real Effects of Monetary Policy.
What does the situation just described have to do
with monetary policy or the cost of inflation? The
answer to this question begins with a seminal insight
of Sargent and Wallace (1981): The government’s
budget constraint enforces a connection between
fiscal policy and monetary policy. For the purposes
of their analysis, Sargent and Wallace define monetary policy as consisting of the central bank’s choice
of a combination of base money and government
debt policies that is consistent with the fiscal
authority’s policies regarding taxes and government
spending.7 They assume that these fiscal policy
5

This point also has been made by Darby (1984), among others. During
1948-97, the average ex post real (CPI-deflated) yield on three-month
Treasury bills was 1.1 percent. This yield is widely used as an empirical
proxy for the risk-free real interest rate: The short term presumably
ensures that the ex post real rate is quite close to the ex ante rate and
that the premium for interest risk is minimal. Of course, the average
real interest rate that the government actually paid was higher, because
the average term of the bonds it issued exceeded three months. However, even the average ex post real yields on bonds with terms of ten
years or more fall well short of the average output growth rate.

6

The term “bond seigniorage” seems to have been coined by Miller
and Sargent (1984).

7

An alternative interpretation of the Sargent-Wallace policy assumptions
is that the fiscal authority controls debt policy but conducts it in a way
that passively accommodates the fiscal authority’s active decisions
concerning taxes and spending as well as the monetary authority’s

FEDERAL R ESERVE BANK OF ST. LOUIS

decisions leave the government with a fixed real
primary deficit. They show that under this assumption a permanent tightening of monetary policy
(a permanent decrease in the base money growth
rate) is not feasible and a temporary tightening
must eventually cause the inflation rate to rise. The
logic behind this result is simple. A monetary tightening reduces the amount of inflation tax revenue
and leads to a gradual accumulation of government
debt. At some point the debt accumulation must
cease and the increased debt service costs must
be financed by increased revenue from base money
seigniorage.
In the Sargent-Wallace (1981) model the real
interest rate was assumed to be fixed at a level above
the output growth rate. However, Miller and Sargent
(1984) and Wallace (1984) conduct similar analyses
in models in which the real interest rate is endogenous, and the former analysis encompasses situations in which it is lower than the real growth rate.
Miller and Sargent sketch out a model that implies
that, under certain conditions, a permanent tightening of monetary policy can lead to a permanent
decrease in the inflation rate and a permanent
increase in the real interest rate. The explanation
for this result grows out of the fact that when the
real interest rate is relatively low the government
can earn revenue from bond seigniorage. A decrease
in the inflation rate reduces the amount of base
money seigniorage revenue and forces the government to issue more debt to increase its revenue
from bond seigniorage. The increase in the debt
stock causes the real interest rate to rise.8 It is this
situation—one where there is an inverse relationship
between inflation rates and real interest rates—that
we study in this paper.
We now turn to the welfare consequences of
permanent changes in inflation in these equilibria.

Bullard and Russell

2.1.2 The Cost of Inflation. Across Samuelsoncase steady states of models in which the households are intragenerationally homogeneous, such
as Espinosa-Vega and Russell (1998a), policyinduced decreases in the real interest rate are
welfare-reducing. When the real interest rate is
lower than the output growth rate, the tendency
of a lower real interest rate to increase household
welfare by increasing the real wage (because a lower
real interest rate produces a larger capital stock) is
more than offset by its tendency to increase the
relative price of future consumption.9 Thus, models
of monetary policy that support Samuelson-case
steady states seem to provide a potential contribution to the literature on the cost of inflation.10
In the research program that led to the current
paper, we began by reconstructing the Espinosa-Vega
and Russell analysis in a multi-period calibrated
model that allows us to talk credibly about magnitudes. Our previous research—Bullard and Russell
(1999)—had established that plausible calibrations
of a relatively simple, nonmonetary version of this
model produce realistic-looking low-real-interestrate steady states.11 In the present paper we find
that plausible calibrations of a richer version of the
model—a version that includes both money and
government debt—support realistic-looking steady
states across which permanent increases in the
base money growth rate produce higher inflation
rates, lower real interest rates, and lower levels of
welfare for households.
9

Part of the reason for this is that in Samuelson-case equilibria, capital
is overaccumulated: The marginal return to capital is smaller than the
marginal cost of maintaining the capital stock via investment. A reduction in the real interest rate increases the capital stock and increases
the severity of this “dynamic inefficiency.”

10

The dynamic inefficiency of the steady states in our model helps
explain why our estimates of the size of the Feldstein effect are relatively low. In the Feldstein and Abel models, the fact that increases in
the inflation rate increase the effective tax rate on capital income is
almost unambiguously welfare-reducing. In our model, in contrast,
higher capital income tax rates tend to reduce welfare because they
increase the distortion of the saving and labor supply decisions (as in
Feldstein and Abel), but they tend to increase welfare because a higher
tax rate on capital income tends to reduce the degree of capital overaccumulation.

11

In the postwar U.S. economy the average real rate of return on capital
seems to be substantially higher than the average output growth rate.
In Bullard and Russell (1999) we show that augmenting the basic model
by adding capital income taxes and/or intermediation costs at plausibly
calibrated levels can produce realistic-looking steady states in which
the real rate of return on capital exceeds the output growth rate but
the real interest rate on government bonds is lower. The model in the
current paper includes both these features and produces a baseline
steady state of this type.

active decisions about the growth rate of the base money supply
(which determines government revenue from currency seigniorage).
This assumption seems consistent with modern U.S. monetary and
fiscal arrangements. Congress and the Administration make active
decisions about taxes and spending and the Federal Reserve makes
active decisions about the base money growth rate. The Treasury then
passively issues the bonds necessary to cover any resulting deficit.
8

The Miller-Sargent (1984) analysis has been refined and extended by
Espinosa-Vega and Russell (1998a,b), who study the real interest rate
effects of permanent changes in monetary policy across Samuelsoncase steady states of a pure exchange model (1998a) and in a model
with production and capital (1998b). In both models, a permanent,
policy-induced increase in the inflation rate can result in a permanent
decrease in the real interest rate on government debt. In the latter
model, the increase in the inflation rate is also associated with a permanent increase in the level of output.

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Figure 1
Dependence of Government Revenue on the Real Bond Rate
GY

0 24

02

10

0 16

0 12

0 08

0 04
rb
–2

2

4

6

8

10

10

In a basic version of the model presented below—
one where we abstract from capital income taxation—the mechanisms work as we have described
them but the quantitative real interest rate and
welfare effects of moderate increases in the inflation
rate are relatively small.12 The small size of these
effects is easily understood. We have seen in the
models that, when the inflation rate increases, the
government earns additional revenue from currency
seigniorage and consequently needs less revenue
from bond seigniorage. As a result, the government
needs to borrow less, the real stock of bonds declines,
and the real interest rate falls to allow private debt
to replace some of these bonds in the portfolios of
savers. However, in the U.S. economy the stock of
base money is quite small relative to output, so the
ratio of base money seigniorage to output is also
quite small. As a result, in a plausibly calibrated
model a moderate increase in the inflation rate will
produce a relatively small increase in the amount
of revenue from currency seigniorage and thus a
relatively small decrease in the amount of bond
12

Although the changes in the real interest rate that are produced are
small relative to our main results in this paper, the welfare cost these
changes produce are about as large as most of the inflation-cost estimates that appear in the literature.

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seigniorage. This small decrease in bond seigniorage
can be produced by a small decrease in the real
stock of government bonds and thus a small decline
in the real interest rate on these bonds.
However, when nominal capital income taxation
is included in the model, as it is in this paper, these
effects are greatly magnified—they are an order of
magnitude larger, in fact. As we have seen, the formal
analyses of this argument conducted by Feldstein
(1997) and Abel (1997) are based primarily on the
fact that increases in effective capital income tax
rates increase the spread between the before-tax
and after-tax real return rates on capital. The revenue
implications of these tax rate increases are a distinctly secondary consideration in those papers.
In our analysis, in contrast, the increase in capital
income tax revenue that occurs when the inflation
rate rises is the principal driving force behind our
results: Real interest rates have to fall substantially
to restore equilibrium. Under plausible calibrations,
this revenue increase is much larger than the
inflation-induced increase in revenue from currency
seigniorage. It is large enough to cause a substantial
decline in the real interest rate and a large decrease
in household welfare.

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2.2 A Graphical Description
A simple graphical description of the mechanism
we describe is presented in Figure 1. The lowest
curve in the figure describes the ratio of total government revenue to output as a function of the beforetax real interest rate on government debt (hereafter,
the real bond rate) in the baseline parameterization
of our model. The inflation rate is held fixed at its
baseline value of 4 percent. The tax rates on labor
and capital income are also held fixed at their baseline values.
One might expect the government revenue curve
to be uniformly downward-sloping, since lower real
interest rates are associated with higher real wages
and the U.S. government gets most of its revenue
from labor income taxes. Since the U.S. tax system
taxes net rather than gross capital income, however,
decreases in the real interest rate cause capital
income tax revenues to decline sharply. In addition,
at relatively low real bond rates, further declines in
the rate produce substantial declines in the revenue
from bond seigniorage. As a result, there exists a
real bond rate below which further decreases in the
rate cause the revenue-output ratio to fall. In our
baseline calibration, this rate is roughly 2.5 percent.
Equilibrium in the model occurs at a real bond
rate at which the ratio of government revenue to
output is equal to the government’s target for the
expenditures share of output. The expenditures
target is indicated by the horizontal line in the figure.
The equilibrium real bond rate on which we focus
is the one on the left side of the government revenue
curve: Its value is 1 percent. Although there is an
alternative equilibrium rate on the right side of the
curve, its level is counterfactually high and it produces implausible values for other endogenous
variables.
Now suppose that the monetary authority
increases the base money growth rate, and thus the
inflation rate, by 10 percentage points. If capital
income tax revenues were indexed to inflation, this
would affect total government revenue only by
increasing the revenue from currency seigniorage.
The increase in revenue would be small and the
government revenue curve would shift upward by
a small amount, producing the curve in Figure 1 that
lies just above the baseline curve. The new equilibrium value of the real bond rate would be slightly
lower (roughly 0.3 percentage points) than the
original value.
Under the actual U.S. tax system, however, the

Bullard and Russell

increase in the inflation rate produces a relatively
large increase in the amount of capital income tax
revenue. As a result, the total revenue curve shifts
upward by a relatively large amount, producing the
curve in Figure 1 that lies well above the baseline
curve. The left side of the new curve intersects the
expenditures target line at a point well to the left of
the original intersection point, indicating a decrease
of 2.4 percentage points in the before-tax real interest
rate on government debt. The after-tax real bond
rate falls by a larger amount, 3.6 percentage points,
because the increase in the effective tax rate on capital income increases the size of the wedge between
the two rates. The spread between the before-tax
and after-tax values of the real rate of return on
physical capital widens by 1.8 percentage points.
As we have indicated, however, only a small part of
our estimate of the welfare cost of inflation is attributable to the increase in these rate spreads.

2.3 Empirical Plausibility
Is it plausible to believe that permanent increases
in the inflation rate can produce substantial permanent declines in before-tax real interest rates? During
the past few years, a number of authors have used
recent developments in time series analysis to study
the long-run relationship between the money growth
rate and/or the inflation rate and the levels of real
variables such as the real interest rate, output, and
investment. The papers in question include King
and Watson (1992, 1997), Weber (1994), Bullard and
Keating (1995), Ahmed and Rogers (1996), Serletis
and Koustas (1998), Koustas (1998), and Rapach
(2003). As in the case of most literature that conducts
empirical tests of propositions from macroeconomic
theory, the results reported are mixed and the evidence cannot be regarded as conclusive. Nevertheless, the literature provides plenty of evidence that
indicates that money may not be long-run superneutral and that the direction and magnitude of the
long-run effects of inflation on real variables may
be consistent with the implications of our model. A
key aspect of these papers is that they distinguish
permanent from temporary movements in nominal
variables. Since the experiment we study (and that
most of the inflation cost literature studies) is a
permanent change in the inflation rate that alters
the steady state of the model, these studies provide
the appropriate empirical counterpart.
King and Watson (1992, 1997) use postwar U.S.
data to study the long-run relationship between
the money growth rate and the level of output, and
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Bullard and Russell

between the inflation rate and nominal interest rate,
under a range of alternative identifying assumptions.
They find that there is a broad range of plausible
identifying assumptions under which (i) the hypothesis that money is superneutral can be rejected and
(ii) the relationship between the rate of money
growth and the level of output is significantly positive. When they assume that money is contemporaneously exogenous—the most common identifying
assumption in this literature—they find that a permanent 1-percentage-point increase in the money
growth rate tends to increase the level of output by
3.8 percent. As we shall see in section 5, this is
almost identical to the percentage increase in output that results, in our model, from a permanent
1-percentage-point increase in the money growth
and inflation rates starting from the baseline inflation
rate. Under the analogous identifying assumption
regarding inflation and nominal interest rates, the
authors find that the simple Fisher relationship can
be rejected easily and that a 1-percentage-point
increase in the inflation rate tends to reduce the
real interest rate by more than 80 basis points. As
we have seen, this estimate is roughly twice the size
of the effect our model produces in the vicinity of
the baseline steady state. Alternative identifying
assumptions produce smaller estimates, however.
Weber (1994) uses similar data and methodology
to study the relationships between money growth
and output/interest rates in the Group of Seven countries. He finds that superneutrality can be rejected,
under a wide range of alternative identifying assumptions, for all of these countries except France. Weber
also finds that the data for the United States and the
United Kingdom are strongly inconsistent with the
simple Fisher relationship, with increases in the
inflation rate producing substantial decreases in
the real interest rate. The evidence for the other
countries is less conclusive.13
Bullard and Keating (1995) use bivariate models
to study the long-run relationship between the rate
of inflation and the level of output using postwar
data for 58 countries. They find evidence of statistically significant departures from superneutrality
13

There is a large literature that uses more traditional econometric
methods to investigate the relationship between ex ante real return
rates on assets and the expected rate of inflation. Most of these studies
find that these variables are strongly negatively correlated in the short
run and/or the long run. A good example is Huizinga and Mishkin
(1984). See Marshall (1992) and Boyd, Levine, and Smith (2001) for
more complete descriptions of this literature.

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M AY / J U N E 2 0 0 4

for a number of developed countries with relatively
low average inflation rates, though not for the United
States. In each of these countries an increase in the
inflation rate is associated with an increase in the
level of output.14 Rapach (2003) uses trivariate
models to study the long-run relationship between
the inflation rate, the real interest rate, and the level
of output in 14 OECD countries. He finds that for
each of these countries, increases in the inflation
rate produce statistically significant decreases in the
real interest rate. For seven countries, higher inflation rates produce statistically significant increases
in the level of output. For the other seven countries
(including the United States) the output responses
vary in sign but are not statistically significant.
Ahmed and Rogers (1996) use vector autoregressive methods to study the long-run relationship
between the inflation rate and the levels of output,
consumption, and investment using U.S. data for the
past 100 years. They find that permanent increases
in the inflation rate are associated with large permanent increases (decreases) in the ratio of investment
(consumption) to output. They view these results
as inconsistent with superneutrality or the simple
Fisher relationship. Their point estimate is that a
permanent, 1-percentage-point increase in the inflation rate causes the consumption share of output
to fall by 2.5 percentage points and the investment
share of output to rise by 1.0 percentage points.15
The effects generated by our model are qualitatively
similar, although the magnitudes are somewhat
different. In our model, a permanent increase in
the inflation rate from 4 percent to 5 percent causes
the consumption share of output to fall by 1.6 percent and the investment share to rise by 1.3 percent.

3. A GENERAL EQUILIBRIUM LIFECYCLE MODEL
3.1 Overview
Our model can be succinctly described as the
result of a hypothetical meeting between Sargent
and Wallace and Auerbach and Kotlikoff. Auerbach
14

For Germany, Austria, and the United Kingdom, the estimated effects
are clearly significant. For Japan and Spain, the estimated effects are
large but only marginally significant.

15

When Ahmed and Rogers (1996) confine their analysis to data from
the postwar period, they find that the departures from superneutrality
are qualitatively similar, and remain statistically significant, but are
much smaller in size.

FEDERAL R ESERVE BANK OF ST. LOUIS

and Kotlikoff (1987) were pioneers in the use of
multi-period OLG models to study issues in public
finance, but neither they nor their successors have
used these models to study issues in monetary economics.16 The principal differences between our
model and the Auerbach-Kotlikoff model are that
our model includes monetary elements and that it
allows for productivity growth and capital depreciation. As we have noted in the previous section,
Sargent and Wallace (1981, 1982, 1985) were pioneers in the use of two-period OLG models to study
questions in monetary theory and policy. We have
adopted many aspects of their approach, perhaps
the most important of which is their emphasis on
the role of the government budget constraint in helping determine the real effects of changes in monetary policy. In addition, since the source of money
demand in our model is a reserve requirement, our
analysis might be considered an application of the
legal restrictions theory of money that was developed by Wallace (1983, 1988) and has been applied
repeatedly by Sargent and Wallace. However, we do
not expect readers to take our reserve requirement
assumptions seriously as a deep theory of the
demand for money: Instead we view them as providing a proxy for money demand from all sources.
In this sense, our money demand specification is
similar to the cash-in-advance specifications that
are common in the cost-of-inflation literature.17

3.2 Primitives

Bullard and Russell

date can be consumed or stored. If stored they are
called “capital goods” and can be used in production
during the following period. Capital goods depreciate at a net rate of δ ∈[0,1] per period whether or
not they are used in production.
At each date, an arbitrary number of competitive
firms have access to a technology that uses capital
and effective labor to produce the consumption
good. The aggregate stock of capital goods available
for use in production at the beginning of date t is
denoted K(t). Since the technology exhibits constant
returns, it suffices to describe the aggregate production function

where L(t) is the aggregate supply of effective labor
and k(t) ; K(t) /L(t) is the ratio of capital to effective
labor. The parameter λ ≥ 1 is the gross rate of growth
of labor productivity, and the parameter α ∈(0,1)
governs the capital share of output.
3.2.3 Preferences. A household’s preferences
are defined over intertemporal bundles that include
the quantities of the single good that it consumes
during each period of its life and the quantity of
leisure enjoyed in each period. The consumption
and leisure choices of a member of generation t
at date t+j are denoted ct (t+j ) and ,t (t+j ), j=0,
…,n – 1, respectively.
The preferences of the households are described
by the standard utility function

(

U {ct (t + j ), lt (t + j )}nj =−01

3.2.1 Demographics. A generation of identical

households is born at each discrete date t=…,–2,
–1,0,1,2,… and lives for n periods. Successive generations of households are identified by their birthdates and differ from each other only in their populations, which grow at gross rate ψ ≥ 1 per period.
Each household is endowed with a single, perfectly
divisible unit of time per period and must allocate
this time unit between labor and leisure. A household in its i th period of life has an effective labor
productivity coefficient ei, i=1,…,n. If this household supplies l units of labor during this period,
then its effective labor supply is ei l.
3.2.2 Goods and Technologies. There is a
single good. Units of the good available at a given
16

An exception is Altig and Carlstrom (1991).

17

See Haslag (1995) for a discussion of some fairly general conditions
under which cash-in-advance and reserve requirement economies
are allocationally equivalent.

Y (t ) = λ(1−α )( t −1) K(t )α L(t )1−α ,

(1)

(2)

n −1

)

βj
ct (t + j )η lt (t + j )1−η
j =0 1 − γ

=∑

[

]

1−γ

,

where γ >0, η >0, and β ;1/(1+ρ), with ρ > –1.
We require ct (t+j) ≥ 0 and ,t(t+j) ∈[0,1] for all j=0,
…,n – 1 and for all t. These preferences imply that
households’ elasticity of intertemporal substitution
in consumption, σ, is the reciprocal of their coefficient of relative risk aversion ν, where ν ;1– η (1– γ ).
Since this is an OLG model, no restrictions need
be placed on the value of ρ other than ρ > –1.
Although ρ is often described as the “(pure) rate of
time preference,” a more meaningful measure of
the households’ relative valuation of current versus
future consumption is their effective time preference
rate ϕ ;1– (1+ρ)–1/γ. If a household with an effective time preference rate of ϕ is faced with a zero
net real interest rate, then it will choose an average
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Bullard and Russell

lifetime consumption growth rate of approximately
–ϕ.18
The parameter η is the elasticity of intratemporal substitution of consumption and leisure. It is also
the dominant parameter governing the share of
households’ time that they devote to providing labor.
We require households to retire from the labor force
at an age n* ≤ n; that is, ,t (t+j )=1 for j=n*– 1,…,
n – 1.

3.3 Markets
3.3.1 Inputs Markets. The firms rent capital
and hire effective labor at rental and wage rates
equal to these inputs’ respective marginal products.
The rental rate is r(t)=αλ (1– α)(t – 1)k(t)α – 1 and the
wage rate is w(t)=λ (1– α)(t – 1)(1– α)k(t)α .
3.3.2 Asset Markets. There are four basic types
of assets in the model: physical capital, consumption loans, government (consumption) bonds, and
fiat currency. For purposes of simplicity, all loans
and bonds are assumed to have terms of one period.
We assume that households hold any assets other
than government bonds indirectly: Their direct
holdings consist of deposits issued by perfectly
competitive financial intermediaries. The intermediaries use these deposits to make loans to households, to purchase capital goods from households
(in order to rent them to firms next period), and to
purchase fiat currency. The financial intermediaries
incur a constant real cost per unit of goods lent or
used to acquire capital. This cost, which is denoted
ξ ∈(0,1), is assumed to be incurred during the period
when the loans are repaid or the capital goods are
recovered from storage. Households purchase bonds
directly from the government without incurring
any transactions costs.19
The intermediation cost assumption is intended
to act as a crude proxy for the costs associated with
risky private lending—including, perhaps, a risk
premium. At the calibration stage, the assumption
helps us do a better job of mimicking the observed
structure of interest rates on private and government
18

19

The easiest way to see this is to consider a two-period endowment
model with inelastic labor supply and preferences given by
u=Σ1i=0(1– γ )–1β ict (t+i)1– γ . The first-order conditions imply ct (t+1)=
(β R(t))1/γ ct (t), where R(t) is the gross real interest rate between dates t
and t+1. In this case the effective time preference rate ϕ is exactly
equal to the arithmetic inverse of the consumption growth rate the
household chooses when faced with a zero net real interest rate.
Thus, ϕ=–(ct (t+1)/ct (t) –1)|R(t)=1, which, from the first-order condition, is ϕ=1– β1/γ , or 1–(1+ρ)–1/γ .
We assume that households who attempt to make private loans
directly would face prohibitively high transactions costs.

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M AY / J U N E 2 0 0 4

liabilities.20 It has little effect on our estimates of
the welfare cost of inflation (see section 6.3.1).
Financial intermediaries are legally required to
hold a minimum fraction φ ∈(0,1) of their liabilities
in the form of real balances of fiat currency (reserves).
We confine ourselves to the study of equilibria in
which fiat currency is not return-competitive, so
that households do not hold it directly and intermediaries do not hold excess reserves. As we have
indicated, however, we use reserve demand as a
proxy for base money demand from all sources.
3.3.3 Government Intervention in Markets.
The government in the model is a consolidated
federal, state, and local entity. At date t the government must finance a real expenditure of G(t) ≥ 0
by a combination of direct taxation and seigniorage.
The goods that comprise the expenditure are
assumed to leave the economy. We will assume
that the level of the expenditure must be constant
relative to output: that is, the government chooses
G(t) so that G(t)/Y(t)=g for some g ≥ 0. Thus, the
expenditure must grow at the same rate as output,
which is λψ (gross) per period in a steady state.
The government issues two types of liabilities:
fiat currency and one-period consumption bonds.
The nominal quantity of fiat currency outstanding
at the end of date t is denoted H(t). The currency
price of a unit of the consumption good at date t is
denoted P(t). Aggregate real currency balances at
date t are M(t)=H(t)/P(t). The real rate of return on
currency balances is Rh(t)=P(t)/P(t+1) and the gross
inflation rate is Π(t)=1/Rh(t)=P(t+1)/P(t). We assume
that the government issues just enough additional
fiat currency, each period, to allow the total nominal
stock to grow at a constant rate: H(t)=θ H(t –1) for
some θ ≥ 1. Nominal revenue from currency seigniorage at date t is simply H(t) – H(t –1)=(1 – 1/θ ) H(t).
Real revenue from this source is S c(t) ; M(t) – Rh(t –1)
M(t –1)=(1 – 1/θ ) M(t).
The aggregate real market value of the consumption bonds issued during period t is denoted B(t).
The gross real interest rate that the government pays
on these bonds is denoted Rb(t). Real government
revenue from bond seigniorage (net extension of
real indebtedness) is S b(t) ; B(t) – Rb(t –1) B(t –1).21
20

Recent work on financial intermediation in macroeconomic models
includes Boyd and Smith (1998), Bernanke and Gertler (1989),
Greenwood and Williamson (1989), Williamson (1987), and DíazGiménez et al. (1992). Our approach is most closely related to the
latter paper.

21

In official government budget statistics, bond seigniorage is not
regarded as revenue. Thus, the empirical analog of bond seigniorage
revenue is the government budget deficit.

FEDERAL R ESERVE BANK OF ST. LOUIS

Bullard and Russell

The government collects the bulk of its revenue
using three direct proportional taxes: a tax on real
labor income levied at rate τ w ∈[0,1), a tax on the
nominal interest income of households levied at
rate τ i ∈[0,1), and a “corporate income tax” on firms’
nominal returns to capital levied at rate τ c ∈[0,1).
Aggregate real labor income tax revenue at date t
is T l(t) ; τ ww(t)L(t). The government taxes the net
nominal interest that households receive on government bonds or intermediary deposits. Nominal
revenue from this source is τ i [Rd(t –1)/Rh(t –1) – 1]
A+(t –1)P(t –1), where A+(t) represents households’
aggregate gross real asset holdings at date t and Rd
is the gross real rate of return to deposits.
Real revenue from interest income taxation is T i(t)
; τ i[Rd(t –1) – Rh(t –1)]A+(t –1). The government also
taxes the net nominal returns paid by the firms to
the financial intermediaries, after adjustment for
depreciation. Thus, the corporate income tax produces nominal revenue of τ c(Rkn(t –1) /Rh(t –1)–1)
K(t)P(t –1), where Rkn is the gross real rate of return
to capital net of depreciation, Rkn(t)=Rk(t) – δ, Rk is
the gross real rate of return to capital, Rk(t)=1+
r(t+1), and r(t+1) is the marginal product of capital.
The real revenue from corporate income taxation is

(

)

T k (t ) ;τ c R kn (t − 1) − R h (t − 1) K(t ) .
Our tax structure is intended to provide a crude
but parsimonious representation of the current U.S.
tax system. This representation captures two important features of the U.S. system for taxing capital
income: double taxation of dividend income and
the fact that household income from interest and
capital gains is taxed on a nominal basis. By levying
the labor tax on real labor income, we are taking a
conservative approach so that we do not overstate
the impact of inflation on welfare. We will match
revenues from taxes on capital to the data on the
sources of government revenue, and then we will
allow all remaining government revenue to come
from labor income taxation.
The government budget constraint can be written
(3)

gY (t ) = T l (t ) + T i (t ) + T k (t ) + S c (t ) + S b (t ) .

3.4 Market Clearing
3.4.1 The Structure of Real Interest Rates.
Our assumptions about money demand, financial
intermediation, and capital income taxation determine the interest rate structure of our economy.
In the equilibria that we study, the lowest gross real

return rate in our economy is Rh(t), the gross real
rate of return on currency. The highest gross real
rate of return is the gross pre-depreciation return
rate on capital, which is Rk(t)=1+r(t+1), where
r(t+1) is the marginal product of capital. The gross
real rate of return on capital, net of depreciation,
is Rkn(t) ; Rk(t) – δ. Since firms are taxed on their
nominal net-of-depreciation returns to capital, the
after-tax gross real rate of return they pay to the
financial intermediaries is Rka(t) ; (1– τ c )Rkn(t)+
τ cRh(t).22 Arbitrage implies that Rcl(t), the gross real
rate of return that the intermediary receives on
consumption loans, must be equal to Rka(t).
Because financial intermediation is costly, intermediaries are not willing to pay Rka(t) to depositors.
The real intermediation cost is ξ per unit of loans
or capital intermediated, so the gross real return
rate net of this cost is Rkc(t) ; Rka(t) – ξ. In addition,
intermediaries must allocate a fraction φ of their
deposits to the acquisition of fiat currency reserves.
They pay household depositors a reserve-ratioweighted average of the real return rate on fiat
currency and the real return rate on loans net of
intermediation costs: This rate is Rd(t) ; (1– φ )
Rkc(t)+φ Rh(t). Since government bonds are not
intermediated, arbitrage implies that their gross
real interest rate, which we denote Rb(t), must be
equal to Rd(t). Finally, households must pay taxes
on their nominal interest income at a rate of τ i, so
the gross after-tax real rate of return on deposits is
Rda(t) ; (1– τ i )Rda(t)+τ i Rh(t). Since the government
taxes interest income from all sources, Rda(t) must
be equal to Rba(t), the gross after-tax real interest
rate on government bonds.
To summarize, our steady-state asset return
structure obeys the following chain of inequalities:
(4)
R h < R da = R ba < R d = R b < R kc < R cl = R ka < R kn < R k .
The associated gross nominal interest rates are
equal to the gross real rates divided by Rh. The monetary authority determines Rh through its conduct of
monetary policy. The equilibrium conditions of the
model can be thought of as determining the equilib22

The gross nominal return to capital employed at date t –1 is
Rkn(t –1) /Rh(t –1), so at date t the firms have to make a nominal tax
payment to the government of τ c((Rkn(t –1) /Rh(t –1) ) –1)K(t –1) P(t –1).
Firms’ total real net-of-depreciation earnings are Rkn(t –1) K(t –1) .
Dividing the former expression by P(t ) to put it into real terms and
then subtracting it from the latter expression produces the gross rate
of return expression given in the text. A similar calculation defines
Rda below.

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rium value of Rk, and the capital income tax, intermediation cost, and money demand parameters
then determine the remainder of the interest rate
structure.23
3.4.2 Household Decisions. Households
maximize (2) subject to a lifetime budget constraint
that we will now define. We will let at (t+j ), j=0,
…, n –1, denote the demand for assets, at date t+j ,
of a household born at date t. Households can
borrow or lend in any period of life. If they borrow
at date t, then they pay the gross real rate Rka(t). If
they lend by holding deposits with the financial
intermediary, then they earn the gross real after-tax
return Rda(t). The budget constraints of an agent
born at date t are

as a positive number, so that A(t)=A+(t) – A–(t).
The liabilities of the financial intermediaries are
then K(t+1)+A–(t). A household’s asset demand
problem can have a corner solution for a particular
life period j, in which case the household sets
at (t+j)=0.
3.4.3 Equilibria. Households hold aggregate
real deposits D(t) with financial intermediaries.
The intermediaries use a fraction of these deposits
to acquire fiat currency reserves: φ D(t)=M(t). The
remainder of the deposits are lent to firms and
households: (1– φ )D(t)=A–(t)+K(t+1). The moneymarket clearing condition is
(6)

(5)

M (t ) =

φ
A − (t ) + K(t + 1) .
1− φ

[

]

ct (t ) + at (t ) = (1 − τ w )w(t )e1(1 − lt (t )),

The credit-market clearing condition is

ct (t + j ) + at (t + j ) = (1 − τ w )w(t + j )e j +1(1 − lt (t + j ))

(7)

+ˆR(t + j − 1)at (t + j − 1)
for j=1,…, n – 2 and
ct (t + n − 1)
= (1 − τ w )w(t + n − 1)en (1 − lt (t + n − 1))
+ˆR(t + n − 2)at (t + n − 2),
where w(t) is the before-tax real wage at date t, and

ˆR(t +

ka
R (t + j ) if at (t + j ) < 0,
j ) =  da
R (t + j ) if at (t + j ) ≥ 0.

Aggregate net household asset holdings at date
t are
n −2
A(t ) ;∑ ψ t − j at − j (t ) ,
j =0

where the population at date t has been normalized
to unity. We can decompose A(t) into A+(t), the net
aggregate asset demand of the households whose
net asset demand is non-negative (net creditors) at
date t, and A–(t), the net aggregate asset demand of
the agents whose net asset demand is negative (net
debtors) at date t. The first group earns a gross rate
of return Rda(t)=Rba(t), while the second group must
pay interest at gross rate Rka(t). We will define A–(t)
23

In practice, we fix Rb and Rh at their postwar U.S. averages and find a
parameterization of the model that has an equilibrium that supports
these values, as we will discuss. This parameterization determines
the rest of the interest rate structure.

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A(t ) = M (t ) + K(t + 1) + B(t ),

since some household assets may take the form of
government debt. These last two conditions can be
combined, producing the condition
(8)

B(t ) = A + (t ) −

1
[ A − (t ) + K(t + 1)].
1− φ

The marginal product condition for the capital
rental rate at date t can be used to express the capitallabor ratio k(t+1) as a function of the rental rate
r(t+1) and thus of the gross pretax, pre-depreciation
capital return rate Rk(t). The value of k(t), which
depends on Rk(t –1), determines the equilibrium
wage rate w(t) through the marginal product of labor
condition. The values of Rh(t) and Rk(t) determine
the structure of real return rates, and together with
the values of w(t) they provide the data necessary
for the households to solve their decision problems.
The households’ leisure choices imply values for L(t),
the aggregate supply of effective labor, and thus for
K(t)=k(t)L(t).
Equation (3), the government budget constraint,
involves B(t) and M(t). We can substitute equations
(6) and (8) into this constraint. As we have seen, the
quantities of labor and capital income tax revenue
that appear in the government budget constraint
also depend on the wage rate, the household labor
supply decision, and the household asset demand
decisions. After we make these substitutions, the
consolidated government budget constraint becomes

FEDERAL R ESERVE BANK OF ST. LOUIS

Bullard and Russell

(9)
gY (t ) = τ w(t ) L(t ) +
w

{
A (t − 1)
{R (t ) − φR (t − 1)} +
1− φ
τ ( R (t − 1) − R (t − 1)) + 


K(t ) 1
+
R (t ) − φR (t − 1)) 
(

1 − φ


}

A + (t − 1) τ i [ R d (t − 1) − R h (t − 1)] − R b (t ) +
−

b

c

h

kn

h

h

b

A + (t ) − A − (t ) − K(t + 1).
In equilibrium, the level of output at date t
depends on real returns prevailing at date t –1, which
determine the capital-labor ratio k(t), and L(t), which
determines the capital stock given k(t). Thus, given
the solution to the firms’ and households’ decision
problems, the right-hand side of the resulting
equation can be written entirely as a function of
{Rh(t)}, {Rk(t)}, and the parameters of the model:
(10)

[

]

gY (t ) = Z {R h (t )},{R k (t )}, F , ∆ ,

where F and ∆ are sets of parameters defined below.
It is readily seen that if Rh(t) and Rk(t) are dateinvariant then the value of the function Z will grow
at a rate equal to the steady-state output growth rate.
Consequently, the steady-state version of the equilibrium budget constraint can be written

[

]

g = ζ R , R , F ,∆ .
h

k

We will confine ourselves to the study of steady-state
equilibria.
As we indicated in Figure 1, if Rh (and thus the
inflation rate) and the parameters of the model are
held fixed, then the function ζ takes the form of a
downward-opening paraboloid in Rk or (equivalently)
Rb. Provided the ratio G /Y is low enough, there will
consequently be two steady states, one associated
with a relatively low real interest rate and the other
associated with a relatively high one. In this paper
we focus on the steady states that are associated
with relatively low real interest rates, which provide
a better match for the data.24
In steady-state equilibria, the capital-labor ratio
and the real wage grow at a gross rate of λ , while
24

For most of the calibrated specifications we study, the alternative
steady state produces unrealistically high values for the rate of return
on government debt and the debt-to-GDP ratio.

the levels of real aggregates such as output, asset
demand, the capital stock, and real balances grow
at a gross rate of λψ. Money prices will rise at a gross
rate of θ /λψ, where θ is the gross growth rate of the
stock of fiat currency. Thus, the steady states we
study are quantity-theoretic in the sense that the
rate of money growth dictates the inflation rate
through the standard quantity theory equation.
It is possible, of course, that for given values of
the inflation rate, the direct tax rates, and the other
parameters of the model, equation (10) will not have
real solutions. To fit our model to the data, we need
to solve the agents’ decision problems and equation
(10) repeatedly for a wide variety of parameter values.
For this reason, our approach to calculating steady
states of calibrated versions of our model is slightly
different from the approach implicitly described
by the discussion presented above. When we search
for plausible values of our model’s “deep parameters”
we hold Rh, Rb, and the other parameters of the
model fixed at values suggested by the data, and
we treat the revenue-output ratio g as endogenous.
We then adjust the values of the deep parameters
in an attempt to match data-derived targets for many
of the model’s endogenous variables—including a
target for g. We now turn to describe this calibration
process in detail.

4. CONFRONTING THE DATA
4.1 Calibration Strategy
Our goal is to find a specification of the model
that is plausible in two senses: in the sense that the
values of the parameters are not out of line with
published estimates and/or values used elsewhere
in the calibration literature, and in the sense that
the steady-state values of endogenous variables
provide a convincing match for the data. We divide
the parameters of our model into two sets. The first
set, which we refer to as the fixed parameter vector F,
consists of parameters whose values are not very
controversial because they map into the data in a
simple, direct way. We choose values for these
parameters, element by element, based on data for
the postwar period.
The second set of parameters, the deep parameter
vector ∆, consists of parameters that do not map
into the data directly. Although many of these parameters appear in other calibrated general equilibrium
models, the question of their appropriate values is
unsettled and controversial, largely because empirical estimates vary widely from study to study. Our
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Bullard and Russell

Table 1
Targets on Observable Quantities
Endogenous variable

Target

Range

Source

K/Y

3.32

[2.32, 4.32]

Cooley and Prescott (1995)

I/K

0.076

[0.066, 0.086]

Cooley and Prescott (1995)

B/Y

0.47

[0.255, 0.686]

U.S. data, 1959-94

hcg

0.015

[0.01, 0.03]

Laitner (1992)

alt

0.154

[0.075, 0.33]

Authors’ calculations

I /Y

0.06

[0.05, 0.07]

Díaz-Giménez et al. (1992)

M/Y

0.0592

[0.041, 0.078]

U.S. data, 1959-94

g

0.151

[0.121, 0.18]

U.S. data, 1959-94

Tk/G

0.119

[0.036, 0.201]

U.S. data, 1959-94

m

SOURCE: U.S. data were obtained from the 1996 Economic Report of the President.

approach to setting these parameters is somewhat
novel: We select them jointly, using an iterative nonlinear optimizing procedure (a genetic algorithm)
to find a vector of values for the deep parameters
that supports a steady state that produces endogenous variables whose values come as close as possible to a vector of targets based on postwar data.
The target variables we select are natural ones from
the perspective of our model.

tax gross real return rate on federal government
bonds is close to zero, we seek a parameterization
that produces Rba=1.25 The relationship between
Rb and Rba then requires us to set the interest income
tax rate τ i at 0.2. Our life-cycle labor productivity
profile is based on estimates constructed by Hansen
(1993).26

4.3 The Deep Parameter Vector
The deep parameter vector is

4.2 The Fixed Parameter Vector
(12)

The fixed parameter vector is
(11)

[

]

F = {ei }i =1, n*, λ ,ψ , R h , R b ,τ i .
n

Thus, the fixed parameters are the labor efficiency
profile {ei}ni=1, the age of retirement n*, the gross
productivity growth rate λ , the gross labor force
growth rate ψ, the gross real return rate on money
Rh (or, equivalently, the gross inflation rate Π=1/Rh ),
the gross before-tax real interest rate on government
bonds Rb, and the tax rate on interest income τ i .
We set n*, the retirement age, to household age
44 (figurative age 65). We set the gross productivity
growth rate at λ =1.015, the gross rate of labor force
growth at ψ=1.017, the gross real rate of return on
currency at Rh=0.9615 (implying a 4 percent inflation rate), and the before-tax gross rate of return
on government bonds at Rb=1.01. All four of these
values are based on postwar data. The choices of
Rh, λ , and ψ imply a value for θ, the base money
supply growth rate, that satisfies Rh=λψ /θ.
Since our estimate of the postwar-average after48

M AY / J U N E 2 0 0 4

[

]

∆ = ρ,γ ,η,α ,δ , ξ ,φ ,τ w ,τ c .

Thus, the deep parameters are the pure rate of time
preference ρ (or the discount factor β=[1+ρ]–1), the
indifference-curve convexity parameter γ , which
helps determine the intertemporal consumption
substitution elasticity σ=[1– η (1– γ )]–1, the intratemporal labor-leisure substitution elasticity (or
labor share of time) η, the capital share of output α,
the net depreciation rate δ, the unit intermediation
25

We constructed this estimate using marginal tax rate data provided
by Joseph Peek of Boston College. We thank him for his cooperation.

26

The Hansen data are collected from samples taken in 1979 and 1987.
The data separate males from females. We average the data from the
two years, and we also average the data across males and females
using weights of 0.6 and 0.4. The resulting profile is a step function,
because the data are collected for age groupings. We fit a fifth-order
polynomial to this step function. This yields the smooth profile ei – 20
=m0+m1i+m2i 2+m3i 3+m4i 4+m5i 5 for i=21,…,76, with the vector
of coefficients m=[–4.34, 0.613, –0.0274, 0.0063, –0.717 × 10–5,
0.314 × 10–7]. This profile peaks at agent age 28 (figurative age 48), when
productivity is about 1.6 times its level at agent age 1 (figurative age
21). Productivity in the final year of life is virtually the same as in the
first year of life.

FEDERAL R ESERVE BANK OF ST. LOUIS

cost ξ, the reserve ratio φ, the labor income tax rate
τ w, and the corporate income tax rate τ c.
4.3.1 Targets. The endogenous variables whose
values we target are listed in Table 1. Most of the
target values are widely cited estimates of postwar
averages, so we will not discuss them in much
detail. In some cases, the closeness of a particular
variable to a target depends largely on the value
of one parameter: When this is the case, we will
identify the relevant parameter. It should be emphasized, however, that in each of these cases the
parameter in question also plays a role in the determination of other endogenous variables.
The estimates of the average capital-output ratio
Κ /Y and the average investment-capital ratio Ι /K are
due to Cooley and Prescott (1995). These estimates
are based on a broad definition of capital that
includes consumer durables and government capital.
We target the equilibrium bonds-to-output ratio Β /Y
at the average postwar ratio of gross federal debt to
output. The money-output ratio Μ /Y is targeted at
the average postwar ratio of the monetary base to
output. Since we are using bank reserve demand as
a proxy for base money demand from all sources,
the value of Μ /Y is largely determined by the reserve
ratio φ.
The target for intermediation costs relative to
output, Im /Y, is based on estimates of the size of the
U.S. financial intermediation sector that were constructed by Díaz-Giménez et al. (1992). These estimates are summarized in Figure 2. They indicate that
the quantity of resources devoted to financial intermediation is quite large—roughly 5 to 7 percent of
GDP in the early 1980s. Our target for intermediation
costs relative to output is in the middle of this range.
The value of the unit intermediation cost ξ plays a
key role in determining whether we hit this target.
Laitner (1992) reports evidence that indicates
that the average lifetime consumption growth rate
of U.S. households is not very different from the
aggregate consumption growth rate. Consequently,
we set the target for hcg, households’ net lifetime
consumption growth rate, at 0.015, which is the
net rate of technological progress (from F) and thus
the steady-state net growth rate of aggregate per
capita consumption. In OLG models the lifetime
consumption growth rate can be very different from
the aggregate consumption growth rate, so this target
imposes a significant constraint on our parameter
choices. Our target for alt, the average share of
households’ time devoted to providing labor, is based
on our own calculations.27 As we have indicated,

Bullard and Russell

Figure 2
Financial Intermediation in the United States
Financial Intermediation± GDP ratio (percent)
10

8

6

4

2
1958 1961 1964 1967 1970 1973 1976 1979 1982 1985 1988 1991 1994
Year
Upper Bound
Lower Bound

NOTE: The value of financial intermediation services provided
in the U.S. economy is large. The boxes and triangles represent
upper (total product basis) and lower (value added basis)
bounds, respectively, as calculated by Díaz-Giménez et al. (1992).
The lines are simple midpoints based on linear interpolation
between data points and extrapolation of existing trends (solid
line) and no trend (dotted line) at the end of the sample.

the choice of η essentially determines the value of
this variable.
Our target for g, the ratio of government expenditures to output, is the average postwar value of consolidated government revenue, net of transfers and
government investment, relative to GDP.
That leaves only the sources of government revenue to be determined. We want the revenue coming
to the government from the corporate profits tax to
look like it does in the data, so that we do not overemphasize this feature of the model economy. Accordingly, we target Tk/G, the ratio of corporate profits tax
revenues to total government expenditures, to match
the average value of this ratio in postwar data.28
27

The target value is based on a 24-hour day, a 40-hour work week, ten
vacation days and ten holidays per year, and a 70 percent labor force
participation rate. The 24-hour day assumption seems reasonable
because the utility function implies that if leisure hours are zero then
the marginal utility of leisure is infinite.

28

In our model, government revenue comes from five sources: a tax on
labor income, a tax on household interest income, a tax on corporate
profits, currency seigniorage, and bond seigniorage. The personal interest income tax rate is an element of F. The volume of currency and
bond seigniorage revenue is determined by the interest rates Rh and
Rb, which are also part of F, and by the ratios of money and bonds to
output, both of which we have targeted. By setting a target for Tk/G,
we leave all remaining government revenue to come from the tax on
labor, τ w, an element of ∆. This tax is levied in real terms and is not
affected by inflation.

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Bullard and Russell

Table 2
Baseline Parameter Values
ρ

γ

η

α

δ

ξ

φ

τw

τc

–0.223

37.4

0.154

0.26

0.0439

0.018

0.0169

0.11

0.0742

NOTE: Values of deep parameters in the baseline steady state.

Our parameter-selection algorithm also allows
us to indicate ranges around the target values that
we regard as plausible. These ranges are also displayed in Table 1. Although these ranges have some
effect on the operation of the algorithm, the values
it selects turn out to be very close to our targets.
4.3.2 Parameter Choices. A complete description of our parameter-selection algorithm is presented in the appendix, along with a detailed
description of the results it generates. The baseline
parameter values we obtain using this algorithm
are displayed in Table 2. The characteristics of the
associated steady state are described in Tables 3, 4,
and 5. We discuss the parameter values first, before
discussing the fit to the data in the next section.
Although our baseline value for ρ may seem
quite low, household preferences regarding lifetime
consumption paths are much more accurately summarized by the value of the effective time preference
rate ϕ, which is a nonlinear function of ρ and γ
(see section 3.2.3). Our baseline values for these
two parameters imply an effective time preference
rate of –0.0067. This value produces very plausiblelooking consumption behavior: In particular, it is
largely responsible for the fact that households’
lifetime consumption growth rate is so close to the
aggregate consumption growth rate. Our value for
ϕ is quite close to the value (–0.0098) implied by
Hurd’s (1989) widely cited econometric estimates
of γ and ρ, and it is even closer to a recent direct
estimate of ϕ (–0.0078) obtained by Barsky et al.
(1997) using experimental methods.
Similarly, while our baseline value for γ may
seem high, household preferences regarding substituting consumption across periods are much more
accurately summarized by σ, the elasticity of intertemporal substitution in consumption (EISC), which
is a nonlinear function of γ and η (again, see section
3.2.3). Our values for these two parameters produce
σ=0.151. This EISC value is well within the range
of published estimates. It falls particularly closely
in line with widely cited econometric estimates due
50

M AY / J U N E 2 0 0 4

to Hall (1988) and with recent laboratory estimates
due to Barsky et al. (1997).29
The question of the appropriate value for the
EISC is highly controversial. Many empirical studies
have produced estimates significantly higher than
the value we use: Attanasio and Weber (1995), for
example, report a point estimate of 0.56. On the
other hand, an argument for EISC values much lower
than ours can be based on the fact that under an
expected-utility interpretation of the preferences
we employ, the coefficient of relative risk aversion
is the reciprocal of the EISC.30 Researchers working
with stochastic models typically find that it takes
very high degrees of risk aversion to explain the
observed differential between risky and risk-free
return rates (the equity premium). Kandel and
Stambaugh (1991), for example, report that they
need a relative risk aversion coefficient of 29 to
explain the risk-free rate and the equity premium
using standard preferences, while Campbell and
Cochrane (1999) use a local relative risk aversion
coefficient of 48.4 to accomplish the same task using
habit-formation preferences. Later in this paper,
after we report estimates of the welfare cost of inflation that are implied by the baseline specification
of our model, we will also report alternative cost
estimates implied by specifications with EISC values
equal to the Attanasio-Weber and Kandel-Stambaugh
29

In Hall’s (1988) introductory summary of his results, he asserts that σ
is “unlikely to be much above 0.1” (p. 340); later in the paper he says
it is “probably not above 0.2” (p. 350). Barsky et al. (1997) report a
point estimate of 0.18.

30

Thus, our estimate of σ would be associated with a relative risk aversion coefficient of approximately 6.6. While this value is well within
the (very wide) range of published estimates, and satisfies the MehraPrescott (1985) plausibility criterion by being below 10, most economists would probably regard it as uncomfortably high. There is no
uncertainty in our model, however, and there are good reasons to
believe that reluctance to substitute consumption intertemporally (a
low value of σ ) is not in fact closely associated with aversion to risk.
Indeed, Barsky et al. (1997, p. 568) conclude that for their experimental
subjects “there is no significant relationship, either statistically or
economically, between risk tolerance and intertemporal substitution.”

FEDERAL R ESERVE BANK OF ST. LOUIS

Bullard and Russell

Table 3
Baseline Steady-State Characteristics
Variable

Model

Target

Aggregate performance

λψ

1.032

Fixed

1/Rh

1.04

Fixed

Technological progress

λ

1.015

Fixed

Labor force growth

ψ

1.017

Fixed

ϕ

–0.0067

Open

Real output growth
Inflation

Preferences
Effective rate of time preference
CRRA

ν

6.6

Open

EISC

σ

0.151

Open

Individual consumption growth

hcg

0.0188

0.015

Lifetime average agent time devoted to labor

alt

0.1539

0.154

K/Y

3.33

3.32

Bonds-output ratio

B/Y

0.48

0.47

Money-output ratio

H/Y

0.0591

0.0592

Asset holdings
Capital-output ratio

Technology
Capital share
Depreciation rate
Investment-capital ratio

α

0.26

Open

δ

0.0439

Open

I/K

0.0762

0.076

NOTE: The term “fixed” in a target entry means we set these quantities directly based on U.S. data. The term “open” in a target entry
means we did not fix or target these quantities directly. More characteristics are given in Tables 4 and 5.

estimates.31 These alternative estimates indicate
that the value of EISC is qualitatively unimportant
to our conclusions, in the sense that our welfare cost
estimates are still an order of magnitude larger than
estimates in the existing literature.
Our baseline value for α, the capital share of
output, is quite close to the value of 0.25 that is used
by Auerbach and Kotlikoff (1987) and has become
standard in the literature on calibrated life-cycle
models. Participants in the real business cycle literature typically use higher values for α: Cooley and
Prescott (1995), for example, use α=0.4. We will
estimate the welfare cost of inflation in an alternative specification that uses this capital share value.
Again, it turns out that the particular α-value we
use is not qualitatively important for our results.
31

Since the Campbell-Cochrane (1999) preferences are not standard
(that is, not intertemporally separable CES), the local intertemporal
substitution elasticity may not be equal to the reciprocal of the local
coefficient of relative risk aversion.

5. CHARACTERISTICS OF THE BASELINE
ECONOMY
5.1 A Quantitative Match for the Data
The characteristics of our baseline steady state
are summarized in Tables 3, 4, and 5. The steady
state does a remarkably good job of matching the
data along the dimensions we have selected. The
only detectable discrepancy between a variable and
its target involves households’ lifetime consumption
growth rate, which is a bit less than 0.4 percentage
points higher than the target value, as shown in
Table 3. Since our target for this variable was not
based on a precise estimate of its value, we do not
view a discrepancy of this magnitude as a problem.
We included hcg on our list of targets to avoid ending
up with a baseline economy in which the lifetime
consumption growth rate was substantially (multiple
percentage points) higher or lower than the aggreM AY / J U N E 2 0 0 4

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Bullard and Russell

Table 4
Baseline Steady-State Characteristics
Variable

Model

Target

Im/Y

0.0599

0.06

Government-output ratio

G/Y

0.151

0.151

Revenue from firms

Tk/G

0.119

0.119

Tw/Y

0.081

Open

Household interest tax

i

T /Y

0.037

Open

Corporate profits tax

Tk/Y

0.018

Open

Bond seigniorage

s

B /Y

0.010

Open

Currency seigniorage

Cs/Y

0.004

Open

Intermediation
Intermediation-output ratio
Government size

Government revenue sources
Household labor tax

NOTE: This is a continuation of Table 3.

Table 5
Baseline Steady-State Characteristics
Rates of return
h

R

da

ba

R ,R

d

b

R ,R

Rkc

Rka,Rcl

Rkn

Rk

Target

Fixed

Fixed

Fixed

Open

Open

Open

Open

Real

0.9615

1.0003

1.0100

1.0108

1.0288

1.0342

1.0781

Nominal

1.0000

1.0403

1.0504

1.0513

1.0700

1.0756

1.1213

NOTE: This is a continuation of Table 3.

gate consumption growth rate—a common occurrence in previous work with calibrated versions of
life-cycle models.

5.2 Real Rates of Return
Our model produces rate-of-return differentials,
as shown in Table 5, that can be compared with
average return rates in the data. In our model, the
counterpart to the return on a basket of stocks is Rka,
since corporate profits taxes are deducted from firms’
earnings before they pay dividends and the capital
gains on firms’ stock presumably reflect market
adjustments for depreciation. The “equity premium”
in our model is then the difference between Rka and
Rb, the before-tax real interest rate on government
bonds. In our baseline steady state this difference is
52

M AY / J U N E 2 0 0 4

188 basis points. Eight of these basis points are due
to the reserve requirement; the remaining 180 are
due to the cost of financial intermediation. Campbell,
Lo, and MacKinlay (1997, Table 8.1) report that the
equity premium in U.S. data, measured as an average
of annual excess returns over a long time horizon,
is 418 basis points with an approximate 95 percent
confidence band of [64,756]. Thus, although our
baseline equity premium accounts for a bit less than
half of their point estimate, it is well within their 95
percent confidence band.
As we indicated in section 2, an important element of our approach to identifying the welfare
costs of inflation is the assumption that capital is
overaccumulated—a situation implied by the fact
that in our baseline steady state the real interest
rate on government debt is lower than the output

FEDERAL R ESERVE BANK OF ST. LOUIS

growth rate. As we have also indicated, our steadystate values for both these variables are close to
estimates of their values based on postwar U.S. data.
In an influential paper, Abel et al. (1989) note
that in stochastic models an average risk-free real
interest rate lower than the average output growth
rate is not a sufficient condition for capital overaccumulation. They derive a sufficient condition for
efficiency of a steady state in any model, stochastic
or otherwise. The condition is that gross capital
income is always larger than gross investment. They
use data from the national income and product
accounts to argue that, in the United States, gross
capital income exceeded gross investment in every
year from 1929 to 1980. They conclude, on this basis,
that capital has not been overaccumulated in the
United States.
If we calculate gross capital income using the
definition that Abel et al. employed in their empirical
analysis, we find that gross capital income exceeds
gross investment in our baseline steady state.32 Thus,
our steady state actually passes the Abel et al. test
for efficiency. Nevertheless, our baseline steady state
has too much capital, and policy-induced increases
in the real interest rate increase household welfare.
The source of this conundrum is the fact that the
theoretical analysis presented by Abel et al.
abstracts from capital income taxes, intermediation
costs, or other factors that might drive a wedge
between income paid by firms and income received
by households. In our model, by contrast, we use
tax and intermediation-cost assumptions that are
based on analysis of postwar data. We suspect that
proper accounting of taxes and intermediation
costs would reverse the Abel et al. conclusion that
gross capital income has always exceeded gross
investment.33,34
32

33

Equivalently, the baseline marginal product of capital, net of depreciation, exceeds the baseline output growth rate. The ratio of gross investment to output is [K(t+1) – K(t)+δ K(t)] /Y(t), which is (λψ –1+δ )(K /Y)
in a steady state. Our baseline value of this ratio is 0.253—a value
consistent with calculations presented by Cooley and Prescott (1995).
The baseline ratio of gross capital income to output is (Rk–1)K /Y=0.26,
which exceeds our baseline ratio of investment to output. Abel et al.
(1989) report a much lower estimate of the ratio of investment to output. One reason for this is that in performing their calculations they
used data on gross investment in private business capital, as opposed
to the broader concept of capital used by Cooley and Prescott (1995),
which includes government capital and consumer durables. Using
this narrower concept, the gross investment figure in the data declines
to 0.16. For additional discussion of this question and related questions,
see Bullard and Russell (1999).
The dynamic efficiency literature does not provide any conclusive test
that applies to cases in which gross capital income fluctuates above
and below gross investment.

Bullard and Russell

While our baseline steady state matches postwar U.S. data along a number of other dimensions,
a more complete description of its features would
take us too far afield.

6. THE WELFARE COST OF INFLATION
6.1 Definition and Measurement
6.1.1 Assessing Welfare Costs. Many analyses
of the cost of inflation compare a steady state
with a given inflation rate with a Pareto optimal
Friedman-rule steady state. This approach amounts
to assuming that inflation is the only source of
distortions in the economy. Our model also has an
optimal Friedman-rule steady state. In this steady
state, the tax rates on labor and capital income are
zero, the inflation rate and the nominal interest rate
on government bonds are zero, and the combined
real stocks of fiat currency and government debt
are just large enough to support a real interest rate
equal to the output growth rate (so that currency
and bond seigniorage revenue is also zero). If government expenditures are positive then they are
financed by lump-sum taxes.
For a practical assessment of the costs of inflation, a steady state of this type does not seem very
interesting, because it is so unlike the actual U.S.
economy. A procedure for estimating inflation costs
that was based on this steady state would ignore
the fact that the economy is distorted in many ways
that do not involve inflation; it would also ignore the
fact that moderate changes in the inflation rate—
changes of the sort usually contemplated by policymakers—would not eliminate distortions caused or
aggravated by inflation. Our alternative approach
is to model the most important sources of deviation
from the Pareto optimum and study the ways in
which inflation interacts with them.
As we have indicated, two sources of distortion
34

In our model, if the real rate of return on capital, net of depreciation
and intermediation costs but not taxes, is lower than the output growth
rate (as in our baseline case) then capital is overaccumulated and our
welfare-cost analysis always goes through. However, the case in which
the real return rate net of depreciation and intermediation costs is
higher than the output growth rate—but the real return rate net of
depreciation, intermediation costs, and taxes is lower than the output
growth rate—is considerably more complicated. In this case capital is
not overaccumulated: Maintaining the capital stock at its steady-state
level does not reduce aggregate consumption on the margin. However,
the tax-induced return rate distortion reduces the welfare of households by artificially increasing the cost of future consumption, and
policies that tend to increase the real interest rate (such as a decrease
in the inflation rate) may increase household welfare even though
they reduce aggregate consumption.

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are particularly critical to our analysis. The first is
the fact that the government issues bonds at a real
interest rate lower than the output growth rate—a
policy that amounts to levying a tax on bond holders
at a rate equal to the difference between these two
rates. Although this tax is conceptually similar to
the “inflation tax,” it turns out to have much broader
welfare implications, partly because the real stock
of government bonds is much larger than the real
stock of currency and partly because the real interest
rate on government bonds plays a much more fundamental role in determining the structure of real rates
of return on other assets. The second distortion is
the fact that the government taxes nominal capital
income—particularly, the fact that the effective tax
rate on capital income increases with the inflation
rate. This policy means that increases in the money
growth and inflation rates would produce, if all else
were held constant, large increases in the volume
of government revenue. Under our assumptions
about fiscal policy behavior, equilibrium is restored
by large declines in the volume of government borrowing and large decreases in the real interest rate
on government bonds—decreases that have very
adverse effects on household welfare.
6.1.2 Calculating Welfare Costs. Our welfare
cost calculations are based on comparing the steady
states of two economies that share exactly the same
environment, preferences, and technology, including
common values of all parameters except the base
money growth rate θ. One economy has a higher
money growth rate, and thus a higher inflation rate
(a lower value of Rh ), than the other. A typical household in the high-inflation economy will be worse
off, in a welfare sense, than a typical household in
the low-inflation economy. We measure the magnitude of the welfare difference by calculating the
amount of consumption-good compensation necessary, at each date, to make the agents in the highinflation economy indifferent between staying in
that economy or moving to the low-inflation economy. This measure of the welfare cost of inflation
is conceptually similar to measures used by Cooley
and Hansen (1989) and others. However, the agent
heterogeneity in our model makes our calculations
slightly more complicated.
Our procedure compares the welfare levels
produced by particular rates of inflation to the levels
produced by benchmark inflation rates that exceed
the Friedman-rule rate. In one set of calculations,
the benchmark inflation rate is our baseline rate and
the associated steady state is our baseline steady
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state. In the other set of calculations, the benchmark
inflation rate is zero: The associated steady state is
the one generated by this inflation rate when all
the other parameters are set at their baseline values.
In each case, we begin by calculating the lifetime
utility of a representative household from an arbitrary generation t in the steady state associated with
the benchmark inflation rate. Next, we solve the
model for the new steady state associated with a
different inflation rate, and we record the consumption and leisure choices of a representative household from the same generation t. We hold these
consumption and leisure quantities fixed and imagine
giving the household annual compensation, in units
of the consumption good, until its augmented lifetime consumption-leisure package gives it the same
utility level as in the benchmark steady state. The
quantity of consumption-good compensation given
to the household during each period of its life is
assumed to grow at a gross rate of λ , the (exogenous)
steady-state growth rate of per capita consumption.
The final steps of our procedure are (i) to calculate
the total amount of consumption good compensation
necessary, at an arbitrary date t, to compensate
each household alive at that date in the manner
just described; (ii) to calculate the total amount of
output produced at the same date in the benchmark
steady state; and (iii) to express the former value as
a percentage of the latter value.

6.2 Results
6.2.1 Welfare Costs Relative to Baseline
Cases. The triangles in Figure 3 display the welfare

costs of a range of alternative inflation rates, relative
to a benchmark inflation rate of 4 percent. These
cost estimates represent the principal results of our
analysis. The triangle at the point with coordinates
(4,0) represents our baseline steady state. Lower
inflation rates yield welfare benefits to households
relative to the benchmark inflation rate, so the
welfare cost estimates associated with these rates
are negative.
Since increases in the inflation rate reduce the
welfare of households, the line formed by the triangles is upward-sloping. The gradient linking the
inflation rate to the welfare cost is surprisingly steep.
Over the range of inflation rates considered, a 1
percent increase in the annual inflation rate increases
the welfare cost of inflation by more than 1 percent
of output per year. As we have noted, these cost estimates are an order of magnitude larger than most

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Table 6
Recent Estimates of the Welfare Cost of Inflation
Study

Features

Inflation comparison

Welfare cost

10% vs. optimal

0.387%

Cooley/Hansen (1989)

RBC model with cash-in-advance

Gomme (1993)
·
Imrohoroğlu/Prescott (1991)

Endogenous growth with cash-in-advance

8.5% vs. optimal

0.0273%

Idiosyncratic labor income risk

10% vs. 0%

0.9%

Dotsey/Ireland (1996)

Endogenous growth with cash-in-advance

10% vs. 0%

1.73%

Lucas (2000)

Representative agent with shopping time

10% vs. optimal

1.3%

This paper

Life-cycle economy with financial
intermediation

10% vs. 0%

12.4%

NOTE: Some recent studies of the welfare cost of inflation. Costs are expressed as the compensating consumption necessary to make
agents indifferent between the two inflation regimes. The cost calculated in this paper is an order of magnitude larger than those from
the earlier literature.

other estimates from the literature. Table 6 summarizes some of the previous estimates.35
There are no triangles in the figure for inflation
rates lower than 2.5 percent. The reason for this is
that, once the inflation rate falls below this level, the
government faces a revenue shortage: No steadystate real interest rate produces enough revenue to
meet our target value for G/Y. We adopt two different
strategies for addressing this situation. The simplest
strategy involves modifying our baseline steady state
by holding fixed all the parameters of the model
except the inflation rate and accepting whatever
level of G/Y turns out to be consistent with a benchmark inflation rate of zero. We can then calculate
the welfare cost of inflation relative to this zeroinflation steady state.36 The results of these calculations are indicated by the boxes in Figure 3. Over
the range of inflation rates considered, the increase
in the welfare cost as the rate of inflation rises is
again better than 1 percent of real output per per35

36

One interpretation of the results reported by Lacker and Schreft (1996)
would place the welfare cost of 10 percent versus 0 percent inflation
at 4.27 percent of output. Other interpretations, however, are consistent
with the lower cost estimates reported in the papers listed in Table 6.
Lacker and Schreft (1996) emphasize resource-costly credit and the
impact of inflation on real returns.
The steady state at zero inflation inherits most of the quantitative
properties of the steady state at 4 percent inflation, so we do not report
these properties here. The principal exception is government revenue
as a fraction of real output, which is about 11 percent in the zero
inflation case versus 15.1 percent in the baseline case. At the cost of
some complications, we could use the Friedman-rule inflation rate—
a deflation rate equal to the output growth rate—as a benchmark rate
without changing our qualitative conclusions. However, a zero rate of
inflation has often been used as a benchmark in the literature, and it
has often been proposed as a practical target for monetary policy.

Figure 3
The Welfare Cost of Inflation
4
Z
W
18
16
14
12
10
8
6
4
2
0
–2
–4
0

2

4

6

8

10

12

14

4

centage point increase in the inflation rate. These
results illustrate the fact that even when the initial
inflation rate is low, the marginal distortion produced
by increases in the inflation rate can be quite large.
6.2.2 Welfare Gains from Lower Inflation:
An Alternative Approach. A second approach to
confronting the revenue shortage that arises when
the inflation rate is allowed to fall below 2.5 percent
is to raise direct tax rates to recover the lost revenue.
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Figure 4
Disinflation with Distorting Taxes
W
1
0
–1
–2
–3
–4
–1

0

1

2

3

4

q

This approach sacrifices comparability with the
results reported in Table 6, since the experiments
that produce these results often assume either that
there are no direct taxes or that any direct tax rates
are fixed. However, this alternative approach may
give us better insight into the practical problems
of disinflation from relatively low initial inflation
rates.
Figure 4 illustrates how the need to raise other
distortionary taxes affects the welfare benefits of
disinflation from low inflation rates. For simplicity,
we consider a tax increase scenario in which the lost
revenue is made up by increasing all three tax rates
(τ w, τ i, τ c ) equally in percentage point terms.37
The welfare benefit from further reductions in
inflation declines dramatically once the initial inflation rate falls below 2.5 percent. The total welfare
benefit achieved by moving from 2.5 percent inflation to zero inflation is less than 0.2 percent of the
baseline level of real output. While this benefit estimate remains large by the standards of the other
papers listed in Table 6, it is quite small compared
with the results reported in this paper for disinflation from higher initial inflation rates.
The bottom line of this aspect of our analysis is
that when the initial inflation rate is low, the welfare
gains from reducing the inflation rate are largely
offset by the welfare losses caused by more severe
37

An alternative scenario in which the lost revenue is recovered exclusively by increases in the labor income tax rate produces similar results.

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distortions from direct taxes. And while the gains
from moving to inflation rates below 2.5 percent
are not trivial, achieving them requires a degree of
coordination between fiscal policy and monetary
policy that is not necessary when disinflating from
higher initial inflation rates.
6.2.3 Decomposing the Welfare Cost of
Inflation. As we have indicated, much of the literature on the welfare cost of inflation has concentrated
on what might be called “purely monetary” costs.
In our analysis, in contrast, most of the distortions
that are aggravated by higher inflation are not
directly connected to money demand. From a policy
perspective we think our approach is the more useful one, since it allows policymakers to use the total
distortion caused by inflation, taking other features
of the economy as given, as the yardstick by which
judgments are made. In this section of the paper,
however, we attempt to apportion our welfare cost
estimates by source to allow easier comparisons
with other studies and to provide additional intuition for our results.
To repeat, the three basic sources of inflation
costs in our model are (i) monetary costs associated
with the fact that higher inflation reduces the rate of
return on money, (ii) tax-distortion costs associated
with the fact that higher inflation increases the effective tax rate on capital income (the “Feldstein effect”)
and reduces the after-tax real rate of return on capital,
and (iii) return-distortion costs associated with the
fact that higher inflation produces a decrease in
government borrowing that reduces the before-tax
real return rate on capital (the “Miller-Sargent effect”).
We will begin by attempting to isolate the purely
monetary welfare cost, using a procedure as closely
analogous to Feldstein’s (1997) as we can arrange
in the context of our model. In particular, we look
for a steady-state equilibrium in which the inflation
rate has increased by 10 percentage points, the
before-tax real interest rate on government bonds
is unchanged from the baseline case, and the ratio
of government revenue to output is unchanged from
the baseline case. We avoid the Feldstein effect by
nominalizing the pretax returns to capital using
the baseline inflation rate of 4 percent instead of
the new inflation rate of 14 percent. The revenue
gain that the government enjoys as a result of the
increase in the inflation rate is offset by equalpercentage-point reductions in all three of the direct
tax rates. This experiment produces a result similar
to Feldstein’s: There is actually a small welfare gain
from higher inflation—0.2 percent of output—
because the inflation tax on bank reserves is slightly

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less distortionary than the direct taxes it replaces.
The next step in our decomposition procedure
is to identify the welfare costs that are due to the
Feldstein effect. Again we increase the inflation rate
by 10 percentage points, holding the pretax real
government bond rate at its baseline level. This time,
however, we nominalize pretax capital income at
the new inflation rate. Again we offset the resulting
increase in government revenue by reducing the
three direct tax rates. The before-tax real return rate
on capital is virtually unchanged, but the real interest
rate facing household savers—the after-tax real
return rate on government bonds or intermediary
deposits—falls by almost exactly 1 percentage point.
The welfare cost of inflation is approximately 1.3
percent of output. Given the small monetary benefit,
the total Feldstein-effect cost of inflation is roughly
1.5 percent of output.
Finally, we move to the new steady state associated with the much-larger welfare cost estimate we
reported in Figure 3. We begin by restoring the direct
tax rates to their baseline levels: The increase in
inflation-tax and capital-income-tax revenue that
was previously offset by a reduction in these tax rates
is now offset by a decline in pretax real interest rates
that reduces government revenue from bond seigniorage. The pretax real return rate on capital falls by
1.7 percentage points, the pretax real interest rate
on government debt falls by 2.4 percentage points,
and the after-tax real deposit rate falls by 3.6 percentage points.38 As we have indicated, the welfare
cost of inflation is roughly 11.2 percent of output.
On the basis of this decomposition, we can conclude that about 85 percent of the inflation cost we
describe (9.7 percentage points of the 11.2 percent
of output) is caused by the decline in the before-tax
real interest rate, while the Feldstein effect accounts
for about 15 percent of the cost and the purely
monetary cost is negligible. However, the small size
and perverse sign of the monetary cost hinges partly
on the way in which that cost is defined. If we give
back the additional currency seigniorage revenue
produced by an increase in the inflation rate by
allowing the pretax real interest rate to fall, rather
than by increasing direct tax rates, then the pretax
real capital and real bond return rates fall by 20 and

30 basis points, respectively, and the after-tax real
deposit rate falls by 25 basis points. The monetary
cost of inflation rises to 0.6 percent of output, which
amounts to approximately 5 percent of the total welfare cost.39 The Miller-Sargent effect now accounts
for about 80 percent of the total cost of inflation.
6.2.4 Moderate Changes in the Inflation Rate.
As we have indicated, reporting the results of
experiments in which the inflation rate is permanently increased by 10 percentage points or more
is a standard practice in the welfare cost of inflation
literature. One reason for this is that, in much of the
literature, the marginal welfare effects of changes
in the inflation rate are so small that it takes larger
changes to generate effects of any practical significance. In our model, however, the effects of smaller
changes in the inflation rate on welfare and other
endogenous variables are quite substantial. Moreover, from a practical point of view, reporting the
effects of moderate changes in the inflation rate
seems more interesting than reporting the effects
of changes that are very large relative to modern
U.S. historical experience.
Table 7 reports the effects on a variety of endogenous variables of a permanent, 1 percent increase
in the inflation rate, starting from the baseline inflation rate of 4 percent. The before-tax real rate of
return on capital and the before-tax real interest
rate on government bonds fall by 38 and 43 basis
points, respectively, while the real interest rate on
bank deposits (which is also the after-tax real rate on
bonds) falls by 53 basis points. The level of output
rises by 3.9 percent. Most of the increase in output
is due to a large (9.3 percent) rise in investment:
Aggregate consumption increases by only 0.8 percent. Government spending increases in proportion
to the increase in output; the capital stock increases
in proportion to the increase in investment. The
real wage increases by 1.8 percent and aggregate
labor hours rise by 2.1 percent.40
39

One can think of this alternative monetary cost estimate as an estimate of the component of the welfare cost of inflation that has nothing
to do with the fact that inflation changes the effective tax rate on
capital income. Thus, our results suggest that 95 percent of the total
welfare cost of inflation is associated, directly or indirectly, with this
feature of the tax system.

38

40

It should be emphasized that these are level effects: In the new steady
state, these variables continue to grow at exogenously determined rates
that are invariant to changes in the inflation rate. Output, consumption,
and investment grow at the exogenous output growth rate, while labor
hours grow at the exogenous labor force growth rate and the real wage
grows at the exogenous productivity growth rate. Also, these are, of
course, steady-state comparisons, and so it would take time for these
impacts to occur.

Real interest rate declines of this magnitude are quite moderate by
comparison with historical data from high-inflation periods. During
1973-79, for example, the average inflation rate was 9.1 percent
(CPI-U) and the average real government bond rate was –2.0 percent
(ex post real yield on 3-month T-bills). In our baseline specification, a
steady-state inflation rate of 14 percent is associated with a real government bond rate of –1.4 percent, while an inflation rate of 9.1 percent
produces a real government bond rate of –0.5 percent.

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Table 7
Real Effects of a Permanent 1-Percentage-Point Increase in the Inflation Rate
Variable

% Change

Variable

% Change

Before-tax real MPK

–0.38

Real wage

+1.8

Before-tax real bond rate

–0.43

Labor hours

+2.1

After-tax real deposit rate

–0.53

Output

+3.9

Consumption

+0.8

Investment

+9.3

Consumption growth

–0.08

First 5 periods

+1.5

Last 5 periods

–3.7

Welfare

–1.3

NOTE: The figures for return rates are changes in percentage points. The figures for output, consumption, investment, the real wage,
labor hours, and first- and last-five-periods consumption are percent changes in levels. The figure for consumption growth is the
percentage point change in the lifetime growth rate. The welfare cost figure is the required consumption compensation as a percent
of the initial level of output.

The decline in the real interest rate makes it
more difficult for households to consume during
the later years of their lives. Although households’
lifetime consumption growth rate falls by only 0.1
percent, this change has a big effect on their consumption levels at the beginning and end of their
lives. Households’ average consumption during the
first five years of life rises by 1.5 percent, but their
consumption during their last five years falls by 3.7
percent. The welfare loss from the 1 percent increase
in the inflation rate amounts to 1.3 percent of output. The small increase in aggregate consumption
does not suffice to compensate households for the
increase in their labor hours and the decrease in
the slope of their lifetime consumption path. Households work harder, but most of their increased work
effort goes to support accumulation of additional
capital that produces low marginal returns.
The relationship between the size of the welfare
cost of inflation and the magnitude of the increase
in the inflation rate is a little less than linear: The
welfare cost of a 10-percentage-point increase in
the inflation rate is only 8.7 times larger than the
cost of a 1-percentage-point increase in the inflation
rate. For other variables the departure from linearity
is more pronounced. The percentage point decline
in the real interest rate produced by a 10-percentagepoint increase in the inflation rate is only six times
larger than the decline produced by a 1-percentagepoint increase in inflation. Roughly the same ratio
holds for the percentage increases in the levels of
output, investment, and work effort. For the level
of aggregate consumption, the ratio is only 3.7.
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6.3 Alternative Parameterizations
In this subsection, we report the results of
welfare-cost experiments that are conducted using
alternative parameterizations of our baseline economy. These experiments are intended to explore the
robustness of our results to changes in the values
of parameters whose baseline values are potentially
controversial.
6.3.1 Intermediation Costs. As we indicated
in the introduction, we introduce intermediation
costs primarily because they allow our baseline
steady state to do a better job of matching postwar
data. These costs allow the steady-state values of
endogenous variables from our nonstochastic model
economy to more closely resemble long-run averages of variables from an actual economy that is
presumably stochastic.41 Since the magnitude of
the unit intermediation cost is not affected by
changes in the inflation rate, there is no reason to
expect changes in the value of the intermediation
cost to have substantial effects on our welfare cost
estimate.
As a simple test to confirm the robustness of
our results to dropping the cost of intermediation,
we calculate the effects of a permanent increase in
41

Ríos-Rull (1994, 1995, 1996) studies a general equilibrium life-cycle
model with aggregate production and return risk but no cost of intermediation. Since the model does not generate a significant equity
premium, it does not solve the problem of reconciling the high real
average rate of return on equity with the relatively low real interest
rate on government debt. See Bullard and Russell (1999) for a more
detailed discussion of the impact of intermediation costs in a nonstochastic model.

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the inflation rate starting from the steady state that
our model produces when the intermediation cost
is set at zero but none of the other baseline values
are changed. (This new steady state is not a very
good match for postwar data along some of the
dimensions we have described.) The cost of a 1percentage-point increase in the inflation rate is
1.1 percent of output, while the cost of a 10percentage-point increase is 9.8 percent of output.
Although the differences between these estimates
and our original estimates are not entirely inconsiderable, they would not affect our conclusions in
any important way.
6.3.2 Intertemporal Substitution in Consumption. Our parameter selection procedure
produces relatively low values for the intertemporal
elasticity of substitution in consumption and the
pure rate of time preference. Some economists
might argue that households with the preferences
we describe are implausibly resistant to intertemporal substitution and/or place an implausibly high
value on future consumption relative to current
consumption. It turns out that by reducing the value
of the indifference curvature parameter γ —which
increases the value of σ associated with a fixed
value of η—and increasing the pure time preference
rate ρ so as to keep the ratio of government expenditures to output constant, we can create a family of
alternative steady states that match postwar data
nearly as well as our baseline steady state. To investigate the robustness of our results to different substitution elasticities and time preference rates, we
examined the characteristics of a member of this
family of specifications with an IESC of 0.56—a
point estimate due to Attanasio and Weber (1995)
that is substantially larger than our baseline value
for σ. The corresponding value of the pure time
preference rate is –0.048.42 The welfare cost of a
1-percentage-point increase in the inflation rate is
now 1.1 percent of output, while the cost of a 10percentage-point increase in inflation becomes 8.3
percent of output. Although these estimates are
somewhat smaller than our original estimates
(particularly in the latter case), the differences
remain too small to affect our conclusions.43
42

Hurd (1989) estimates the difference between the risk-free real interest rate facing households and the pure time preference rate at 4.1
percent. This estimate is widely used in the literature on calibrated
OLG models. Since our estimate of the risk-free rate facing households is zero, the associated estimate of the pure time preference
would be –0.041.

43

We also conducted welfare-cost experiments from a baseline steady
state with σ=1/29, an estimate based on Kandel and Stambaugh

Bullard and Russell

An interesting feature of these alternative experiments is that the changes in the values of other
endogenous variables that result from increases in
the inflation rate are smaller, and in some cases
different in sign, than the changes produced by our
original experiments. For example, when the inflation rate is increased by 1 percentage point, the
before-tax real government bond rate falls by only
15 basis points (compared with 43 basis points) and
the level of output rises by only 0.3 percent (compared with 3.9 percent). In the 10-percentage-point–
increase case, moreover, the real bond rate falls by
only 0.7 percentage points (compared with 2.4
percentage points) and the level of output falls by
3.4 percent (compared with rising by 24.1 percent).
The small size of the changes in the pretax real
bond rate are attributable to the fact that when σ is
high, aggregate saving is very sensitive to changes
in the real interest rate, so that a small reduction in
the rate produces a large decline in the real stock
of bonds and a large decrease in the revenue from
bond seigniorage. The changes in output are small
because small declines in the pretax real rate produce
small increases in the capital stock—increases that
are largely offset, or more than offset, by the decrease
in the capital stock that is caused by the increase in
the effective tax rate on capital income. The changes
in welfare remain large because households with
large values of σ are very sensitive to small changes
in the slope of their lifetime consumption paths.
However, the Feldstein effect becomes a much larger
component of the cost of inflation, accounting for
a bit more than half the total cost: 4.3 percentage
points of 8.3 percent of output.
The results presented in this subsection demonstrate that it is possible to believe that inflation has
very high welfare costs without believing that permanent increases in the inflation rate produce large
permanent increases in the level of output. In addition, these results make it possible to believe that
the Feldstein effect is nearly as large as Feldstein’s
(1997) estimate, while at the same time believing
that the total cost of inflation is substantially larger.
6.3.3 Capital Share of Output. Our best-fit
value for α, the capital share of output, is somewhat
lower than values used in the literature on real
business cycles. Cooley and Prescott (1995), for
example, recommend a value of 0.4 for this param(1991). The welfare costs of 1-percentage-point and 10-percentagepoint increases in the inflation rate are 1.4 percent and 13.8 percent
of output, respectively.

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eter. We will investigate the robustness of our results
to changes in the capital share by examining an
alternative steady state in which α is increased to
0.4 but the other parameters retain their baseline
values. (Again, this alternative steady state is not a
good match for postwar data along some dimensions.) The welfare costs of 1-percentage-point and
10-percentage-point increases in the inflation rate
fall to 0.7 percent and 7.0 percent of the initial
steady-state level of output, respectively. Although
these cost estimates are substantially smaller than
the estimate produced by our baseline steady state,
they remain large enough, relative to other values
that have appeared in the literature, to support our
qualitative conclusions.44

7. QUALIFICATIONS
7.1 The Magnitude of Our Cost Estimates
The continuing interest in academic research
on the cost of inflation grows out of the fact that most
of the cost estimates the literature has produced
are quite small—too small to satisfy the intuition of
many economists and far too small to explain the
abhorrence with which inflation is regarded by many
members of the business and policy communities.
Our cost estimates, on the other hand, may be large
enough to produce the opposite problem: If inflation
is really this costly, it seems hard to understand why
monetary policymakers would ever allow the inflation rate to rise above very low levels.
Our model provides one explanation for the
persistence of moderately high inflation rates that
seems natural to us: Higher inflation rates produce
higher levels of output and employment. Policymakers typically assume that policies that increase
output and hours worked also increase public welfare. Economic theory does not necessarily concur,
and we think our model provides an empirically
plausible counterexample.
It must be noted, however, that our cost estimates
are founded on some basic assumptions that may
not be very reasonable in practice, and that more
realistic assumptions could reduce the size of the
estimates substantially. Our principal defense for
44

One partial explanation for the decline in the cost estimates here, and
also in the zero-intermediation-cost case, is that the initial G /Y ratio
is substantially smaller than in the baseline steady state. Since the
inflation-cost-generating mechanism we describe works through the
government budget constraint, lower values of G /Y tend to produce
lower cost estimates. A more thoroughgoing respecification that kept
this ratio constant would produce substantially higher estimates.

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these assumptions is that analogous ones have
been adopted by most other participants in the
inflation-cost literature, so that adopting them facilitates comparisons with the literature. In addition,
these assumptions have not been considered very
controversial.
One of our most important assumptions is that
changes in monetary policy are not accompanied
by changes in the active elements of fiscal policy
(expenditure or tax policy). Most of the previous
literature makes the somewhat weaker assumption
that changes in monetary policy do not result in
changes in government expenditures. In the “monetary cost” literature, the increased seigniorage revenue produced by higher inflation rates is usually
returned to the public via lump-sum taxes; Feldstein
(1997) and Abel (1997) assume that inflation-induced
increases in government revenue are offset by
decreases in direct tax rates. We follow our predecessors by assuming that changes in the inflation rate
do not result in changes in government expenditures
(relative to output), but we also assume that there
are no changes in direct tax rates. We are able to
make this assumption because in our model the
increased government revenue generated by higher
inflation can be offset by reductions in government
borrowing that decrease the amount of revenue
from bond seigniorage.
We think the assumption that the government
does not respond to changes in monetary policy by
changing direct tax rates is quite plausible for estimating the welfare effects of small or moderate
changes in the inflation rate—much more plausible,
in fact, than the alternatives just described. However,
this assumption begins to seem much less plausible
when applied to large changes. One reason for this
is that in our model, large changes in the inflation
rate produce huge changes in the volume of government borrowing. When the inflation rate rises by
10 percent, for example, a steady-state government
budget deficit amounting to 1 percent of output
becomes a steady-state budget surplus of 5.5 percent
of output. (The government dissipates the surplus
by lending to the public.45)
If we assume that large increases in government
revenue are partly offset by cuts in direct tax rates,
then the pretax real interest rate becomes less sensitive to increases in the inflation rate and the welfare
45

The government budget deficit is equal to the amount of revenue
from bond seigniorage. In our model, a permanent 1 percent increase
in the inflation rate cuts the steady-state budget deficit from 1 percent
of output to 0.5 percent of output.

FEDERAL R ESERVE BANK OF ST. LOUIS

costs of such increases become smaller. Suppose
we assume, for example, that when the monetary
authority increases the inflation rate by 10 percentage points the fiscal policy authority responds by
allowing the deficit-output ratio to fall by only half
the amount just described—a decline that still leaves
the government with a very substantial surplus—
and offsets the rest of the revenue increase by equalpercentage-point reductions in the three direct tax
rates. In this case, the pretax real bond rate falls by
only 1.5 percentage points instead of 2.4 percentage
points, and the welfare cost of the 10-percentagepoint increase in inflation is only 7.0 percent of
output. Smaller deficit reductions produce smaller
cost estimates.46
We have also followed most of the previous literature by confining our analysis to comparisons of
steady states. Thus, we are estimating the costs of
permanent changes in the inflation rate produced
by permanent and perfectly credible changes in
monetary policy. A more complete analysis of the
welfare implications of changes in inflation would
study costs (or benefits) incurred during the transition path from one steady state to another, and it
would also incorporate the fact that there is inevitably
uncertainty about exactly what the new inflation
target is and whether the monetary authority will
persist in trying to reach it. While uncertainty about
policy implementation is beyond the scope of this
paper, we have done preliminary research on the
properties of transition paths. Our findings indicate
that in our model, a complete or nearly complete
transition from one steady state to another is likely
to take quite a long time. Thus, our results should
not be interpreted as suggesting that the welfare
gains from lower inflation can be realized quickly,
and it is not entirely inconceivable that a transition
analysis might reveal that a permanent decrease in
the inflation rate imposes large costs on households
whose lives overlap the date of the policy change
or who are born in the years immediately following
the change.
We can cite one interesting piece of evidence
which suggests that transition analysis is unlikely
to have any dramatic effect on our conclusions.
Suppose we imagine that the shift from the old
steady state to the new steady state occurs instantly
at some date T, so that the households who are
46

A policy of holding the deficit-output ratio fixed produces an
unchanged pretax real bond rate and thus duplicates the Feldstein
effect, yielding a welfare cost of 1.2 percent of output.

Bullard and Russell

alive at date T—the members of generations T, T –1,
T – 2,…,T – 54, who have 55, 54,...,1 years left to
live, respectively—switch immediately from the
consumption-leisure bundles associated with the
old steady state to the bundles associated with the
new one. We can then use our utility function to
conduct across-steady-state comparisons of the
welfare of these 55 cohorts of households during
the remaining years of their lives. In our baseline
economy, the “remaining welfare” of the members
of each cohort is higher in a steady state with a 3
percent inflation rate than in the baseline steady
state with its 4 percent inflation rate. Thus, if the
transition path between the steady states is monotonic, as our preliminary results also suggest, then
the benefits of a disinflation undertaken at a date T
should start accruing immediately to all members
of the society.

7.2 Modeling the Tax System
Our assumptions about the tax system are at
best a crude approximation of the complex and
nonlinear array of taxes imposed by U.S. federal,
state, and local governments. We have adopted the
conservative approach of allowing a large fraction
of government expenditures to be financed by a tax
on real labor income—a tax whose effective rate
does not depend on the rate of inflation. This decision probably causes us to understate the historical
welfare cost of inflation: Actual income taxes are
levied on nominal income in a progressive manner
and, prior to the 1980s, “bracket creep” allowed
increases in inflation to increase both effective labor
income tax rates and government labor income tax
revenues. We also ignore the historical effect of
“bracket creep” on income from interest and capital
gains. (In the case of capital gains, the tax reforms
of the 1980s reduced this effect but did not eliminate
it entirely.) On the other hand, our assumption that
the corporate profits tax acts analogously to the
interest income tax as a tax on nominal returns to
capital is at least partly counterfactual: Under the
U.S. tax system, the effective corporate profits tax
rate is not directly increased by inflation. However,
we think this assumption is reasonable, as a first
approximation, for two reasons. First, our corporate
profits tax is intended partly as a proxy for a tax on
capital gains, which is absent from our model: The
effective tax rate on capital gains does increase with
higher inflation. Second, the fact that the U.S. tax
system uses historic cost depreciation allows inflation to increase the effective tax rate on corporate
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Bullard and Russell

profits indirectly, by reducing the real value of depreciation allowances.47
Our model also abstracts from another important
feature of the U.S. tax system, which is that households may deduct mortgage interest payments (and
before the 1980s, other interest payments) from
their taxable incomes. But our tax assumptions
account for this effect by taxing households on their
net interest income. In our general equilibrium environment, the net asset position of the households
is essentially the capital stock of the economy.
Similarly, our model does not distinguish returns
paid by firms as dividends from returns paid as
interest: Under the U.S. tax system, firms are taxed
on the former but not the latter. As a result, it may
seem that we are overstating the extent of double
taxation of capital. We address this problem by
choosing a relatively low corporate profits tax rate—
a rate that allows us to duplicate the observed ratio
of corporate profits tax revenue to government
expenditures in our baseline equilibrium.
In sum, we think our tax assumptions provide
an approximation of the U.S. tax system that is adequate for our purposes. However, further research
on the nature of the interaction between inflation
and the tax code in general equilibrium models is
certainly warranted.48

8. CONCLUDING REMARKS
In this paper, we use a dynamic general equilibrium model to estimate the welfare cost of inflation
in the U.S. economy. According to our estimates,
inflation is far more costly than most of the literature to date has indicated. However, our estimates
of the purely monetary component of the cost of
inflation—the component studied in most previous
work on this topic—are of the same order of magnitude as previous estimates. Our much-larger total
cost estimates grow out of the fact that in our model,
47

48

Both these effects are discussed in Feldstein (1997), who concludes
that inflation does indeed increase the effective tax rate on corporate
profits and that, overall, the effect of inflation on the effective tax rate
on income produced by firms in the form of dividends and capital
gains is actually somewhat larger than its effect on the effective tax
rate on interest paid by firms.
Black et al. (1994) also use a calibrated general equilibrium model to
study welfare costs of inflation that are driven largely by inflation’s
interaction with the nominal tax system. The version of their model
most comparable to ours produces costs that are less than one-fifth
the size of our estimates. However, they find that introducing endogenous growth and/or an open economy increases the cost of inflation
significantly. We think these are important directions for future
research in this area.

62

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inflation has a substantial impact on the real rates
of return on nonmonetary assets. Thus, our results
provide a formal interpretation of a view about the
source of inflation costs that is often expressed in
business and policy circles as well as academic
discussions.
In our model, most of the welfare cost of inflation
is attributable to the fact that higher inflation rates
increase the effective tax rate on capital income.
However, the portion of the cost that is driven by
the tendency of increases in the capital tax rate to
widen the spread between the before-tax and aftertax real return rates on capital—a distortion whose
impact has been studied by Feldstein (1997) and
Abel (1997)—is relatively small. Instead, the lion’s
share of the welfare cost of higher inflation is attributable to its tendency to produce a downward shift
in the entire structure of real interest rates, both
before and after taxes. This general decline in real
interest rates is a consequence of our assumption
that fiscal policymakers respond to the increase in
tax revenue that higher inflation produces by reducing government borrowing rather than by cutting
tax rates.
Our results have at least two important implications for further study of inflation costs and related
issues. First, they indicate that abstracting from
general equilibrium considerations may lead to
serious underestimates of the welfare cost of inflation—a conclusion we share with Dotsey and Ireland
(1996). Second, they demonstrate that plausible
alternatives to the standard calibrated dynamic
general equilibrium model may produce very different estimates of the cost of inflation—and, by extension, very different answers to other outstanding
questions in macroeconomics.

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Appendix

CHOOSING PARAMETERS BY MEANS
OF NONLINEAR OPTIMIZATION
As we have indicated in the text, we use a genetic
algorithm to learn about the irregular nonlinear map
between the vector ∆ of “deep parameters” and the
endogenous variables whose values we target.49
Given a candidate vector j at algorithm time s, ∆js,
we can calculate the solution to the agents’ decision
problem, and based on that information, we can
find the implied steady-state equilibrium values for
the targets associated with candidate vector j. We
define a fitness criterion for a candidate vector ∆js
based on deviations of these implied values from
targets. We use a genetic algorithm with real-valued
coding, and operators providing tournament reproduction, three types of crossover, and non-uniform
mutation, as explained below. Because our nonuniform mutation procedure slowly reduces the
mutation rate to zero by time T, separate genetic
algorithm searches can yield different best-fit candidate vectors ∆*
T. We conduct ten such searches and
report the best-fit vectors.
49

A more complete discussion of the principles of genetic algorithms
would take us too far afield. For an introduction, as well as detailed
description of the real-valued approach we use and the associated
genetic operators, see Michalewicz (1994).

We begin by defining a fitness criterion across
the nine targets of our system. We want to consider
a criterion on the order of sum of squared deviations
from target, but we also want the genetic algorithm
to consider the fact that some targets are tighter than
others in that the plausible deviation from them is
smaller. Accordingly, we think of the target ranges
as defining the space of plausible outcomes, and we
design our fitness criterion to penalize candidate
vectors ∆js more severely if they deliver values outside the target range. This will prevent the genetic
algorithm from spending a lot of time searching
areas of the parameter space that are good on many
dimensions but bad on a few dimensions. We assign
penalty points based on deviations from target on
each dimension. The penalty points are assigned
linearly up to the boundary of the target, such that
a candidate vector is penalized one point if a particular value is at the boundary of the target range.
Outside the target range, an appropriately scaled
quadratic penalty in the difference between the value
and target boundary is added to the linear penalty.
If we denote implied values of a candidate vector
∆js by θ ijs, target values by θ *i, and upper and lower
–
target bounds by θ i and θ i , respectively, where i=1,
…,9, then the fitness of the candidate vector, F[∆js],
is given by
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Bullard and Russell

9

[ ] ∑P

F ∆ js =

(A.1)

ijs ,

i =1

where

(
(
(
(

 θ −θ*
i
 ijs
 θ ijs − θ i*
(A.2) Pijs =  *
 θ i − θ ijs
 *
 θ i − θ ijs

) / (θ
) / (θ
) / (θ
) / (θ

i
i
*
i
*
i

) (
−θ )
−θ )
− θ ) + (θ

− θ i* + θ ijs − θ i

)

2

(

/ θ i θ i − θ i*

if θ ijs

i

i

M AY / J U N E 2 0 0 4

if θ ijs > θ i

[ ].
∈[θ ,θ ]

if θ ijs ∈ θ i* ,θ i

i

− θ ijs

)

2

(

/ θ i θ i − θ i*

This definition means that the better-fit vectors will
have lower fitness values, and a vector that delivers
an exact fit on all targets will have a fitness of zero.
The genetic algorithm is an iterative, directed
search procedure acting on a population of j candidate vectors at algorithm time s. At time s, the fitness
of all candidate vectors in the population is calculated. To obtain the next set of candidate vectors,
∆ js+1, we apply genetic operators. The first operator
is tournament reproduction. We select two vectors
at random with replacement from the time s population. The vector with the better fitness value is
copied into the time s+1 population. This operator is
repeated enough times to produce a time s+1
population equal in size to the time s population.
Reproduction provides most of the evolutionary
pressure in the search algorithm, but we need other
operators to allow the system to experiment with
new, untried candidate vectors. Crossover and mutation provide the experimentation and operate on
the time s+1 population before the fitness values
for that population are calculated.
To implement our crossover operators, we consider the time s+1 population two vectors, j and
j+1, at a time, and we implement the crossover
operator with probability p c. If crossover is to be
performed on the two vectors, we use one of three
methods with equal probability. In single-point
crossover, we choose a random integer icross ∈[1,…,9]
and swap the elements of ∆ j,s+1 and ∆ j+1,s+1 where
i ≥ icross. In arithmetic crossover, we choose a random
real a ∈[0,1] and create post-crossover vectors
a∆ j,s+1+(1– a)∆ j+1,s+1 and (1– a)∆ j,s+1+a∆ j+1,s+1.
In shuffle crossover, we exchange elements of ∆ j,s
and ∆ j+1,s based on draws from a binomial distribution, such that if the i th draw is unity, the i th
elements are swapped, otherwise the i th elements
are not swapped. Each of these operators has been
shown to have strengths in the evolutionary programing literature in certain types of difficult search
66

)

*
i

)

i

*
i

if θ ijs < θ i
problems, and we use them all here to improve the
prospects for success.
We implement a non-uniform mutation operator
–
that makes use of upper and lower bounds, δ i and
δ– i, respectively, on the elements of a candidate
vector ∆ j+1,s . This operator is implemented with
probability pm on element δ ij,s+1. If mutation is to
be performed on the element, we choose a pair of
random reals r1,r2 ~ U[0,1]. The new, perturbed
value of the element is then set according to
(A.3)

δ ij ,s +1 + δ i − δ ij ,s +1

new
δ ij ,s +1 = 
δ
 ij ,s +1 − δ ij ,s +1 − δ i


 1− s b  

( T ) 
1 − r2
 if r1 > 0.5,


b




1− s
( T ) 
1 − r2
 if r1 < 0.5,



(

)

(

)

where b is a parameter. With this mutation operator,
the probability of choosing a new element far from
the existing element diminishes as algorithm time
s → T, where T is the maximum algorithm time.
This operator is especially useful in allowing the
genetic algorithm to more intensively sample in
the neighborhood of the algorithm time-s estimate
of the best-fit vector in the latter stages of the search.
We conducted ten genetic algorithm searches
to identify a best-fit deep parameter vector ∆*
T
according to our set of targets defined in Table 1.50
The results are reported in Table A1.
50

We set the parameters in the genetic algorithm, {population, pc,pm,T,b}
as {30, 0.95, 0.11, 1000, 2} based on standards in the evolutionary
programing literature. In our final search, we set T=2500, but we did
not observe a commensurate improvement in performance, and so we
did not pursue higher values of T any further. We set the bounds on
elements δ i ,i=1,…,9, according to [–0.3, 0.1], [1.1,40], [0.075, 0.33],
[0.25, 0.4], [0.025, 0.075], [0.01, 0.04], [0.01, 0.08], [0.01, 0.4],
[0.01,0.25]. This amounts to a set of constraints on the search to values
that are typically viewed as economically plausible. We initialize the
system by choosing elements in an initial population of vectors ∆
randomly from uniform intervals defined by these bounds.

FEDERAL R ESERVE BANK OF ST. LOUIS

Bullard and Russell

Table A1
Results of Nonlinear Optimization
Search

K/Y

I/K

B/Y

hcg

alt

Im/Y

H/Y

G/Y

TK/G

F

1

0.02

0.14

0.00

0.24

0.32

0.01

0.00

0.00

0.05

0.78

2

0.05

0.04

0.00

0.31

0.29

0.00

0.00

0.00

0.00

0.69

3

0.01

0.00

0.00

0.29

0.27

0.00

0.00

0.00

0.00

0.57

4

0.00

0.06

0.00

0.29

0.28

0.01

0.00

0.00

0.01

0.65

5

0.01

0.02

0.00

0.25

0.02

0.00

0.00

0.00

0.00

0.30

6

0.02

0.08

0.00

0.31

0.33

0.00

0.00

0.00

0.02

0.76

7

0.01

0.01

0.00

0.29

0.31

0.00

0.00

0.00

0.00

0.61

8

0.08

0.06

0.00

0.33

0.31

0.00

0.00

0.00

0.00

0.78

9

0.04

0.04

0.00

0.33

0.46

0.00

0.00

0.00

0.03

0.91

10

0.06

0.02

0.00

0.30

0.23

0.00

0.00

0.00

0.01

0.62

NOTE: The fit to the data. The entries are deviations from target, by target and total, in penalty points, for each of the ten searches
we conducted. Columns 2 through 10 are averages across algorithm time s =T populations. Within algorithm time s =T populations,
we found little or no variation across fitness components.

We find that the algorithm time-T population
of parameter vectors ∆*
jT provide a close fit on our
target data. The only quantitatively significant discrepancies from targets occur on individual consumption growth and individual time devoted to
market, and then the implied values are typically
only 0.2 to 0.35 of a penalty point from target,
meaning that implied values on these dimensions
lie away from the target only 20 to 35 percent of
the distance between the target and a target bound.

We found little or no variation among individual
parameters within algorithm time s=T populations.
Across searches, we found some variance, almost
all of it in the preference parameters. The estimates
of the elasticity of intertemporal substitution, for
instance, ranged from a low of 0.114 to a high of
0.185. Search number 5 provided the best overall
fit, so we use the parameters from this search in
the baseline specification of our model.

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