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Editor’s Note

This issue of the Economic Quarterly includes the Richmond Fed’s 2003
Annual Report essay, written by Al Broaddus and Marvin Goodfriend. In this
essay, the authors summarize and build on an approach to monetary policy
that they have developed over many years working here at the Bank. In particular, they discuss how the knowledge gained through the process of reducing
inflation can be applied to the new problem of sustaining price stability. Their
approach draws on the new neoclassical synthesis, an analytical framework
that emphasizes the decentralized price-setting of monopolistically competitive firms. To further illuminate this framework, this issue of the Quarterly
reprints Goodfriend’s primer on the subject. Also in this issue, Bob Hetzel’s
interpretation of how the Fed controls inflation is influenced by certain aspects
of the new neoclassical synthesis but differs somewhat from that approach,
and Yash Mehra examines alternative empirical specifications of a Phillips
curve relationship for explaining inflation behavior.
—John A. Weinberg
Director of Publications

Federal Reserve Bank of Richmond Economic Quarterly Volume 90/3 Summer 2004

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Sustaining Price Stability
J. Alfred Broaddus, Jr., and Marvin Goodfriend

T

he year 2003 was a watershed in Federal Reserve history. In his semiannual testimony to Congress on monetary policy in July, Chairman
Greenspan declared that measures of core consumer inflation had decelerated in the first half of the year to a range that could be considered “effective price stability.”1 The Chairman paused briefly to acknowledge, with
understated satisfaction, the achievement of this goal, which Congress had assigned to the Federal Reserve and the Fed had pursued for over two decades.
He quickly pointed out, however, that the Fed would be confronted now with
new challenges in sustaining price stability—specifically preventing deflation
as well as inflation. Earlier in the year, at the conclusion of its May meeting,
the Federal Open Market Committee (FOMC) had expressed concern for the
first time that inflation might decline too far, saying that “the probability of
an unwelcome substantial fall in inflation, though minor, exceed(ed) that of a
pickup in inflation from its already low level.”2
The case for maintaining price stability—in the United States and elsewhere—is rooted in experience and theory, which indicate that monetary policy best supports employment, economic growth, and financial stability by
making price stability a priority. The full rationale for price stability has been
elaborated elsewhere, and we will refrain from repeating it here.3 This article,
instead, is about how to sustain price stability now that it has been achieved.
We build our argument in several stages. First, we present a framework for understanding the inflation and deflation processes. Our framework, borrowed
from the “new neoclassical synthesis” macroeconomic model, focuses on the
management of the markup of price over marginal cost by monopolistically
This article first appeared in the Bank’s 2003 Annual Report. The authors are President,
and Senior Vice President and Policy Advisor, respectively. Robert Hetzel, Jeffrey Lacker,
Bennett McCallum, Aaron Steelman, and John Walter contributed valuable comments. The
views expressed are the authors’ and not necessarily those of the Federal Reserve System.
1 See Greenspan (2003, 5).
2 See Bernanke (2003) for a discussion of the nature of the deflation risk.
3 See, for instance, Goodfriend and King (2001) and Goodfriend (2004).

Federal Reserve Bank of Richmond Economic Quarterly Volume 90/3 Summer 2004

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Federal Reserve Bank of Richmond Economic Quarterly

competitive firms.4 Next, we provide examples of shocks that are potentially
inflationary or deflationary and explain how interest rate policy actions can
counteract them effectively to maintain price stability.
The Fed’s current hard-won credibility for low inflation is a foundation
of efficient monetary policy because it anchors expected inflation. We review
briefly why inflation scares create problems for monetary policy. Addressing
the challenge noted by Chairman Greenspan, we explain why deflation scares
are equally problematic. Unfortunately, credibility for containing inflation
does not necessarily imply credibility against deflation because while there is
no upper bound on nominal interest rates to resist inflation, there is a lower
bound at zero. We explain how the Fed can use monetary policy—even at the
zero bound—to preempt deflation and acquire credibility against deflation to
complement its anti-inflation credentials.
Communication has come to play an increasingly important and substantive role in the Fed’s conduct of monetary policy because open and effective
communication is a crucial ingredient in building and maintaining credibility
for price stability. Good communication requires clear long-run policy objectives and clarity in conveying the reasoning behind short-run policy actions
aimed at achieving those objectives. In line with our macroeconomic framework, we believe that both purposes would be well served if the Fed publicly
announced an explicit long-run inflation target and made more prominent use
of price-cost gap, employment gap, and output gap indicators in explaining
the stance of monetary policy. In particular, we explain how, in our view, these
changes would help minimize the kind of communication problems the Fed
faced in 2003 in signaling its concern about deflation and its policy intentions
for dealing with the rising risk of deflation at that time.
Having outlined what we want to accomplish in this article, let us emphasize that what follows is our understanding of the issues and our suggestions
for dealing with them. Some of our views are shared by our Fed colleagues,
others are not. This is no cause for embarrassment. Monetary policy and its
effect on the economy is a complex and subtle subject; there is plenty of room
for different approaches and divergent views.

1. THE FUNDAMENTAL PRINCIPLE OF PRICE STABILITY
Our approach to thinking about the maintenance of price stability focuses
on how monopolistically competitive firms set their prices over time.5 This
4 New neoclassical synthesis (NNS) models feature complete microeconomic foundations as
in real business cycle economies and imperfect competition and sticky prices as in New Keynesian
economies. New synthesis models are thoroughly discussed and analyzed in Goodfriend and King
(1997, 2001) and Woodford (2003). The Federal Reserve Board’s FRB-US macromodel shares
many of the central features of the NNS approach (see Brayton et al. [1997]), as does the model
of monetary policy discussed extensively in Clarida, Gal´, and Gertler (1999).
ı
5 Monopolistically competitive firms have the market power to set their product price above
the marginal cost of production.

J. Alfred Broaddus, Jr., and M. Goodfriend: Sustaining Price Stability

5

approach is useful because it highlights how monetary policymakers must
create an environment within which firms choose to maintain stable prices on
average.6
For our purposes, a key feature of price-setting in practice is its discontinuous character. It is costly for a firm producing a distinctive product to
determine the exact price that maximizes its profits at every point in time.
Forecasts of demand and cost conditions are expensive to obtain. Moreover,
pricing must compete with other claims on management’s time, such as production and marketing decisions. Consequently, pricing gets the attention of
management only every so often.
For all these reasons, a firm is apt to consider changing its product price
only when demand and cost conditions threaten to move its actual markup of
price over cost significantly and persistently away from its profit-maximizing
markup.7 Given a firm’s current product price, higher production costs compress its markup, and lower production costs elevate its markup. Production
costs, in turn, increase with the hourly wage a firm must pay its workers and
decrease as labor productivity (output per hour) rises.8
Potential inflation arises when a significant compression of markups is
widely expected by firms to persist. In this case, firms raise product prices
over time to cover higher expected costs. Potential deflation develops if firms
expect significantly elevated markups to persist. Competition for product
market share in this latter case induces firms to pass along lower costs via
lower prices.
Such reasoning implies the fundamental principle of price stability: inflation will remain low and stable if and only if departures from profit-maximizing
markups are expected to be relatively small and transitory across firms, so firms
are content to raise prices at the existing low inflation rate on average. Note
that we consider low and stable inflation to be “effective price stability,” in
keeping with Chairman Greenspan’s characterization.
The historical record shows that in the long run competition among firms
for labor pushes real wages (nominal wages adjusted for inflation) up at about
the same rate as labor productivity grows. Consequently, real production costs
in the aggregate are stable in the long run. Nominal wages, in turn, tend to rise
at the rate of productivity growth plus the rate of inflation; therefore, nominal
production costs rise at about the rate of inflation in the long run. In the
short run, however, shocks to aggregate demand and productivity can cause
production costs to vary significantly and persistently relative to prices.
6 The term “on average” is important. Obviously, individual firms adjust particular prices in
response to sector- and firm-specific demand and supply conditions as well as the broader pricing
environment.
7 An excessively high markup is counterproductive because it yields too much market share
to competitors; conversely, a markup that is too small does not exploit a firm’s market power
sufficiently.
8 We focus on labor and ignore capital and raw material costs to simplify our exposition.
Labor costs alone account for about two-thirds of the cost of producing goods and services.

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Federal Reserve Bank of Richmond Economic Quarterly
COUNTERACTING SHOCKS TO PRICE STABILITY

This section builds on the fundamental principle of price stability discussed in
the previous section to explain how monetary policy, working through shortterm interest rates, can counteract inflationary or deflationary shocks to the
economy. The argument is straightforward: interest rate policy maintains
price stability by managing aggregate demand so as to stabilize the actual
markup at the profit-maximizing markup on average across firms.9 (What
follows is tightly reasoned but well worth working through, since it describes
the core relationships policymakers must focus on to succeed in maintaining
price stability.)
An inflationary shock generates a sustained acceleration in production
costs, and therefore a compression of the average markup that inclines firms
to raise prices above the previously expected low inflation rate unless the
Fed uses interest rate policy actions to reverse the increase in costs and the
markup compression. A deflationary shock, in contrast, generates a sustained
deceleration or decline in production costs and an increase in the markup that
requires offsetting Fed interest rate actions. Exactly how interest rate policy
works to stabilize the markup is explained below.
For expositional purposes, it is useful to divide shocks with inflationary
or deflationary potential into two categories. We consider first shocks to
expected future income prospects. Subsequently, we take up shocks to current
productivity growth.

Shocks to Expected Future Income Prospects
Whatever the source of optimism or pessimism about the future, shocks to expected future wages and profits are likely to be transmitted to current aggregate
demand.10 Households will want to adjust current as well as future consumption to reflect any changes in expected lifetime resources. And firms will want
to invest more or less currently in response to any changes in expected future
profits.
In these circumstances, optimism about future income prospects is potentially inflationary because it increases the current demand for labor, raises
wages, and compresses markups. On the other hand, pessimism about future
prospects is potentially deflationary because it eases competition in the labor
market, slows wage growth, and elevates markups.
9 See Goodfriend (2002) for an exposition of the mechanics of interest rate policy geared
to maintaining price stability in a new synthesis model. Woodford (2003) presents an extensive
treatment of interest rate policy. Clarida, Gal´, and Gertler (1999) provide a useful survey. We
ı
ignore the zero-bound constraint on interest rate policy in this section, assuming, in effect, that
the shocks are small enough that the zero-bound constraint never binds.
10 Optimism or pessimism regarding job prospects, profitable investment opportunities, taxes,
and war, for example, would all affect future income prospects.

J. Alfred Broaddus, Jr., and M. Goodfriend: Sustaining Price Stability

7

The key point for monetary policy is this: one way or another, profitmaximizing markups will be restored. The shock may dissipate before inflationary or deflationary forces build up. If not, then either the Fed must restore
profit-maximizing markups promptly with interest rate policy actions, or else
firms will attempt to restore these markups by raising or cutting product prices,
whichever the case may be. Clearly, it is better that profit-maximizing markups
be restored by interest rate policy actions without inflation or deflation.
Bottom line: the Fed can offset a potentially inflationary increase in current demand arising from an increase in expected future income prospects
by raising real interest rates to increase the return to saving, raise the cost of
borrowing, and induce households and firms to defer spending. Higher real
rates preempt inflation by reversing the increased current demand for labor,
which reduces the pressure on wages and production costs, and restores profitmaximizing markups. Conversely, by lowering real interest rates, the Fed can
lower the return to saving and the cost of borrowing, stimulate spending, and
offset a potentially deflationary reduction in aggregate demand. Lower real
rates, in turn, preempt deflation by strengthening current labor demand, reversing the downward pressure on wages, and recompressing markups.
The argument above proceeded as if firms were not fully confident that
the Fed would act promptly to stabilize production costs that would otherwise
be affected by shocks to future income prospects. If firms are confident, then
they will meet a temporary increase in demand by working current employees
more intensively or by hiring temporary workers, rather than by raising product
prices. And firms will lay off labor rather than cut prices if they expect the Fed
to stabilize production costs in the face of a shortfall in current demand. Note
that the average markup will tend to be compressed temporarily in the first case
and elevated temporarily in the second case. We will say more below about
why the Fed’s “credibility” for price stability is the foundation of efficient
monetary policy.

Shocks to Current Productivity Growth
Consider next a sequence of current shocks to productivity growth that persists unexpectedly at first, but subsequently comes to be expected to persist.
Initially, unanticipated increases in productivity growth are potentially deflationary, and decreases are potentially inflationary. We take the deflationary
case; the inflationary case is exactly the reverse.
For a given growth rate of wages, accelerated productivity growth lowers
production costs directly. If, at first, the acceleration is not expected to persist,
there is little effect on expected future income and little effect on current aggregate demand. In such circumstances, faster productivity growth also slows
production costs indirectly by reducing current labor demand and slowing the
growth of wages. Two historical examples of these effects are particularly

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Federal Reserve Bank of Richmond Economic Quarterly

noteworthy. Surprisingly persistent strong productivity growth in conjunction
with a weak labor market helped lower production costs and produce disinflation in 2003. Conversely, surprisingly persistent weak productivity growth
helped produce inflation in the 1970s.11
The longer a surprising acceleration or deceleration of productivity growth
persists, the more likely it will come to be expected to persist. If these changes
in expectations are sufficiently pronounced, they have the potential to offset
and reverse the initial risk to price stability arising from the change in productivity growth. This appears to be what happened in the late 1990s when
surprisingly persistent increases in productivity growth apparently came to be
expected and were extrapolated far into the future. The brightening future
income prospects caused aggregate demand to grow even faster than productivity for a time near the end of the decade. Labor markets tightened, real
wages grew about as fast as productivity, and inflation remained low and stable. Indeed, there was concern at the time that inflation might rise if the
increase in demand stimulated by the higher expected future income growth
outstripped the restraining effect of the higher productivity growth on prices.
Whether current shocks to productivity are potentially inflationary or deflationary, the Fed can act to offset that potential with interest rate policy.
Again, the guiding policy principle is to manage aggregate demand to stabilize
production costs so as to sustain profit-maximizing markups on average. The
Fed must reduce real interest rates to defuse the potential for deflation when
a period of faster productivity growth is not expected to persist. In this situation, lower real interest rates must stimulate aggregate demand sufficiently
to offset the weakness in labor markets and thereby allow wage increases to
reflect the higher productivity. Alternatively, if the public comes to regard
a period of faster productivity growth as an increase in trend growth, then
the Fed might have to increase real interest rates to relieve the potential for
inflation. Specifically, interest rates would have to rise enough to limit the
increase in current aggregate demand to what can be satisfied by the current
increase in productivity at the profit-maximizing markup.
Having outlined these policy prescriptions, we want to be quick to acknowledge—as practical policymakers—that implementing them with consistent
success is far from rote. Measuring and predicting the relevant aggregate
variables is difficult enough; estimating and tracking indicators of the average
profit-maximizing markup is even more so. Modeling the transmission of
interest rate policy actions to demand, production costs, and inflation requires
sophisticated econometric techniques. And discerning whether the public
perceives an increase in productivity growth as transitory or more lasting, for
11 Weak productivity growth, however, was only part of the story in the 1970s: inflation rose
long before the extended productivity slowdown began in 1974 and fell briefly thereafter, before
rising again in 1978.

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9

example, is not easy. Tasks like these are as challenging as they are crucial. Some would refer to the judgments involved in this work as the “art” of
monetary policy.

3. THE IMPORTANCE OF CREDIBILITY FOR STABLE PRICES
As the foregoing has already suggested, credibility is an essential component of
effective monetary policy. The long campaign from the late 1970s through the
early 1990s to reduce inflation and establish price stability arguably succeeded
only when the Fed finally acquired credibility for low inflation in the eyes of
the public in the late 1990s. Indeed, the acquisition of this credibility was
essentially equivalent to establishing price stability—two ways to describe
the same achievement. Similarly, the Fed needs to acquire credibility for
sustaining price stability going forward.
The previous section showed how interest rate policy actions can counteract inflationary or deflationary shocks and perpetuate credibility presuming
that it has already been established. In this section we explain why full credibility for maintaining price stability is so useful, and how its absence can
cause serious problems.
Credibility for stable prices produces three critically important benefits.
First, credibility anchors inflation expectations so that nominal federal funds
rate target changes translate clearly into real interest rate changes, which helps
the Fed gauge the likely impact of its policy actions on the economy. Second,
credibility buys time for the Fed to recognize and counteract threats to price
stability. Third, credibility enhances the flexibility of interest rate policy to
respond aggressively to transitory shocks that threaten to destabilize financial
markets and create unemployment.
The absence of credibility, on the other hand, creates problems for monetary policy. The history of post-World War II monetary policy in the United
States features numerous inflation scares marked by sharply rising long-term
bond rates reflecting increased expected inflation premia.12 Inflation scares
create a fundamental dilemma for monetary policy. At the initial nominal federal funds rate target, higher expected inflation lowers the real federal funds
rate and intensifies the inflation scare by stimulating current aggregate demand
and compressing the markup. In these circumstances, the Fed could raise its
nominal federal funds rate target just enough to leave the real rate unchanged;
but that would do nothing to reverse the collapse of confidence.
Inflation scares are dangerous because ignoring them encourages even
more doubt about the Fed’s commitment to low inflation. And restoring credibility for low inflation requires the Fed to weaken labor markets deliberately
12 See Goodfriend (1993). See Orphanides and Williams (2004) for a quantitative, theoretical
analysis of inflation scares in a model of perpetual learning.

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Federal Reserve Bank of Richmond Economic Quarterly

with higher real interest rates in order to slow wage growth, elevate markups,
and induce firms not to raise prices—rarely a popular policy stance with the
public or the political establishment. It is in large part to avoid the risk of recession posed by inflation scares that the Fed has learned to preempt inflation
with interest rate policy.
Unfortunately—and this is a crucial point in appreciating fully the policy
implications of the transition from fighting for price stability to maintaining it—credibility for controlling inflation does not automatically translate
into credibility for preventing deflation. A deflation scare obviously does not
confront the Fed with a choice between contracting employment and loosing
credibility. On the contrary, the way to resist a deflation scare is to reduce real
interest rates in order to stimulate demand, tighten labor markets, raise wages,
and compress the markup. The problem is that given the zero bound on the
nominal federal funds rate, interest rate policy alone might have insufficient
leeway to deter deflation, especially since the federal funds rate is low on average when expected inflation is low. Moreover, the Fed would have to drive
the nominal federal funds rate ever closer to zero to prevent disinflationary
expectations from raising the real federal funds rate. And deflation expectations would actually raise the real federal funds rate at the zero bound and
exacerbate the deflation scare.
In addition, a policy vacuum at the zero bound could encourage ill-advised
fiscal actions. Some fiscal actions would be desirable as we explain below; but
many would not be. For instance, the government might enact legislation that
results in wasteful government spending, inefficient credit subsidies, or forbearance in the banking system related to deposit insurance. The government
might also resort to off-budget policies such as anti-competitive measures to
support wages or prices in particular sectors. All told, such fiscal actions
could lower potential GDP substantially.13 In doing so, they would lower
future income prospects, lower current aggregate demand, contract current
employment, lower wages and production costs, and exacerbate the deflation
problem. This appears to be what happened in the Great Depression of the
1930s.14
Ultimately then, a deflation scare, like an inflation scare, is problematic
because it has the potential to lead to a protracted recession. From this perspective, even those who care mainly about employment and output can understand
why the Fed must establish credibility as a deflation fighter as well as an inflation fighter by making price stability a priority and resisting deviations from
it in either direction.
13 Potential GDP refers to the path of output consistent with the maintenance of price stability.
14 Kennedy (1999) describes U.S. economic policies in the 1930s as a collection of market

interventions taken to support favored sectors of the economy. Cole and Ohanian (2001) model
these interventions and show quantitatively that they can explain the persistence of the Great Depression in the United States.

J. Alfred Broaddus, Jr., and M. Goodfriend: Sustaining Price Stability

11

Moreover, credibility against inflation and credibility against deflation are
mutually supportive: each strengthens the other, and each is weaker without
the other.15 As we pointed out above with respect to inflation scares, policy
must compensate for insufficient credibility in one direction by taking risks
in the other direction. We make this point again as it pertains to establishing
credibility against deflation.

4.

DEFEATING DEFLATION AT THE ZERO BOUND

But how can the Fed establish credibility for preventing deflation given the zero
bound on the nominal funds rate? In brief, the Fed should make arrangements
to overcome operational and institutional obstacles identified below that could
impede the effectiveness of monetary policy at the zero bound. The publication
of a contingency plan for the aggressive pursuit of monetary policy against
deflation at the zero bound would greatly reduce the likelihood and force of
deflation scares and help guarantee that the devastating effects of deflation
experienced earlier in U.S. history will not be repeated.16
But how, specifically, can the Fed confront a deflationary risk when the
funds rate is at the zero bound? Most importantly in our view, the Fed can
continue to inject money into the economy by buying assets and expanding
its balance sheet when conventional interest rate policy is immobilized at the
zero bound.17 Some economists believe that expanding the monetary base
would stimulate spending directly through a monetarist channel of monetary
transmission. Others focus on how Fed purchases of long-term bonds would
stimulate spending by lowering long-term interest rates. Still others believe
that expanding the balance sheet would work by creating expectations of inflation that would push real interest rates below zero if the Fed held the nominal
federal funds rate at zero.
Even though we do not know the relative strength of these three transmission channels, and others that may exist, we do know this: monetary policy
must be able to defeat deflation at the zero bound; otherwise, the government
could eliminate explicit taxes and finance all of its expenditure forever with
money created by the Fed!18 The challenge is to identify and overcome opera15 It is worth pointing out that credibility for price stability is also threatened when Fed
participation in foreign exchange operations with the Treasury creates doubt about whether monetary
policy will support domestic or international objectives. See Broaddus and Goodfriend (1996).
16 Deflations in the early 1920s and in the 1930s were particularly destructive; milder deflations at other times caused less distress.
17 The Fed is not free to expand the size of its balance sheet as long as it targets a federal
funds rate even slightly above zero. In that case, the size of its balance sheet is constrained to
create a scarcity of bank reserves just sufficient to maintain the desired positive federal funds rate.
18 Technically, a deflation trap is not a possible rational-expectations equilibrium if the nominal value of total government liabilities will not decline, even in the presence of sustained deflation.
See Woodford (2003, 133).

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Federal Reserve Bank of Richmond Economic Quarterly

tional and institutional obstacles to the credible implementation of quantitative
monetary policy as opposed to interest rate policy, where “quantitative monetary policy” refers to open market purchases that expand the volume of assets
and monetary liabilities on the Fed’s balance sheet.
What are these operational and institutional obstacles? One problem is
that the bang for the buck of quantitative monetary policy at the zero bound is
unknown and may be relatively weak. It follows that the Fed must be prepared,
if necessary, to overshoot temporarily the long-term, steady state size of its
balance sheet by a wide margin. But to do so, the Fed must have a credible
exit strategy for draining whatever monetary base threatens excessive inflation
after it has successfully concluded its deflation-fighting policy actions.
A second problem is that short-term government securities are perfect substitutes for the monetary base at the zero bound; therefore, the Fed would have
to buy longer-term government securities, private assets, or foreign assets for
quantitative policy to be effective at the zero bound.19 The current outstanding
stock of longer-term government securities together with the prospective flow
of future government borrowing may very well provide sufficient government
securities for the Fed to buy—that is, monetize—to defeat deflation at the zero
bound.
To lock in credibility against deflation, however, the Fed will need more
fiscal support for quantitative policy at the zero bound than it is usually granted
by the fiscal authorities, i.e., Congress and the Treasury. For example, in some
circumstances, there might not be enough outstanding longer-term government
bonds to purchase, or government budget deficits to monetize, to make the
quantitative policy effective. Of course, the Fed could buy other assets. But
buying domestic private assets or foreign assets on the large scale contemplated
here would create other credibility problems.20 Additionally, this strategy
would expose the Fed to capital losses that might leave it with insufficient assets
to reverse a huge expansion of its balance sheet, should that be required.21
The fiscal authorities could enter the process in a number of ways. In
particular, they could support the Fed’s exit strategy by committing to transfer
enough government securities to the Fed—in effect to recapitalize the Fed
if necessary—to allow the Fed to drain whatever base money needed to be
withdrawn from the economy following an aggressive anti-deflation action by
the Fed at the zero bound. In addition, the fiscal authorities could agree to run a
budget deficit to help inject money into the economy. The Fed could monetize
19 When the federal funds rate has been pushed to zero, there is no opportunity cost to
holding currency or bank reserves relative to short-term securities. Hence, the public is indifferent
at the margin between holding cash or short-term securities, and open market purchases of shortterm securities have no effect.
20 See Broaddus and Goodfriend (2001).
21 For instance, long-term bonds purchased to stimulate the economy when interest rates are
near zero suffer large capital losses when interest rates rise as the economy recovers.

J. Alfred Broaddus, Jr., and M. Goodfriend: Sustaining Price Stability

13

short-term debt issued to finance the deficit and then withdraw excess base
money later by selling the debt back to the public. In this way, monetary policy
could be made completely credible against deflation in virtually any situation.
This discussion may strike some readers as far-fetched. But while the
probability is low that a deflationary threat of the magnitude contemplated
here at the zero bound will emerge in the future, if it did, the consequences
of not being fully prepared to deal with it could be exceptionally damaging
to the economy. Consequently, we believe it is essential to have contingency
arrangements of the kind we have just described firmly in place in advance.

5.

IMPROVING COMMUNICATION IN SUPPORT
OF PRICE STABILITY

Up to this point, we have explained the economics of maintaining price stability in the context of a modern macroeconomic model, and indicated the critical
importance of credibility in this effort, including credibility for confronting
the risk of deflation at the zero bound. This last section of our article addresses
a final element in the strategy for maintaining price stability: clear communication with the public regarding both the strategy itself and short-term actions
taken in the defense of price stability.22
The macroeconomic model of the inflation and deflation processes outlined above suggests two substantial opportunities for the Fed to improve its
communication practices in ways that would strengthen its strategy for maintaining price stability. First, the Fed can lock in long-run price stability and
clarify its short-run concerns and policy intentions regarding inflation by publicly announcing an explicit low long-run inflation target. Second, the Fed
can clarify its reasons for taking particular short-run policy actions to preempt potential inflation or deflation by talking in terms of the average gap
between the actual markup and the profit-maximizing markup, and closely
related indicators of labor market tightness, which we identified earlier as
the proximate determinants of price pressures. Our arguments for these two
recommendations are developed below.

Clarifying Short-Run Policy Aims
with an Inflation Target
Although the Fed has made price stability a priority for monetary policy, it
does not publicly and explicitly specify a target range for inflation. Instead, the
Fed signals its concerns about inflation or deflation in its post-FOMC meeting
statements and minutes, and in the Chairman’s monetary policy reports to
22 See Dudley (2003).

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Federal Reserve Bank of Richmond Economic Quarterly

Congress. We believe that the Fed’s experience in the May–June 2003 period
indicates that references to inflationary or deflationary risks cannot reliably
substitute for an explicit long-run inflation target.
The indication in the announcement following the May 2003 FOMC meeting that significant further disinflation would be unwelcome, in our view, effectively put a lower bound on the Fed’s tolerance range or comfort zone for
inflation. At the time, inflation was running at around 1 percent in terms of
the core PCE, one of the Fed’s preferred inflation measures.23 The assertion
of a lower bound seemed prudent given the deflation risk discussed above and
the fact that the federal funds rate at the time was 1 1/4 percent. The Fed’s
statement served two useful purposes—it alerted the public to the small but
real risk of deflation while also asserting implicitly that the Fed would act to
deter further disinflation.
The assertion of the lower bound on inflation, however, came as a surprise
that took the expected future path of the federal funds rate sharply lower and
pulled longer-term interest rates down as well. Commentary in the media
amplified nervousness about deflation well beyond what was justified in the
economic data. In the event, the Fed reduced its federal funds rate target only
25 basis points, rather than the widely anticipated 50 basis points, at the June
FOMC meeting. And longer-term interest rates promptly reversed field.24
Our reading of this episode is that references to the probability of rising or
falling inflation in FOMC policy statements cannot reliably substitute for an
announced, explicit inflation target range. One of the most important lessons
of rational expectations theory is that it is particularly difficult for the public
to gauge the intent of a policy action taken out of context, and, therefore, it
is particularly difficult for the Fed to predict the effect of an unsystematic
policy action.25 We think this reasoning extends to policy announcements
as well. Since the ad hoc implicit announcement of a lower bound on the
Fed’s tolerance range for inflation was unsystematic by definition, it is not
surprising that the announcement caused confusion, nor that the Fed failed to
predict the public’s reaction. In this case the reaction was excessive, but in
another situation there might have been an insufficient reaction.
If an inflation target range had been in place in 2003, the public could
have inferred the Fed’s growing concern about disinflation as the inflation rate
drifted down toward the bottom of the range through the first half of the year.
Expected future federal funds rates and longer-term interest rates would have
moved lower continuously, with less chance of overshooting or undershooting
the Fed’s intended policy stance. We recommend that the Fed publicly commit
to maintaining core PCE inflation within a target range of 1 to 2 percent over
23 See Federal Open Market Committee (1996, 11).
24 See Ip (2003, June 27 and August 15).
25 McCallum (2004) makes a related point.

J. Alfred Broaddus, Jr., and M. Goodfriend: Sustaining Price Stability

15

the long run so that such misunderstandings won’t recur at either end of the
Fed’s tolerance range for inflation.26
The Fed’s assertion of an inflation target might appear to some to usurp a
congressional prerogative. We think otherwise for three reasons.
First, we believe a compelling case can be made that, beyond underlining
the Fed’s long-term responsibilities for price stability, an inflation target would
be a valuable addition to the Fed’s operational communications procedures.
From this perspective, we believe that at least implicitly Congress has already
delegated authority to set an inflation target to the Fed as part of its operational
independence.
Second, as we emphasized earlier, monetary policy best facilitates achievement of the Fed’s other mandated policy goals—such as maximum sustainable
employment, economic growth, and financial stability—by making price stability a priority.
Third, an inflation target would not prevent or hinder the Fed from taking
the kinds of policy actions it takes today to stabilize employment and output
in the short run. What it would do is discipline the Fed to ensure that these
actions are consistent with its commitment to protect the purchasing power of
the currency.27

Clarifying Short-Run Policy Aims
with Gap Indicators
The second opportunity for improved communication noted above is more
effective explanation of the reasons for particular short-term policy actions.
The macroeconomic framework presented above locates the potential for departures from price stability in the sign, size, and expected persistence of
the average price-cost gap between actual markups and the respective profitmaximizing markups. In practice, indicators of the employment gap and the
output gap are also used, in conjunction with preferable but hard-to-measure
price-cost gap indicators, to assess the risks to price stability.28 (Recall that
tightness or slack in the labor market is what causes nominal wages to accelerate or decelerate. Markup dynamics then govern the transmission of these
nominal wage dynamics to the price level.) Recently, the Fed has mentioned
26 While the core PCE, the Fed’s preferred inflation measure internally, seems a straightforward choice for the index on which to base its target measure, the better-known consumer price
index could be used instead. Our framework suggests that the Fed should target a core inflation
index that closely reflects sticky prices set by monopolistically competitive firms.
27 This repeats a point made by Broaddus at the January 1995 FOMC meeting. See Federal
Open Market Committee (1995, 41).
28 The output gap measures aggregate output relative to an estimated potential level of output
consistent with price stability. The employment gap measures aggregate employment relative to an
estimated level of employment believed to be consistent with price stability.

16

Federal Reserve Bank of Richmond Economic Quarterly

only the growth of output or productivity, and the improvement or deterioration in employment in its policy statements, and has rarely if ever mentioned
markups, price-cost gaps, or employment and output gaps.
We recognize that gap indicators are particularly difficult to estimate,
especially in real time. One must measure the average markup, aggregate employment and output and estimate the time-varying levels of these aggregates
believed to be consistent with price stability. And one must forecast future
changes in these gap indicators in order to assess the risks to price stability.
Furthermore, one must decide how to weight the various indicators in the
overall assessment when inevitable inconsistencies occur.
There is a natural reluctance to feature gaps in the Fed’s policy statements
because of the unfortunate experience in the 1960s and ’70s, when calling
attention to employment and output gaps created pressure that ultimately led
to inflationary monetary policy and very poor macroeconomic performance.29
Even so, Fed economists necessarily employ, internally at least, implicit estimates of the price-cost gap, the employment gap, and the output gap to
evaluate the potential for inflation or deflation. Therefore, gaps ought to be
mentioned more prominently in the Fed’s post-FOMC policy statements and
other important regular policy reports such as the FOMC meeting minutes
and the semiannual monetary policy reports to Congress.30 This would help
to avoid confusion in periods such as the recent past when productivity growth
has been rising and fluctuating widely with substantial effects on employment
and production costs.
In the second half of 2003 the Fed had difficulty convincing financial markets of its inclination to maintain a low federal funds rate for a “considerable
period.”31 One reason for this, in our view, was that its policy statements
emphasized explicitly strong real economic growth during the period but paid
insufficient attention to the sizable gap in employment and the cumulative
deflation in unit labor costs that had almost certainly widened the price-cost
gap. The apparent size and likely persistence of these gaps produced the disinflation that occurred in 2003 and constituted the deflation risk that inclined
the Fed to keep the federal funds rate low.
To sum up, we believe that the Fed has much to gain and little to lose by
referring to price-cost, employment, and output gaps more prominently.32 By
communicating more explicitly in terms of gap indicators, the Fed could clarify
29 See, for example, Orphanides (2002).
30 McCallum (2001) discusses conceptual and operational problems involved in measuring

employment gaps and output gaps, and argues that monetary policy should not respond strongly
to such gaps in its monetary policy rule.
31 These words were employed initially in the policy statement following the August 2003
FOMC meeting. See Ip (2003, August 13). The FOMC dropped the “considerable period” language
at its January 2004 meeting, saying instead that it could be “patient” in raising interest rates.
32 Our recommendation is consistent with evidence presented in Kohn and Sack (2003) that
greater clarity in the Fed’s statements about the economic outlook would improve monetary policy.

J. Alfred Broaddus, Jr., and M. Goodfriend: Sustaining Price Stability

17

substantially its views regarding inflationary or deflationary risks and make
expected future federal funds rates conform more closely to its preemptive
policy intentions.
If the Fed clarifies its short-run policy aims with gap indicators, however,
it is critical that it also discipline itself by announcing an explicit long-run
inflation target to deal with any inconsistencies that may appear between gap
indicators and inflation performance. The Fed should acknowledge its definition of price stability to avoid repeating either the inflationary mistakes of the
1960s and ’70s or the deflationary mistakes of the 1930s.

6.

SUMMARY AND CONCLUSION

In this article, we have sought to provide a framework for thinking about
how monetary policy can maintain price stability. The core principle—taken
from the new neoclassical synthesis—is that inflation will remain low and
stable if and only if firms, on average across the economy, expect departures
from their profit-maximizing markups to be relatively small and transitory.
We explained how interest rate policy works to maintain price stability by
managing aggregate demand to offset the effect on production costs of shocks
to expected future income prospects and current productivity.
Monetary policy is most effective when the public is confident that the
Fed will act to stabilize production costs promptly after a shock—what we
referred to as “credibility” for price stability. When the Fed has credibility,
prices are relatively insensitive to cost shocks on average, since firms expect
the Fed to manage aggregate demand to reverse pressures on costs in either
direction promptly. Credibility anchors expected inflation and enables the Fed
to act aggressively to prevent recessions. On the other hand, we indicated how
the absence of credibility raises the risk of recession whenever the economy
is confronted with either an inflation scare or a deflation scare.
The Fed’s current credibility as an inflation fighter is now firmly established, but the zero bound on interest rate policy impedes the extension of that
credibility, in any straightforward way, to deflation. We pointed out, however,
that ultimately monetary policy must be able to deter deflation at the zero
bound; otherwise, the government could eliminate explicit taxes and finance
all of its expenditure forever with money created by the Fed.
We identified several operational and institutional obstacles that the Fed
should address to make quantitative policy (as opposed to interest rate policy)
credible against deflation at the zero bound. In particular, we pointed out that
in order to secure full credibility against deflation, the Fed will need more
fiscal support for quantitative policy at the zero bound than is usually granted
by the fiscal authorities.
Finally, we offered two recommendations for improving the Fed’s communication policy designed to address the kinds of problems the Fed faced in

18

Federal Reserve Bank of Richmond Economic Quarterly

conveying its concerns about deflation in 2003. First, the Fed should commit
publicly to maintaining core PCE inflation within a target range of 1 to 2 percent over the long run. We think that an inflation target should be regarded,
not just as a policy goal, but as an essential part of communication policy.
Second, the sign, size, and expected persistence of price-cost, output,
and employment gap indicators play a central role in gauging the risks to price
stability and in preempting inflation and deflation. We recommend that the Fed
feature such gap indicators more prominently in its statements and discussions
about policy to clarify the potential for inflation or deflation in its outlook, and
to clarify its intentions for dealing with these threats. We emphasize that the
Fed should announce an explicit inflation target so that it does not stray from
price stability under any circumstances.
The role of monetary policy in halting what seemed to be an inexorable
rise in inflation in the 1970s, and subsequently reducing it during the ’80s and
’90s to an acceptable level, is in our view one of the greatest achievements in
the Fed’s history. We hope that our article will help the Fed to surmount its
next challenge—the maintenance of price stability—in the years ahead.

REFERENCES
Bernanke, Ben S. 2003. “An Unwelcome Fall in Inflation?” Remarks before
the Economics Roundtable, University of California, San Diego; La
Jolla, Calif. (July 23).
Brayton, Flint, Andrew Levin, Ralph Tryon, and John C. Williams. 1997.
“The Evolution of Macro Models at the Federal Reserve Board.”
Carnegie-Rochester Conference Series on Public Policy 47 (December):
43–81. Ed. Bennett McCallum and Charles Plosser.
Broaddus, J. Alfred, Jr., and Marvin Goodfriend. 1996. “Foreign Exchange
Operations and the Federal Reserve.” Federal Reserve Bank of
Richmond Economic Quarterly 82 (Winter): 1–19.
. 2001. “What Assets Should the Federal Reserve Buy?” In
The Fiftieth Anniversary of the Accord: Issues in Treasury-Federal
Reserve Relations, Federal Reserve Bank of Richmond Economic
Quarterly 87 (Winter): 7–22.
Clarida, Richard, Jordi Gal´, and Mark Gertler. 1999. “The Science of
ı
Monetary Policy: A New Keynesian Perspective.” Journal of Economic
Literature 37 (December): 1661–707.
Cole, Harold, and Lee Ohanian. 2001. “New Deal Policies and the

J. Alfred Broaddus, Jr., and M. Goodfriend: Sustaining Price Stability

19

Persistence of the Great Depression: A General Equilibrium Analysis.”
Federal Reserve Bank of Minneapolis, Research Department Working
Paper 597 (May).
Dudley, Bill. 2003. “The Need for Clear Communication.” Goldman Sachs
U.S. Economics Analyst (September 12): 1–6.
Federal Open Market Committee. 1995. Transcript, January 31–February 1:
39–59.
. 1996. Transcript, July 2–3.
Goodfriend, Marvin. 1993. “Interest Rate Policy and the Inflation Scare
Problem: 1979–1992.” Federal Reserve Bank of Richmond Economic
Quarterly 79 (Winter): 1–24.
. 2002. “Monetary Policy in the New Neoclassical
Synthesis: A Primer.” International Finance 5 (Summer): 165–91.
Reprinted in Federal Reserve Bank of Richmond Economic Quarterly
90 (Summer 2004).
. 2004. “Inflation Targeting in the United States?”
Forthcoming in Inflation Targeting, ed. Ben S. Bernanke and Michael
Woodford. Cambridge: National Bureau of Economic Research. Also:
NBER Working Paper 9981 (September 2003).
, and Robert King. 1997. “The New Neoclassical Synthesis
and the Role of Monetary Policy.” NBER Macroeconomics Annual 1997,
ed. Ben S. Bernanke and Julio Rotemberg. Cambridge: MIT Press,
231–83.
. 2001. “The Case for Price Stability.” Why Price Stability?
Proceedings from the First ECB Central Banking Conference, ed. A.
Herrero, V. Gaspar, L. Hoogduin, J. Morgan, and B. Winkler. Frankfurt:
European Central Bank. Also: NBER Working Paper 8423 (August).
Greenspan, Alan. 2003. Federal Reserve Board’s Semiannual Monetary
Policy Report to the Congress, testimony before the Committee on
Banking, Housing, and Urban Affairs, U.S. Senate (July 16).
Ip, Greg. 2003. “Fed Fails to Sway Bond Investors—Yields Rise as Market
Holds to Economic View; Rate Cut Found Lacking.” Wall Street Journal
(June 27): A2.
. 2003. “The Economy: Fed Keeps Interest-Rate Target at
1%—Expected Decision Comes with Surprise Commitment to Continue
Very Low Levels.” Wall Street Journal (August 13): A2.
. 2003. “The Economy: Fed Missed Mark On Impact of Cut
on Bond Market.” Wall Street Journal (August 15): A2.

20

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Kennedy, David. 1999. Freedom from Fear: The American People in
Depression and War, 1929–1945. New York: Oxford University Press.
Kohn, Donald L., and Brian P. Sack. 2003. “Central Bank Talk: Does It
Matter and Why?” Finance and Economics Discussion Series 2003–55,
Board of Governors of the Federal Reserve System.
McCallum, Bennett. 2001. “Should Monetary Policy Respond Strongly to
Output Gaps?” American Economic Review 91 (May): 258–62.
. 2004. “Misconceptions Regarding Rules vs. Discretion for
Monetary Policy.” Cato Journal 23 (Winter): 365–72.
Orphanides, Athanasios. 2002. “Monetary Policy Rules and the Great
Inflation.” American Economic Review 92 (May): 115–20.
, and John C. Williams. 2004. “Imperfect Knowledge,
Inflation Expectations, and Monetary Policy.” Forthcoming in Inflation
Targeting, ed. Ben S. Bernanke and Michael Woodford. Cambridge:
National Bureau of Economic Research. Also: NBER Working Paper
9884 (August 2003).
Woodford, Michael. 2003. Interest and Prices: Foundations of a Theory of
Monetary Policy. Princeton: Princeton University Press.

Monetary Policy in the New
Neoclassical Synthesis: A
Primer
Marvin Goodfriend

G

reat progress was made in the theory of monetary policy in the
last quarter century. Theory advanced on both the classical and
the Keynesian sides. New classical economists emphasized the
importance of intertemporal optimization and rational expectations.1 Real
business cycle (RBC) theorists explored the role of productivity shocks in
models where monetary policy has relatively little effect on employment
and output.2 Keynesian economists emphasized the role of monopolistic
competition, markups, and costly price adjustment in models where monetary policy is central to macroeconomic fluctuations.3 The new neoclassical synthesis (NNS) incorporates elements from both the classical and the
Keynesian perspectives into a single framework.4 This “primer” provides an introduction to the benchmark NNS macromodel and its recommendations for
monetary policy.
The author is Senior Vice President and Policy Advisor.
This article originally appeared in International Finance (Summer 2002, 165–191) and is reprinted in
its entirety with the kind permission of Blackwell Publishing [http://www.blackwellsynergy.com/rd.asp?code=infi&goto=journal]. The article was prepared for a conference, “Stabilizing the Economy: What Roles for Fiscal and Monetary Policy?” at the Council on Foreign
Relations in New York, July 2002. The author thanks Al Broaddus, Huberto Ennis, Mark
Gertler, Robert Hetzel, Andreas Hornstein, Bennett McCallum, Adam Posen, and Paul Romer
for valuable comments. Thanks are also due to students at the GSB University of Chicago,
the GSB Stanford University, and the University of Virginia who saw earlier versions of this
work and helped to improve the exposition. The views expressed are the author’s and not
necessarily those of the Federal Reserve Bank of Richmond or the Federal Reserve System.
Correspondence: Marvin.Goodfriend@rich.frb.org.
1 Lucas (1981) and Ljungqvist and Sargent (2000).
2 Prescott (1986) and Plosser (1989).
3 Mankiw and Romer (1991), Mankiw (1990), and Romer (1993).
4 This primer draws on ideas developed in Goodfriend and King (1997, 2001). See also

Brayton, Levin, Tryon, and Williams (1997), Clarida, Gali, and Gertler (1999), and Woodford
(2003).

Federal Reserve Bank of Richmond Economic Quarterly Volume 90/3 Summer 2004

21

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Federal Reserve Bank of Richmond Economic Quarterly

The article begins in Section 1 by presenting a monopolistically competitive core RBC model with perfectly flexible prices. The RBC core emphasizes
the role of expected future income prospects, the real wage, and the real interest rate for household consumption and labor supply. And it emphasizes the
role of productivity shocks in determining output, the real wage, and the real
interest rate.
The NNS model introduced in Section 2 takes costly price adjustment into
account within the RBC core. In the NNS model, firms do not adjust their
prices flexibly to maintain a constant profit maximizing markup. Instead,
firms let the markup fluctuate in response to demand and cost shocks. Markup
variability plays a dual role in the new neoclassical synthesis. As a guide to
pricing decisions, the markup is central to the evolution of inflation. As a “tax”
on production and sales, the markup is central to fluctuations in employment
and output.
Section 3 locates the transmission of interest rate policy to employment
and inflation in its leverage over the markup. That leverage creates the fundamental credibility problem of monetary policy: the temptation to increase
employment by compressing the markup jeopardizes the central bank’s credibility for low inflation. The nature of the credibility problem is discussed
in Section 3 together with the closely related “inflation scare” problem that
confronts monetary policy in practice.
Section 4 traces the effects on employment and inflation of three types of
disturbances: optimism or pessimism about future income prospects, a temporary productivity shock, and a shift in trend productivity growth. It then
tells how interest rate policy can counteract such shocks. The combination
of rational forward-looking price setting by firms, monopolistic competition,
and RBC components in the benchmark NNS model provides considerable
guidance for interest rate policy. The recommended objectives and operational guidance are developed and presented in Section 5. Section 6 addresses
three challenges to these policy recommendations. Section 7 is a summary
and conclusion.

1. THE CORE REAL BUSINESS CYCLE MODEL
The core monopolistically competitive real business cycle model is presented
in four subsections below: First, the representative household’s optimal lifetime consumption plan is derived, given its lifetime income prospects and
the real rate of interest. Second, household labor supply is derived. Third,
employment and income are determined, taking account of the representative
household’s choice of labor supply, firm profit maximization, and the economy’s production technology. Fourth, the real interest rate is determined,
emphasizing its role in clearing the economy-wide credit market and in coordinating aggregate demand and supply.

M. Goodfriend: Monetary Policy Primer

23

Household Consumption5
The economy is populated by households that live for two periods, the present
and the future.6 Households have lifetime income prospects (y1 , y2 ) and access
to a credit market where they can borrow and lend at a real rate of interest r.
A household chooses its lifetime consumption plan (c1 , c2 ) given its income
prospects and the real rate of interest to maximize lifetime utility subject to
its lifetime budget constraint
c2 = −(1 + r)c1 + (1 + r)x

(1)

y2
1+r

is the present (period 1) discounted value of lifetime
where x = y1 +
income prospects.
A household obtains utility from lifetime consumption according to
U (c1 , c2 ) = u(c1 ) +

1
u(c2 )
1+ρ

(2)

where u(c1 ) is utility from consumption in the present, u(c2 ) is utility from
future consumption, U (c1 , c2 ) is the present discounted value of lifetime utility
from consumption, and ρ > 0 is a constant psychological rate of time discount.
For concreteness we work with log utility: u(c) = log c, so that u (c) = 1/c.
To maximize lifetime utility the household chooses its lifetime consumption plan (c1 , c2 ) so that
c2
(1 + r) = (1 + ρ)
(3)
c1
where the household’s choices for c1 and c2 exhaust its lifetime budget constraint (1).7 Below we see how lifetime income prospects are determined and
how the real interest rate adjusts to reconcile desired aggregate household
consumption with aggregate output.

Household Labor Supply
The representative household must also choose how to allocate its time to
work and leisure. In deciding how much to work, a household takes the real
hourly wage in terms of consumption goods w as given in the labor market.
5 Fisher (1930) and Friedman (1957) pioneered the theory of household consumption.
6 As will become clear below, it is not necessary to specify the length of the two periods in

order to explain the mechanics of the forward-looking benchmark NNS model and its implications
for monetary policy. The features of the NNS model highlighted here are qualitatively consistent
with those of a fully dynamic version of the model specified as a system of difference equations
connecting periods of relatively short duration.
7 To maximize lifetime utility, a household must choose c and c so that what it requires in
1
2
c
future consumption to forgo one more unit of current consumption, (1 + ρ) c2 , equals the interest
1
rate, 1 + r, at which it can transform a unit of current consumption into future consumption by
lending.

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Federal Reserve Bank of Richmond Economic Quarterly

The household has a time budget constraint
l+n=1

(4)

where l is time allocated to leisure, n is time allocated to work, and the amount
of time per period is normalized to 1. A household gets utility directly from
leisure. Leisure taken in the present and the future contributes to lifetime
utility as does consumption. Again we work with log utility so that utility
from leisure is given by v(l) = log l and v (l) = 1/ l.
The allocation of time in a given period that maximizes the household’s
utility is the one for which the marginal utility earned directly by taking leisure
equals the marginal utility earned indirectly by working
1/ l = w/c.

(5)

Using time constraint (4) to eliminate leisure l in (5) we can express
the household’s willingness to supply labor ns as a function of household
consumption c and the real wage w
c
(6)
ns = 1 − .
w
Household labor supply (6) has three important features. First, holding
the wage w constant, household labor supply is inversely related to household
consumption. This makes sense because if the household is able to consume
more goods, say, because its lifetime income prospects have improved, then
it will wish to consume more leisure as well. Second, holding consumption
fixed, labor supply varies directly with the real wage. This also makes sense
because, other things the same, a higher hourly wage increases the opportunity
cost of leisure and makes work more attractive. Third, if both consumption
and the real wage rise equiproportionally, then the effects on labor supply
are exactly offsetting. We see below that this last feature of labor supply is
important to account for some aspects of long-run economic growth.

Firms, Employment, and Output
There are a large number of firms in the economy, each producing a different
variety of consumption goods. Because their products are somewhat different,
firms are monopolistically competitive. Each firm has enough pricing power
in the market for its own output that it can sustain a price somewhat above
the marginal cost of production. Firms face a constant elastic demand for
their products, which means that the profit maximizing markup of price over
marginal cost is a constant µ∗ > 1, invariant to shifts in demand or in the cost
of production.8 For the remainder of Section 1, we assume that firms adjust
their prices flexibly to maintain the constant profit maximizing markup µ∗ at
8 This point can be verified with a little algebra.

M. Goodfriend: Monetary Policy Primer

25

all times. The demand for all varieties of goods is symmetric, so consumption
is treated as a single composite good.
Firms produce consumption goods c from labor input n according to the
production technology
c =a·n

(7)

where a is labor productivity per hour in units of consumption goods. Productivity a fluctuates and grows over time with technological progress.
The markup of price over the marginal cost of production is defined as
P
(8)
MC
where P is the dollar price of a unit of consumption goods, and MC is the cost
in dollars of producing a unit of consumption goods. According to production
technology (7), 1/a hours of work is needed to produce a unit of c. If the
hourly wage is W dollars, then the marginal cost in dollars (unit labor cost) of
producing a unit of consumption goods is W/a. Substituting for MC in the
definition of the markup and rearranging yields
a
a
µ=
=
(9)
W/P
w
µ=

where w is the real wage.
Note that (9) uses only the production technology and the definition of
the markup to express the markup µ in terms of productivity a and the real
wage w. We see immediately from (9) that the equilibrium real wage w ∗ is
determined as
w ∗ = a/µ∗ .

(10)

If firms adjust their product prices to maintain markup constancy, the
real wage grows and fluctuates only with productivity a. Since the profit
maximizing markup exceeds unity, µ∗ > 1, the real wage is less than labor
productivity w∗ < a. Firms are content to stop hiring before bidding the real
wage up to the marginal product of labor because they maximize monopoly
profit by restricting their own output somewhat.
To determine equilibrium employment n∗ , use (7) and (10) to substitute
for c and w in labor supply function (6)
a·n
ns = 1 −
(11)
a/µ∗
and equate desired labor supply ns to labor utilized by firms n to find equilibrium employment n∗
n∗ =

1
.
1 + µ∗

(12)

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Federal Reserve Bank of Richmond Economic Quarterly

Notice that equilibrium employment n∗ depends only on the profit maximizing markup µ∗ and not on productivity a. The reason is that productivity a
affects consumption c and the real wage w proportionally given hours worked
n, so that the productivity effects operating through consumption and the real
wage in labor supply function (6) are exactly offsetting. This feature of the
core RBC model is necessary to account for some fundamental facts about
long-run economic growth. For instance, labor productivity in the U.S. economy has grown by more than 2 percent per year for over 100 years; and output
and the real wage have both grown at roughly the same rate. Yet the fraction of
time allocated to work has changed relatively little during that same period.9
Equilibrium output c∗ is determined from production technology (7) and
equilibrium employment (12) as
c∗ = a ·

1
1 + µ∗

(13)

where output c∗ grows and fluctuates proportionally with productivity a.

The Real Interest Rate: Coordinating Demand with Supply10
To complete our understanding of the core RBC model, we must check that
households have sufficient income to purchase all the consumption goods that
firms produce each period and that households can be induced to choose a
lifetime consumption plan that matches the current and future production of
consumption goods. The real interest rate plays the central role in aligning
the demand and supply of consumption goods over time.
Households have two sources of income. First, there is wage income
which equals the real wage multiplied by hours worked, wn. Second, there
is profit income which equals firms’ revenue from sales minus the wage bill,
an−wn. Profits are positive because w < a. Since households own the firms,
total household income each period is the sum of wage income and profit
income wn + (an − wn) = an, which is exactly the value of consumption
goods produced and sold each period. Thus, households do indeed earn enough
income each period to buy the goods produced in each period. It follows
that the lifetime consumption plan (c1 , c2 ) that matches the current and future
1
1
∗
∗
supply of consumption goods given by (13), c1 = a1 · 1+µ∗ and c2 = a2 · 1+µ∗ ,
also satisfies the lifetime budget constraint (1).
The real interest rate r ∗ that makes desired lifetime consumption match
the intertemporal supply of consumption goods is found by substituting the
9 Romer (1989).
10 Fisher (1930).

M. Goodfriend: Monetary Policy Primer

27

∗ ∗
current and future supply of consumption goods (c1 , c2 ) into condition (3)
∗

(1 + r ) = (1 + ρ)

a2 ·
a1 ·

1
1+µ∗
1
1+µ∗

= (1 + ρ)

a2
a1

(14)

where we see that the equilibrium real interest rate r ∗ varies directly with the
growth of labor productivity, a2 .
a1
One can understand the determination of the real interest rate as follows:
When productivity is stagnant (a1 = a2 ), households are satisfied with a flat
lifetime consumption plan as long as the real interest rate equals the psychological rate of time preference (r ∗ = ρ). In that case, the return to lending
exactly offsets the preference for consuming in the present. On the other
hand, if future productivity is expected to be higher than current productivity (a1 < a2 ), then households want to borrow against their brighter future
income prospects to bring some consumption forward in time. In the aggregate, however, households cannot do so because the future productivity has
not yet arrived. As households try to borrow against the future, they drive
the real interest rate up to the point where they are satisfied with the steeply
sloped consumption plan that matches the growth of productivity. The equilibrium real interest rate clears the economy-wide credit market by making
the representative household neither a borrower nor a lender. In so doing, the
equilibrium real interest rate also clears the economy-wide goods market by
inducing the representative household to spend its current income exactly.

2. THE NEW NEOCLASSICAL SYNTHESIS
The new neoclassical synthesis (NNS) builds on the core real business cycle (RBC) model to provide an understanding of fluctuations in employment
and inflation and a framework for thinking about monetary policy. The main
departure is that firms do not adjust their product prices flexibly in the NNS
model to maintain a constant profit maximizing markup. Consequently, the
markup fluctuates in response to shocks to aggregate demand and productivity. The remainder of Section 2 explains why markup variability is central
to fluctuations in inflation and employment in the benchmark NNS model.
Section 3 discusses how monetary policy exerts its leverage over employment
and inflation through the markup. Section 4 considers various shocks in the
NNS model and explains how interest rate policy actions can counteract them.
The recommendations for monetary policy implied by the benchmark NNS
model are spelled out in Section 5.

Firm Pricing Practices, Inflation, and the Markup
It is costly for a firm producing a differentiated product to determine the price
that maximizes its profits at each point in time. Pricing requires information

28

Federal Reserve Bank of Richmond Economic Quarterly

on a firm’s own demand and cost conditions that is costly to obtain. Moreover, that information needs to be assessed and processed collectively by top
management. Management must prioritize pricing decisions relative to other
pressing concerns, so pricing decisions get the attention of management only
every so often.11 Hence, a firm considers whether to change its product price
only when demand or cost conditions are expected to move the actual markup
significantly and persistently away from the profit maximizing markup. For
instance, if higher nominal wages W , or lower productivity a were expected
to compress the markup significantly and persistently, then it would be in
the firm’s interest to consider raising its product price to restore the profit
maximizing markup.
These points can be summarized in four pricing principles:
1) Firms would like to keep their actual markup µ as close to the profit
maximizing markup µ∗ as they can over time, subject to the cost of changing
their product prices.
2) Firms must balance the one-time cost of changing prices against the
benefit of staying close to the profit maximizing markup over time.
3) A firm is more apt to change its product price to restore the profit
maximizing markup the larger and more persistent it expects a deviation of its
actual markup from the profit maximizing markup to be.
4) Firms move their prices with expected inflation on average over time.
The implications of these pricing principles for the economy-wide rate of
inflation π may be summarized as follows:
π = INF(µ1 , Eµ2 ) + Eπ

(15)

where Eπ is the expected trend rate of inflation, and INF(µ1 , µ2 ) is a function
indicating the effect of the current and expected future markup on inflation.12
When the current and expected future markup both equal the profit maximizing markup, then firms move their prices in accordance with expected trend
inflation Eπ , i.e., INF(µ∗ , µ∗ ) = 0. Markup compression (µ < µ∗ ) moves
actual inflation above trend inflation, and markup expansion (µ > µ∗ ) moves
actual inflation below trend inflation.
We characterize increasingly inflationary situations as follows:
A) Absolute Price Stability: µ1 = Eµ2 = µ∗ , Eπ = 0. Current and
expected future markups equal the profit maximizing markup, and expected
trend inflation is zero.
11 Calvo (1983) models price stickiness by assuming that a firm gets opportunities to change

its price on a stochastic basis; this accords with the description of price-setting given here.
12 Calvo’s (1983) pricing model yields a forward-looking inflation process approximately like
(15). See the discussions and derivations in Clarida, Gali, and Gertler (1999), Gali and Gertler
(1999), Goodfriend and King (1997, 2001), and Taylor (1999).

M. Goodfriend: Monetary Policy Primer

29

B) Low Inflation Potential: µ1 < µ∗ , Eµ2 = µ∗ , Eπ = 0. Current
markup is compressed relative to the profit maximizing markup, but the expected future markup is not, and expected trend inflation is still zero.
C) Modest Inflation Potential: µ1 < µ∗ , Eµ2 < µ∗ , Eπ = 0. Markup
compression is expected to persist, but expected trend inflation is still zero.
D) Persistent Trend Inflation: µ1 = Eµ2 = µ∗ , π = Eπ > 0. Current
and expected future markups are at their profit maximizing levels, but expected
trend inflation is positive.

Employment Fluctuations and the Markup
Inflation today is reasonably low and stable in the United States and around the
developed world. Hence, we consider the nature of employment fluctuations
in the NNS model in terms of situations A and B above. In other words, we
suppose that the current markup may be compressed or elevated relative to
the profit maximizing markup, but firms do not expect that gap to persist for
very long. And firms expect zero inflation. The central bank is said to have
“credibility for zero inflation” in these situations. When the central bank has
credibility for zero inflation, firms are disinclined to raise or lower their product
prices in response to a shock to their current markup because they expect the
markup shock to be temporary.13 In such circumstances, the current price level
P is nearly invariant to current shocks or current monetary policy actions.14
In this case current employment and output are determined by the aggregate demand for goods. The reason is two-fold. First, each firm faces
a downward sloping demand for its particular variety of consumption good,
and a firm can sell only as much as households wish to purchase at the going
price. Second, firms are happy to produce and sell as much as households
are willing to buy because labor productivity exceeds the real wage. Hence,
holding product price constant, profits rise with employment, production, and
sales. Since firms can’t sell more than demand will allow and firms are happy
to accommodate demand, aggregate demand governs output in the short run,
and output governs employment given labor productivity.15
We can understand the determination of employment in the benchmark
NNS model from either a Keynesian or a classical perspective. The Keynesian
13 Markup shocks are expected to be transitory because monetary policy is expected to make
them so. See Sections 4 and 5 below.
14 The price level is nearly invariant to current economic conditions because firms choose not
to adjust their product prices to maintain markup constancy. Firms would adjust their prices to
restore markup constancy if they expected that otherwise their markups would deviate persistently
and significantly from the profit maximizing markup. Prices are less flexible in the NNS model
the more confident are firms that monetary policy will manage nominal cost conditions so as to
maintain their profit maximizing markup without any price adjustments. Hence, credibility for low
inflation reinforces price stickiness in the NNS model.
15 Blanchard and Kiyotaki (1987).

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Federal Reserve Bank of Richmond Economic Quarterly

transmission mechanism runs from aggregate demand to employment. The
production technology c = an shows how employment n depends on aggregate demand c and labor productivity a. Firms attract enough labor to meet
demand given labor productivity by offering a nominal wage W sufficient to
induce households to supply the required labor input. Since the price level P
is nearly invariant to current economic conditions, the higher nominal wage
raises the real wage w. According to labor supply function (6) given aggregate
demand c, a higher real wage increases labor supply by raising the opportunity
cost of leisure. When demand falls and firms need less labor, wages fall since
enough labor supply is forthcoming at a lower real wage.
The classical perspective takes the view that actual employment n must
equal labor willingly supplied by households ns regardless of the strength of
aggregate demand. Working in this direction, substitute c = an and w = a/µ
into labor supply function (6), equate n and ns , and solve for employment to
arrive at
1
n=
.
(16)
1+µ
From the classical perspective, employment in the NNS model is determined inversely with the markup, exactly as in the core RBC model.16 The only
difference is that firms adjust their prices continually to maintain a constant
profit maximizing markup µ∗ in the flexible price RBC model and markup
constancy stabilizes aggregate employment in that case. When circumstances
are such that the price level P is sticky in the NNS model, however, the
markup fluctuates with the real wage and labor productivity according to (9),
and employment fluctuates as well according to (16).
Employment varies inversely with the markup in (16) because the markup
drives a wedge between the price of consumption goods and the marginal cost
of production. In effect, the markup is a percentage sales tax administered by
firms, the proceeds of which are distributed as profits to households. As is the
case for any tax, a higher tax rate reduces the supply of the good being taxed,
and a lower tax rate expands the supply of that good. Hence, a compressed
markup expands (and a higher markup contracts) the production and sale of
consumption goods. Alternatively, recall from (9) that a higher markup means
a lower real wage relative to labor productivity; so the markup also acts like
a tax on labor supply because it drives the real wage below the marginal
product of labor. Thus, the labor market perspective provides another way
of understanding why employment fluctuates inversely with the markup. The
classical perspective is compatible with the Keynesian perspective because
the markup shrinks when the wage rises to attract more labor in order to
accommodate an increase in aggregate demand.
16 Rotemberg and Woodford (1999).

M. Goodfriend: Monetary Policy Primer

31

It is useful to sum up this way: In the flexible price RBC model firms
neutralize the effect of aggregate demand and productivity shocks on aggregate employment by adjusting their prices to maintain markup constancy. The
flexible price RBC model is classical in the sense that aggregate output is
determined independently of aggregate demand. We saw in Section 1 that
the real interest rate adjusts in the flexible price RBC model to make household demand for aggregate consumption conform to the aggregate supply of
consumer goods. In the NNS model, fluctuations in aggregate demand can
induce fluctuations in employment and output. In that sense the NNS model is
Keynesian. But since the NNS model has the classical RBC model at its core,
we call it the new neoclassical synthesis, recalling Paul Samuelson’s designation for the original attempt to synthesize classical and Keynesian economics
in the 1950s. Since firms maintain the profit maximizing markup on average over time in the NNS model, the NNS model behaves like the flexible
price RBC model on average but with leeway for monetary policy to influence
aggregate demand and stabilize employment and inflation.

3.

INTEREST RATE POLICY, CREDIBILITY,
AND INFLATION SCARES

As is common practice, assume that the central bank implements monetary
policy in the NNS model with a short-term nominal interest rate policy instrument R. By definition, the real interest rate r is R − Eπ , the money
interest rate paid or earned on a loan above and beyond the compensation for
expected inflation. In practice, a central bank’s influence over the real interest
rate is limited for two reasons. It exercises direct control of only the nominal rate. Expected inflation is variable, possibly highly variable if the central
bank has little credibility for low inflation, so control of the nominal interest
rate translates loosely into control of the real interest rate. Moreover, longerterm interest rates are what matter for economic activity, and a central bank
influences long-term interest rates only indirectly via the management of its
short-term nominal interest rate policy instrument. We ignore these important
complications to focus on the essence of interest rate policy in what follows.
In order to understand the mechanism through which interest rate policy
actions are transmitted to the economy, we must first specify the context in
which policy is acting. Continue to assume that the central bank has credibility
for zero inflation so that Eπ = 0 and the price level P is nearly invariant to
current shocks and interest rate policy actions. In this case the central bank’s
choice of nominal interest rate target R translates into a target for the real
interest rate r. Moreover, in this case the public expects the future markup to
be at its profit maximizing level Eµ2 = µ∗ . Recall that current and future
productivity (a1 , a2 ) are given by technology, independently of interest rate

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Federal Reserve Bank of Richmond Economic Quarterly

policy. In this context, (13) says that expected future household consumption
1
∗
is anchored by future income prospects at c2 = a2 1+µ∗ .
In order to trace the effect of an interest rate policy action on current
macroeconomic variables, use (3) to express current desired consumption c1
1
∗
in terms of expected future consumption c2 = a2 1+µ∗ and the real interest rate
target r
c1 =

1+ρ
1
.
· a2
1+r
1 + µ∗

(17)

Expression (17) reveals the nature of the leverage that interest rate policy
exerts on aggregate demand: Current consumption c1 is inversely related to
the real interest rate target r when expected future consumption is anchored
1
at a2 1+µ∗ . An increase in the real interest rate target depresses current aggregate demand by raising the opportunity cost of current consumption in terms
of future consumption. The contraction in aggregate demand is reflected in
reduced current employment n1 , a low current real wage w1 , and an elevated
current markup µ1 . Conversely, a cut in the real interest rate target expands
current aggregate demand, raises the real wage, and compresses the markup.
The transmission mechanism can be understood from either the Keynesian
or the classical point of view. From the Keynesian perspective, interest rate
policy exerts leverage over employment and output because production is demand determined in the short run. From the classical perspective, that leverage
derives from the fact that aggregate demand influences wages, which in turn
influence the markup, which behaves like a variable tax rate in the RBC setting.
The leverage that interest rate policy actions exert on employment creates
the fundamental credibility problem of monetary policy. The credibility problem arises from a basic tension in the new neoclassical synthesis. On one hand,
firms set their prices so as to maintain a profit maximizing markup on average
over time. From the household’s point of view, however, the markup acts like a
tax on consumption and labor supply that reduces welfare. Therefore, the central bank has an incentive to pursue expansionary monetary policy on behalf
of households to undo the markup tax. That temptation is greatest when the
central bank’s credibility for low inflation is most secure, since then employment can be expanded with little immediate increase in inflation or inflation
expectations. The problem is that by giving in to this temptation the central
bank undercuts its own credibility. If firms come to expect the markup to be
compressed persistently, they will raise prices to restore the profit maximizing
markup. Inflation and inflation expectations will rise, and the central bank
will lose credibility for low inflation. In short, credibility for low inflation
is fundamentally fragile in the new neoclassical synthesis because the public recognizes the central bank’s temptation to pursue expansionary monetary
policy to depress the markup and expand employment.17
17 Barro and Gordon (1983), Chari, Kehoe, and Prescott (1989), and Sargent (1986) discuss
credibility issues in models other than those of the new neoclassical synthesis.

M. Goodfriend: Monetary Policy Primer

33

From time to time the public comes to doubt the central bank’s commitment to low inflation. The history of monetary policy in the United States
contains numerous “inflation scares” marked by sharply rising long-term bond
rates reflecting increased expected inflation premia.18 Inflation scares create
a fundamental dilemma for monetary policy. At the initial nominal interest
rate target R, expected higher inflation lowers the implied real interest rate
target r = R − Eπ and exacerbates the inflation scare by stimulating current
demand and compressing the markup. The central bank could raise R just
enough to offset the effect of expected higher inflation on the real rate. However, neutralizing the effect of higher inflation expectations on the real interest
rate target does nothing to fight the collapse of credibility itself.
If the inflation scare persists, a central bank must react by raising its real
interest rate target. That is, the central bank must raise R by more than the
increase in Eπ . A higher real interest rate target counteracts the inflation scare
by contracting current aggregate demand, reducing employment, lowering real
wages, and widening the markup. According to (15), tight monetary policy
works by elevating the current and expected future markup significantly above
the profit maximizing markup. In the contractionary environment, firms move
prices up more slowly than expected inflation, and expected inflation comes
down as credibility for low inflation is restored.
Inflation scares are costly because ignoring them or raising R only enough
to cover the increase in Eπ can encourage even more doubt about the central
bank’s commitment to low inflation. But raising r to restore credibility for
low inflation only works by contracting employment, output, and consumption to widen the markup significantly and persistently enough to encourage
firms to slow the rate of inflation. For this reason, central banks have been
reluctant to react promptly to inflation scares. In the past such hesitation led
to “stagflation,” when rising inflation encouraged by insufficiently preemptive
policy would eventually be accompanied by a period of rising unemployment
after the central bank set out to restore its credibility for low inflation.

4.

FLUCTUATIONS AND STABILIZATION POLICY

In this section we consider three shocks that cause fluctuations in employment
and output because firms choose not to adjust prices to maintain markup constancy. Again we assume that the central bank has credibility for low inflation.
Inflationary situations A or B prevail, there are no inflation scares, and the current price level P is nearly invariant to current economic shocks and interest
rate policy actions. We consider the effects of optimism or pessimism about
future income prospects, a temporary productivity shock, and a shift in trend
18 See Goodfriend (1993) and Chari, Christiano, and Eichenbaum (1998).

34

Federal Reserve Bank of Richmond Economic Quarterly

productivity growth. In each case we trace the effect of the shock holding the
central bank’s real interest rate target fixed, then we consider how interest rate
policy might react to stabilize employment and inflation.

Optimism and Pessimism about Future Income Prospects
According to the analysis of consumption in Section 1, a household plans
lifetime consumption to satisfy (3) and to exhaust its lifetime budget constraint
(1). Using these two conditions, we can write current aggregate demand c1 in
terms of lifetime income prospects (y1 , y2 ) and the central bank’s real interest
rate setting r
c1 =

1+ρ
y2
(y1 +
).
2+ρ
1+r

(18)

Since current output and income are demand determined when the price
level P is nearly invariant to current shocks and policy actions, we can set
y1 = c1 in (18) and solve for c1 in terms of y2 and r
1+ρ
· y2 .
(19)
1+r
According to (19), households transmit increased optimism or pessimism
about future income prospects y2 (whether in future wage or profit income) to
current consumption, employment, and output. The reason is that households
want to allocate any expected change in lifetime resources to both current
and future consumption. Moreover, because current income is demand determined, there is a secondary (multiplier) effect on current income that amplifies
the initial impact of increased optimism or pessimism about the future. Both
the primary and secondary effects are captured in (19).
Although households react to increased optimism or pessimism by attempting to borrow or lend in the credit market, ultimately any change in
current aggregate demand must be reflected in an equal change in current production. Collectively, households cannot borrow from the future to consume
more in the present because it is impossible to bring goods forward in time.
Nor is it possible to store goods for future consumption in this benchmark
NNS model. However, the real interest rate does not react to conditions in
the credit market because the central bank intervenes by injecting or draining
cash to maintain its nominal interest rate target R. In so doing, interest rate
policy actually facilitates the transmission of optimism or pessimism about
the future to current employment and output.
In principle, interest rate policy can counteract the effect on current employment and output of increased optimism or pessimism about the future.
For instance, according to (19), a lower real interest rate target r can stabilize
current consumption, employment, and output against increased pessimism
about future income prospects. At best, however, stabilization policy can only
c1 =

M. Goodfriend: Monetary Policy Primer

35

be partially effective because it is difficult to recognize shocks promptly and
because policy actions affect spending with a lag.

A Temporary Productivity Shock
Aggregate productivity grows on average over time as a result of technological progress. However, productivity growth fluctuates over time because the
invention and implementation of technological improvements do not occur
smoothly. We can think of a temporary shock to productivity as involving a
period in which productivity grows more rapidly or more slowly than its longrun average, but is expected to return shortly to its long-run growth path. To
analyze the effect of a temporary productivity shock in the benchmark NNS
model, we abstract from trend productivity growth and consider a shortfall of
current productivity a1 with no effect on expected future productivity a2 .
The adverse shock to current productivity expected to be temporary has
little effect on lifetime income prospects and, therefore, on current aggregate
demand. Hence, the negative productivity shock causes firms to hire more
labor to meet the initial demand. Real wages rise as firms bid for more labor.
Household wage income rises at the expense of profit income, but aggregate
real income remains largely unchanged.
The markup is compressed directly because lower productivity raises
marginal cost and indirectly because the real wage is elevated. Firms are
inclined to raise prices to restore the profit maximizing markup, but the price
level does not change much if the negative productivity shock is not too large
and is expected to be temporary.
Again the central bank can stabilize employment and inflation fully, in
principle. According to (14) and (17), it does so by raising the real interest rate
to contract current aggregate demand enough to stabilize the current markup
at µ∗ . When the markup is stabilized, current output, income, consumption,
and the real wage all fall proportionally with productivity.

A Shift in Trend Productivity Growth
To understand the effect of shifting trend growth, suppose that current and
future productivity are related by a2 = (1 + g) · a1 , where g is the trend growth
rate, and current productivity a1 is taken as given. Assume that interest rate
policy is expected to keep the actual markup at the profit maximizing markup
in the future so that µ2 = µ∗ . In this case, future income prospects vary
1
directly with the growth rate g since y2 = (1 + g)a1 1+µ∗ .
Shifting trend productivity growth affects current variables in the same
way as changing optimism or pessimism about future income prospects. Substituting the above expression for y2 into (19), we see that for a given real
interest rate target r, current aggregate demand, output, and employment all

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Federal Reserve Bank of Richmond Economic Quarterly

move in the same direction as the trend growth rate g. For instance, an increase in trend growth raises current aggregate demand, raises current labor
demand, raises the real wage, and compresses the markup. Contrary to popular belief, an increase in trend productivity growth is inflationary at the initial
real interest rate target because it compresses the current markup.
According to (14) the central bank can stabilize the current markup, employment, and inflation against a shift in trend productivity growth by moving
its real interest rate target point for percentage point with the growth rate g. To
see this, substitute (1 + g)a1 for a2 in (14) and note that r ∗ =ρ + g.19 Higher
trend growth requires a higher real interest rate target to give households an
incentive not to consume the proceeds prematurely. Instead of providing a
reason to keep interest rates low, higher trend productivity growth actually
requires a higher real interest rate target on average over time to stabilize the
markup and maintain credibility for low inflation.

5. WELFARE MAXIMIZING MONETARY POLICY
The benchmark NNS model presented here recommends that interest rate
policy should stabilize the markup at its profit maximizing level in order to
stabilize the price level and make employment and output behave as in the core
RBC model with perfectly flexible prices. The recommended policy is referred
to as “neutral” because it stabilizes the price level, neutralizes fluctuations in
employment and output that would otherwise occur due to sticky prices, and
makes aggregate demand conform to fluctuations in productivity as in a pure
real business cycle.
Neutral monetary policy is recommended because it maximizes household
welfare.20 This can be understood in four steps:
1) The central bank can only stabilize the markup at the value that maximizes firm profits µ∗ . Firm price adjustments will undo any attempt by the
central bank to move the markup permanently away from µ∗ .
2) It is feasible for monetary policy to stabilize the markup at µ∗ . Interest
rate policy can do so by making aggregate demand c conform to movements
in productivity a given the production technology c = an so as to stabilize
1
employment at n∗ = 1+µ∗ .
3) Household labor supply ns is invariant to productivity a when the
markup is stabilized at its profit maximizing value µ∗ . A greater abundance of consumption makes households want to take more leisure, but a
higher real wage raises the opportunity cost of leisure just enough to neutralize the overall effect of productivity on desired labor supply. Thus, household
19 The approximate one-for-one correspondence is an implication of log utility.
20 Goodfriend and King (1997, 2001), Ireland (1996), and Woodford (2003).

M. Goodfriend: Monetary Policy Primer

37

welfare is maximized when consumption moves with productivity at the profit
maximizing markup.
4) Household welfare would be reduced if monetary policy were to allow
the markup µ to fluctuate around the profit maximizing markup µ∗ . It is true
that households would be better off in periods when the markup tax is low.
But the markup tax would have to average as much time above as below µ∗ to
be consistent with firm profit maximization on average over time. With diminishing marginal utility, the utility gain from above average consumption and
leisure would be insufficient to offset the utility loss from below average consumption and leisure. Among other things, such logic means that interest rate
policy would reduce welfare if it moved the markup to smooth consumption
against productivity shocks.
The key characteristics of neutral monetary policy are these:
First, neutral policy stabilizes employment at the “natural rate,” n∗ =
1
.21 In effect, neutral policy enables the macroeconomy to operate as if
1+µ∗
firms adjusted their prices costlessly and continuously to maintain the profit
maximizing markup at all times.
Second, when employment is stabilized at the natural rate n∗ , actual output
moves with “potential output” y ∗ = an∗ , where potential output grows and
fluctuates over time with productivity a. In other words, neutral policy aims to
eliminate the “output gap,” the difference between actual and potential output.
Third, the consistent pursuit of neutral policy perpetuates low inflation
according to (15) if the central bank has already attained credibility for low
inflation by its past policy actions.
Fourth, low inflation confers a number of benefits in addition to its consistency with neutral policy.22 For instance, low inflation produces low nominal
interest rates and less economization on the use of currency; low inflation
minimizes costly pricing decisions; low inflation minimizes relative price distortions; and low inflation guards against disruptive inflation scares.
Fifth, a central bank can implement neutral policy by maintaining price
stability. There is no need to target the profit maximizing markup directly in
practice. The reason is that an economy in which firms show little inclination
to raise or lower prices on average is one in which the profit maximizing
markup is realized on average.
Sixth, price stability can be maintained by consistently raising the real
interest rate target to preempt inflation and lowering it to preempt deflation.
In practice, interest rate policy should utilize measures of the output gap,
employment relative to the natural rate, and unit labor costs to help recognize
and preempt potential departures from price stability.23
21 Friedman (1968).
22 Khan, King, and Wolman (2003).
23 McCallum (1999).

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Federal Reserve Bank of Richmond Economic Quarterly

Seventh, according to (14) the real interest rate target r that consistently
achieves price stability shadows the real interest rate r ∗ that supports pure
real business cycles. Price stability must be maintained by activist interest
rate policy that makes aggregate demand conform to potential output to keep
µ = µ∗ , and makes the real interest rate move with expected productivity
growth a2 /a1 .
Eighth, an inflation target facilitates the implementation of neutral monetary policy in three ways.24 An inflation target mandated by the legislature
helps secure credibility for low inflation against the temptation to stimulate
employment excessively. A mandated target for low inflation reduces the incidence of destabilizing inflation or deflation scares. And an inflation target
enables the central bank to cut its interest rate instrument more aggressively to
stimulate economic activity when necessary without fear of an inflation scare.

6.

CHALLENGES TO THE POLICY RECOMMENDATIONS

According to the benchmark NNS model, credible price stability keeps output
at its potential and employment at its natural rate. So from this perspective
even those who care mainly about output and employment can support strict
inflation targeting. Yet the benchmark NNS model presented in this paper is
only one of many possible specifications of the new synthesis model. Taking
other features of the macroeconomy into account might overturn the strong
implication that price stability is always welfare-maximizing monetary policy.
The purpose of this section is to consider briefly three additional aspects of
the macroeconomy and whether they call for optimal departures from strict
inflation targeting.25

Nominal Wage Stickiness
Empirical studies of wage and price dynamics suggest that nominal wages
exhibit about the same degree of temporary rigidity as do nominal prices.26
Yet, nominal wages are perfectly flexible in the benchmark NNS model and
are determined in perfectly competitive labor markets. So it is worth asking
to what extent nominal wage stickiness might overturn the strict inflation targeting policy prescription. Consider a temporary adverse productivity shock.
With flexible nominal wages, stabilization of the markup and the price level
24 Bernanke, Laubach, Mishkin, and Posen (1999), Haldane (1995), Leiderman and Svensson

(1995), and Svensson (1999).
25 Goodfriend and King (2001) consider a number of reasons to depart from perfect markup
constancy and price stability in an NNS model: fully dynamic multi-period pricing, distortions
involving monetized exchange, variable labor supply elasticities, and government spending shocks.
They argue that optimal departures arising from these sources are likely to be quantitatively minor.
26 Taylor (1999).

M. Goodfriend: Monetary Policy Primer

39

calls for aggregate demand to contract proportionally with productivity. At
the optimum, employment is unchanged because the markup is perfectly stabilized. The nominal and the real wage both fall with productivity, exactly
offsetting the effect of lower productivity on marginal cost and the markup.
And the economy settles temporarily at the reduced potential output with a
perfectly stabilized price level.
Things don’t work out as neatly if nominal wages are sticky. In order to
maintain price stability, monetary policy must now steer output below potential. Monetary policy must push employment below the natural rate to offset
the adverse effect of lower productivity on marginal cost. This is possible because labor is more productive at the margin the less it is utilized, i.e., there is
diminishing marginal physical product of labor.27 In the presence of nominal
wage stickiness it is no longer feasible for monetary policy to both stabilize
the price level and keep output at potential. In principle, then, a negative
productivity shock could present the central bank with a short-run tradeoff
between price stability and output stability (relative to potential) when both
nominal wages and prices are sticky. In general, such a tradeoff would call
for a departure from strict inflation targeting.
There are two reasons, however, why such situations should be of relatively
little concern in practice. First, an inflation target between 1 and 2 percent
per year and trend productivity growth of around 2 percent produces average
nominal wage growth in the 3 to 4 percent range. Such high average nominal
wage growth should keep the economy safely away from situations in which
significant downward nominal wage rigidity, as opposed to slower nominal
wage growth, is required to keep price inflation on target and output at its
potential.28 If the economy were to suffer a protracted productivity growth
slowdown, then the central bank could stick to its inflation target and maintain
markup constancy by allowing slower nominal wage growth to match the
slower productivity growth. Downward nominal wage stickiness should not
present a problem in this case. Upward nominal wage stickiness would not
cause problems either. If nominal wages were temporarily rigid upward in the
face of a favorable productivity shock, then the central bank could stick to its
inflation target by steering the economy temporarily above potential output.
Second, implicit or explicit long-term relationships govern most labor
transactions in developed economies. For reasons analogous to those discussed in Section 2, it can be efficient for firms to fix nominal wages for a
period of time and to consider wage changes only at discrete intervals. Yet it
would be inefficient for either firms or workers to allow temporary nominal
27 Production technology (7) is specified as linear in labor for expositional purposes only.
A more realistic specification such as c = a(n)α , 1>α>0, would exhibit diminishing marginal
product of labor.
28 Vinals (2001).

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Federal Reserve Bank of Richmond Economic Quarterly

wage rigidity to upset the terms of otherwise efficient long-term relationships.
And there is scope for firms and workers to neutralize the effect of wage
stickiness since wages already resemble installment payments in the context
of long-term relationships.29 Hence, firms and workers could be expected to
arrange future transactions to undo any effects of nominal wage stickiness.30
If the price level is stabilized in the face of a negative productivity shock,
those firms whose nominal wage is temporarily sticky will appear to pay an
excessive real wage. However, this logic suggests that non-adjusting firms
record a “due from” to be transferred from workers to the firm in the future.
In this way, “effective” real wages fall as much for firms that do not adjust
their nominal wages as for those firms that do adjust. To the extent that such
behavior is widespread, there is little reason to depart from strict inflation
targeting because nominal wages are sticky.31
From this perspective the consequences for monetary policy of stickiness
in wages and prices are sharply different. We can expect firms and workers to neutralize the allocative consequences of temporarily sticky nominal
wages in the context of long-term relationships in the labor market. But spot
transactions predominate in product markets. There, temporarily sticky prices
can cause the average markup to fluctuate significantly and persistently over
time with adverse consequences for employment and inflation. The adverse
consequences of temporarily sticky product prices need to be eliminated by
neutral monetary policy that supports price stability.

Extreme Asset Price Fluctuations
Some analysts suggest that interest rate policy should react directly to asset
prices in order to preempt extreme fluctuations such as those experienced in
Japan and the United States in recent years.32 They would urge a central
bank to take such action even if it has full credibility for low inflation. Such
advice amounts to a recommendation to risk recession or deflation in order
to preempt what may become an unsustainable increase in asset prices. It is
certainly debatable whether that risk would ever be worth taking.
The main problem with this recommendation, however, is that it is virtually
impossible to put into practice.33 The reason boils down to this: When asset
prices first appear to be surprisingly elevated, the central bank is disinclined
to react directly to them because asset prices are not yet so high as to be
29 Hall (1999).
30 Barro (1977).
31 Goodfriend and King (2001).
32 Interest rate policy ordinarily takes indirect account of asset prices in so far as they help

forecast aggregate demand.
33 Bernanke and Gertler (1999), Goodfriend (2003), and Greenspan (2002).

M. Goodfriend: Monetary Policy Primer

41

clearly unsustainable. However, interest rate policy cannot react aggressively
to asset prices after they become clearly unsustainable either. At that point a
collapse of asset prices itself, even without a tightening of policy, could put the
economy into recession. The best way to handle extreme fluctuations in asset
prices is to make sure that supervisory and regulatory safeguards are in place
to prevent a precipitous asset price correction from immobilizing financial
institutions and markets, and to make sure that monetary policy is sufficiently
sensitive to the risk of recession and deflation after a correction takes place.

The Zero Bound on Interest Rate Policy
This potential challenge to strict low inflation targeting stems from the fact
that nominal interest rates cannot go below zero because neither banks nor the
public will lend money at negative nominal interest when bank reserves and
currency are costless to carry over time. The zero bound on nominal interest is
a potential problem for monetary policy in a low inflation environment for two
main reasons. First, if expected inflation is nearly zero, then the central bank
cannot make real short-term interest negative if need be to fight deflationary
shocks. Second, when short-term nominal rates are zero, further disinflation
raises real short-term interest rates and worsens the deflationary pressure.
One could keep nominal short-term interest rates safely away from zero
by targeting inflation at 3 or 4 percent per annum; but that would mean accepting the costs of excessive inflation forever. Moreover, such a high inflation
target would invite credibility problems. An inflation target between 1 and 2
percent is a good compromise. Inflation is kept low, but far enough from zero
to avoid deflation. One could conceivably raise the inflation target temporarily whenever more leeway for negative real interest was thought necessary to
fight a recession. However, a policy that resorted to higher inflation in such
circumstances would cause inflation expectations to rise whenever the economy weakened. Variable inflation expectations would be difficult to manage.
Inflation scares would again become a significant source of shocks to the economy. Strictly targeting inflation between 1 and 2 percent could firmly anchor
expected inflation and still give a central bank leeway to push the real shortterm rate 1 to 2 percentage points below zero. Evidence from U.S. monetary
history suggests that such leeway would be enough to enable a central bank to
preempt deflation and stabilize the economy against most adverse shocks.34
Moreover, other effective monetary policy options are available if short-term
nominal rates become immobilized at the zero bound.35
34 Reifschneider and Williams (2000) and Vinals (2001).
35 Goodfriend (2000) and McCallum (2000).

42
7.

Federal Reserve Bank of Richmond Economic Quarterly
CONCLUSION

Economists and central bankers will surely make further progress on the theory
and practice of monetary policy in the future. Nevertheless, it seems clear that
price stability will continue to be regarded as the foundation of good monetary
policy. For almost two decades low and relatively stable inflation around the
world has proved its worth. In the United States the period included the two
longest peacetime cyclical expansions and two mild recessions in 1990–91
and in 2001. The benchmark new neoclassical synthesis model provides a
theoretical case for price stability that supports the practical case derived from
experience. Theory reinforces practice and strengthens the view that price
stability should be a priority for monetary policy.
The benchmark NNS model explains why price stability works well, and
why price stability is desirable from the perspective of household welfare.
A credible commitment to low inflation prevents inflation or deflation scares
that are destabilizing for both output and prices. Price stability is welfaremaximizing monetary policy because it anchors the markup at its profit maximizing value and thereby prevents fluctuations in employment and output that
would otherwise occur due to sticky prices.
As an operational matter we saw how interest rate policy actions work
to implement price stability by stabilizing the markup, and how interest rate
policy secures credibility for low inflation. By anchoring expected future
inflation we saw how such credibility strengthens the leverage that interest
rate policy exerts over current aggregate demand. In so doing, credibility
for low inflation helps monetary policy make aggregate demand conform to
movements in potential output.

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Policy.” Journal of Monetary Economics 3 (July): 305–16.
, and David Gordon. 1983. “Rules, Discretion, and Reputation in a Model of Monetary Policy.” Journal of Monetary Economics
12: 101–22.
Bernanke, Ben, and Mark Gertler. 1999. “Monetary Policy and Asset Price
Volatility.” Federal Reserve Bank of Kansas City Economic Review 4th
Quarter: 17–51.
Bernanke, Ben, Thomas Laubach, Fredrick Mishkin, and Adam Posen. 1999.
Inflation Targeting: Lessons from the International Experience. Princeton:
Princeton University Press.

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Blanchard, Olivier, and Nobuhiro Kiyotaki. 1987. “Monopolistic Competition
and the Effects of Aggregate Demand.” American Economic Review 77
(September): 647–666.
Brayton, Flint, Andy Levin, Ralph Tryon, and John Williams. 1997. “The
Evolution of Macro Models at the Federal Reserve Board.” CarnegieRochester Conference Series on Public Policy 47 (December): 43–81.
Calvo, Guillermo. 1983. “Staggered Prices in a Utility Maximizing Framework.” Journal of Monetary Economics 12: 383–98.
Chari, V. V., Patrick Kehoe, and Edward Prescott. 1989. “Time Consistency
and Policy.” Modern Business Cycle Theory, ed. Robert Barro. Cambridge: Harvard University Press: 265–305.
Chari, V. V., Larry Christiano, and Martin Eichenbaum. 1998. “Expectation
Traps and Discretion.” Journal of Economic Theory 81 (August): 462–92.
Clarida, Richard, Jordi Gal´, and Mark Gertler. 1999. “The Science of Moneı
tary Policy: A New Keynesian Perspective.” Journal of EconomicLiterature 37 (December): 1661–1707.
Fisher, Irving. [1930] 1986. The Theory of Interest. Fairfield, N.J.: Augustus
M. Kelley.
Friedman, Milton. 1957. A Theory of the Consumption Function. Princeton:
Princeton University Press.
. 1968. “The Role of Monetary Policy.” American Economic
Review 58 (March): 1–17.
Gal´, Jordi, and Mark Gertler. 1999. “Inflation Dynamics: A Structural
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Econometric Analysis.” Journal of Monetary Economics 44 (October):
195–222.
Goodfriend, Marvin. 1993. “Interest Rate Policy and the Inflation Scare
Problem: 1979–92.” Federal Reserve Bank of Richmond Economic
Quarterly 79 (Winter): 1–24.
. 2000. “Overcoming the Zero Bound on Interest Rate Policy,”
Journal of Money, Credit, and Banking 32 (November): 1007–35.
. 2003. “Interest Rate Policy Should Not React Directly to
Asset Prices.” Asset Price Bubbles: Implications for Monetary, Regulatory, and International Policies, ed. W.C. Hunter, G.G. Kaufman, and M.
Pomerleano. Cambridge: MIT Press: 445–57.
, and Robert G. King. 1997. “The New Neoclassical Synthesis and the Role of Monetary Policy.” NBER Macroeconomics Annual
12, ed. Ben Bernanke and Julio Rotemberg. Cambridge: MIT Press:
231–83.

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. 2001. “The Case for Price Stability.” Why Price Stability?
ed. A. Herrero, V. Gaspar, L. Hoogduin, and B. Winkler. Proceedings
from the First ECB Central Banking Conference, Frankfurt: European
Central Bank. Also: NBER Working Paper 8423 (August).

Greenspan, Alan. 2002. “Economic Volatility.” Remarks at a symposium in
Jackson Hole, Wyoming, sponsored by the Federal Reserve Bank of
Kansas City (August).
Haldane, Andy, ed. 1995. Targeting Inflation. London: Bank of England.
Hall, Robert E. 1999. “Labor-Market Frictions and Employment Fluctuations.” Handbook of Macroeconomics, ed. John B. Taylor and Michael
Woodford. Amsterdam: Elsevier Science B.V.: 1137–70.
Ireland, Peter. 1996. “The Role of Countercyclical Monetary Policy.”
Journal of Political Economy 104 (August): 704–24.
Khan, Aubhik., Robert G. King, and Alexander Wolman. 2003. “Optimal
Monetary Policy.” Review of Economic Studies 70 (4): 825–60.
Leiderman, Leonardo, and Lars Svensson, eds. 1995. Inflation Targets.
London: Center for Economic Policy Research.
Ljungqvist, Lars, and Thomas J. Sargent. 2000. Recursive Macroeconomic
Theory. Cambridge: MIT Press.
Lucas, Robert E., Jr. 1981. Studies in Business Cycle Theory. Cambridge:
MIT Press.
Mankiw, N. Gregory. 1990. “A Quick Refresher Course in Macroeconomics.”
Journal of Economic Literature 28 (December): 1645–60.
, and David Romer, eds. 1991. New Keynesian Macroeconomics, 2 vols. Cambridge: MIT Press.
McCallum, Bennett T. 1999. “Issues in the Design of Monetary Policy
Rules.” Handbook of Macroeconomics, ed. John B. Taylor and Michael
Woodford. Amsterdam: Elsevier Science B.V.: 1483–1530.
. 2000. “Theoretical Analysis Regarding the Zero Bound on
Nominal Interest Rates.” Journal of Money, Credit, and Banking 32
(November): 870–905.
Plosser, Charles I. 1989. “Understanding Real Business Cycles.” Journal of
Economic Perspectives 3 (Summer): 51–77.
Prescott, Edward. 1986. “Theory Ahead of Business Cycle Measurement.”
Federal Reserve Bank of Minneapolis Quarterly Review 10 (Fall): 9–22.
Reifschneider, David, and John Williams. 2000. “Three Lessons for Monetary Policy in a Low Inflation Era.” Journal of Money, Credit, and
Banking 32 (November): 936–66.

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Romer, David. 1993. “The New Keynesian Synthesis.” Journal of Economic
Perspectives 7 (Winter): 5–22.
Romer, Paul. 1989. “Capital Accumulation in the Theory of Long-Run
Growth.” Modern Business Cycle Theory, ed. Robert Barro. Cambridge:
Harvard University Press: 51–127.
Rotemberg, Julio, and Michael Woodford. 1999. “The Cyclical Behavior of
Prices and Costs.” Handbook of Macroeconomics, ed. John B. Taylor
and Michael Woodford. Amsterdam, Elsevier Science B.V.: 1051–1135.
Sargent, Thomas J. 1986. Rational Expectations and Inflation. New York:
Harper and Row.
Svensson, Lars E. O. 1999. “Inflation Targeting as a Monetary Policy Rule.”
Journal of Monetary Economics 43 (June): 607–54.
Taylor, John B. 1999. “Staggered Price and Wage Setting in Macroeconomics.” Handbook of Macroeconomics, ed. John B. Taylor and Michael
Woodford. Amsterdam: Elsevier Science B.V.: 1009–50.
Vinals, Jose. 2001. “Monetary Policy Issues in a Low Inflation Environment.”
Why Price Stability? ed. Herrero, V. Gaspar, L. Hoogduin, and B.
Winkler. Proceedings from the First ECB Central Banking Conference,
Frankfurt: European Central Bank.
Woodford, Michael. 2003. Interest and Prices: Foundations of a Theory of
Monetary Policy. Princeton: Princeton University Press.

How Do Central Banks
Control Inflation?
Robert L. Hetzel

A

round 1980, a dramatic change occurred in the intellectual consensus
over the control of inflation. A consensus emerged that central banks
are responsible for the behavior of inflation. Prior to then, most of
the economics profession had viewed inflation as a hydra-headed monster,
which sprang from innumerable sources.1 Eclectic-factors theories of inflation, which explained inflation without any necessary reference to monetary
policy, possessed an elaborate taxonomy of causes. Demand-pull inflation,
which arose from excessive spending, could originate with government deficits
or investment booms fueled by speculative activity. Cost-push inflation, which
arose from the exercise of private monopoly power, could originate with labor unions or large corporations. Supply-shock inflation could come from
weather, government regulation, or the restrictions imposed on oil exports
by OPEC. Wage-price-spiral inflation emerged from inflationary expectations
independent of monetary policy.2
The author gratefully acknowledges criticism from Marvin Goodfriend, John Weinberg, and
Alex Wolman. The views in this paper are the author’s, not those of the Federal Reserve
Bank of Richmond.
1 For example, see Ackley (1961), Burns (1979), Blinder (1980), and the 1980 Economic
Report of the President, Chapter 2, “Controlling Inflation.” For a longer view, see Humphrey
(1999). Velde (2004) argues that the older debate continues. He divides the current debate into
two camps. One camp attributes the post-War behavior of inflation of monetary policy, and the
other attributes it to the fortuitous behavior of real shocks.
Cagan (1974) borrowed the term, “hydra-headed monster,” for a book on inflation (1974
Economic Report of the President, 21):
During the 8 years the rate of inflation came in various forms—sometimes led by wages,
sometimes by prices, by foods, by oil; sometimes it was domestic and sometimes imported. Many programs have been launched to stop it—without durable success. Inflation
seemed a Hydra-headed monster, growing two new heads each time one was cut off.
2 Goodfriend and King (1997, 236–7) commented on views of policymakers in the 1960s and
1970s:
Policy advisers worried about a wage-price spiral and were concerned that inflation could
develop a momentum of its own . . . [M]onetary policy was regarded as a powerful instrument, but one ill-suited to controlling inflation . . . While monetary policy could control

Federal Reserve Bank of Richmond Economic Quarterly Volume 90/3 Summer 2004

47

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Federal Reserve Bank of Richmond Economic Quarterly

The hypothesis that inflation emerges from a wide variety of nonmonetary phenomena without the intermediation of central bank money creation
implies that only infrequently is monetary policy the appropriate instrument to
control inflation. The clash of a restrictive monetary policy and the powerful
nonmonetary forces that drive inflation would, it was believed prior to 1980,
force up interest rates. Although inflation would subside, the cost would be
a socially unacceptable level of unemployment (Burns 1979). Only when all
sorts of controls, formal and informal, failed to control inflation did governments turn to central banks to control inflation. As a last resort, they gave
central banks instrument independence, that is, the independence necessary
to move their instrument (the interbank rate) to whatever extent necessary to
control inflation. Opinion changed when central banks not only succeeded in
controlling inflation, but also did so at a socially acceptable cost.
What is special about central banks is their monopoly over the creation of
the monetary base—the medium used to arrange for finality of payment. For
this reason, the disastrous experiments with nonmonetary control of inflation
prior to 1980 demonstrated that inflation is a monetary phenomenon. The
quantity theory expresses this idea.3 There are two hallmarks of quantity
theory analysis. One is that the monetary transmission mechanism works
through portfolio rebalancing. The other is that the price level is a monetary
phenomenon.
Sections 1 and 2 exposit these ideas in a way that is applicable to central
bank use of the interest rate as a policy variable.4 If inflation is a monetary
phenomenon, the policy procedures of the Federal Reserve possess a characterization in terms of monetary control.5 However, such a characterization
is not obvious. Because the Federal Open Market Committee (FOMC) uses
the funds rate rather than the monetary base or bank reserves as its policy
variable, money is endogenously determined. Furthermore, the minutes of
FOMC meetings (Board, Annual Reports) suggest that the FOMC does not
use money as an indicator variable, but instead appears to use a real variable,
typically a growth gap or an output gap.6
inflation in theory, the practical view was that inflation was mainly governed by psychological factors and momentum.
See also Hafer and Wheelock (2001).
3 For an historical overview of the quantity theory, see Humphrey (1974).
4 The central bank engages in whatever open market operations are necessary to achieve a
value of the monetary base compatible with the adjustable peg it sets for the rate on lending in
the interbank market.
5 With an interest rate as the policy variable, monetary control does not imply an exogenous
money stock. The monetary control that assures price stability provides for increases in the nominal quantity of money that equal the sum of two components. The first is the increase in real
purchasing power demanded by the public that would occur with complete price flexibility. This
increase abstracts from changes due to monetary shocks interacting with monetary nonneutrality.
The second is the value of the central bank’s inflation target. (See footnotes 11 and 12.)
6 All statements about FOMC practices are inferences made by the author based on a variety
of empirical studies and official records. The FOMC does not itself explicitly characterize its
procedures.

R. L. Hetzel: How Do Central Banks Control Inflation?

49

Section 3 discusses FOMC procedures. Deflation and zero short-term
interest rates in Japan have led some to question the ability of central banks
to end deflation.7 Section 4 discusses policy procedures that are robust to
the zero-bound problem, that is, the inability of the central bank to lower the
nominal interest rate below zero. Section 5 argues that the FOMC should
formulate policy as a strategy for achieving explicit objectives.

1.

REAL MONEY DEMAND AND PORTFOLIO BALANCE

Modern monetary economics began with the portfolio theory of money demand.8 Money is one asset in a portfolio that includes bonds and capital.
For the individual to be satisfied with the allocation of assets within his (her)
portfolio, equality must hold between the rates of return to these assets. Formula (1) uses the portfolio balance equation in Friedman (“The Optimum
Quantity of Money,” 1969). The initial expression is the marginal rate of return to money. It is the sum of the marginal nonpecuniary services of money
(MN P Sm ) minus the cost imposed by expected inflation (π ∗ ), or plus the
return due to expected deflation. The second expression is the marginal return
to bonds. The explicit yield paid on bonds is rB, and MN P SB is the marginal
nonpecuniary services yielded by bonds. The third expression is the marginal
return to physical capital. The explicit yield on capital is rK , and MN P SK is
the marginal nonpecuniary services yielded by capital.
MN P Sm − π ∗ = rB + MN P SB − π ∗ = rK + MN P SK

(1)

All three assets yield liquidity services. The nature of these liquidity services is important for understanding the portfolio rebalancing that occurs from
money creation that is independent of a prior change in money demand. The
liquidity services yielded by money reduce transactions costs by economizing
on time. For example, carrying additional money allows one to make cash
Until 1980, the stability and low interest elasticity of the real M1 demand function rendered
M1 a feasible indicator and target for monetary policy (Hetzel and Mehra 1989). The nationwide
introduction of NOW accounts in 1981 made real M1 demand much more interest sensitive. This
interest sensitivity made M1 unsuitable as a target for controlling the price level. To use M1 as
an intermediate target for controlling inflation would have required setting its value based on a
forecast of interest rates—a practical impossibility. Even with such a forecast, the policymaker
would still have to estimate the magnitude of changes in real M1 demand due to changes in the
opportunity cost of holding it. After the mid-1990s, sweep accounts made measurement of M1
impossible. In the early 1990s, M2 velocity rose when the public used small time deposits to
purchase stock and bond mutual fund shares (Hetzel 1992). Since then, real M2 demand has also
been highly interest sensitive.
Because central banks do not use money as an indicator or target, an “out of sight, out of
mind” confusion about the role of money in price level determination can arise. The important
point is that the nature of the public’s demand for real money (degree of stability and interest
sensitivity) possesses no implications for the nature (monetary or nonmonetary) of the price level.
7 See Hetzel (2003a and 2004) for a discussion of Japanese monetary policy.
8 For an overview, see McCallum and Goodfriend (1987).

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Federal Reserve Bank of Richmond Economic Quarterly

purchases that otherwise would have necessitated a trip to the bank or the sale
of an asset.
The liquidity services yielded by capital are nonmonetary in character.
Liquidity now refers to the degree of access to credit. For example, a liquid
asset can facilitate access to credit by furnishing collateral. Some assets (like
inventories) are more liquid than are others (like buildings). Additional liquidity in the form of access to credit reduces the need for the liquidity offered
by monetary assets. Goodfriend (2001) refers to the sum of the nonpecuniary
services of money, bonds, and capital as broad liquidity.
One can use (1) to think about how the need for monetary control constrains the way that the central bank sets its interest rate target. That is, how
does the central bank set its interest rate target (r T = rB ) in a way that avoids
money creation that sets off portfolio rebalancing by the public? The central
bank must fulfill two conditions. The first is credibility for its inflation target.
For example, if the public raises its expectation of inflation when the central
bank lowers its interest rate target, changes in the interest rate target do not
correspond to the same changes in the real (inflation-adjusted) interest rate.
Expressed generally, the second condition is that the central bank must
vary its interest rate target in a way that respects the working of the price
system. A central part of the price system is the real rate of interest. Movements in the real rate induce individuals to accept an unequal intertemporal
distribution of consumption produced by the unequal intertemporal distribution of production. Fisher (1930) expressed the real rate of interest as the
intertemporal price of consumption. One specific way to express this price is
(2).9 The real rate is rr. The subscripts indicate consumption in current and
future periods. The constant rate of time preference that individuals possess
for current over future consumption is ρ.
c2
−1
(2)
c1
The natural rate of interest is the real interest rate that would exist in the
absence of monetary disturbances. With the perfect price flexibility captured
by the real business cycle core of the economy, the real rate of return on
money, bonds, and capital would follow variations in the natural rate. To
avoid monetary emissions that force portfolio rebalancing, the central bank
must vary its interest rate target (r T ) so that the real value of its interest rate
target tracks the natural rate. In doing so, it maintains equality across the asset
yields in (1) at a level equal to the natural rate.
rr = (1 + ρ)

9 The formula assumes log utility for consumers and certainty about the future (Goodfriend
2002). The formula for the real rate of interest in an economy with money includes terms that
capture the value of the increased leisure (reduced shopping time) that derives from foregoing a
unit of consumption by holding additional money balances.

R. L. Hetzel: How Do Central Banks Control Inflation?

51

The real world counterpart to the quantity theory conceptual experiment
of an exogenous increase in money is a failure by the central bank to move its
interest rate target in a way that tracks the natural rate. Assume, for example,
that a rise in productivity growth makes the public believe that it will be better
off in the future relative to the present. Because individuals desire to smooth
consumption, they will want to consume more today. To prevent aggregate
demand from exceeding the productive potential of the economy, the central
bank must raise its interest rate peg in line with the natural rate.10
In contrast, assume that the central bank puts inertia into interest rate
changes by smoothing the interest rate around a base value.11 Interest rate
smoothing (keeping the real rate below the natural rate) requires money creation. Monetary policy is expansionary.12 However, this situation cannot
persist (Friedman, “The Role of Monetary Policy,” 1969). The increase in
money that allows the divergence between the real and natural rates creates
no additional productive capacity. Ultimately, the additional money creation
will raise the price level, and the central bank will have to allow its interest
rate target to rise fully to reflect the rise in the natural rate.13

2. THE PRICE LEVEL IS A MONETARY PHENOMENON
In the above example, the nominal quantity of money increased without a prior
increase in the demand for the real quantity of money. The price level had
to increase to maintain equilibrium in the market for the quantity of money.
That is, the price level adjusted to endow the nominal quantity of money with
the real purchasing power desired by the public.14
This section suggests a heuristic way to think about how a central bank
limits money creation when it uses a short-term interest rate as its policy
variable. Equivalently, one can ask how a central bank that uses the interest
10 Note that the increase in the interest rate raises the opportunity cost of holding money.
That increase limits the increase in the public’s demand for real money. By using the interest rate
as its policy variable—as long as it successfully tracks the natural rate—the central bank allows
the nominal quantity of money to change in line with changes in the demand for real money.
11 The central bank can only smooth around a base that adjusts over time in line with the
natural rate plus the central bank’s inflation target. For example, the base value could equal an
average of the prior period’s interest-rate and the interest rate that would have existed in the prior
period in the absence of monetary shocks (the prior natural rate plus the value of the inflation
target).
12 Expansionary monetary policy in combination with sticky prices stimulates real output temporarily. Adjusted for the trend, real output is high relative to its expected future value. The
resulting expected fall in output keeps the real rate temporarily below the natural rate.
13 Central bank policy actions occur as part of a strategy for achieving targets. This story
assumes that the central bank allows drift in the price level (Goodfriend 1987; Hetzel 1995).
14 The price level functions as part of the price system, that is, to clear markets. For a small
country with a pegged exchange rate, changes in the price level equilibrate the balance of trade.
An empirical implication of the quantity theory is that changes in the price level serve different
roles for countries under fixed, rather than floating, exchange rates.

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Federal Reserve Bank of Richmond Economic Quarterly

rate as a policy variable provides a “nominal anchor,” so that the price level
possesses a unique equilibrium value.15
The answer offered in Section I is that the central bank must tie down the
way that the public forms its expectation of the future price level. It must
also set its interest rate target in a way that tracks the natural rate. The Fisher
(1907) formula summarizes these two tasks.
The nominal interest rate, which is the exchange rate between current and
future dollars, is the product of the two factors shown in (3). The first is the
(gross) real interest rate, which is the real exchange rate of current for future
goods. The second is the ratio of the expected future price level to the current
price level (asterisk indicates expected).16
rt = (1 + rrt )

∗
Pt+1
−1
Pt

(3)

The nominal-real distinction gives (3) content by explaining which variable the central bank must control and which variable it must accept as given
by the price system. In the rearrangement of (3) as (4), the superscript N on
the real rate indicates the natural rate (the value that obtains with complete
price flexibility). To control money creation in a way that is consistent with its
inflation objective, the central bank must make the expectation of the future
∗
price level (Pt+1 ) conform to its inflation target.17 The central bank must also
move its interest rate target (rtT ) with changes in the natural rate (rrtN ).
Pt =

1 + rrtN
1 + rtT

∗
Pt+1

(4)

As long as the central bank maintains the two right-hand factors of (4)
unchanged, it will stabilize the inflation rate. Expectations will then drive
money and prices. Money will increase at a rate given by the sum of the central
bank’s inflation target and the growth rate of real money demand consistent
with price flexibility (or with no monetary shocks).18
15 The welfare of individuals depends only upon real variables (physical quantities and relative
prices). It follows that only the central bank can give nominal variables well-defined equilibrium
values. The price level is a nominal variable—the money price of goods. (The number of dollars
required to purchase a standardized basket of goods.) The seminal work on nominal determinacy
in a monetary regime of interest rate targeting is in Sargent and Wallace (1974), Dotsey and King
(1983) and McCallum (1986).
16 Formula (3) is an approximation.
17 With base drift in prices, the central bank ties down the way that the public forms its
expectation of the future price level in response to shocks rather than the expectation itself (McCallum 1986; Goodfriend 1987; Hetzel 1995).
18 Write the equation of exchange using percentage changes.

˙
˙ ˙
M = π + k + y,

(5)

R. L. Hetzel: How Do Central Banks Control Inflation?
3.

53

FOMC PROCEDURES: INTEREST RATE
AND GROWTH GAPS

To understand the procedures that the central bank uses to track the natural rate
and, in the process, to control money creation, one needs to think about gaps
between the real rate and the natural rate. The assumption that the price level
is a monetary phenomenon implies that such gaps are “transitory.” Changes
in the price level will undo the changes in real money that permit the gaps.
At the same time, the assumption that a gap can exist at all requires some
power by the central bank to alter real money and force portfolio rebalancing
by the public. One needs a theory of monetary nonneutrality to explain this
power and to give content to the characterization of “transitory.” To avoid
interrupting the flow of the discussion of monetary policy procedures, I have
placed a discussion of monetary nonneutrality in Appendix B.
How does the central bank move the funds rate in a way that eliminates
real-rate/natural-rate gaps? In principle, it could respond to deviations of
the price level from a targeted value. Long lags, evidenced by the length of
time between the initiation of an expansionary monetary policy and the onset
of inflation, could make that procedure destabilizing (Friedman 1960). In
principle, the central bank could solve a model of the economy with a real
business cycle core to determine the natural rate that would exist with complete
price flexibility. A credible central bank could then set its interest rate peg at
a value equal to the sum of the natural rate and its inflation target. In practice,
the necessary models do not exist.
Policymakers must fall back on some indicator. Over a time period that
varies positively with the degree of instability in money demand, they could
look for changes in the trend rate of growth of money. However, noise in
money demand and also the interest sensitivity of money demand has meant,
in practice, that the interval of time required to ascertain that a change in trend
money growth has occurred is impracticably long.
In practice, the FOMC appears to use a growth-gap indicator: the difference between actual “underlying” real growth and trend real growth.19 “Underlying” growth abstracts from transitory influences on real growth such as
weather and strikes. Under this interpretation of monetary policy setting, the
FOMC assesses the reliability of its estimate of the growth gap by observing
where M is money; π , inflation; k, the inverse of the income velocity of money; y, real output;
and the dot indicates a percentage change. As a consequence of its interest rate peg, the central
˙ ˙
bank accommodates changes in the public’s demand for real money k + y . The assumption that
the central bank varies its interest rate peg so that the real rate equals the natural rate implies that
no monetary emissions occur that require a change in inflation different from the central bank’s
target. Given credibility, expected inflation will equal the central bank’s inflation target, which will
then control both inflation and money growth (beyond changes to real money demand).
19 The statements here come from the documentary and empirical evidence in Hetzel (2004c).
See comments in Appendix A and footnotes 6 and 7.

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Federal Reserve Bank of Richmond Economic Quarterly

measures of change in excess capacity, especially, the unemployment rate.
For example, if the growth gap is positive, the unemployment rate should be
falling. The FOMC moves the funds rate above its prevailing value in response
to a positive growth gap, and conversely.
The FOMC appears to use this pragmatic search procedure for changing
the funds rate to discover the natural rate.20 It can do so because there is a
correspondence between the real rate/natural rate interest gap and the growth
gap. Failure of the central bank to align the real rate that corresponds to its
interest rate peg with the natural rate allows a growth gap to emerge.
These procedures for tracking the natural rate require that the public’s
expectation of inflation be stable at a value equal to the central bank’s target
for inflation. A major innovation of the post-1979 operating procedures was
the emphasis on credibility. The FOMC raised the funds rate in response to
sharp increases in bond rates construed as indicating a rise in inflationary expectations to a level inconsistent with its implicit inflation target. Goodfriend
(1993) documents these episodes of “inflation scares.” Note that the FOMC
apparently does not target directly a discrepancy between actual and targeted
inflation, but rather between expected and targeted inflation.21

4. THE ZERO BOUND PROBLEM
The zero-bound problem refers to the fact that there is a lower bound of zero
on nominal interest rates. If an expectation of deflation exists, the negative
value of that expectation places a floor on the real rate of interest. The central
bank can lose its ability to track the natural rate if it falls below this floor.
In this situation, the central bank can continue to stabilize the price level by
changing from an interest rate to a reserves instrument.
Consider again FOMC procedures for setting an interest rate instrument.
To achieve its inflation objective, the FOMC requires procedures for discovering the associated unique “nominal natural rate of interest.” With credibility,
this interest rate equals the value of the central bank’s inflation target plus the
natural rate. The central bank uses its growth gap procedures to discover the
value of the natural rate.
Consider now the analogue of these procedures for a reserves instrument.
A trend rate of growth of reserves exists that varies positively with the trend rate
20 Economists often characterize as “activist” a monetary policy that uses a measure of real
economic activity, such as an output gap, as an indicator variable for adjusting an interest-rate peg
(for example, Orphanides 2003a). However, real variables offer information on the natural rate of
interest. Tracking the natural rate with procedures that use real variables as indicators is more
aptly characterized as a “neutral” policy. Such a monetary policy respects, rather than supplants,
the working of the price system.
21 What is relevant for current price-setting behavior is expected inflation. Orphanides (2003c)
concludes that the FOMC targets expected inflation.

R. L. Hetzel: How Do Central Banks Control Inflation?

55

of growth of real output. There is a corresponding rate of reserves growth that
equals this rate plus the targeted inflation rate. Analogous to the interest rate
case, the central bank could use a growth gap indicator to adjust judgmentally
reserves growth rates up or down from the prevailing value to keep the growth
gap equal to zero on average over time. In this way, the FOMC would maintain
reserves growth equal to the reserves demand consistent with trend real growth
and targeted inflation.
In the case of an interest rate instrument, the central bank privatizes control
over reserves provision by turning the decision on the quantity of reserves over
to the financial market (subject, of course, to setting both the funds rate and
the public’s expectation of inflation consistently with its inflation target). It
takes direct control over the setting of the interest rate. In the case of a reserves
instrument, the central bank turns (real) interest rate determination over to the
private market while taking direct control over reserves provision.22 There is
no clear economic reason for preferring a reserves instrument to an interest
rate instrument except for the advantage of the former in dealing with the zero
bound problem.23
Critics of quantitative procedures for the implementation of monetary
policy have argued that the central bank becomes impotent to force portfolio
rebalancing and stimulate expenditure at a low or zero interest rate. The public
will supposedly hoard the money the central bank creates through open market
purchases.24 The idea of a liquidity trap gains apparent plausibility from the
fact that at a zero short-term interest rate money and short-term government
securities are perfect substitutes because both pay no interest. (At the margin,
money ceases to yield more liquidity services than bonds.) However, the liquid
assets in the public’s portfolio then become the total of money and bonds. The
central bank can still increase liquidity through purchases of illiquid assets
that increase this total. That increase will stimulate expenditure because the
public will not forego the holding of income-yielding assets for assets whose
marginal yield is zero.
22 The reserves targeting procedures could include a tolerance band for allowable interest rate
fluctuations. However, just as in the case of the gold standard before the establishment of the Fed,
volatility of short-term rates would not pass on to long-term rates.
23 According to the logic laid out in Poole (1970), reserves control would produce the changes
in real rates required by real shocks faster than with interest rate control. Interest rate control
would accommodate changes in the demand for real money with changes in money faster than
with reserves control.
24 The idea of a liquidity trap goes back to Keynes. In comparing classical and Keynesian
economics, Mundell (1968, Chapter 12) referred to the tradition of “classicists and romanticists.”
For Keynesians (romanticists), the issue was not how to limit aggregate demand to the production
of goods and services, but rather how to increase production by increasing aggregate demand
through deficit spending. With respect to a liquidity trap, the “romanticist” position is that a
liquidity trap allows costless (noninflationary) seigniorage. When the central bank exchanges noninterest-bearing government debt (money) for interest-bearing government debt (bonds), the public
simply hoards the additional money.

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Federal Reserve Bank of Richmond Economic Quarterly

Consider again the portfolio balance equation (1), with rB = MN P Sm =
MN P SB = 0, and −π ∗ = rK + MN P SK . Assume that the central bank
purchases an illiquid asset—for example, shares in a mutual fund holding equities. The public will rebalance its portfolio through the purchase of physical
assets like land and equities. The rise in their price will raise their value as collateral (MN P SK rises while rK falls) and thus facilitate the access to credit
of the holders of these assets. Increased liquidity from increased access to
credit augments the portfolio rebalancing effect by decreasing the demand for
the liquidity services of money. The increase in the price of physical capital
relative to its replacement cost stimulates investment.25

5.

RULES VERSUS DISCRETION

Robert Lucas (1981, 255) expressed the prevailing consensus in academia
about the desirability of basing policy on an explicit strategy.
[O]ur ability as economists to predict the responses of agents rests, in
situations where expectations about the future matter, on our understanding
of the stochastic environment agents believe themselves to be operating
in. In practice, this limits the class of policies the consequences of which
we can hope to assess in advance to policies generated by fixed, well
understood, relatively permanent rules (or functions relating policy actions
taken to the state of the economy). . . .[A]nalysis of policy which utilizes
economics in a scientific way necessarily involves choice among alternative
stable, predictable policy rules, infrequently changed and then only after
extensive professional and general discussion, minimizing (though, of
course, never entirely eliminating) the role of discretionary economic
management.

Lucas (1981, 255) also noted:
I have been impressed with how noncontroversial it [the above argument
for rules] seems to be at a general level and with how widely ignored it
continues to be at what some view as a “practical” level.

One problem with moving to a rule that incorporates an explicit strategy is
a lack of agreement over those aspects of monetary policy that have rendered
policy largely stabilizing since the early 1980s. The FOMC could make policy
in a way that leaves a record that allows learning about the systematic aspects
25 For further discussion, see Goodfriend (2001) on broad money. The transmission of the
impact of monetary policy on the spending of the public continues to operate through asset prices
and interest rates, but one must consider a range of assets broader than Treasury bills (Brunner
and Melter 1968). Reserves, rather than the funds rate, become the policy instrument.

R. L. Hetzel: How Do Central Banks Control Inflation?

57

of policy. Such learning would require that the FOMC make an ongoing effort
to record the systematic part of monetary policy and deviations from it.26
The FOMC would begin by making its inflation objective explicit. The
FOMC secretary would then take responsibility for distilling the strategy most
representative of FOMC practice in achieving that objective. This strategy
would organize discussion of the Bluebook.27 The Bluebook would make
explicit the behavior of whatever indicators the FOMC uses regularly. The
Greenbook would predict the behavior of the future funds rate path based on
the FOMC’s inflation objective and on the strategy chosen by the Bluebook
as most representative of FOMC practice.28
The Bluebook would also assess recent past actions of the FOMC in terms
of the strategy assumed representative of FOMC behavior. In particular, it
would flag deviations from the assumed strategy arising from one-time special
factors and events. Deviations might include financial market instability and
the foreign exchange value of the dollar. Finally, the Bluebook would make
regular assessments of the reasons for missing the FOMC’s objectives.

6.

SUMMARY

If the price level is a monetary phenomenon, then the way that the central
bank controls monetary base and money creation determines the behavior of
inflation. Even when a central bank does not employ reserves as an instrument
or money as an indicator, its operating procedures possess a characterization in
terms of monetary control. The central bank achieves that control by keeping
the public’s expectation of inflation equal to its inflation target and by varying
the funds rate in a way that causes the real interest to track the natural rate.
This tracking emerges from procedures that move the funds rate away from
its prevailing value in response to an estimated growth gap.
By maintaining expected inflation equal to its inflation target, money and
inflation grow in line with the inflation target. By maintaining the real rate of
interest equal to the natural rate, the central bank prevents monetary emissions
that force undesired changes in prices.
26 The answer to the question posed in the title to this article (“How Do Central Banks
Control Inflation?”) depends upon the strategy central banks follow. This proposal, if adopted,
would make that strategy explicit.
27 The staff of the Board of Governors circulates the Bluebook prior to FOMC meetings. It
suggests alternative FOMC directive language and presents arguments supporting the alternatives.
28 The Greenbook, which the Board staff circulates prior to FOMC meetings, contains forecasts of macroeconomic variables. These forecasts are judgmental.

58

APPENDIX A:

Federal Reserve Bank of Richmond Economic Quarterly

MONETARY POLICY
PRE- AND POST-VOLCKER

Prior to 1979 and Paul Volcker’s chairmanship, the FOMC used the output gap
(the difference between actual and trend output) as an indicator for setting the
funds rate. The FOMC raised the funds rate only when an estimated negative
output gap approached zero. It benchmarked the level of the trend line for
real output using a year in which full-employment prevailed, assumed to be
4 percent. However, because 4 percent turned out to be too low an estimate,
the FOMC consistently overestimated the appropriate height of the trend line
for real output (Mayer 1999; Orphanides 2003b and 2003c). Phillips curve
estimates of inflation based on overly pessimistic estimates of the output gap
produced forecasts for inflation that were consistently too low (Orphanides
and van Norden 2003). The assumption that inflation arose from real forces
unrelated to monetary policy caused the FOMC to accept historically high
inflation rates as necessary to avoid a high level of unemployment.
In the early 1980s, the FOMC began to rely on an estimate of the gap
in the growth rate of real output relative to potential output. Starting in the
1980s, “bond market vigilantes” forced bond rates up whenever real output
grew strongly. The sensitivity of the FOMC to bond rates as indicators of
inflationary expectations meant that the FOMC raised the funds rate whenever
economic activity quickened.
A search of FOMC transcripts and staff materials circulated to the FOMC
for the years 1983 through 1997 revealed only very infrequent mention of
an output gap. There was a single reference in FOMC meetings in each
of the years 1988, 1992, 1993, and 1994 and three references in 1995 and
1996. In contrast, the use of the term “sustainable” as a characterization of the
desirable growth rate of output was ubiquitous. For example, the Directive
issued at the January 28, 2004, FOMC meeting stated, “The Federal Open
Market Committee seeks monetary and financial conditions that will foster
price stability and promote sustainable growth in output” (italics added).
Hetzel (2004b) relates changes in the funds rate to a proxy for the growth
gap. For the period from 1982 on, Orphanides (2003c) finds that a growth gap
does a better job than an output gap in explaining the behavior of the funds
rate. For the earlier stop-go period, the output gap is superior. Mehra (2002)
finds evidence for both sorts of gaps in the latter period.
With the establishment of full credibility after 1995, the FOMC gained
more latitude in moving the funds rate. This would allow a departure from
growth gap procedures beginning with the Asia crisis in fall of 1997. Credibility gives the FOMC the latitude to wait before raising the funds rate until
growth has reduced the magnitude of the current negative output gap.

R. L. Hetzel: How Do Central Banks Control Inflation?

APPENDIX B:

59

MONETARY NONNEUTRALITY

Monetary nonneutrality arises from a coordination failure.29 When the central
bank creates and destroys money in an erratic way that forces unpredictable
changes in the price level, individual price setters lack a coordinated way to
move their dollar prices to maintain the real purchasing power desired by the
public while also preserving relative prices. Individual price setters do not
capture the externalities from being the first to change their dollar prices to
discover the price level that would prevail with perfect price flexibility. They
therefore make quantity adjustments initially.
As explained by Friedrich von Hayek (1945), in competitive markets the
price system allows the efficient allocation of resources by communicating
information widely dispersed among individuals. The individual firm can set
its output based only on the market price for its product and the prices of its
labor and capital inputs. The price system fails to provide any comparable
mechanism for economizing on the information needed to move individual
dollar prices to the level appropriate for providing the real purchasing power
the public desires.
When a firm (with some transitory market power) sets the dollar price of
its product, it is solely concerned with the ratio of its dollar price to other
dollar prices. That is, it only cares about relative prices—the rate of exchange
of its product with other products. However, there is another dimension to its
dollar price. The average of the dollar prices set by firms must be at the level
that endows the nominal quantity of money with the real purchasing power
that the public desires. How do individual firms set their dollar prices in a way
that collectively creates the right amount of purchasing power?
The coordinating mechanism that maintains the average of individual dollar prices at the level that delivers the public’s desired purchasing power is
a common expectation of the future price level. Of course, the central bank
must validate that expectation by pursuing a monetary policy resulting in a
consistent rate of money creation. The main responsibility of a central bank
is to provide this coordination for the setting of dollar prices. The more explicit the central bank is about its inflation objective, the better it fulfills this
responsibility.
What happens when erratic money creation by the central bank forces
unpredictable changes in the price level? For example, assume that the central
bank attempts to lower equity prices through a “high” real interest rate made
possible by money destruction. The central bank provides no guide for the
29 Ball and Romer (1991) explain monetary nonneutrality using a model of fixed menu costs
and coordination failure.

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Federal Reserve Bank of Richmond Economic Quarterly

duration of the policy or the required fall in asset prices. A specific example
would be Fed policy in 1928 (Friedman and Schwartz 1963). The resulting
monetary contraction will require a lower price level, but the nature of the
policy renders the ultimate price level unpredictable. Associated changes in
real money demand produced by interest rate and real output changes and
financial market instability will likely render money an unreliable guide to the
appropriate price level.
Consider an individual firm. Assume that its customers face search costs
so that the firm possesses some short-term, but no long-term, market power.
If the firm lowers its price in the absence of an aggregate shock, it will expect
initially only a small increase in demand. Profits will fall because the firm
sells about the same amount, but at a lower price. However, over time, demand
will increase. If the firm’s price was appropriate before, it will then sell too
much. While its sales increase, it sells each unit of output at a loss.
Given monetary contraction, all firms should lower their dollar prices in
tandem to maintain sales. However, there is no way to coordinate a common
fall in dollar prices that preserves relative prices. Each individual firm faces
the prospect of lowering its price in an isolated fashion and incurring the losses
described above. Another way to make this point is to note that the firm that
lowers its price first confers a positive externality by increasing the purchasing
power of money.
This story of price stickiness captures the spirit of the Friedman-Lucas
(Lucas 1972) critique of the Phillips curve understood as a menu of choices
between inflation and unemployment. Unanticipated changes in aggregate
nominal demand created by the central bank affect real output while anticipated changes do not. Anticipated changes are those associated with a common
expectation of inflation consistent with central bank monetary policy (money
creation). For example, inflation consistent with an announced, credible inflation target will not affect output. The common expectation set up by the
central bank guides firms in setting their dollar prices in a coordinated way to
preserve real purchasing power while allowing freedom to set relative prices.

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Company.
Ball, Laurence, and David Romer. 1991. “Sticky Prices as Coordination
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Accommodation.” Development in an Inflationary World, ed. J. Flanders
and A. Razin. New York: Academic Press.
Board of Governors of the Federal Reserve System. “Minutes of Federal
Open Market Committee Meetings.” Annual Reports, various issues.
Broaddus, J. Alfred, Jr., and Marvin Goodfriend. 2003. “Sustaining Price
Stability.” Federal Reserve Bank of Richmond Annual Report.
Brunner, Karl, and Allan H. Meltzer. “Liquidity Traps for Money, Bank
Credit and Interest Rates.” Journal of Political Economy 76 (July 1968):
8–24.
Burns, Arthur F. 1979. The Anguish of Central Banking. Belgrade,Yugoslavia:
Per Jacobsson Foundation.
Cagan, Phillip. 1974. The Hydra-Headed Monster: The Problem of Inflation
in the United States. Washington, D.C.: American Enterprise Institute for
Public Policy Research.
Dotsey, Michael, and Robert G. King. 1983. “Monetary Instruments and
Policy Rules in a Rational Expectations Environment.” Journal of
Monetary Economics 12 (September): 357–82.
Fisher, Irving. 1907. The Rate of Interest. New York: Macmillan.
. 1930. The Theory of Interest. New York: Macmillan.
Friedman, Milton. 1960. A Program for Monetary Stability. New York:
Fordham University Press.
. 1969. “The Role of Monetary Policy.” The Optimum
Quantity of Money, ed. Milton Friedman. Chicago: Aldine.
. 1969. “The Optimum Quantity of Money.” The Optimum
Quantity of Money, ed. Milton Friedman. Chicago: Aldine.
, and Anna J. Schwartz. 1963. A Monetary History of the
United States, 1867–1960. Princeton: Princeton University Press.
Goodfriend, Marvin. 1987. “Interest Rate Smoothing and Price Level TrendStationarity.” Journal of Monetary Economics 19 (May): 335–48.
. 2001. “Financial Stability, Deflation, and Monetary
Policy.” Bank of Japan Institute for Monetary and Economic Studies
Monetary and Economic Studies 19 (February ): 143–67.
. 2002. “Monetary Policy in the New Neoclassical Synthesis:
A Primer.” International Finance 5 (July): 165–91.
, and Robert G. King. 1997. “The New Neoclassical Synthesis.” NBER Macroeconomics Annual, ed. Ben S. Bernanke and Julio
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Hafer, R. W., and David C. Wheelock. 2001. “The Rise and Fall of a Policy
Rule: Monetarism at the St. Louis Fed, 1968–1986.” The Federal
Reserve Bank of St. Louis Review 83 (January/February): 1–24.
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Hetzel, Robert L. 1992. “How Useful Is M2 Today?” Federal Reserve Bank
of Richmond Economic Review (September/October): 12–26.
. 1995. “Why the Price Level Wanders Aimlessly.” Journal
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Reserve Bank of Richmond Economic Quarterly 89 (Summer): 21-52.
. 2004a. “A Proposal to Stabilize the Japanese Price Level.”
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. 2004b. “Post-1983 Federal Reserve Monetary Policy.”
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. 2004c. “An Analytical History of the Monetary Policy of
the Federal Reserve System.” Federal Reserve Bank of Richmond,
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, and Yash Mehra. 1989. “The Behavior of Money Demand
in the 1980s.” Journal of Money, Credit, and Banking 21 (November):
455–63.
Humphrey, Thomas M. 1974. “The Quantity Theory of Money: Its Historical
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Richmond Economic Review 60 (May/June): 2–19.
. 1999. “Mercantilists and Classicals: Insights from Doctrinal
History.” Federal Reserve Bank of Richmond Economic Quarterly 85
(Spring): 55–82.
Lucas, Robert E., Jr. 1972. “Expectations and the Neutrality of Money.” In
Studies in Business-Cycle Theory. Cambridge: The MIT Press.
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Mayer, Thomas. 1999. Monetary Policy and the Great Inflation in the United
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, and Marvin Goodfriend. 1987. “Demand for Money:
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Macmillan Press: 775–80.
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Taylor Rule.” Journal of Monetary Economics 50 (July): 983–1022.
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Predicting the Recent
Behavior of Inflation Using
Output Gap-Based Phillips
Curves
Yash P. Mehra

M

any analysts believe that strong productivity growth has played
an important role in the favorable inflation performance of the
U.S. economy since the mid-1990s. Inflation, as measured by the
behavior of the GDP deflator, hovered mostly near a low of 2 percent in the
second half of the 1990s and has decelerated further during the past three years.
Some policymakers think that, as a result of the continuing strong productivity
and weak labor market, inflation may remain low throughout 2004, despite
the continued strong pickup in economic activity.1
The traditional output gap-based Phillips curve relates current inflation to
lagged inflation, supply shocks, and a measure of excess demand such as the
level of the output gap. This Phillips curve is likely to overestimate inflation
in the second half of the 1990s unless one revises upward estimates of real
potential output made possible by the ongoing acceleration of productivity
growth. However, in recent speeches, a few policymakers have highlighted
two other potential anti-inflationary consequences of the recent surge in productivity. One is that the recent surge in productivity accompanied by weak
labor markets has reduced unit labor costs, leading to possible downward pressures on inflation.2 The other potential consequence stems from the ensuing
I would like to thank Bob Hetzel, Ray Owens, and Roy Webb for many helpful comments.
The views expressed are those of the author and do not necessarily represent the views of
the Federal Reserve Bank of Richmond or the Federal Reserve System. All errors are mine.
1 See, for example, recent speeches by Bernanke (2003, 2004).
2 Fed Governor Ben Bernanke (2004), among others, has emphasized this factor in the recent

evolution of inflation, as he observes:
Recently . . . labor productivity has grown even more quickly than the cost of employing
workers, with the result that unit labor costs have declined in each of the past three

Federal Reserve Bank of Richmond Economic Quarterly Volume 90/3 Summer 2004

65

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Federal Reserve Bank of Richmond Economic Quarterly

behavior of aggregate demand. The strong productivity growth and the resulting surge of real potential output imply aggregate demand must grow fast
enough to absorb higher potential output. Otherwise, disinflationary pressures
may develop.3
In order to investigate the above-noted potential anti-inflationary consequences of acceleration of productivity, this article augments the traditional
output gap-based Phillips curve to include two additional variables: the cyclical component of a markup variable defined as the markup of prices over
unit labor costs and the change in the output gap. The markup allows for the
short-term influence of a productivity-induced decline in unit labor costs on
inflation, whereas the “rate of change” specification implies inflation depends
also on how fast aggregate demand is growing relative to potential (called here
the “demand growth gap”). I estimate the modified Phillips curve and examine whether it predicts the recent deceleration of inflation.4 I also examine
the robustness of the results of using wage share, rather than the markup, to
capture the short-term influence of productivity-induced decline in unit labor
costs on inflation.5
Some analysts have argued that Phillips curves are not useful for predicting inflation. In particular, Atkeson and Ohanian (2001) present evidence indicating that one-year-ahead inflation forecasts from several NAIRU
(nonaccelerating-inflation rate of unemployment) Phillips curves are no more
accurate than those from a na¨ve model that predicts inflation next year will
ı
be the same as it had been over the past year. Sims (2002) points out that
the results in Atkeson and Ohanian arise entirely from having the forecast
evaluation period restricted to 1984–1999, a period when inflation was very
stable. I examine the robustness of the results in Atkeson and Ohanian along
another dimension. Their forecasting exercise predicts the one-year-ahead
inflation rate conditional on just past values of a real activity variable and the
inflation rate, thereby ignoring the potential contribution of the future values
years. . . . A decline in production costs must result in lower prices for final consumers,
an increase in price-cost markup for producers, or both (“Monetary Policy,” 3).
Ball and Moffitt (2001) have also emphasized the role of weak labor markets in explaining
the recent behavior of inflation.
3 See, for example, Kohn (2003), who argues that, as a result of the “jobless recovery,”
rapid productivity growth has been associated with weak growth in aggregate demand, resulting in
a falling inflation rate.
4 It should be noted that the hypothesis that inflation may depend on a change in the output
gap is not new. Gordon (1983), in fact, uses such a Phillips curve to explain U.S. inflation dynamics over almost a century from 1892 to 1980. The role of such a Phillips curve in explaining
the most recent inflation dynamics is, however, left unexplored. Similarly, the hypothesis that inflation may be influenced by unit labor costs is not new either, having been previously examined by
Gordon (1988) and Mehra (1991, 1993, 2000), among others. The empirical evidence in previous
research on the importance of unit labor costs in explaining inflation has, however, been mixed,
as I find even here.
5 Many analysts argue that labor share can better capture the influence of the productivity-led
decline in unit labor costs on inflation. See, for example, Gal´ and Gertler (2003).
ı

Y. P. Mehra: Output Gap, Markup, and Inflation

67

of real activity over the forecast horizon.6 Their exercise may be a reasonable
way to construct the forecast because, in real time, forecasters usually do not
have information about the future values of the indicator variable. However,
it is plausible that a forecast including this extra information may be more
accurate than the one ignoring it. As a robustness check, I take the other
extreme and generate one-year-ahead predictions of the inflation rate under
the counter-factual assumption that the forecaster knows actual values of the
indicator variable over the forecast horizon. I then investigate whether the
Phillips curve still generates less accurate predictions of the inflation rate than
does the na¨ve model.
ı
The empirical work presented here estimates the modified Phillips curve
over two sample periods, 1961Q1 to 1995Q4 and 1961Q1 to 2003Q4, using
the chain-weighted GDP deflator as the measure of inflation.7 It suggests
the following conclusions. First, the estimated coefficients that appear on
the output gap and its rate of change are significant and correctly signed,
suggesting there is a “rate of change effect.” Inflation is predicted to rise
when the output gap is positive and when aggregate demand increases faster
than real potential output. Second, the markup, which is usually defined as
the excess of the price level over unit labor costs, has a slow-moving trend and
is not statistically significant when included in the estimated Phillips curve.
However, the cyclical component of the markup when included in the Phillips
curve is significant and appears with a negatively signed estimated coefficient,
meaning inflation is predicted to fall if the cyclical markup is high. If the
Phillips curve includes the wage share instead of the markup, the estimated
coefficient on the wage share is positive, suggesting inflation is predicted to
fall if the wage share declines.
Third, the predictions of the one-year-ahead inflation rate conditional on
actual values of the explanatory variables suggested by traditional and modified Phillips curves track actual inflation well, outperforming those based on
the na¨ve model that predicts inflation using only its past values.8 This result
ı
holds over 1980–2003 as well as over 1984–1999, a period when inflation was
stable. The results also indicate demand growth and output gap variables help
most in generating accurate predictions of the inflation rate. The markup (or
the wage share) does not improve the predictive accuracy if it is included in
6 Their forecasting exercise also assumes that the NAIRU is constant over the sample pe-

riod 1959–1999, because one of the indicator variables used is the unemployment rate, not the
unemployment gap.
7 In order to check whether results regarding the influences of additional factors on inflation
are not simply due to the ongoing episode of productivity surge, the shorter sample period exludes
the most recent period of productivity surge.
8 The predictions, however, are dynamic in the sense that lagged values of the inflation rate
used are those predicted by the model.

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Federal Reserve Bank of Richmond Economic Quarterly

the modified Phillips curve. Together these results suggest that Phillips curves
are useful for predicting inflation.
Regarding sources of the recent deceleration of inflation, the correlations
summarized in the estimated modified Phillips curve suggest one plausible explanation of the recent behavior of inflation. As noted at the outset, inflation,
after hovering near a low of 2 percent in the second half of the 1990s, decelerated further during the past three years. In the second half of the 1990s, the
demand growth gap stayed close to the 2 percent range, as aggregate demand
grew just fast enough to absorb the productivity-induced increase in potential.
However, during the period 2000–2002, aggregate demand did not grow fast
enough to absorb higher potential output, creating a declining demand growth
gap and negative output gap. The recent deceleration is well predicted by the
behavior of a Phillips curve that includes these two gap variables. However,
the contribution of the markup (or wage share) in improving the prediction
of the inflation rate since the mid-1990s remains negligible, suggesting the
markup is not providing information beyond that contained in the gap variables. These results suggest that the weak demand growth gap together with
the resulting negative output gap trump the cyclical markup (or wage share)
as the major source of the recent deceleration of inflation.
The plan of this article is as follows. Section 1 discusses two modifications
to the conventional expectations-augmented Phillips curve. It also provides an
overview of the data including graphs of key variables that enter the Phillips
curve, the estimation procedure, and the empirical specifications estimated
here. Section 2 presents the new empirical work, and Section 3 contains
concluding observations.

1.

MODEL AND THE METHOD

Traditional and Modified Phillips Curves
The traditional reduced-form Phillips curve relates current inflation to lagged
inflation, supply shocks, and a measure of excess demand such as the level of
output or unemployment gap. Following Gordon (1985, 1988) and Stockton
and Glassman (1987), the traditional output gap-based Philips curve can be
derived from the following reduced-form price and wage equations.
pt = h0 + h1 (w − q)t + h2 xt + h3 spt ,

(1.1)

(w − q)t = k0 + k1 pte + k2 xt + k3 swt , and

(1.2)

pte = g(L) pt ,

(1.3)

where all variables are in natural logarithms and where p is the price level; w
is the nominal wage; q is labor productivity; x is a demand pressure variable;

Y. P. Mehra: Output Gap, Markup, and Inflation

69

p e is the expected price level; sp represents supply shocks affecting the price
equation; sw represents supply shocks affecting the wage equation; g(L) is a
lag operator; and is the first difference operator. Equation (1.1) describes
the price markup behavior: prices are marked over productivity-adjusted wage
costs and are influenced by cyclical demand and the exogenous supply shocks.
This equation implies that productivity-adjusted wages determine the price
level, given demand pressures. Equation (1.2) is the wage equation: wages
are assumed to be determined by cyclical demand and expected price level, the
latter modeled as a distributed lag on past prices as in (1.3). The wage equation,
together with the price expectation equation (1.3), implies that productivityadjusted wages depend upon past prices, cyclical demand, and supply shocks.
If we substitute the price expectation equation (1.3) into the wage equation
(1.2) and the resulting wage equation into the price equation (1.1), we get the
traditional reduced-form Phillips curve of the form given in (2).

pt = a0 + a1 (L) pt + a2 xt + a3 SSt ,

(2)

where SS represents supply shocks, a1 (L) is a lag operator, and other variables
are defined as before. The parameters ai , i = 0, 1, 2, in (2) are functions of
the parameters in the underlying price and wage equations. Equation (2) says
current inflation depends on lagged inflation, cyclical demand, and supply
shocks.
The key feature of the Phillips curve (2) is that current inflation does
not directly depend on the productivity-adjusted wage once we control for
the influences of lagged inflation and the cyclical demand on inflation. This
feature rests on the assumption that wages adjust one-for-one with productivity
each period, so that the productivity-adjusted wages depend only on lagged
inflation and the cyclical demand (as hypothesized in (1.2) and (1.3)). Under
this specification, productivity-adjusted wages have no independent influence
on inflation once we allow for the influences of lagged inflation and the cyclical
demand.
The assumption above—wages adjust one-for-one with productivity each
period—may not hold in practice, especially during a period when productivity
is undergoing a structural shift. In that case, the productivity-adjusted wage
may change due to reasons other than those captured in the wage equation
(1.2) and hence may play an independent role in determining inflation in the
short run. Thus, an acceleration of productivity growth that is accompanied
by anemic wage growth may lead to lower inflation if firms pass through the
productivity-induced declines in unit labor costs in lower product prices.
In order to motivate the empirical specification of the influence of productivity on inflation, note first that “the price markup hypothesis” that underlies
(1.1) can be summarized in the following price equation:

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Federal Reserve Bank of Richmond Economic Quarterly

p t = b0 + b w w t − b q q t ,

(3.1)

where all variables are defined as before and the parameters bw and bq measure
the responses of the price level to nominal wages and productivity, respectively.
The price equation (3.1) says the price level declines if nominal wages decline
or productivity rises; the magnitude of the price response depends in part on the
size of the pertinent wage or productivity response coefficient. The assumption
implicit in the inflation specification (1.1) is that the underlying wage and
productivity response coefficients are equal in magnitude but opposite in signs,
an assumption that may not hold in practice.
If we subtract wt and add qt to both sides of the price equation (3.1), we
can rewrite the price equation (3.1) as (3.2).
pt − wt + qt = b0 + (bw − 1)wt − (bq − 1)qt ,

(3.2)

where all variables are defined as before. The left-hand side of the reformulated
price equation (3.2) is the markup, defined as the excess of the price level over
unit labor costs. Equation (3.2) links the markup (mrkt ≡ pt − (wt − qt )) to
the behavior of wages and productivity, given the price level. If we assume
prices are sticky in the short run, then the markup will move in response to
changes in wages and/or productivity. Since in the long run the price level
adjusts to reflect economic fundamentals as envisioned in “the price markup
hypothesis,” a rise in the markup has implications for the near-term behavior
of inflation. Thus, if unit labor costs decline in response to the acceleration
of productivity and the markup rises, then the price level should eventually
decline to reflect lower unit labor costs, leading to lower inflation down the
road. Hence I modify the traditional Phillips curve to include the one-period
lagged value of the markup as in (4).
pt = a0 + a1 (L) pt + a2 xt + a3 SSt + a4 mrkt−1 .

(4)

Under the assumption that the “price markup hypothesis” is valid, the expected sign of the coefficient that appears on the markup should be negative,
suggesting that the high level of the markup is associated with a decline in
the inflation rate. As can be seen, the modified Phillips curve reduces to the
traditional Phillips curve if a4 = 0 in (4).
In some previous work analysts have captured the influence of unit labor
costs on inflation by including wage share in the Phillips curve (Gal´ and
ı
Gertler 2003). The wage share, however, moves inversely with the markup,
and one should obtain similar results using the wage share. Note that the
(log of) wage share is just the (log of) real wage per hour minus the (log of)
output per hour. Using the notation introduced above, the wage share can be
expressed as (5).

Y. P. Mehra: Output Gap, Markup, and Inflation

W St = (wt − pt ) − qt ≡ −{pt − (wt − qt )},

71

(5)

where W S is the log of wage share and other variables are defined as before.
Equation (5) shows wage share is just the inverse of the markup. If productivity
rises faster than the real wage, wage share declines, and the markup may move
up if prices are sticky in the short run. The expected sign of the coefficient on
wage share when included in the Phillips curve is positive, implying inflation
is predicted to fall if wage share declines. As a robustness check, I shall
examine results using the wage share also.
In most previous empirical work, the Phillips curve (2) has been estimated
with excess demand measured by the output gap or unemployment gap. I now
consider another modification to the Phillips curve, arguing excess demand
be measured by the level and change in output gap. The main reason for
considering the rate of change specification is that in a reformulated version of
this Phillips curve inflation depends explicitly on the excess of the growth rate
of aggregate demand over that of potential. This reformulation better captures
the potential demand channel consequence of the ongoing acceleration of
productivity, emphasized by Kohn (2003). Consider the Phillips curve (4)
augmented to include the change in output gap as in (6).9
pt = a0 a1 (L) pt + a2 yt + a3 SSt − a4 mrkt−1 + a5 yt ,

(6)

where y is now the output gap and where all other variables are defined as
before. Following Gordon (1983), I reformulate the inflation equation (6) as
follows. Note first that the level of the output gap is linked to the growth rate
of nominal GDP via the following identity.
yt ≡ yt−1 + ( Yt − pott ) − pt ,

(7)

where Y is nominal GDP and pot is real potential output. If we substitute (7)
into (6) and rearrange terms, we get the modified Phillips curve (8).
pt

= (1/(a2 + a5 ))[a1 (L) pt + (a2 + a5 )( Yt − pott )
+a2 yt−1 + a3 SSt + a4 mrkt−1 ,

(8)

where all variables are defined as before. According to equation (8), among
other things, inflation depends on the contemporaneous “demand growth gap”
9 A theoretical model consistent with a structural Phillips curve—in which current inflation
depends also on a change in the output gap—appears in Mankiw and Reis (2001). Under the
assumption that information is sticky, they derive a Phillips curve in which inflation depends on
the level and change in the output gap, besides depending on past expectations of the current
inflation rate.

72

Federal Reserve Bank of Richmond Economic Quarterly

defined as the excess of the growth rate of nominal aggregate demand over
that of real potential output,10 besides depending on the “level” of the output
gap. In this framework, the estimated coefficient on the lagged output gap
indicates the presence of an output “level effect,” while the difference between
the coefficient on the “demand growth gap” and the output gap indicates the
relative size of the “rate of change effect.” An interesting implication of
this Phillips curve is that during the period when there is an outgoing shift
in productivity indicating higher real potential output near term, aggregate
demand has to grow fast enough to absorb higher potential output. If aggregate
demand fails to keep up with higher potential output, disinflationary pressures
may develop, even when there may be no slack as measured by the level of
the output gap. To illustrate this point further, the most recent estimates of
potential output prepared by the Congressional Budget Office indicate real
potential output rising at a 3.5 percent annual rate since the mid-1990s. This
trend growth rate of 3.5 percent is one percentage point higher than the trend
rate for the preceding period of 1990 to 1994. This upward shift in the trend
growth rate of real potential implies aggregate demand now has to grow at a
higher rate than before, otherwise deflationary pressures will develop.

A Visual Look at Some Data: Demand Growth Gap,
Output Gap, Markup, and Wage Share
I estimate the modified Phillips curve (8) using quarterly data from 1959Q1
to 2003Q4. Inflation is measured by the behavior of the chain-weighted GDP
deflator. In most previous work, potential output has been estimated fitting a
deterministic time trend to real output. I, however, use estimates of potential
output prepared by the Congressional Budget Office. I consider two supply
shock variables: one associated with change in the relative price of imports
and the other arising as a result of the imposition and removal of President
Nixon’s price controls. The effects of price controls are captured by means
of two dummies: PC1 defined to be unity from 1971Q3 to 1972Q4 and zero
otherwise, and PC2 defined to be unity from 1973Q1 to 1974Q4 and zero
otherwise. The relative import price series is the GDP deflator for imports
divided by the implicit GDP deflator. The nominal wage series is compensation per man hour, and the productivity series is output per man hour, both
of the nonfarm business sector.11 The inflation equations are estimated with
an instrumental variables procedure. The instruments used are: a constant;
10 Gordon (1983) calls it “adjusted nominal growth.” I think the term “demand growth gap”

better captures the way inflation depends on how fast aggregate demand is growing relative to
potential supply.
11 The empirical work here is done using revised, not real-time, data. Hence the conclusions
regarding the predictive accuracy of the Phillips curve must be viewed with caution.

Y. P. Mehra: Output Gap, Markup, and Inflation

73

Figure 1
10.0

Panel A: Actual Inflation and Demand Growth Gap (CBO)

7.5
5.0
2.5
0.0
-2.5
1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001
Actual inflation

0.050

Demand Gap

Panel B: Output Gap

0.025
0.000
-0.025
-0.050
-0.075
-0.100
1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001

contemporaneous change in military expenditures; and four lagged values of
the inflation rate, change in the federal funds rate, gap variables, and change
in the relative price of imports.12
Figures 1 through 5 provide a visual look at the behavior of some key
variables that enter the modified Phillips curve. Panel A of Figure 1 charts
the demand growth gap and actual inflation. Both variables measure changes
defined over four-quarter periods and are smoothed further by taking the fourquarter moving average of the variables. Figure 1 illustrates that actual inflation and the demand growth gap have moved together over time. Inflation
steadily increased in the late 1960s and the 1970s, accompanied by steadily
expanding demand growth gap. Similarly, a declining demand growth gap
12 I do present results of the test that the instruments used are not correlated with the resid-

uals of the estimated Phillips curves. That test is implemented regressing the residuals from the
instrumental variables regression on the instruments. See Table 1 (p. 15) which reports the significance levels of the pertinent Chi-square statistic, x 2 , defined as T times the R 2 from this
regression and distributed Chi-square with (K-1) degrees of freedom, where T is the sample size
and K is the number of instruments.

74

Federal Reserve Bank of Richmond Economic Quarterly

Figure 2

4.55

Panel A: Actual and Trend Markup (HP)

4.50
4.45
4.40
4.35
4.30
1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001
Actual

0.05

Trend

Panel B: Cyclical Markup

0.04
0.03
0.02
0.01
0.00
-0.01
-0.02
-0.03
-0.04
1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001

accompanied the steady decline in inflation observed during the 1980s and the
1990s. In particular, during the second half of the 1990s, inflation was stable
and so was the demand growth gap. However, for most of the past three years
aggregate demand has not kept up with real potential output and hence the
resulting decline in the demand growth gap has accompanied the most recent
decline in the inflation rate.
Panel B of Figure 1 charts the level of the output gap. The output gap is
not smoothed. During the past three years the output gap has been negative
and remains so currently, despite last year’s upturn in the demand growth gap.
Panel A of Figure 2 charts the markup defined as the excess of the price
level over productivity-adjusted wage (markup = pt − (wt − qt )). As can be
seen, the markup displays a slow-moving trend. I de-trend the markup, using
the Hodrick-Prescott (1997) filter. Panel B of Figure 2 charts the cyclical
component of the markup. As can be seen, for much of the 1990s the cyclical
markup has been positive. Furthermore, in recent quarters the cyclical component has reached levels not seen in the recent past. As of the fourth quarter
of 2003, the cyclical component is above 4 percent.

Y. P. Mehra: Output Gap, Markup, and Inflation

75

Figure 3

4.55

Panel A: Actual and Trend Markup (Price Equation)

4.50
4.45
4.40
4.35
4.30
1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001
Actual

0.04

Trend

Panel B: Cyclical Markup (Price Equation)

0.02
0.00
-0.02
-0.04
-0.06
1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001

As indicated in Figure 2, the markup series has a slow-moving trend.
One simple explanation of the trend in the markup series is suggested by
the price equation (3.2), which is that the firms do not pass through part of
the productivity-led decline in unit labor costs in lower product prices. In
order to explain this point further, note that the markup, as formulated in
the price equation (3.2), is constant if the coefficients that appear on wage
and productivity variables are unity, as will be the case if there is perfect
competition. However, if in practice these coefficients are different from
unity, then the markup may have trend if wage and/or productivity series have
trend.
In order to explore this source of trend in the markup series, I present
below the price equation (3.2), estimated using aggregate data on the price
level, nominal wages, and average productivity over the whole sample period
1959Q1 to 2003Q4.

pt − wt + qt = 3.1 − . 04 wt + . 34 qt + µt .
(2.9)

(6.7)

(9)

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Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Cyclical Markup: HP versus Price Equation
0.042

0.028

0.014

0.000

-0.014

-0.028

-0.042

-0.056
1959 1963

1967

1971

1975

1979
HP

1983

1987

1991

1995

1999 2003

Price

As can be seen, the estimated coefficient that appears on the wage variable is not
economically different from zero, but the one that appears on the productivity
variable is different from zero. Since the productivity variable has a trend,
the estimated price equation implies the observed trend in the markup arises
because not all of the productivity gain passes through in lower prices.13
Panel B in Figure 3 charts the residuals from the estimated price equation
(9), which is the measure of the cyclical markup.14 This measure of the cyclical
markup appears similar to the one estimated using the HP filter, as shown in
Figure 4. The simple correlation between these two cyclical measures of the
markup is 0.84. I consider results with both these measures.
13 The empirical evidence here that the estimated coefficient on productivity in the price
equation is not unity is in line with the evidence in Bils and Chang (2000). Using the U.S.
manufacturing data, they estimate industry price equations and find product prices respond weakly
to declines in marginal costs driven by increases in labor productivity, suggesting not all of the
gain in productivity shows up in the form of lower product prices. They attribute this result to
the presence of imperfect competition. It is plausible that similar forces might be at work at the
aggregate level.
14 For generating the cyclical markup I have set the wage response coefficient in the estimated
markup equation to zero, thereby implicitly assuming the wage response coefficient in the price
equation is unity.

Y. P. Mehra: Output Gap, Markup, and Inflation

77

Figure 5 Wage Share

Ratio of Real Wage to Productivity; Non-farm Business Sector
110.0

100 in 1996

107.5

105.0

102.5

100.0

97.5
1959

1963

1967

1971

1975

1979

1983

1987

1991

1995

1999

2003

Figure 5 charts the wage share calculated using the nonfarm business sector data on the nominal average hourly compensation, price level, and average
productivity. As shown in equation (5), the wage share can be expressed as
the ratio of the real wage to the average product of labor.15 A look at Figure
5 indicates that the wage share series calculated using the nonfarm business
sector data does not have as noticeable a trend as the markup series shown
in Figure 2. However, the wage share does show a distinct decline in recent
years, indicating productivity has grown faster than the real wage. Since in
previous research many analysts have used the wage share to explain inflation dynamics, as a robustness check, I also examine results using the wage
share.16
15 Wage share is usually calculated as total labor compensation (W ∗ n) divided by total factor
income (p ∗ y). One can then express the wage share as the ratio of real wage to the average
product of labor, as shown: Wage share = (W ∗ n) / (P ∗ y) ≡ (W/P )/ (y/n) ≡ (W/P )/(q), where
W is the nominal wage; n is the number of hours; y is real output; P is the price level; and q
is the average product of labor. The wage share declines if productivity rises faster than the real
wage.
16 See, for example, Gal´ and Gertler (2003).
ı

78
2.

Federal Reserve Bank of Richmond Economic Quarterly
EMPIRICAL RESULTS

This section reports and discusses empirical estimates of the modified Phillips
curve (8). It also examines whether the estimated Phillips curve predicts the
behavior of inflation during the 1980s and the 1990s.

Estimated Phillips Curves
Table 1 reports estimates of the traditional and modified Phillips curves over
two sample periods, 1961Q2 to 1995Q4 and 1961Q2 to 2003Q4. The shorter
sample period excludes observations pertaining to the most recent subperiod
of productivity surge. The estimated coefficients (with t-values in parentheses) reported are those that appear on the demand growth gap, output gap,
cyclical markup, lagged inflation, and the relative import price inflation. The
coefficient on lagged inflation reported is the sum of coefficients that appear
on four lagged values of the inflation rate.
Rows 1 and 2 present estimates of the traditional Phillips curve that relates
current inflation to the contemporaneous output gap, lagged inflation, and the
relative import price inflation. As can be seen, the estimated coefficients
appearing on the output gap, lagged inflation, and import price inflation have
positive signs and are statistically significant, suggesting current inflation is
positively correlated with the contemporaneous output gap, lagged inflation,
and import price inflation. These results hold over both the sample periods.
Rows 3 and 4 present estimates of the modified Phillips curve that allow
inflation to depend on the change in the output gap, but not on the markup. As
can be seen, the estimated coefficient that appears on the demand growth gap
has a positive sign and is statistically significant, meaning inflation is predicted
to rise if aggregate demand grows faster than real potential output. The other
estimated coefficients that appear on the output gap, lagged inflation, and the
relative import price inflation remain correctly signed and significant. The
point estimates of the coefficient on the contemporaneous demand growth gap
are in a 0.10 to 0.14 range, implying the current quarter predicted increase in
inflation following a one percentage point rise in the demand growth gap is
0.10 to 0.14 of a percentage point. These estimates suggest that the cumulative
predicted increase in inflation over one year, resulting from a one percentage
point sustained increase in the demand growth gap, is about 0.4 to 0.6 of a
percentage point.17
Rows 5 through 8 present the modified Phillips curve estimated with the
demand growth gap and cyclical markup.18 Rows 5 and 6 present estimates
17 In Gordon (1983) the estimate of the cumulative increase in inflation over the year resulting
from a sustained rise in the demand growth gap is 0.4 of a percentage point, which is near the
low end of the range estimated here.
18 The actual markup, when included in the estimated Phillips curve, is never significant.

As can be seen from Figures 1 and 2, the markup series has a slow-moving trend whereas the
inflation rate series appears stationary over the whole sample period.

Y. P. Mehra: Output Gap, Markup, and Inflation

79

Table 1 Conventional and Modified Reduced-form Phillips Curves
GDP Inflation
Row
No.

End
Period

Output
Gap
(d1 )

1

1995Q4

2

2003Q4

3

1995Q4

4

2003Q4

5

1995Q4

6

2003Q4

7

1995Q4

8

2003Q4

9

1995Q4

10

2003Q4

Demand
Growth
Gap
(d2 )

Cyclical
Markup

Lagged
Inflation

Import
Prices

(d3 )

(d4 )

(d5 )

00.90
(21.30)
00.91
(24.20)

0.07
(4.60)
0.06
(5.20)

00.85
(20.30)
00.86
(22.20)

0.07
(5.30)
0.07
(5.30)

0.03
(2.90)
0.03
(3.10)
0.03
(3.50)
0.03
(3.70)

0.10
(2.10)
0.10
(2.10)

0.04
(3.90)
0.03
(3.90)

0.14
(2.80)
0.11
(2.30)

−0.03
(1.90)
−0.02
(1.20)

00.82
(18.90)
00.85
(20.70)

0.06
(4.50)
0.06
(5.30)

0.05
(3.10)
0.04
(2.10)

0.13
(2.80)
0.11
(2.40)

−0.05
(1.90)
−0.03
(2.10)

00.78
(18.90)
00.83
(19.40)

0.06
(4.60)
0.06
(5.30)

0.04
(4.20)
0.04
(4.40)

0.14
(3.40)
0.12
(3.20)

0.02
(1.70)
0.02
(1.70)

00.81
(19.40)
00.83
(20.80)

0.06
(4.60)
0.06
(5.20)

R2

x2

0.84

0.80

0.86

0.67

0.86

0.84

0.87

0.72

0.86

0.42

0.87

0.47

0.87

0.53

0.88

0.48

0.86

0.63

0.87

0.78

Notes: With the exception of the coefficients in rows 9 and 10, the estimated coefficients
(with t-values in parentheses) are from reduced-form Phillips curves of the form pt =
d0 + d1 yt−1 + d2 ( Yt − pott ) + d3 mrkt−1 + d4 pt−1 + d5 SSt , where all variables
are in their natural logs and where p is the price level; Y is nominal GDP; pot is real
potential output; y is the output gap; ( Yt − pott ) is demand growth gap; and SS is
relative import prices. The coefficients reported in rows 9 and 10 are from Phillips curves,
estimated using wage share instead of the markup. The reported coefficient on lagged
inflation is the sum of the estimated coefficient on its four lagged values. The inflation
equations are estimated over the sample periods that all begin in 1961Q2 but end as
shown above, using an instrumental variables procedure. The instruments are: a constant;
four lagged values of the inflation rate, output gap variables, changes in the federal funds
rate, and relative import prices; and change in the current nominal defense expenditure.
The estimated inflation equations also included the Nixon price control dummies. The
significance level of the test that the instruments are not correlated with the residuals of
the Phillips curve is x 2 .

generated using the cyclical markup based on the HP filter, and rows 7 and 8
present estimates with the cyclical markup generated using the estimated price
equation. The estimated coefficient that appears on the markup has a negative
sign and is significant, especially over the shorter sample period, meaning

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Federal Reserve Bank of Richmond Economic Quarterly

inflation is predicted to decline if the markup is high. In the longer sample
period, the markup—though it continues to appear with a correctly signed
estimated coefficient—is not significant if the Phillips curve is estimated using
the cyclical markup based on the HP filter.19
The point estimates of the coefficient that appears on the cyclical markup
fall in a –0.02 to –0.05 range, suggesting that in response to a one percentage
point increase in the markup, the cumulative predicted decline in the inflation
rate over the year is about 0.10 to 0.20 of a percentage point, which is not
large in magnitude. Moreover, augmenting the Phillips curve to include the
cyclical markup does not much improve the explanatory power of the inflation
regression, as measured by the R-squared statistic. (Compare estimates in
rows 3 and 4 with those in rows 5 through 8, Table 1).20 Despite these caveats,
the estimated Phillips curve with the markup is capable of generating the
prediction of a significant fall in the inflation rate during periods of high
cyclical markups, which may be periods when productivity is accelerating but
wage growth remains anemic.21
Rows 9 and 10 present estimates of the coefficients from the modified
Phillips curve that includes the wage share rather than the markup. The estimated coefficient on the wage share is positive, suggesting that inflation is
predicted to decline if the wage share declines. The size of the estimated
coefficient on the wage share appears to be of the magnitude found using the
cyclical markup. All the remaining variables appear with correctly signed
estimated coefficients and are significant in the estimated Phillips curve.
19 The serial correlation coefficients estimated using the residuals series from the estimated
modified Phillips curve are small, indicating serial correlation is not a problem. The significance
level of the Chi-squared test of the null hypothesis that instruments are uncorrelated with the
residuals (reported in Table 1) indicates that the null is not rejected.
20 In fact, the explanatory power of the regressions as measured by the R-squared statistic
does not improve much if demand growth gap and markup variables are added into the traditional
Phillips curve. However, these two variables significantly enter the modified Phillips curve. The
significance level of the F statistic, testing the null hypothesis that the estimated coefficients on
these two variables are zero, falls in a 0.00 to 0.03 range and leads to the rejection of the null.
Together these results, however, do imply that the quantitative contribution of these two variables
in predicting inflation may not be large, as we see later.
21 In some previous research the potential influence of unit labor costs on inflation has been
investigated, using cointegration and error correction methodology (Mehra 1991, 1993, 2000). In
particular, the influence of unit labor costs on inflation is investigated in two steps. In step one,
the cointegrating (long-run) relationship between the price level and unit labor costs is investigated,
resulting in an estimated price equation like (3.1) in which wage and productivity response coefficients are assumed to be opposite in sign but equal in magnitude. The residual series from the
estimated price equation is the error-correction variable, which measures the gap between the actual price level and the price based on unit labor costs—a variable similar in spirit to the cyclical
markup used here. In the second step, the inflation equation is estimated including, among other
variables, the lagged value of the error-correction variable. In previous research the error-correction
variable is generally found to be insignificant, suggesting unit labor costs have no direct influence
on inflation (Gordon 1988; Mehra 1993, 2000). The new empirical evidence here indicates that
the error-correction variable estimated without imposing unitary coefficient restrictions on the price
equation is somewhat more favorable to the view that productivity-led declines in unit labor costs
may matter for the short-term behavior of inflation.

Y. P. Mehra: Output Gap, Markup, and Inflation

81

Predicting the Behavior of Inflation During the 1980s
and the 1990s: Are Phillips Curves Useful?
Panel A in Figure 6 charts the dynamic, one-year-ahead predictions of the
inflation rate generated using the rolling regression estimates of the modified
Phillips curve with the markup over the period 1980–2003.22 As indicated
before, these predictions are conditional on actual values of the explanatory
variables suggested by the Phillips curve. Panel B charts the dynamic predictions of the inflation rate generated using a na¨ve model that predicts inflation
ı
using only four lagged values of the inflation rate. Actual inflation rates are
also charted there. As can be seen, the estimated modified Phillips curve tracks
actual inflation fairly well. The na¨ve model, however, tends to overpredict
ı
inflation, first during the early 1980s and then in the second half of the 1990s.
Table 2 presents the statistical evidence on the relative accuracy of inflation predictions. It presents the mean error (ME) and the root mean squared
error (RMSE) of the prediction from several different Phillips curves including the one in which the unemployment rate, not the output gap, is the main
activity variable as in Atkeson and Ohanian (2001). The predictive accuracy
is evaluated over 1980–2003 as well as over the period 1984–1999 covered in
Atkeson and Ohanian. The relative accuracy is evaluated by computing the
ratio of the RMSE of the prediction from a given Phillips curve with the RMSE
of the na¨ve model’s prediction. The na¨ve inflation model is said to generate
ı
ı
more accurate predictions of inflation than a given Phillips curve if the ratio is
above unity. The Phillips curves considered here are: the traditional Phillips
curve that relates current inflation to the contemporaneous output gap, lagged
inflation, and supply shocks; the traditional Phillips curve augmented to include demand growth gap; the traditional Phillips curve augmented to include
both demand growth gap and markup or wage share; the traditional Phillips
curve augmented to include just the wage share; and the NAIRU Phillips curve
that relates current inflation to four lagged values of the unemployment rate
and the inflation rate.
If we focus on estimates of the ratio reported for the sample period 1980–
2003, we see that the ratio is less than unity for all the Phillips curves considered here. The point estimates of the ratio fall in a 0.5 to 0.9 range, suggesting
the Phillips curves considered here provide more accurate predictions of the
inflation rate than does the na¨ve model. The ratio estimated using predictions
ı
from the traditional output gap-based Phillips curve or the modified Phillips
curve with demand growth gap is close to 0.5, far below unity. The results also
22 The estimation periods that underlie the rolling regressions all begin in 1961Q1 but end
in the year before the forecast period. Thus the Phillips curve is first estimated over 1961Q1 to
1979Q4 and then dynamically simulated over 1980Q1 to 1980Q4 to generate the one-year-ahead
prediction of the inflation rate for 1980. The end of the estimation period is then advanced one
quarter, the Phillips curve re-estimated and dynamically simulated to generate the one-year-ahead
prediction of the inflation rate, and so on.

82

Federal Reserve Bank of Richmond Economic Quarterly

Figure 6 Actual and Predicted Inflation: 1980–2003

Panel A: Modified Phillips Curve: Demand Growth + Markup

10
9
8

Actual
Predicted

7
6
5
4
3
2

–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
-

1

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

Panel B: Naïve Inflation Model

10
9
8

Actual
Predicted

7
6
5
4
3
2

–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
-

1

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

indicate the markup or wage share does not aid much in improving the RMSE
of the prediction as do the output gap and supply shock variables (compare
RMSEs across models in Table 2).
If we focus on estimates of the ratio for the period 1984–1999, they suggest qualitatively similar inferences about the relative predictive accuracy of
the Phillips curve and the na¨ve model. The prediction of inflation from the
ı
modified Phillips curve with demand growth gap has the lowest RMSE, outperforming the na¨ve model’s prediction by a substantial margin. The ratio of
ı
the RMSEs for these two models is 0.56 (see Table 2). In contrast, the ratio of
the NAIRU Phillips curve and na¨ve models’ RMSEs is 0.88, not too far below
ı
unity, suggesting the NAIRU Phillips curve does not aid much in improving
accuracy relative to the na¨ve model.23 Together these results suggest Phillips
ı
curves are useful for predicting inflation.
23 The relative poor accuracy of the NAIRU Phillips curve may be due to the use of the

unemployment rate rather than the unemployment gap, implicitly assuming a constant NAIRU over
the sample period.

Y. P. Mehra: Output Gap, Markup, and Inflation

83

Table 2 Test of Relative Predictive Accuracy
Panel A: Sample Period 1980–2003
Model
Na¨ve
ı
Traditional Phillips
Traditional Phillips
+ Demand Growth
+ Demand Growth
+ Demand Growth
+ Wage Share

ME

0.91
0.53

0.56

−0.00
0.05
0.20
0.03

0.48
0.51
0.52
0.55

0.53
0.56
0.57
0.62

0.80

0.88

ME

NAIRU Phillips Curve

−0.48
−0.10

−0.20

Curve
Curve
Gap
Gap + Markup
Gap + Wage Share

RMSE

RATIO

RMSE

RATIO

−0.41
−0.21

0.66
0.43

0.65

−0.13
−0.10
0.13
0.04

0.37
0.42
0.40
0.38

0.56
0.64
0.60
0.65

−0.25

0.58

0.88

Panel B: Sample Period 1984–1999
Model
Na¨ve
ı
Traditional Phillips
Traditional Phillips
+ Demand Growth
+ Demand Growth
+ Demand Growth
+ Wage Share

Curve
Curve
Gap
Gap + Markup
Gap + Wage Share

NAIRU Phillips Curve

Notes: ME is mean prediction error; RMSE is the root mean squared error; and RATIO
is the ratio of Phillips Model/Na¨ve Model RMSEs. The traditional Phillips curve relates
ı
current inflation to contemporaneous output gap, lagged inflation, and supply shocks. The
NAIRU Phillips curve relates current inflation to four lags of inflation and unemployment
rate. The prediction of inflation used is the dynamic, one-year-ahead predicted inflation
rate generated using the Phillips curve model and conditional on actual values of other
explanatory variables. If the RATIO is below unity for a Phillips curve model, it implies
the Phillips curve model generates more accurate predictions of the inflation rate than
does the Na¨ve model.
ı

Predicting the Behavior of Inflation
since the Mid-1990s
Table 3 focuses on the behavior of inflation since the mid-1990s. The column
labeled (2) presents the inflation predictions generated using the traditional
output gap-based Phillips curve and estimates of potential output prepared by
the Congressional Budget Office. As can be seen, the traditional Phillips curve
still tends to overestimate inflation somewhat. The bias measured by the mean

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Federal Reserve Bank of Richmond Economic Quarterly

Table 3 Actual Predicted Inflation 1995–2003
Year

ME
RMSE

Pred.

Pred.

Pred.

Pred.

DGG

OG

mrk

(1)
1995
1996
1997
1998
1999
2000
2001
2002
2003

Act.

(2)

(3)

(4)

(5)

(6)

(7)

(8)

1.90
1.80
1.50
1.10
1.50
2.20
2.40
1.40
1.50

2.50
1.90
1.90
1.50
2.00
2.70
2.10
2.00
1.70

2.30
1.90
1.90
1.40
1.90
2.50
1.70
1.80
1.60

1.50
1.30
1.40
1.60
2.50
3.30
2.20
1.80
1.30

1.70
1.50
1.50
1.30
2.00
2.70
1.80
1.60
1.20

1.10
3.10
2.40
2.10
2.60
0.90
−1.00
0.70
2.30

−1.30
−0.10
0.90
1.90
3.00
1.70
−1.70
−2.40
−1.50

3.10
3.60
2.30
0.00
−0.70
−3.10
−1.70
1.60
4.00

−0.33
0.42

−0.21
0.35

−0.22
0.56

−0.04
0.35

Notes: The predicted values are the dynamic, one-year ahead forecasts of the GDP inflation rate (4Q to 4Q) generated using rolling regression estimates of the modified Phillips
curve reported in Table 1. The forecasts are conditional on actual values of nominal GDP
growth, potential output, wage growth, productivity growth, and import prices. Act. is
actual inflation; Pred. is the predicted inflation rate, DGG is demand growth gap; OG is
the output gap; mrk is the cyclical markup (price equation); ME is the mean prediction
error; and RMSE is the root mean squared error.
The predicted values given in column (2) are from the traditional Phillips curve; those
given in column (3) are from the Phillips curve augmented to include demand growth
gap; those given in column (4) are from the Phillips curve augmented to include demand growth gap plus the markup; and those in column (5) are from the Phillips curve
augmented to include demand growth gap plus the wage share.

prediction error is -0.33, one-third of a percentage point, and the root mean
squared error is 0.44.24
The inflation predictions generated using the modified Phillips curve are
presented in the columns labeled (3), (4), and (5). The predictions in column
(3) are from the Phillips curve with the demand growth gap, those in column
(4) are from the Phillips curve with the demand growth gap and markup, and
those in column (5) are from the Phillips curve with the demand growth gap
and wage share. Augmenting the Phillips curve to include the demand growth
gap does improve the predictive accuracy. The Phillips curve with the demand
24 Note that the prediction bias is larger in magnitude if one does not allow for productivityled increases in potential real output since the mid-1990s. Under the counterfactual assumption that
real potential output continues to increase at its earlier trend growth rate of 2.5 percent since the
mid-1990s, the inflation rates predicted using the traditional Phillips curve for the years 2000,
2001, 2002, and 2003 are 3.0, 2.5, 2.6, and 2.4 percent, respectively. The mean prediction error
is -0.67 of a percentage point, and the RMSE is 0.74.

Y. P. Mehra: Output Gap, Markup, and Inflation

85

growth gap has a lower mean error and lower root mean squared error than the
Phillips curve without the demand growth gap. But further augmenting the
Phillips curve to include the cyclical markup or wage share does not aid much
in improving the predictive accuracy of the long-range inflation forecasts.
Table 3 also presents the underlying data on the demand growth gap, output gap, and cyclical markup over the period since the mid-1990s. Regarding
sources of the recent deceleration of inflation, the correlations summarized in
the estimated modified Phillips curve suggest one plausible explanation of the
recent behavior of inflation.25 As can be seen in Table 3, inflation, after hovering mostly near a low of 2 percent in the second half of the 1990s, decelerated
further during the past three years. In the second half of the 1990s, the demand
growth gap stayed close to the 2 percent range as aggregate demand grew just
fast enough to absorb the productivity-induced increase in potential. However,
during the most recent period, 2000–2002, aggregate demand did not grow
fast enough to absorb higher potential, creating a declining demand growth
gap and a negative output gap. The recent deceleration is well predicted by the
behavior of the Phillips curve that includes these two gap variables. However,
the contribution of the markup (or wage share) in improving the prediction
of the inflation rate since the mid-1990s remains negligible, suggesting the
markup is not providing information beyond that contained in the gap variables. Together these results suggest a weak demand growth gap together
with the resulting negative output gap, trumping the cyclical markup (or wage
share) as the major source of the recent deceleration of inflation.

Generating a Conditional Prediction
of the Inflation Rate for 2004
What do the Phillips curves estimated here imply about the behavior of inflation during 2004? In order to answer this question, I generate the conditional
prediction of the inflation rate for 2004. During the past two years productivity has increased at an average annual rate of 4.5 percent, whereas nominal
wages have increased at an average annual rate of 2.4 percent, implying an average annual decline of 2.5 percent in unit labor costs. Aggregate demand, as
measured by nominal GDP, has grown at an average annual rate of 5 percent.
Potential output, as estimated by the Congressional Budget Office, has grown
at a 3.5 percent annual rate. If productivity, wages, aggregate demand, and
potential output continue to grow in 2004 at rates observed during the past two
years, the point estimate of the conditional prediction of inflation for 2004,
generated using the Phillips curve with demand growth gap and markup, is
25 There may be other structural models that are consistent with the correlations summarized

in the modified Phillips curve. Hence one may come up with other explanations of the recent
behavior of inflation.

86

Federal Reserve Bank of Richmond Economic Quarterly

1.0 percent. The conditional prediction of the inflation rate is 1.5 percent if
the modified Phillips curve excludes the markup. Last year the GDP deflator
grew 1.5 percent. The ensuing behavior of inflation this year would provide
further evidence on the predictive accuracy of the Phillips curve that includes
the markup.

3.

CONCLUDING OBSERVATIONS

This article makes two modifications to the traditional output gap-based Phillips
curve. It includes the cyclical component of a markup variable defined as the
markup of prices over unit labor costs, and it allows inflation to depend also on
a change in the output gap. The markup allows for the short-term influence of
productivity-induced decline in unit labor costs on inflation, and the “rate of
change” specification implies inflation depends also on how fast aggregate demand is growing relative to real potential output. The results indicate demand
growth gap and the level of the cyclical markup enter the traditional Phillips
curve with significant and correctly signed estimated coefficients. Inflation
is predicted to increase if aggregate demand grows faster than real potential
output, and it is predicted to fall if the markup is high.
The predictions of the one-year-ahead inflation rate conditional on actual
values of the explanatory variables suggested by the traditional and modified
output gap-based Phillips curves track actual inflation well over 1980–2003,
outperforming those based on a na¨ve model that predicts inflation using only
ı
lagged inflation. These results imply output gap-based Phillips curves are
useful in predicting inflation.
As a result of the recent acceleration of productivity, the trend growth rate
of real potential output has increased since the mid-1990s. This upward shift
in the trend growth rate of potential output implies aggregate demand needs
to grow at higher rates than before in order to stabilize inflation. Inflation
remained low in the second half of the 1990s and decelerated further during
the past three years. This deceleration of inflation is well predicted by the
modified Phillips curve that assigns a key role to demand growth and the output
gap. The demand growth gap remained stable in the 2 percent range in the
second half of the 1990s, but it declined considerably over the period 2000–
2002, creating a negative output gap over the recent period. The negative
predicted effect of these two gap variables on the inflation rate trumps the
cyclical markup as the major source of the recent deceleration of inflation.
The cyclical component of the markup or the wage share, when added into
the traditional and modified Phillips curves, appears with a correctly signed
negative estimated coefficient and is generally significant. However, in the
past the markup or wage share has not helped in improving the accuracy of the
long-range inflation prediction if the estimated Phillips curve includes demand
growth and output gap variables. This may be due to the fact that the markup

Y. P. Mehra: Output Gap, Markup, and Inflation

87

or wage share is also influenced by cyclical demand, besides productivity, and
hence is highly correlated with the cyclical measures of excess demand. So,
the marginal predictive content of the markup or wage share is small once we
control for the influence of cyclical demand on inflation.

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