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FEDERAL RESERVE BANK OF ST. LOUIS

Inflation Targets and
Inflation Targeting
Laurence H. Meyer
here is widespread agreement that price
stability (in practice, low and stable inflation)
should be an objective of monetary policy.
This agreement is reflected both in the mandates
set for monetary policy by governments and in the
practice of central banks. Several other important
questions about the objectives for monetary policy
are less settled: Should there be other objectives?
If there are multiple objectives, should one of the
objectives take priority? And how explicit should
the objectives be?
Central banks typically operate under one of two
types of mandate. A hierarchical mandate makes
price stability the primary objective for monetary
policy and subordinates other potential objectives.
A dual mandate recognizes two objectives—price
stability and full employment—and puts them on
an equal footing. Either regime could make the price
stability objective more precise by setting an explicit
numerical target for inflation.
Thus we can describe a typical central bank’s
mandate and objectives in terms of two sets of
alternatives: between a hierarchical or a dual mandate, on the one hand, and an implicit or explicit
inflation objective, on the other hand. During the
1990s, a number of central banks adopted a framework that is called inflation targeting, combining
a hierarchical mandate and an explicit inflation
objective. The United States, in contrast, combines
a dual mandate and an implicit inflation objective.
Most of the discussion in the United States on
the subject of mandates and objectives has been
about whether to identify inflation as the single or
primary objective and whether to move to a formal
inflation-targeting regime.1 The title of my lecture—
“Inflation Targets and Inflation Targeting”—is
intended to differentiate between two options for
changing the policy mandate for the Federal Reserve.
One option, which I favor, is setting an explicit
numerical target for inflation within the context of
our current dual mandate. The other option, which I

T

Laurence H. Meyer is a member of the Board of Governors of the
Federal Reserve System. These remarks were originally presented at
the University of California at San Diego Economics Roundtable, San
Diego, California, July 17, 2001.

© 2001,

T H E F E D E R A L R E S E R V E B A N K O F S T. L O U I S

do not favor, is moving to an inflation-targeting
regime—that is, also substituting a hierarchical
mandate for our current dual mandate. The purpose
of this lecture is therefore to explain the benefits
of an explicit inflation target in the context of the
Federal Reserve’s dual mandate and to set out the
operational steps for implementing such a target.
Before proceeding, let me note that the views
that I am presenting here are my own. I am not
speaking for the Board of Governors or the Federal
Open Market Committee (FOMC).

THE EVOLUTION OF MONETARY
POLICY MANDATES
A good starting point is a survey of mandates
around the world. I will begin by discussing the
evolution of the mandate in the United States,
including the precise language related to the dual
mandate, the way in which the price stability objective has been interpreted, and proposed legislation
that would have amended the mandate. Then I
sketch an inflation-targeting regime and discuss
some common elements and differences among
the inflation-targeting regimes of developed economies around the world.

The Evolution of Policy Objectives in
the United States
In the United States, it took quite some time for
the Congress to establish a precise set of objectives
for monetary policy. In fact, remarkably little about
policy objectives was included in the original Federal
Reserve Act in 1913. The only policy objectives of
the Fed, as identified in that statute, were “to furnish
an elastic currency [and] to afford means of rediscounting commercial paper.” The absence of any
mention of price stability undoubtedly reflected
confidence that the gold standard, under which the
United States was operating, would promote price
stability. The intent of providing an elastic currency
and of rediscounting commercial paper was to
expand the supply of money and credit to accommodate expansions in production and the accompanying demand for credit. Given that the immediate
impetus of the founding of the Federal Reserve was
the Panic of 1907, promoting financial stability was
a clear focus. The framers’ intention was that the
Federal Reserve would provide banks with a source
of liquidity through rediscounting to meet deposit
withdrawals.
1

See, for example, Bernanke et al. (1999) and Gramlich (2000).

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On several occasions during the 1920s and
1930s, the Congress debated a price-stability objective for the Fed. The Fed opposed such a mandate
and it was not adopted. Congress did take a step
toward a more explicit treatment of policy objectives
in the Employment Act of 1946. This act identified
the objectives for the government in general, but not
specifically for the Fed. Still, the act was generally
viewed as applying to the Fed, as a part of government. The objectives identified in the act were “to
promote maximum employment, production, and
purchasing power.” Although this set of objectives
could be interpreted as including both full employment and price stability, the title of the bill and the
specific language suggests that the priority at the
time was more to maintain full employment than
to promote price stability. Such a focus on stabilizing
employment and a relative inattention to inflation
was perhaps an understandable reaction to the Great
Depression when, for a decade, high unemployment
and falling prices were the major problems facing
the U.S. economy.
The specific mandate for the Federal Reserve
was first added to the Federal Reserve Act in 1977,
although that same language had been included in
a 1975 concurrent resolution of the Congress. The
1977 amendment required the Board of Governors
and the FOMC to “maintain the growth of monetary
and credit aggregates commensurate with the economy’s long-run potential to increase production,
so as to promote effectively the goals of maximum
employment, stable prices, and moderate long-term
interest rates.” This language makes the objective
of price stability explicit. Because the Fed can contribute to moderate long-term interest rates principally by achieving low and stable inflation, that
objective is generally not viewed as an independent
one. In addition, the goal of maximum employment
is usually interpreted as maximum sustainable
employment—meaning the highest level of employment that can be maintained without upward
pressure on inflation. The mandate is therefore
interpreted as a dual mandate: full employment
and price stability.
The Federal Reserve has not set an explicit,
numerical objective for inflation. Paul Volcker offered
the following definition of price stability in 1983:
A workable definition of reasonable “price
stability” would seem to me to be a situation
in which expectations of generally rising
(or falling) prices over a considerable period
are not a pervasive influence on economic
2

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and financial behavior. Stated more positively, “stability” would imply that decision
making should be able to proceed on the
basis that “real” and “nominal” values are
substantially the same over the planning
horizon—and that planning horizons should
be suitably long.2
Alan Greenspan has described the price stability objective in a similar way: “We will be at price
stability when households and businesses need not
factor expectations of changes in the average level
of prices into their decisions.”3
These definitions make clear a commitment
to low inflation. But they leave open whether, for
example, the inflation rate prevailing today—about
2.5 percent for the core consumer price index (CPI)
measure of consumer prices—is consistent with
this definition. Is policy going to be set to lower inflation over time, and if so, by how much? These definitions also leave open the possibility of changing
interpretations as the FOMC membership changes
over time.
The Fed often prefers to state its objective without specifically mentioning price stability. This is
perhaps because the emphasis on price stability is
taken by some as carrying a hint of restrictive policy
and as an inclination to always be leaning against
cyclical increases in demand. The Fed sometimes
prefers to state its objective simply as promoting
maximum sustainable growth. Stating its objective
in this way allows the Fed to offer a more positive
message and leaves implicit the price stability objective in two ways. First, if the economy were to grow
above a sustainable rate for long enough, overheating and higher inflation would eventually follow.
Second, price stability contributes to a high and
perhaps faster rate of growth in productive capacity,
a point I will return to below. Nevertheless, I prefer
to state the Fed’s objectives as full employment and
price stability. In my view, the Fed has no growth
objective. At full employment, the rate of growth
will automatically be the maximum sustainable
rate the economy is capable of achieving and a rate
largely independent of monetary policy, except
insofar as monetary policy is successful in achieving
price stability.
In recent years, bills have been introduced on a
few occasions that would have made price stability
2

Volcker (1983).

3

Greenspan (1994).

FEDERAL RESERVE BANK OF ST. LOUIS

the sole or primary objective for monetary policy
and required the Fed to set an explicit numerical
inflation target. In 1989, 1991, and 1993, Representative Steve Neal, Chairman of the House Banking
Committee’s Subcommittee on Domestic Monetary
Policy, introduced resolutions instructing the Federal
Reserve “to adopt and pursue monetary policies
leading to, and then maintaining, zero inflation.”
In the 1991 and 1993 versions, zero inflation was
defined as “when the expected rate of change of
the general level of prices ceases to be a factor in
individual and business decisionmaking.” While
these resolutions did not pass, the definition of
price stability in the 1991 and 1993 resolutions was,
undoubtedly not by accident, nearly identical to the
language used by Chairman Greenspan and to the
concept articulated earlier by Chairman Volcker.
A second set of bills was introduced by Senator
Connie Mack and Representative Jim Saxton in 1995
and 1997. These bills instructed the Fed to set an
explicit numerical definition of price stability and
to “maintain a monetary policy that effectively
promotes long-term price stability.” Representative
Saxton introduced a significantly revised version
of these bills in 1997 and 1999, mandating price
stability as the “primary goal” of the Federal Reserve
and requiring the Fed to establish an explicit numerical definition of inflation. Senator Mack reintroduced his version in 1999.
I interpret these bills as attempts to push the
United States toward a full inflation-targeting regime.
Indeed, the Mack versions would establish an inflation-targeting regime among the strictest in the
world, given that it would have established price
stability as the sole objective of monetary policy,
not simply a hierarchical set of objectives. The
Saxton version is more in line with hierarchical
mandates employed in many inflation-targeting
regimes. These bills were, therefore, vigorously
opposed by advocates of the dual mandate. Perhaps
because these bills formed the backdrop to the
debate in the United States about the policy mandate, little discussion has taken place on the merits
of moving to an explicit numerical inflation target
in the context of the prevailing dual mandate. Of
course, another explanation for the lack of debate
is that few are unhappy with macroeconomic performance under the current regime.

Mandates in Inflation-Targeting Regimes
New Zealand in 1990 became the first country
to establish a formal inflation-targeting regime.

Canada followed in 1991, the United Kingdom in
1992, and Australia and Sweden in 1993. Subsequently, Finland and Spain adopted inflation targeting (before becoming members of the European
Monetary Union), and in the last few years several
developing countries have adopted this approach.
Although the European Central Bank (ECB) does
not identify itself as an inflation-targeting regime,
the Maastricht Treaty set price stability as the ECB’s
primary objective and the ECB has set an explicit
numerical target for inflation.
What Is an Inflation-Targeting Regime?
Inflation-targeting regimes generally identify price
stability as the primary objective, usually in the
context of a hierarchical mandate. They set an
explicit numerical target for inflation and set a
period over which any deviation of inflation from
its target is to be eliminated, although some regimes
provide escape clauses and other flexibility related
to the pace of return to price stability.
The inflation target is sometimes set as a point
and sometimes as a range. In most cases, the inflation objective is set for a measure of overall consumer price inflation, the point or midpoint of the
ranges is generally around 2 percent, and the ranges
(where employed) are generally 2 percentage points
wide—typically 1 percent to 3 percent. The time
period prescribed for return to the inflation target
following departures is sometimes explicit and
sometimes not, generally in the range of 18 months
to 2 years.
Examples of Inflation-Targeting Regimes. In
New Zealand, the first inflation-targeting regime, the
numerical target is set jointly by the Minister of
Finance and the Governor of the central bank and
is currently a range of 0 percent to 3 percent, the
widest of any of the ranges in inflation-targeting
regimes. New Zealand is quite well-known for
establishing performance contracts for government
officials, and this approach is followed in the law
governing the operation of the central bank: The
statute allows the Governor to be dismissed if inflation performance is inadequate.
The Bank of Canada operates under the vaguest
legal mandate among inflation-targeting central
banks. Its statute requires it to regulate “credit and
currency in the best interests of the economic life
of the nation.” Despite the absence of a precise legal
mandate, the details of the Bank’s monetary policy
objectives are reached by agreement between the
Bank and the Department of Finance. This agreement has set price stability as the principal objective
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for monetary policy. To implement this objective,
the agreement sets the range for inflation as 1
percent to 3 percent and identifies the midpoint
as the explicit target.
The Reserve Bank of Australia has a mandate
most closely resembling ours, though it is even
broader and more open-ended. Their legislative
mandate is “to [promote] stability of the currency
of Australia;…[maintain] full employment in
Australia; and…[foster] economic prosperity and
welfare of the people of Australia.” The explicit
inflation target, 2 percent to 3 percent, is set by
the central bank and applies to the average inflation
rate over a business cycle. Although Australia is
counted among inflation-targeting countries, it
has a dual mandate rather than a hierarchical one.
Indeed, it is a model for the combination I prefer:
an explicit inflation target within a dual mandate.
The mandate in the United Kingdom is hierarchical. Article 11 of the Bank of England Act sets the
objectives for monetary policy as follows: “to maintain price stability” and “subject to that, to support
the economic policy of Her Majesty’s Government,
including its objectives for growth and employment.” The explicit target, set by the Chancellor of
the Exchequer (the equivalent of the Minister of
Finance in many countries or the Secretary of the
Treasury in the United States), is currently 2.5 percent and the target is for retail prices excluding
mortgage interest payments. The Governor of the
Bank of England must write a letter to the Chancellor
if inflation deviates by more than 1 percentage point
from the target.
The ECB does not view itself as an inflationtargeting central bank. However, the Maastricht
Treaty—the equivalent of the statute establishing
the objectives for a central bank—identifies price
stability as the principal objective in the context of
a hierarchical mandate. Article 105 of the Maastricht
Treaty states that “the primary objective of the
[European System of Central Banks (ESCB)] shall
be to maintain price stability. Without prejudice to
the objective of price stability, the ESCB shall support
the general economic policies in the community
with a view to contributing to the objectives of the
Community laid down in Article 2.” The objectives
mentioned in Article 2 include “sustainable and
non-inflationary growth,” a “high level of employment,” and “raising the standard of living” among
member states. The ECB’s Governing Council sets
the explicit numerical inflation target. This is currently set with an explicit ceiling of 2 percent and
4

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an implicit lower bound of 0 percent. This is the
case of a range rather than a point, with no preference stated for the midpoint.
The Evolution of Inflation-Targeting Regimes.
Over their short history, inflation-targeting regimes
have evolved to give central banks greater flexibility
in conducting monetary policy. Mervyn King calls
regimes which take no account of output gaps
(where the coefficient on the output gap is zero in
the loss function) “inflation nutters.”4 That language
suggests that entirely ignoring output stabilization
is now viewed as an extreme position and not as a
desirable option for central banks. Lars Svensson
argues that there has, in fact, been a convergence
toward “flexible inflation targeting”—meaning
inflation-targeting regimes that in practice take into
account deviations in both output and inflation
from their respective targets.5 Such an evolution
has brought many inflation-targeting regimes closer
in practice to a dual mandate regime.

THE CASE FOR A DUAL MANDATE
The appropriate goals for monetary policy
depend on the structure of the economy and the
preferences of the citizenry. My support for a dual
mandate reflects my views about the structure of
the economy and about the public’s preferences.
These can be summarized as follows:
1. Low and stable inflation (“price stability”) is
essential to good macroeconomic performance and hence should be an objective of
macroeconomic policy.
2. The central bank is uniquely responsible for
the inflation rate in the long run.
3. Monetary policy can make some contribution
to lowering the variability of output relative
to potential.
4. The public desires both low and stable inflation and a low variability of output relative
to potential.
The first two points, of course, are shared by
most central bank mandates. The case for the dual
mandate includes the third and fourth points.

Price Stability as a Policy Objective
As I noted at the outset, it is widely agreed that
low and stable inflation is desirable. Several costs
4

King (1997).

5

Svensson (1999).

FEDERAL RESERVE BANK OF ST. LOUIS

of high and variable inflation have been identified.
These costs typically arise from distortions in economic decisionmaking arising from high or variable
inflation rates and result in lower levels of output
than would otherwise be the case. I won’t elaborate
in detail about these costs here, because I take as a
starting point the agreement that price stability is
an important, if not the singular, objective for monetary policy.6 But the key point is that price stability
is not an end in itself; it is important because it
contributes to a higher level of output and perhaps
faster growth in output.

Monetary Policy and Inflation
Few economists would disagree that inflation
is, as Milton Friedman taught us long ago, always
and everywhere a monetary phenomenon. This
was earlier interpreted as a statement about a tight
relationship between money growth (controlled by
the central bank) and inflation. Today, it is recognized that even if the relationship between money
growth and inflation has weakened, perhaps because
of financial innovations, central banks can achieve
their inflation targets by adjusting their preferred
instrument, typically some short-term interest rate.
Hence, monetary policy still determines the rate of
inflation in the long run. While it is also well understood that supply shocks—such as abrupt changes
in the price of energy or food unrelated to the overall balance between aggregate demand and supply—
can result in short-run changes in inflation, such
changes in inflation can persist only if central banks
accommodate them. Central banks therefore must
accept full responsibility for inflation in the long
run and have the tools to achieve price stability.

The Ability to Stabilize Output
While monetary policy can achieve a long-run
inflation target, economic theory suggests that it
cannot affect the level of output or its growth rate
in the long run, other than by maintaining low and
stable inflation. Therefore, the objective of price
stability should be assigned to monetary policymakers, but the objective of high and rising living
standards should not be. On the other hand, the
Congress and the Administration have many opportunities to affect the level and growth in potential
output—including the size of the structural budget
deficit relative to output, the details of the tax code,
and the composition of government spending.

Whether central banks should accept responsibility for stabilizing output relative to potential is
more controversial. Milton Friedman, for example,
has always questioned the ability of central banks
to stabilize output relative to potential and worried
that attempting to do so could be counterproductive,
given the “long and variable lags” between policy
actions and the economic effects. Economists agree
that monetary policy cannot “fine tune” the economy to ensure that the full employment objective
is continuously maintained. However, a considerable
amount of research supports the contention that
monetary policy can reduce the variability of output
around its full-employment level.7

Preferences
Households and businesses are presumed to
prefer low and stable inflation to high and variable
inflation. But they also prefer high and rising real
income per capita and output that is consistently
close to the economy’s maximum sustainable level
of output. This is often expressed in terms of a loss
function where the loss to society is expressed as a
weighted average of squared deviations of inflation
from its target and of output from its potential level.
The squaring of the deviations ensures that deviations on either side of the target are treated equivalently as losses.8 The weights, a and 1– a, indicate
the relative intensity of the public’s distaste for
deviation from their preferred rates of inflation and
output. The loss to society, L, can be expressed as
(1)

L=a(π – π*)2+(1– a)( y – y*)2,

where π is the rate of inflation, π* is the target rate
of inflation, y is the level of output, and y* is the
target level of output or potential output.
6

For a discussion of the case for price stability, see Fischer (1996).

7

Much of this research involves simulations of empirical macroeconomic models with alternative policy rules. The simple policy rules
used in these exercises mimic the systematic aspects of the response
of discretionary policy to changes in the macroeconomy. For example,
Taylor has shown that Federal Reserve policy actions in recent years
have been broadly similar to what a simple policy rule would have
prescribed. These exercises therefore demonstrate the ability of
simple rules—and by extension, discretionary monetary policy more
broadly—to both reduce the variability of output and achieve a longrun inflation target. See Taylor (1999) for a series of papers involving
simulations of models with various policy rules.

8

Squaring the deviations from target values also penalizes larger deviations more than proportionately compared with smaller ones.

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Tradeoff Between Inflation and Output
Variability
Although it is possible in principle to achieve
price stability and full employment simultaneously,
an inevitable tradeoff between the variability of
output and the variability of inflation exists.9 This
tradeoff is most obvious in the case of a supply
shock, for example an abrupt increase in the price
of oil. An adverse supply shock typically raises
inflation and lowers aggregate demand (by reducing the purchasing power of consumers), thereby
moving inflation up and output down. This gives
rise to a well-known dilemma for monetary policy:
Should monetary policy ease to reduce the decline
in output or tighten to counter the rise in inflation?
The structure of the economy is such that the quicker
monetary policy tries to return inflation to its target
(to reduce the variability of inflation), the greater
the variability in output.
The choice of a hierarchical versus a dual mandate may be the most important consideration determining where a country ends up along this tradeoff.
That is, countries with hierarchical mandates are
more likely to end up with lower inflation variability
at the expense of higher output variability.10 A dual
mandate, therefore, provides flexibility for the
central bank to select the point along this tradeoff
that matches the public’s preference.

Focusing Policymakers on What They
Can Achieve
An argument often made for a hierarchical
mandate is that identifying price stability as the
sole or primary objective focuses monetary policy
on what it can achieve and, thereby, reduces political
pressure to pursue goals that are not achievable. To
be sure, wide agreement exists that central banks
can achieve low and stable inflation and should be
held accountable for doing so. There is also agreement that central banks cannot raise the level or
growth of potential output (other than through
achieving their price stability objective) and should
therefore not be held accountable for these dimensions of macroeconomic performance. But the
public also cares about the variability of output
relative to potential, and the conduct of monetary
policy inevitably will affect output variability. Therefore, in my view, the importance of keeping monetary policy focused on what it can do supports the
case for a dual mandate that explicitly recognizes
both price stability and output stabilization as objectives for monetary policy.
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Is There a Single Long-Run Objective?
It is sometimes argued, however, that price
stability can be the only objective for monetary
policy in the long run, again placing price stability
on a higher plane than full employment. In the long
run, theory holds that the economy gravitates to
full employment by self-equilibrating forces, principally through the effects of price flexibility. That is,
if the economy is operating at a level of output below
full employment, the price level will tend to fall,
and at least for a given value of the nominal money
supply, this will tend to stimulate aggregate demand.
Over time, this process will raise aggregate demand
to a level consistent with full employment. Hence,
policymakers do not have to be concerned with full
employment in the long run, leaving price stability
as their unique long-run concern.
But this view is misleading in a couple of
respects. First, monetary policymakers should be
concerned about two long-run properties of the
economy. One is price stability and the other is the
variability of output around full employment. Policy
has to be judged by its success in both dimensions.
Second, policy is made in the short run, not the long
run. The speed of return of output to its potential
level is influenced by policy decisions and cannot
be treated with indifference. It may just take too long
and waste too many resources in the interim to rely
on the self-equilibrating forces of the economy.
Policymakers will therefore have to take into account,
in practice, both objectives in their policy actions.
Still, a meaningful difference in the interpretation of the two objectives remains. A central bank
can achieve the inflation target, with considerable
precision, in the long run, meaning on average over
a period of years. But it cannot be expected to maintain the economy continuously at full employment.
The full employment objective might therefore be
better interpreted as an output stabilization objective. It instructs the central bank to work to reduce
the variability of output around its full employment
level.

The Need for Flexibility
The purpose of a hierarchical mandate is to
impose constraints on the operation of monetary
policy, constraints that proponents believe enhance
9

Levin, Volker, and Williams (1999) analyze the output-inflation volatility frontier in four different macroeconomic models.

10

For some supporting evidence, see Cecchetti and Ehrmann (1999).

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credibility, focus policy on what monetary policy
can achieve, and reduce political pressures for
policy to aim at impossible-to-achieve and potentially destabilizing output goals, such as a level of
output above the economy’s maximum sustainable
rate. However, those same constraints might interfere with the pursuit of other legitimate objectives
of monetary policy, specifically with policy adjustments to reduce the variability of output around
potential output.
Most inflation-targeting regimes explicitly recognize that returning inflation to its target too rapidly
following some departure could result in excessive
variability of output. The solution has been to
encourage a gradual return to the inflation target
by explicitly or implicitly setting a policy horizon
over which policymakers commit to return inflation
to its target. Setting fixed horizons for the return to
the inflation target, independent of the size or the
nature of the shock, clearly reduces the flexibility of
monetary policy. To be fair, many regimes explicitly
note that the policy horizons need not be fixed or
include escape clauses that would allow greater
flexibility, for example, in response to a supply
shock. But setting a policy horizon is intended to,
and does, constrain policy responses. It may therefore interfere with an appropriate balancing of the
full-employment and price-stability goals. This is
especially the case if the mandate is hierarchical,
where other objectives can be pursued only if the
inflation objective is achieved.

The Taylor Rule and the Dual Mandate
The Taylor rule is a useful characterization of
U.S. monetary policy.11 According to the Taylor rule,
monetary policymakers should adjust the target for
the short-term interest rate in response to deviations
of output and inflation from their respective targets
and in response to changes in inflation. It is therefore well aligned with a dual mandate. The Taylor
rule can be written as
(2)

R=r*+π+c[( y/y*) –1]+d(π – π*),

where R is the target nominal policy rate, r* is the
equilibrium real level of the policy rate (consistent
with price stability and full employment), y is output,
y* is the level of potential output, π is inflation, π*
is the target for inflation, and c and d are the parameters that describe the response of the policy rate
to deviations of output and inflation from their
respective targets.

The Taylor rule is consistent with the loss function described in equation (1) because the rule
prescribes an adjustment of the federal funds rate
in response to the deviations from target values that
are presumed to give rise to costs to society. The
Taylor rule also helps to make the point that policymakers can operate with an output stabilization
goal and still ensure that inflation is, on average,
consistent with the inflation target in the long run.12
A strict version of inflation targeting would be
one based on a loss function, taking into account
only losses associated with inflation deviating from
its target. In terms of equation (1), that would mean
that a=0—that is, no costs were associated with
deviation of output from its potential level. Based
on a simple model, we could derive an optimal
policy response to shocks, based on this loss function and the more general one where costs are
assigned to deviations from both price stability and
full employment. If policy is set assuming a=0 (as
would be the case in a very strict inflation-targeting
regime), it is clear that policy will be suboptimal if
the true loss function does assign a cost to deviating
from full employment.13
The more difficult question is: How suboptimal
are inflation-targeting regimes that recognize the
costs of excessive output variability, but nevertheless
constrain monetary policymakers from responding
to deviations of output from its target, except when
the inflation target has already been met or when
policymakers can project that it will be met in a
reasonable period? In my view, such regimes are
likely to remain suboptimal, compared with a more
flexible dual-mandate regime.

Transparency, Accountability, and the
Dual Mandate
As I noted, transparency about monetary policy
requires a full and accurate account of the objectives. But pretending that inflation is the only objective, while taking account of output variability in
practice, only makes for less-transparent policy and
ensures that the central bank will have difficulty
communicating the rationale for its policy actions.
11

Taylor (1993).

12

A Taylor rule could also be consistent with a regime that set inflation
as the sole objective. In this case, the output gap terms would be viewed
as a predictor of inflation, allowing policymakers to take preemptive
action to contain the threat of higher inflation, in addition to directly
responding to higher inflation itself.

13

See Kim and Henderson (2000).

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I remember the first conference I attended after
joining the Board of Governors. Two foreign central
bankers—each from inflation-targeting countries—
lectured me about how “good” central bankers acted
in public. They each told me that a disciplined
central banker would never admit to having a stabilization objective and never admit that there was a
cost of lowering inflation. Such admissions, they
warned, would only undermine the public’s confidence in a central banker’s commitment to price
stability. I responded that this lesson in central banking surprised me. I would not have thought obfuscating about policy objectives or the way monetary
policy affects the economy would have enhanced
the credibility of a policymaker. I still don’t.

THE CASE FOR AN EXPLICIT
INFLATION TARGET
An explicit inflation target would, in my view,
give added precision to an already mandated objective. Three of the arguments for inflation-targeting
regimes, it seems to me, also support an explicit
inflation target within a dual mandate. First, an
explicit inflation target would improve the transparency and accountability of monetary policy.
Second, it might help, at the margin, to anchor
inflation expectations. Third, it would help to institutionalize recent good monetary policy. It would
also, in my view, make the decisionmaking process
more coherent. Indeed, moving in this direction
would extract most of the benefits of an inflationtargeting regime without suffering the loss of flexibility inherent in its hierarchical mandate.

Improving Transparency and
Accountability
Transparency is an important goal for monetary
policymakers for two reasons. First, a more transparent policy may be a more effective one. Monetary
policy works both through the setting of a target
short-term nominal interest rate and by the expectations policymakers induce in the markets, wittingly
or unwittingly, about the course of future policy. To
the extent that market participants correctly anticipate future policy moves, long-term interest rates
will move in response to expectations of future
moves in short-term rates, in effect, speeding the
response of aggregate demand to monetary policy.
Second, central bank independence has to be balanced by accountability. More precise goals increase
both the transparency and the accountability of
monetary policy.
8

N OV E M B E R / D E C E M B E R 2 0 0 1

Anchoring Inflation Expectations and
Increasing Credibility
Anchoring inflation expectations at the targeted
rate of inflation is an important goal for monetary
policy. However, whether an explicit inflation target
or a formal inflation-targeting regime would boost
the credibility of the central bank’s commitment to
price stability is more debatable. In my judgment,
credibility is primarily earned by performance. In
addition, there is little empirical evidence to suggest that either explicit inflation targets or inflationtargeting regimes lower the cost of disinflation by
directly lowering inflation expectations. Still, at the
margin, such a target might enhance the ability of
the Fed to anchor inflation expectations and perhaps
also enhance the ability of the Fed to pursue its stabilization objective without undermining the public’s
confidence in its commitment to low inflation.

Institutionalizing Good Monetary
Policy
Most observers would rate monetary policy in
the United States over the last two decades as very
good. Good policy, in turn, depends on the combination of a well-defined mandate, a disciplined
strategy for achieving the mandate, and the quality
of the FOMC and its staff working to implement
the strategy. The Chairman has considerable influence over the policy outcome, disproportionate to
the one vote he or she casts, so that the quality of
the chairman is especially important. The Federal
Reserve has been fortunate to have strong leadership
for many years under both Paul Volcker and Alan
Greenspan. A more fully articulated mandate could
help ensure that policy remains well focused and
disciplined as the leadership of the Fed changes.

Facilitating the Policymaking Process
The Fed staff routinely shows policymakers the
prescriptions from several Taylor-rule-type policy
reaction functions, and such a rule is explicitly
incorporated into the Fed’s large-scale model used
for policy analysis. The staff has never asked FOMC
members about their preferences for a numerical
inflation target and instead often employs the target
that John Taylor used in the policy rule he introduced in 1993. I have great regard for John, but this
seems to be a rather unusual way for a policy rule
to be run at the Fed.
More important, if the target is implicit, and

FEDERAL RESERVE BANK OF ST. LOUIS

therefore imprecise, members of the FOMC inevitably will each make policy decisions in pursuit of
different inflation targets. It seems to me that the
internal discussion of policy would be more coherent
if policymakers agreed in advance on an inflation
objective. There would still be differences in policy
preferences at FOMC meetings due, for example, to
different views about the economic outlook, different views about the structure of the economy, and
different views about the sustainable level of the
unemployment rate or the maximum sustainable
rate of growth in output. But, provided that all FOMC
members agreed to seek the objective chosen by the
majority, an explicit target would prevent members
from pulling in different directions because of different inflation objectives.

even allowing for the convergence that has been
under way. I believe we could retain that flexibility
with an explicit inflation target because of our historical commitment to a dual mandate and because
there would be no presumption that the fundamental strategy for conducting monetary policy, summarized by the Taylor rule, would change. At the
same time, I believe transparency and accountability
are appropriate goals for monetary policymakers
and that an explicit inflation target would contribute
to each of these goals, even if it would not have had
much effect on the actual course of policy in recent
years.

Retaining Flexibility with the Dual
Mandate

A natural question in the case of a dual mandate
is whether both objectives should be made explicit.
Some members of the Congress, for example, might
encourage the Fed to adopt an explicit objective for
full employment to balance an explicit inflation
objective. Although I support an explicit objective
for inflation, it would not be constructive, in my
view, to set an explicit numerical target for full
employment.
The central bank is capable of achieving an
inflation objective, at least on average over a period
of years. In contrast, if we define full employment
in terms of a threshold for the unemployment rate
consistent with maximum sustainable employment,
the central bank has no choice about what this
threshold should be.14 It is determined by the structure of the economy, including the effectiveness of
institutions and markets in matching vacancies and
unemployed workers, and by policies, such as the
levels of unemployment compensation and minimum wage rates.
Because institutions and markets evolve and
labor market policies change, it would be inappropriate to set a fixed numerical objective for full
employment. That does not rule out central banks
being more transparent about their estimate of the
unemployment rate that is consistent with maximum sustainable employment, though no central
bank has ventured into this territory. That is perhaps
not surprising. Indeed, it would be difficult to do so
because there is considerable debate—both inside
and outside central banks—about the usefulness of
a “full employment rate of unemployment” as a

The key issue for me is whether setting an
explicit inflation target would reduce the flexibility
of policymakers to pursue a dual mandate and select
the preferred point along the tradeoff between output and inflation variability. That is, would making
the p* in the Taylor rule explicit inevitably also lead
to a change in the relative responses to deviations
from the output and inflation targets (the c and d
parameters in equation (2))? Specifically, would
implementing an explicit inflation target inevitably
also raise the response parameter on the inflation
gap relative to that on the output gap? In my view,
the answer is that this need not be the case, but I
agree that there is some risk of this outcome. It
seems to me, however, that it is less likely if the move
to an explicit inflation target is taken in the context
of a reaffirmation of the dual mandate.

If It Ain’t Broke, Don’t Fix It
As I noted above, most observers believe that
monetary policy has been excellent in recent years.
Why, then, change the underlying framework for
policy, especially when this change is not likely to
have much of an influence on the conduct of monetary policy?
The case for moving to an explicit inflation
target within our current dual mandate is that it
extracts most of the potential benefits of inflationtargeting regimes without necessarily reducing the
flexibility of policy. I believe that the Fed remains
more responsive to deviations of output from its
target than most inflation-targeting central banks,

Should the Full Employment Objective
Be Explicit Also?

14

This threshold is often referred to as the non-accelerating inflation
rate of unemployment or the NAIRU.

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guide to policy and, even among those who believe
this is an important and useful concept, about what
that rate may be today and how it tends to change
over time. So the issue here is not simply one of
transparency and accountability.
In addition, political considerations may be at
work. At times, an increase in the unemployment
rate may be required to sustain stable, low inflation.
Rare is the leader of a monetary policy committee
who relishes going to the legislature and reporting
that the central bank is concerned that too many
people have jobs.
The uncertainty about the threshold unemployment rate also suggests a differing degree of intensity in the response of monetary policy to deviations
of inflation and output to their respective targets.
That uncertainty derives from our inability to precisely pin down two key parameters—the threshold
unemployment rate and the trend rate of growth in
potential output. As a result, there is a subtle difference between the two objectives in the dual mandate.
One objective—price stability—can be well defined
and is fully under the control of monetary policymakers, at least over a period of time. The other—
full employment—is set by the structure of the
economy, not policymakers, and cannot be precisely
pinned down numerically at any point in time and
can vary over time.

PRACTICAL CONSIDERATIONS
Let us now assume that a decision has been
made to move to an explicit inflation target. Several
steps would be required to implement such a decision. First, we would have to decide who would set
the explicit target. Second, a specific price index
would have to be selected to serve as the basis for
the inflation target. Third, we would have to decide
whether the target should be a point or a range.
Fourth, we would have to decide on the level of the
point or the values that establish the range.

Who Should Set the Inflation Target?
Among inflation-targeting regimes, there is a mix
of practices with respect to who sets the numerical
target for inflation. In almost all cases, the government identifies price stability as a target, either as
the single target or as part of a hierarchical mandate.
In about half the cases, the explicit numerical target
for inflation is set by the government, typically the
finance ministry, generally in consultation with the
central bank; in about half the cases, the target is
10

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set by the central bank, often in consultation with
the finance ministry.
The United States already has a mandate that
includes price stability. The existing law therefore
seems to be compatible with the Federal Reserve
setting an explicit numerical inflation rate consistent
with the notion of price stability. Thus, the FOMC
could move in this direction without any amendment to the Federal Reserve Act. Perhaps the setting
of an explicit inflation target by the Federal Reserve
might be analogous to its earlier setting of numerical money growth ranges. In 1978, the Congress
instructed the Fed to report an objective for money
growth. The FOMC then decided unilaterally on the
numerical ranges. In 2000, the Congress amended
the Federal Reserve Act to remove the requirement
that the Fed report to the Congress on the ranges
for monetary aggregates. In the case of an inflation
objective, the Congress has already imposed a pricestability objective. All the FOMC would be doing is
communicating back to the Congress and the public
its interpretation of that objective.
Nevertheless, such a move would likely be interpreted as an important change in the conduct of
monetary policy. Consequently, if the FOMC desired
to move in this direction, extensive prior consultations would be appropriate, especially with the
Congress, but also with the Administration. It might
also be constructive to get feedback from a wider
audience on a proposal to set an explicit inflation
target before proceeding in this direction.
It would, however, be problematic for the United
States to follow the approach in many inflationtargeting countries of having the ministry of finance
(in our case, the Treasury Department) set the inflation target. Such an approach is more comfortable
politically in a parliamentary system, in which the
legislative and executive branches are always controlled by the same party or coalition. It seems
unlikely that the Congress would delegate this
responsibility to the Treasury Department. Even
regular consultation with the Treasury Department
about a specific goal under the approach I have
mentioned here might raise questions unless the
Congress explicitly authorized it.

Choosing a Specific Price Index
Most broad measures of inflation move roughly
in concert over time. Nevertheless, the differentials
among the most widely used aggregate measures of
inflation generally are not stable over long periods.
Therefore, it does make some difference which

FEDERAL RESERVE BANK OF ST. LOUIS

measure is selected for the target. All inflationtargeting central banks use a measure of consumer
price inflation for their target. In the absence of a
complete model of the cost of inflation to guide the
choice, the use of consumer price measures seems
appropriate because these measures are the most
relevant to the calculation of real income for households, because the welfare of households is ultimately the goal for monetary policy, and because
measures of consumer price inflation are often the
most visible of inflation measures.
In the United States, this would mean a choice
between the consumer price index (CPI) and the
price index for personal consumption expenditures.
The CPI is the most widely recognized measure of
consumer price inflation, but the Federal Reserve
has expressed the view that the measure based on
personal consumption expenditures has advantages
as a measure of trends in consumer price inflation.
Setting the inflation rate in terms of the price index
for personal consumption expenditures would further
elevate this measure in the public consciousness.
A related decision is whether to set the target in
terms of overall inflation or in terms of core inflation—that is, consumer price inflation net of the
direct influence of movements in energy and food
prices, which tend to be volatile. Focusing on core
inflation might increase the likelihood that monetary policy would respond to underlying inflation
developments that promised to be persistent, and
not on transitory changes in inflation. Nevertheless,
most inflation-targeting regimes set their explicit
inflation target in terms of overall inflation. As long
as policy is focused on achieving a longer-run inflation outcome, as opposed to meeting the target each
quarter or even each year, a target for overall inflation can work well because swings in energy and
food prices that lead to shorter-run inflation blips
tend to dissipate or wash out over longer periods.
In this case, it would also be useful, as is the practice
at some inflation-targeting central banks, to monitor
movements in core inflation as a guide to whether
current monetary policy is well aligned with the
longer-term objective for overall inflation. Weighing the pros and cons, policy might be better and
the communication to the public might be most
clear if the target itself was expressed in terms of
the core inflation rate.

Point or Range
Practice differs among inflation-targeting central
banks, with about half setting their targets as points

and the other half as ranges. Among those who
adopt ranges, some also identify the midpoint of
the range as the specific target. I prefer a point target.
This provides a more precise anchor for inflation
expectations and a more specific target for monetary policymakers. If a range is selected, questions
will arise about the differing implications of movements of inflation inside the range and outside the
range and, in the absence of explicitly identifying
the mid-point as the target, about where within the
range policymakers would prefer inflation to gravitate. If there is indifference about movements inside
the range, this will tilt policy toward allowing greater
variability of inflation.

What Level?
If the objective is price stability, this may seem
like a pointless question. But it is an important issue
for two reasons. First, assuming that the official
indexes are biased upward, true price stability will
be achieved at some positive rate for measured
inflation. Second, there are considerations that favor
allowing some small positive rate of true inflation,
rather than true price stability.
In 1995, the Boskin Commission estimated that
the measurement bias for the CPI was between 0.8
and 1.6 percentage points. Since then, the Bureau of
Labor Statistics has made a series of methodological
improvements in the CPI, lowering the bias. In 1999,
the Congressional Budget Office estimated that the
cumulative effects of these improvements had been
to reduce the measurement error to a point estimate
of 0.8 percent. Therefore, in terms of the CPI, if this
were the only consideration, the target could be set
at 1 percent to allow for measurement error (and
also a round number). This also suggests that the
target should not be fixed in time, but should be
adjusted over time to take into account changes in
the estimated bias.
There are a couple of reasons to consider setting
an inflation target above the level consistent with
true price stability. If there is resistance to declines
in nominal wages, a small amount of wage inflation
may enhance the flexibility of real wages and facilitate the movement to equilibrium in the labor market.15 Whether this requires positive price inflation
will depend on the variance of the wage changes,
the degree of nominal wage rigidity, and the rate of
growth of labor productivity. In addition, a positive
rate of inflation increases the flexibility of mone15

See Akerlof, Dickens, and Perry (1966).

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tary policy by allowing policymakers to drive real
interest rates below zero. Particularly in light of the
latter consideration, I would set the inflation target
at what I refer to as true price stability plus a small
cushion. Specifically, for the CPI, I would set it at 2
percent, 1 percentage point for the measurement
error and 1 percentage point for the cushion.16 This
would correspond roughly to a 1.5 percent inflation
rate for the price index for personal consumption
expenditures, based on recent differentials of this
measure relative to the inflation rate for the CPI.
The precise magnitude of the cushion should also
be subject to adjustment over time to reflect ongoing
research about its optimal size.

Time Horizon
There should be no fixed time horizon for
returning inflation to its target when deviations
occur. Such a horizon would be arbitrary, in some
cases might not be credible, and potentially would
constrain the ability of the FOMC to pursue the dual
mandate. On the other hand, it would be useful to
use a measure for inflation that smoothes over
transient shocks and that is not subject to potential
problems with seasonal adjustment. For that reason,
I would favor a year-over-year measure of the inflation rate—for example, a 12-month CPI or price
index for personal consumption expenditures—for
evaluating performance relative to the target.

CONCLUSION
It is widely agreed that price stability is an important objective of monetary policy and that central
banks should be held responsible for that objective.
That said, central banks differ over whether they
should set an explicit inflation target and whether
they should acknowledge and take responsibility
for other objectives, specifically full employment
or output stabilization.
An explicit inflation target would give added
precision to an already mandated objective and
would thereby improve the transparency of and
accountability for monetary policy. Moving to an
explicit inflation target would, in my view, be consistent with the current statute governing the objectives of monetary policy in the United States and
would, in turn, require no fundamental change in
the current Federal Reserve strategy for implementing monetary policy.
The most important question that has to be
addressed in order to assess the costs and benefits
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of a move in this direction is whether it could be
accomplished without reducing the flexibility the
Fed now has to pursue a dual mandate. In my view,
if the explicit mandate is set in the context of a
reaffirmation of the dual mandate, the flexibility
now enjoyed by U.S. monetary policy will likely be
maintained. A second question is whether moving
in this direction would matter much for the conduct
of monetary policy in the United States. I believe the
answer to that question is that it would not matter
much today, with the current Chairman and the
current FOMC. But moving in this direction would
provide some greater assurance of continuity in
policy. In addition, it would have the virtue of
enhancing transparency and accountability.

REFERENCES
Akerlof, George; Dickens, William and Perry, George. “The
Macroeconomics of Low Inflation.” Brookings Papers on
Economic Activity, 1996, 1, pp. 1-59.
Bernanke, Ben S.; Laubach, Thomas; Mishkin, Frederic S.
and Posen, Adam S. Inflation Targeting: Lessons from
the International Experience. Princeton, NJ: Princeton
University Press, 1999.
Cecchetti, Stephen G. and Ehrmann, M. “Does Inflation
Targeting Increase Output Volatility? An International
Comparison of Policymakers’ Preferences and Outcomes,”
in Klaus Schmidt-Hebbel, ed., Monetary Policy: Rules and
Transmission Mechanisms, Proceedings of the Third
Annual Conference of the Central Bank of Chile, 1999.
<www.bcentral.cl>.
Fischer, Stanley. “Why Are Central Banks Pursuing Long-Run
Price Stability,” in Achieving Price Stability: A symposium
sponsored by the Federal Reserve Bank of Kansas City,
Jackson Hole, WY, August 1996, pp. 7-34.
Fuhrer, Jeffrey C. and Sniderman, Mark S., eds., “Monetary
Policy in a Low Inflation Environment.” Summary of a
conference sponsored by the Federal Reserve Banks of
Boston, New York, Cleveland, Richmond, Atlanta, St. Louis,
16

See Fuhrer and Sniderman (2000) for a series of papers on the implications of a zero nominal bound for the nominal interest rate for setting inflation targets. The paper by Reifschneider and Williams in that
volume provides some support for the 1 percentage point cushion I
have suggested. They conclude: “[I]n very low inflation environments…
the zero bound could prove to be a significant constraint on policy…
With the effectiveness of open market operations diminished at times,
the economy would likely experience a noticeable increase in the
variability of output and employment, particularly if policymakers
were to pursue an inflation target of 1 percent or below.”

FEDERAL RESERVE BANK OF ST. LOUIS

and Minneapolis, and the Board of Governors of the
Federal Reserve System, 18-20 October 1999. Journal of
Money, Credit, and Banking, November 2000, 32(4, Part
2), pp. 845-69.
Gramlich, Edward M. “Inflation Targeting.” Speech delivered
before the Charlotte Economics Club, Charlotte, NC, 13
January 2000. <www.federalreserve.gov/boarddocs/
speeches/2000/20000113.htm>.
Greenspan, Alan. Statement before the Subcommittee on
Economic Growth and Credit Formulation of the Committee on Banking, Finance, and Urban Affairs, U.S. House
of Representatives, 22 February 1994.
Kim, Jinill and Henderson, Dale. “Exactly How Suboptimal
Are Inflation Targeting and Nominal Income Targeting.”
December 2000. <www.people.virginia.edu/~jk9n/
hk3001219.pdf>.
King, Mervyn. “Changes in U.K. Monetary Policy: Rules
and Discretion in Practice.” Journal of Monetary
Economics, June 1997, 39, pp. 81-97.
Levin, Andrew T.; Volker, Weiland and Williams, John C.
“Robustness of Simple Monetary Policy Rules Under
Model Uncertainty,” in John B. Taylor, ed., Monetary
Policy Rules. Chicago: University of Chicago Press, 1999.
Svensson, Lars E.O. “How Should Monetary Policy Be
Conducted in an Era of Price Stability?” in New Challenges
for Monetary Policy: A symposium sponsored by the
Federal Reserve Bank of Kansas City, August 1999, pp.
195-259.
Taylor, John B. “Discretion Versus Policy Rules in Practice.”
Carnegie-Rochester Conferences Series on Public Policy,
December 1993, 39, pp. 195-214.
___________, ed. Monetary Policy Rules. A National Bureau
of Economic Research Conference Report. Chicago:
University of Chicago Press, 1999.
Volcker, Paul. “Can We Survive Prosperity?” Speech given at
the Joint Meeting of the American Economic and
American Finance Associations, San Francisco, CA, 28
December 1983.

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FEDERAL RESERVE BANK OF ST. LOUIS

Equity Financing of the
Entrepreneurial Firm

Figure 1
Venture Capital Raised and Nasdaq IPOs
Billions $
100

Frank A. Schmid

90
80

n entrepreneur is an individual with a
project blueprint and limited wealth. If
launching the project requires expenses
that exceed the entrepreneur’s initial wealth, he
needs outside financing. Entrepreneurs differ from
“hired management” in that they are indispensable
for the firm’s day-to-day operations. This is because
entrepreneurs add value to companies perpetually,
rather than by handing over the project blueprints.
Outside financing is fraught with the problem
of asymmetric information between the entrepreneur (who is a firm insider) and the (outside) investor.
Asymmetric information between management and
investor is considered the most significant problem
in corporate finance.1 Typically, the problem of
asymmetric information is modeled in finance
literature as one that pertains to the use of free
cash flow by management or to management’s
project choice.2 Asymmetric information about the
use of free cash flow can take on a variety of forms.
First, cash flow might be unobservable. In this case,
the diversion of free cash flow for personal use by
management goes unnoticed by the investor. If cash
flows are unobservable, the outside equity holder
has no bargaining power over the allocation of free
cash flow to dividend payments. Second, management’s use of free cash flow might be observable,
but not verifiable. This is when the outsider can
observe management directing free cash flow to
its own benefit, but cannot verify these actions in
court. Third, management’s actions might be
observable and verifiable, but compliance might
not be enforceable. Examples of non-enforceability
are cases where it is prohibitively costly for investors
to go to court, or where court rulings are rendered
worthless because the culprit is subject to limited
liability or has limited wealth.3
In spite of the problems of asymmetric information outlined above, outside equity financing of the
entrepreneurial firm has achieved a rapid increase
over the past decade (see Figure 1). Venture capital
funds, which finance privately held start-ups, raised

A

Frank A. Schmid is a senior economist at the Federal Reserve Bank of
St. Louis. William Bock and Judith Hazen provided research assistance.

© 2001,

T H E F E D E R A L R E S E R V E B A N K O F S T. L O U I S

70
Venture Capital

60
50
40
30
20

Nasdaq IPOs

10
0
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000

NOTE: Annual observations; last observation: 2000.
SOURCE: Venture Economics & National Venture Capital
Association, <http://www.ventureeconomics.com>;
Nasdaq, <http://www.marketdata.nasdaq.com>.

a record $92.3 billion in 2000. This is a thirty-fold
increase relative to 1990. At Nasdaq, initial public
offerings raised an all-time high of $53.6 billion in
2000, which is 24 times as much as in 1990.
This article analyzes equity financing of the
entrepreneurial firm against the background of
observable but non-verifiable cash flow. The study
covers three organizational forms: the limited partnership, the private corporation, and the public
corporation. The legal type of the firm determines
the outside equity financing options that are available to the entrepreneur. By definition, initial public
offerings are available to the (henceforth) public
corporation only, whereas venture capital is possible
for both the limited partnership and the privately
held corporation.
The analysis shows that venture capital financing is superior to public offerings when the entrepreneur has low initial wealth relative to the size of
the project and is equivalent otherwise. This result
highlights the importance of private equity in
financing entrepreneurial enterprises. The GrammLeach-Bliley Act of 1999 allows banks to expand
1

See Hart (1995), Jensen (2000), and Myers (2000).

2

See Zingales (2000).

3

For causes of lack of observability, verifiability, or enforceability and
their consequences for contractual arrangements, see Hart (1995) or
Milgrom and Roberts (1992).

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the scope of their activities in this arena. The law
allows financial holding companies to provide
equity financing to nonfinancial firms for up to ten
years. In particular, the act defines a framework in
which financial holding companies can sponsor
private equity funds that provide venture capital to
entrepreneurial firms. While it is not the purpose of
this article to study the consequences of the GrammLeach-Bliley Act on venture capital financing, the
analysis suggests that venture capital is a significant
financing instrument. The Gramm-Leach-Bliley Act
helps improve the supply side in the venture capital
market by broadening the spectrum of institutions
that are allowed to provide private equity to firms
that do not (or not at this stage) seek to raise capital
in an initial public offering.
The following analysis uses a simple model of
the entrepreneurial firm as proposed by Myers
(2000). While the analysis of the limited partnership
draws heavily on Myers, the examination of the
corporation differs from Myers most significantly
in its simplicity and its focus on the most basic
differences among the organizational forms. The
model shows that private corporations face less
stringent financing constraints than limited partnerships or public corporations. The result emphasizes
the importance of the private corporation as a legal
form. While the model helps explain the choice of
the legal form by the entrepreneur, it cannot explain
transitions among legal forms. For instance, the
analysis offers no insights into why and when a
private corporation might go public.

A BRIEF LITERATURE OVERVIEW
The literature on financing the entrepreneurial
firm is diverse. This is because the characteristics
that define the entrepreneurial firm are multifold.
Moreover, some of these characteristics are not
unique to the entrepreneurial firm but hold for
other companies as well. In the following we briefly
describe six major economic problems associated
with financing the entrepreneurial firm that have
been dealt with in finance literature.
First, there is the problem of project choice or,
synonymously, asset substitution. If the entrepreneur holds the equity and the outsider holds the
debt, the insider has an incentive to choose excessively risky projects. This is because the debt holder
shares the downside risk, but not the upside risk.
By increasing project risk, the entrepreneur can
shift part of the additional risk to the debt holder.
The classic study in this area is Jensen and Meckling
16

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(1976). Note that the problem of asset substitution
is not confined to the entrepreneurial firm. For
instance, hired management of publicly traded
firms might acquire stock or stock options in the
firm as part of its compensation package.
Second, there is the problem of private control
benefits. Management might take pleasure in being
in control of the operations. The total value of the
firm consists of its “social value,” which is its fair
market value, and the “private value,” which is the
value of the management’s control benefits. The
distinction between private and social values is
important when it comes to the allocation of control rights between management and outside
shareholders. Two seminal studies in this area are
Grossman and Hart (1988) and Harris and Raviv
(1988). For a textbook treatment, see Hart (1995).
Note that private control benefits are not confined
to the entrepreneur, but can apply to hired management as well.
Third, there is the problem of managerial
entrenchment. Managerial entrenchment is not
confined to the entrepreneurial firm, but might hold
true for the firm with hired management as well.
On one hand, the higher the fraction of equity
owned by management, the closer the interests of
management might be aligned to the interests of
the outside shareholders. On the other hand, the
more voting power management has, the more
insulated it is from the disciplining forces of the
market for corporate control. Entrenchment allows
management to employ corporate resources for
private benefits, for instance, through empire building or consumption of perquisites. Morck, Schleifer,
and Vishny (1988) and McConnell and Servaes
(1990) provide empirical evidence for managerial
entrenchment. Zwiebel (1996) shows in a theoretical
model how entrenched management can employ
dividend payments as a means of committing to
paying out free cash flow and keeping outside
investors from intervening.
Fourth, free cash flow might be non-verifiable.
When free cash flow is non-verifiable, the insider
has the opportunity to divert it to consumptive use,
for instance, by financing perquisites. Again, this
problem is not confined to the entrepreneurial firm.
On the other hand, non-verifiability of cash flows is
seen as a significant problem in corporate finance
and it earns considerable attention in finance literature. One thread of literature analyzes the role of
debt as a way of forcing management to pay out free
cash flow. Hart (1995) summarizes this literature in

FEDERAL RESERVE BANK OF ST. LOUIS

a textbook treatment. Another thread of literature
looks at the role of dividend payments as a device
to discipline management by maintaining a sufficient level of debt. The aforementioned paper by
Zwiebel (1996) fits into this category. Finally, a
recent paper by Myers (2000) studies the role of
dividend payments in an all-equity financed firm.
He shows that dividend payments can be viewed as
advance compensation on the outsider’s equity
investment. The dividend payment at the end of
the fiscal year compensates the investor for the
opportunity cost of capital that he incurs in the
upcoming fiscal year.
Fifth, there is the problem of risk sharing.
Entrepreneurs typically are risk-averse individuals
who have most of their human capital and financial
wealth invested in the firm. Outside equity is a
means of sharing risk as it allows the entrepreneur
to limit his exposure to the enterprise. For details,
see a recent theoretical paper by Kirilenko (2001).
Sixth, there is the problem of asset complimentarity. In the entrepreneurial firm, management
owns an asset that is complimentary to the firm’s
operating assets. This means that the entrepreneur’s
human capital and the operating assets are worth
more in combination than in isolation. Complimentarity between the managerial asset and the operating assets is an attribute that is confined to the
entrepreneurial firm. While hired management is
dispensable, the entrepreneur is not. Myers (2000)
briefly discusses this point.

A SIMPLE MODEL OF THE
ENTREPRENEURIAL FIRM
In the following analysis, the entrepreneur is
defined as a person who owns human capital that
is complementary to the operating assets of a firm
(a “project”). As mentioned above, assets are complementary if they are more valuable when used in
combination than in isolation.4 The entrepreneur
can add value to the firm only by being in control
of the day-to-day operations. He is indispensable
for the operations because of his unique inventive
and managerial skills. As opposed to a hired manager, the entrepreneur cannot be removed from the
firm without hurting the project’s net present value
(NPV) of continuation. To keep matters simple, we
assume that removing the entrepreneur from the
firm reduces the NPV of continuation to zero or, put
differently, lowers the going concern value to the
level of the liquidation value.

The need for outside financing arises from the
entrepreneur’s wealth constraint. In terms of the
model, the entrepreneur’s initial wealth, w, falls
short of the investment needed to start up the firm,
–
K , which we assume to be exogenous. The amount
–
K – w needs to be financed by an (outside) investor.
The liquidation value of the operating assets is
–
observable, verifiable (at zero cost), and equal to K
in every fiscal year. Because the operating assets
do not depreciate, there is an infinite investment
horizon. There is no uncertainty in the model.
The project generates perpetual free cash flow
equal to
yt = y = (1 + κ ) ⋅ r ⋅ K
at the end of every fiscal year t (t=1,…,∞), where r
is the marginal cost of capital (for the entrepreneur
and the investor) and κ >0 captures the value that
the entrepreneur adds continually to the firm
through his human capital. The condition κ >0
implies that the project has positive NPV at the outset (i.e., the beginning of fiscal year 1), as well as
positive present value (PV) of continuation at the
end of every fiscal year. We assume that there are
no (other) positive-NPV projects becoming available
to the entrepreneur once the project has been
started. Thus, there is no productive use for internally generated funds.
The fundamental problem of financing the
entrepreneurial firm is the entrepreneur’s ability to
divert free cash flow. By virtue of being in control
of the operations, the entrepreneur can route free
cash flow into personal accounts (where it earns r
at the margin). The amount of free cash flow that
the entrepreneur diverts in fiscal year t is denoted
zt. Because all fiscal years are identical, we can write
the following:
z t = z for all t , t = 1,..., ∞ .
We assume that while cash flows are observable
(at zero cost) to outside investors, they are not verifiable (or verifiable only at prohibitively high costs).
Were the project’s cash flows verifiable (at zero cost),
the problem of asymmetric information in financing
the entrepreneurial firm would not exist. Because
the entrepreneur would be able to commit to dividend payments, any positive-NPV project would
be financed. However, with cash flows being non4

See Hart (1995) for details on asset complementarity and its implications for firm organization.

N OV E M B E R / D E C E M B E R 2 0 0 1

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REVIEW

verifiable, the entrepreneur’s inability to commit to
future dividends leads to underinvestment. We will
show that for sufficiently low levels of initial wealth,
w, or, equivalently, sufficiently low levels of project
profitability, κ, there are positive-NPV projects that
are not undertaken.
The investor can provide outside financing
through debt or equity. In this article, only equity
financing is considered.5 The firm may be organized
into a limited partnership or a corporation. The
corporation may be private or public. Limited partnerships and private corporations tend to have few
equity holders, with the entrepreneur being one of
them. The public (traded) corporation is typically
modeled in finance literature as a corporation with
dispersed equity holders. The outside investor, in
this case, is a multitude of small shareholders whose
subjective probabilities of being pivotal to corporate
decisionmaking may be viewed as zero. For simplicity, we assume that, in the limited partnership and
the private corporation, the firm outsider is a single
investor (or, equivalently, a group of block holders
who act as a single investor).
In the next section, the problem of equity
financing is analyzed for the limited partnership.
In subsequent sections the firm is modeled as either
a private or a publicly traded corporation. The analysis shows that the legal form is critical for the degree
of bargaining power the parties have over the fiscal
year’s free cash flow, once the parties are invested.
It turns out that this ex post bargaining power is
greatest for the outside investor in the private corporation. Consequently, the private corporation
faces the least restrictive outside equity constraint.

The Limited Partnership
The limited partnership consists of a general
partner—the entrepreneur—and one or more
limited partners, which are the outside investors.
For simplicity we represent the firm outsiders by
a single investor (or, equivalently, a small set of
block holders that act as a single investor). Because
there is no uncertainty in the model, the difference
between the general and the limited partners lies
solely in the decision rights over liquidation, which
is the only dimension of project choice in this
model. Generally, in limited partnerships the outside
investor can withdraw his funds (at the end of the
fiscal year), but cannot demand liquidation of (all
or parts of) the operating assets.
It is immaterial to the mechanics of the model
whether partial liquidation is an option or whether
18

N OV E M B E R / D E C E M B E R 2 0 0 1

the project can be liquidated in full only. If partial
liquidation is possible, the periodic free cash flow
of the project, y, decreases by the percentage of the
liquidated assets. The assumption of full liquidation,
on the other hand, would mean that any liquidation,
even if in part, reduces κ to zero, and with it the PV
of continuation.6
The (outside) investor contributes the fraction
–
x to the initial fixed investment, K , while the
entrepreneur contributes the fraction 1– x:
x K = K − w ⇔ (1 − x ) K = w .
We define x∼ to be the fraction of equity held by
the investor. This fraction x∼ might be smaller than,
equal to, or greater than the fraction of capital supplied by the investor, x, depending on whether the
entrepreneur sells the equity at a premium, at par,
or at a discount.
The partnership contract specifies that dividends are paid at the end of the fiscal year:
dt = d = y − z for all t , t = 1,..., ∞ .
Note that the fraction 1– x∼ of the dividend payment
goes to the firm insider.
Because all fiscal years are identical, we can
write the PV of the future dividend stream at the
beginning of any fiscal year as7:
y−z d
= .
r
r
Investor’s Continuation Constraint. The
(outside) investor remains invested if the NPV of
doing so is non-negative. In deriving this continuation constraint, we assume that the partnership
contract allows the investor to withdraw his funds
at the end the fiscal year, which means that there is
no vesting period. Upon demand, the entrepreneur
has to pay to the investor the cash equivalent of
∼ of the liquidation value of the operatthe fraction x
ing assets. Note that if the investor withdraws his
funds, the entrepreneur has no incentive to pay
dividends for the respective fiscal year. The investor
remains invested in the firm for (at least) one more
5

Hart (1995) presents an extensive treatment of debt financing of the
entrepreneurial firm.

6

The assumption of total liquidation has the advantage of being analo–
gous to the assumption that a fixed amount of operating assets, K , is
needed to start the project.

7

Note that

d ∞
d
.
≡∑
r t =1 (1 + r ) t

FEDERAL RESERVE BANK OF ST. LOUIS

fiscal year if (and only if) the sum of this fiscal
year’s dividend payment and the PV of all future
dividend payments is greater than or equal to the
liquidation value. This yields the following continuation constraint for the firm outsider:
d

˜x ⋅ (d + r ) ≥ ˜x K

⇔ d+

d
≥ K.
r

In equilibrium, the investor’s continuation
constraint is satisfied at equality because the entrepreneur does not pay more in dividends than is
needed to keep the outside equity capital in the
firm:
d

rK

˜x ⋅ K = ˜x ⋅ (d + r ) ⇔ d = 1 + r .
Investor’s Participation Constraint. The minimum level of dividend payments that satisfies the
investor’s continuation constraint need not fulfill
the investor’s participation constraint, i.e., his willingness to invest in the first place. For instance, if
the outside equity were offered at par (which would
imply x∼=x), the investor’s participation constraint
would be violated. This is because, for x∼=x, the
–
investor’s capital contribution, x K , exceeds the PV
of the dividend stream, xd/r:

xK > x

1
d
=xK
.
1+ r
r

Because the entrepreneur cannot commit to
dividend payments greater than what is needed to
keep the outside equity capital in the firm, the
investor is unwilling to finance the project in the
first place. On the other hand, the entrepreneur
can induce the investor to participate by issuing
–
equity at a discount. Upon contributing x K in cash,
–
the investor receives equity claims equal to x∼ K ,
x∼>x.
Note that, technically, the entrepreneur can
issue equity at a discount by putting part of his own
–
contribution, w=(1–x) K , into equity reserves while
selling the outside equity at face value.
The entrepreneur chooses the minimum x∼ that
meets the investor’s participation constraint:
rK 

r x K = ˜x d = ˜x
.
1 + r 

This implies x∼=x(1+r) and consequently:
x̃ d = x (1 + r ) d = x (1 + r ) ⋅

rK
=xrK.
1+ r

By issuing equity at a discount, the entrepreneur
transfers the following amount to the investor at
inception of the project:
( x̃ − x )

d
d
d
= ( x [1 + r ] − x ) = r x = x d .
r
r
r

Technically, the entrepreneur can do this by transferring an amount equivalent to one dividend payment, d, to the reserves. The implied transfer to the
investor at the amount x·d increases the return on
–
the outsider’s investment, x K , by an amount sufficient to fulfill his participation constraint. At the
same time, the investor’s continuation constraint
remains satisfied at equality.
In the Appendix we show that, in competitive
capital markets, the investor cannot do better than
break even. This implies that the investor has no
incentive to renegotiate the partnership contract
at the end of the fiscal year. By renegotiating the
contract, the investor cannot improve his position
beyond the break-even point, which is what fulfills
his participation constraint.
Entrepreneur’s Participation Constraint.
Because the (outside) investor breaks even, the
entrepreneur’s participation constraint is equivalent
to the NPV decision rule:
y
− K ≥ 0.
r
–
–
–
For y/r ≡ z/r+d/r and K ≡ x K +(1–x)K , we obtain
NPV ≥ 0 ⇔

z d
+ − x K − (1 − x ) K ≥ 0 .
r r
With d/r ≡ (1– x∼)d/r+x∼d/r, we can write
NPV ≥ 0 ⇔

NPV ≥ 0 ⇔

d
d
z
+ (1 − ˜x ) + ˜x − x K − (1 − x ) K ≥ 0 .
r
r
r

After rearranging terms we obtain
(1)

NPV ≥ 0 ⇔

d
z
+ (1 − ˜x ) − (1 − x ) K ≥ 0 .
r
r

The entrepreneur’s participation constraint
states—according to inequality (1)—that the PV of
the diverted free cash flow, z/r, plus the received
dividend payment, (1–x∼)d/r, must not be lower
–
than the initial cash contribution, (1– x)K .
There is another way to read the entrepreneur’s
participation constraint. Adding and subtracting
xd/r from inequality (1) yields
NPV ≥ 0 ⇔

d
d
z
+ (1 − x ) − (˜x − x ) − (1 − x ) K ≥ 0 .
r
r
r

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REVIEW

THE LIMITED PARTNERSHIP—
A NUMERICAL EXAMPLE
Assume the following values for the exogenous
variables in the limited partnership:
K = 100; w = 70; r = 0.1; κ = 0.4 .
Note that the project has positive NPV:
y
(1 + κ ) r K
−K ≡
− K = 140 − 100 = 40 > 0 .
r
r
If the entrepreneur invests all his initial wealth,
the fraction of equity provided by the outsider
reads
x≡

K −w
= 0.3 .
K

Factoring in the equity discount, the outsider is
assigned the following fraction of voting stock:
x̃ ≡ (1 + r ) x = 0.33 .

The entrepreneur diverts the following amount
into private accounts at the end of every fiscal
year:
z ≡ y − d = 14 −

10
= 4.90 .
1.1

The outside equity constraint is fulfilled because
the entrepreneur’s initial wealth exceeds the
equity discount granted the outsider:
0.7 =

w
r
>
= 0.09 .
K
1+ r

If (and only if) the entrepreneur’s initial wealth
––
amounts to not more than 9.09 percent of the
amount needed to purchase the operating assets,
the outside equity constraint is violated.
The investor breaks even. The outsider’s
return equals the opportunity cost of capital:
x̃ ⋅ d 0.33 ⋅ 9.09
= 10 percent .
=
0.3 ⋅100
x⋅K

Dividend payments per fiscal year amount to
d≡

r K 0.1⋅100
=
= 9.09 .
1+ r
1.1

For x∼ ≡ x(1+r), we can write
NPV ≥ 0 ⇔

d
z
+ (1 − x ) −
r
r
d
( x [1 + r ] − x ) − (1 − x ) K ≥ 0 .
r

After rearranging terms, we obtain
d
z
+ (1 − x ) − x d − (1 − x ) K ≥ 0 .
(2) NPV ≥ 0 ⇔
r
r

Inequality (2) states that the PV of the diverted free
cash flow, z/r, plus the dividend payment on the
initial capital contribution, (1– x)d/r, must not fall
short of the sum of the capital transfer to the investor,
(x∼ –x)d/r ≡ xd, and the initial capital contribution,
–
(1–x)K .
Outside Equity Constraint. Similar to the debt
capacity constraint in debt financing, there is an
outside financing constraint for equity. The constraint emerges from the entrepreneur’s limited
wealth. The more constrained the entrepreneur is,
the higher the fraction of equity claims he has to
20

N OV E M B E R / D E C E M B E R 2 0 0 1

grant the outsider. The outside equity constraint
states that the fraction of equity claims held by
the outsider, x∼, is limited to values less than one:
x∼<1. For x∼ ≡ x(1+r), this inequality results in:
x<

1
.
1+ r

With x being equal to the fraction of equity injected
by the outsider, we obtain
1
K −w
.
<
1+ r
K
After rearranging terms, the outside equity constraint reads
w
r
>
.
K
1+ r
The inequality states that the fraction of outside
equity in total liabilities must exceed a threshold
that is solely determined by the marginal cost of
(equity) capital. Because this condition is independent of the profitability of the project, κ, positive-NPV

FEDERAL RESERVE BANK OF ST. LOUIS

projects will not get financed if the entrepreneur’s
initial wealth is sufficiently low.
Optimal Level of Outside Equity Financing.
As shown, the outside equity constraint sets an
upper limit to the fraction of outside equity in total
equity. This does not imply that the entrepreneur
finances the highest fraction possible through outside equity. In fact, the entrepreneur is indifferent
between investing all his initial wealth, w, or investing any amount e, 0<e<w, that satisfies the outside
equity constraint. As assumed, the entrepreneur
and the investor face the same opportunity cost of
capital. Because the investor breaks even, there is
no difference in the costs of capital to the entrepreneur with respect to outside versus inside equity.

The Corporation
The corporation may be privately held (private
corporation) or publicly traded (public corporation).
We start out with the private type and maintain the
assumption from the partnership model that the
firm outsider is a single investor (or, equivalently,
a small set of block holders that act as a single
investor). In a subsequent section, we compare
this organizational type to the public corporation,
assuming that the outsider is a multitude of small
shareholders.
There are important differences between limited
partnerships and corporations with regard to the
outside equity holder’s control rights. First, while
in the limited partnership the investor can withdraw
his funds at the end of the fiscal year, in the corporation the investor can pull his funds only if he has
command over the majority of votes that is necessary for liquidation.8 This is because shareholders
cannot sell in the aggregate, even though they can
trade shares with each other. Consequently, in the
corporation, minority investors are “locked in,”
which makes them vulnerable to opportunistic
behavior by the entrepreneur. Second, unlike the
limited partnership, the corporation enables the
outside investor—if he has command over the
necessary majority of votes—to remove the entrepreneur from the firm at the annual, end-of-fiscal-year
shareholder meeting.
Note that, as in the partnership model, the
optimal outcome demands the entrepreneur to be
in control of the operations. Also, liquidation (in
full or in part) is generally suboptimal because the
going concern value always exceeds the liquidation
value.
The distribution of voting rights influences the

balance of power between insider and outsider
when bargaining over the free cash flow at the end
of the fiscal year. In the following we look at two
cases of voting rights distribution, one in which the
outsider has command over a simple majority of
votes, and one in which the entrepreneur holds the
majority. (We exclude the borderline case of each
party holding 50 percent of the votes.) The outcome
of this bargaining process determines the dividend
payments, which in turn determines the firm’s outside equity financing capacity.
Dividends and Allocation of Voting Rights.
In the case where the investor holds the majority
of votes, the outsider has the power to remove the
entrepreneur from the firm or, equivalently, liquidate the firm.9 On the other hand, the entrepreneur has the power to refuse to contribute his
human capital to the firm henceforth. Any of these
two non-cooperative actions by the investor or
the entrepreneur would reduce the PV of next
–
fiscal year’s free cash flow from (1+κ ) rK /(1+r) to
–
∼
rK /(1+r), with the fraction x going to the investor
and the fraction 1– x∼ going to the entrepreneur.
Moreover, we assume that, if the entrepreneur were
removed (at the end of the fiscal year), the entrepreneur would have no incentive to pay dividends for
the current fiscal year. Because cash flows are not
verifiable, the entrepreneur would divert all of the
fiscal year’s free cash flow into personal accounts
before leaving.
Nevertheless, the parties have an incentive to
cooperate because cooperation generates a surplus that the parties can share. The cooperative
outcome may be modeled as a Nash bargaining
solution. In a Nash bargaining solution, each party
is assigned the same degree of bargaining power,
and thus they share the surplus from cooperation
evenly. In fact, each party receives what it would
receive if the parties did not cooperate plus half the
gains from cooperation.10
The surplus from cooperation at the end of the
fiscal year equals the PV of the entrepreneur’s value
–
added in the next fiscal year, (κ rK )/(1+r). In sharing
the surplus evenly, the entrepreneur pays out
8

We assume that there is no supermajority rule in place, which means
that all decisions are made with a simple majority.

9

Removing the entrepreneur from the firm would result in a PV of
continuation of zero, which is equivalent to liquidation.

10

For details on the Nash bargaining solution, see Dagan, Volij, and
Winter (2000). For a textbook example of a Nash bargaining solution
in a corporate finance context, see Hart (1995).

N OV E M B E R / D E C E M B E R 2 0 0 1

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–
κ rK /(2(1+r)) to the investor, in addition to what
the investor would receive in the noncooperative
–
outcome, x∼rK /(1+r).11 Consequently, the firm’s
total dividend payment equals

κ r K r K (1 + κ ) r K
+
=
.
1+ r 1+ r
1+ r
Note that the dividend payment equals the PV of
the free cash flow of the next fiscal year. This implies
the following for the amount, z, that the entrepreneur
diverts for personal use:
z = (1 + κ ) r K −
⇔

(1 + κ ) r K
1+ r

z (1 + κ ) r K
=
.
r
1+ r

In the case where the entrepreneur holds the
majority of votes, the outsider has no bargaining
power once he is invested. Because the investor
has no ex post bargaining power, the entrepreneur
has no incentive to pay dividends. Thus, an initial
private equity offering in which less than 50 percent
(plus one vote) of the shares are up for sale will fail.
(The entrepreneur would have to offer the shares
for free, which raises no funds.)
Investor’s Participation Constraint. The
–
(outside) investor expends the amount x K at the
inception of the project and receives a dividend
–
payment equal to rK (κ+2x∼ )/(2(1+r)). Thus, the
investor’s participation constraint reads

that the outsider’s participation constraint is satisfied
at equality.
Because the fraction of equity held by the
entrepreneur, 1– x∼ , can be zero, there is no upper
∼ ≡ x(1+δ )
bound on δ ; this means that, for any 1≥ x
>1/2, there is a value δ>–1 at which the investor
breaks even. We assume that the entrepreneur can
divert any excess amount raised in the private equity
offering, which is analogous to our assumption
that the entrepreneur can divert free cash flow.
Note that there is a lower bound on the equity
discount: δ>–1. The fraction of capital injected by
the investor, x, must be positive and so must be the
fraction of (voting) equity that emanates from this
initial capital contribution, x∼ .
Entrepreneur’s Participation Constraint. The
–
entrepreneur expends the amount (1– x)K at inception of the project, receives periodic dividend payments equal to
(1 − x̃ ) r K
κrK
+
,
1+ r
2 (1 + r )
–
and can divert the amount (1+κ )r2K /(1+r) into
personal accounts at the end of every fiscal year.
Thus, the entrepreneur’s participation constraint
reads
(1 + κ ) r K (1 − ˜x ) K
κK
−
+ (1 − x ) K ≥ 0 .
+
1+ r
1+ r
2 (1 + r )
Substituting x(1+δ ) for x∼ yields
1
κ (r + )
2 +r.
δ≤
x

r K (κ + 2˜x )
.
rxK≤
2 (1 + r )
Let δ /(1+δ ), δ>–1, be the percentage discount
(or premium, if negative) at which the entrepreneur
issues the equity to the outsider; then we can write
the investor’s participation constraint as follows:
rxK≤

r K (κ + 2x [1 + δ ])
.
2 (1 + r )

Rearranging terms yields

δ ≥r−

κ
.
2x

The entrepreneur’s participation constraint is subject to 1>x∼ ≡ x(1+δ )>1/2, which demands that
the outside investor holds more than 50 percent of
the voting stock. Remember that the entrepreneur
chooses the discount (premium) such that the
investor merely breaks even or, in other words, such
22

N OV E M B E R / D E C E M B E R 2 0 0 1

As with the investor’s participation constraint discussed in the preceding section, the entrepreneur’s
participation constraint is subject to 1>x∼ ≡ x(1+δ )
>1/2, which demands that the outside investor
holds more than 50 percent of the voting stock.
Outside Equity Constraint. The entrepreneur’s
limited wealth imposes an outside equity constraint
on the firm. It is this constraint that necessitates
outside equity and—at the same time—may impose
an upper bound on the fraction of outside equity
in total liabilities. The outside equity constraint
states that the fraction of equity claims held by
the outsider, x∼ , must not exceed unity: x∼ ≤ 1. For
∼ ≡ x(1+δ ), this inequality results in
x
11

Note that this outcome fulfills the investor’s continuation constraint
by exceeding the opportunity cost of capital.

FEDERAL RESERVE BANK OF ST. LOUIS

x≤

1
.
1+ δ

From the discussion of the investor’s participation
constraint, we know that the outsider breaks even,
which implies the following equality for the percentage by which the fraction of equity claims held by
the outsider, x∼ , exceeds the fraction of the equity
capital contributed by the outsider, x:

δ =r−

κ
.
2x

Inserting the right-hand-side expression into the
above inequality yields
x≤

1

κ
1+ r −
2x

entrepreneur anticipates the investor’s ex post
bargaining power and issues the equity at the lowest discount (or highest premium) that fulfills the
investor’s participation constraint. Thus, if the
project gets financed, the entrepreneur reaps all the
NPV. Also, if the project gets financed, the NPV is
independent of the choice of the legal form. Consequently, the entrepreneur is indifferent about the
legal form if (and only if) this decision is inconsequential to whether the project gets financed.
The only reason why a project of positive NPV
might not get financed is the entrepreneur’s insufficient initial wealth, w. In the limited partnership,
the outside equity constraint (subject to the investor’s
participation constraint being satisfied) reads

.

With x being equal to the fraction of capital injected
–
–
by the outsider, (K – w)/K , we obtain
κ
1+
K −w
2 .
≤
K
1+ r
After rearranging terms, the outside equity constraint
reads
κ
r−
w
2 .
≥
K
1+ r
Except in the case of the limited partnership, the
minimum fraction of initial wealth, w, in total assets,
–
K , that the entrepreneur needs to launch the project
depends not only on the opportunity cost of capital,
r, but also on the project’s profitability, κ.

Limited Partnership Versus Private
Corporation
We use the model to explain the choice between
the limited partnership and the (private) corporation.
We can show that, in the private corporation, the
outside equity constraint is less likely to bind. For
low levels of initial wealth, the entrepreneur may
be unable to attract outside equity when organizing
the project into a limited partnership. The private
corporation, on the other hand, lends greater ex post
bargaining power to the outsider, which increases
the firm’s outside equity capacity. Note that the
model is not dynamic, which implies that it cannot
explain a transition from the partnership to the
corporation, or vice versa.
Assuming competitive capital markets, the outside investor cannot do better than break even. The

(3)

w
r
>
.
K
1+ r

Inequality (3) states that the entrepreneur has to
–
finance more than the fraction w/K of the project’s
–
initial expenses, K , through initial wealth. The threshold level r/(r+1) is solely determined by the opportunity costs of capital, r.
In the (private) corporation, the outside equity
constraint is given by
(4)

κ
r−
w
2 .
≥
K
1+ r

Inequality (4) demands that the ratio of the entrepreneur’s initial wealth, w, to the initial expenses
–
needed to launch the project, K , must meet a
threshold level that is determined by the opportunity cost of capital, r, and the profitability of the
project, κ.
Comparing the constraints across legal forms
shows that the outside equity constraint is more
restrictive in the limited partnership model than in
the private corporation. This is because, in the private
corporation, the ex post bargaining power of the
investor at the end of every fiscal year allows him
to capture—in a Nash bargaining solution—half
the value added of the upcoming fiscal year. For a
sufficiently profitable project, i.e., κ ≥2r, the outside
equity constraint never binds in the corporation
model. Remember that the outside equity constraint
in the limited partnership model is independent of
the project’s profitability.

Going Public
We now analyze the public corporation. In
finance literature, the term public corporation
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THE PRIVATE CORPORATION—
FOUR NUMERICAL EXAMPLES
We assume the same set of values for the
exogenous variables of the private corporation as
we did in the numerical example for the limited
partnership:
K = 100; w = 70; r = 0.1; κ = 0.4 .
As established for the limited partnership, the
project has positive NPV. This is because the
project returns exceed the opportunity cost of
capital by the factor κ=40 percent. As in the
partnership, the outsider has to contribute at
–
–
least the fraction x ≡ (K – w)/K =0.3 to the firm’s
equity capital.
An important difference of the private corporation to the limited partnership is the constraint
x∼ ≡ (1+δ )x>1/2, which demands that the outsider holds the majority of votes. This condition
restricts the entrepreneur in his choice of x (the
fraction of capital contributed by the outsider) and
δ /(1+δ ) (the equity discount). For instance, assume
that the entrepreneur contributes 1– x=0.7 to the
firm’s capital, just as in the numerical example
for the limited partnership. The value of δ at
which the outsider breaks even would then read

δ =r−

κ
= −0.56 .
2x

This would mean that the outside equity is issued
at a discount equal to δ /(1+δ ) ≈ –1.31, or in other
words, at a premium of about 131 percent. At this
premium, though, the outside investor would not
have command over the majority of votes:
0.13 = x ⋅ (1 + δ ) ≡ ˜x <

1
.
2

Consequently, the entrepreneur chooses to contribute a lower fraction to the firm’s equity than
what he is able to. For instance, the entrepreneur
might contribute the fraction 1– x=0.1 only.
For 1– x=0.1, the value of δ at which the
outsider breaks even, reads

δ =r−

24

κ
= −0.12 .
2x

N OV E M B E R / D E C E M B E R 2 0 0 1

This would mean that the outside equity is issued
at a discount equal to δ /(1+δ ) ≈ –0.14, or, in
other words, at a premium of approximately 14
percent. The outsider would end up with x∼ ≡
(1+δ )·x=79 percent of the voting stock.
The dividend payment amounts to
d≡

(1 + κ )rK 1.4 ⋅ 0.1⋅100
=
= 12.72 .
1+ r
1.1

The amount that the entrepreneur diverts
into personal accounts equals
z ≡ y − d = 14 − 12.72 = 1.27 .
The outside investor breaks even:
9 = 0.1⋅ 0.9 ⋅100 = rxK
=

rK (κ + 2x[1 + δ ])
2(1 + r )

=

0.1⋅100 ⋅ (0.4 + 2 ⋅ 0.9 ⋅ [1 − 0.12])
= 9.
2 ⋅1.1

The outside equity constraint is fulfilled:
κ
r−
w
2 = −0.09 .
0.3 = ≥
K 1+ r
Because the project is sufficiently profitable, the
outside equity constraint never binds. For κ ≥ 2r
the entrepreneur is able to attract outside equity
without contributing his own capital. This is in
sharp contrast to the numerical example of the
limited partnership, where the entrepreneur has
––
to contribute more than 9.09 percent of the initial
capital expenditure.
The outside equity constraint is relevant
only if the project is not sufficiently profitable,
i.e., if κ <2r. Even in this case, the outside equity
constraint is less restrictive than in the limited
partnership. For instance, in the partnership the
project cannot be financed if the entrepreneur’s
––
wealth, w, amounts to less than 9.09. In the private corporation, though, the entrepreneur can
attract outside equity for a project with low
profitability κ=0.1 even if his wealth is as low
––
as w=4.54. The entrepreneur would issue the
––
equity at a discount of 4.54, granting the outsider
∼
x=100 of the voting capital.

FEDERAL RESERVE BANK OF ST. LOUIS

represents listed companies with dispersed shareholder structures.
Dispersed shareholders face high costs of collective action. These costs restrain the bargaining
power the shareholders have once they are invested.
We assume that if (and only if) the dividend payments fall short of the opportunity cost of capital,
the shareholders remove the entrepreneur from the
corporation or, equivalently, liquidate the project.
Note that without this assumption, the entrepreneur
pays no dividends.
Investor’s Continuation Constraint. As with
the private corporation, outside equity financing is
possible only if the outside shareholders have command over a majority of votes: x∼ >1/2. Without a
majority of votes, the investor cannot liquidate,
and, consequently, the entrepreneur has no incentive to pay dividends.
In the event of liquidation, the shareholders
can withdraw their fraction of assets. Thus, the
continuation constraint reads

Table 1
Outside Equity Constraints
Legal form

Outside equity constraint

w
r
>
K
1+ r
κ
r−
w
2
≥
K
1+ r
w
r
>
K
1+ r

Limited partnership

Private corporation

Public corporation

w
–
K

Entrepreneur’s initial wealth

r
κ

Marginal cost of capital

Expenses needed to purchase
the operating assets
Project profitability
(percentage by which the
project return exceeds the
opportunity cost of capital)

rK

˜x d ≥ ˜x 1 + r .
This continuation constraint is equivalent to the
continuation constraint in the partnership model.
Investor’s Participation Constraint. Subject to
x∼ >1/2, the (outside) investor’s participation constraint reads
rK 

r x K ≤ ˜x d = ˜x
.
1 + r 

Except for the condition x∼ >1/2, this participation
constraint is identical to the investor’s participation
constraint in the partnership model.
Entrepreneur’s Participation Constraint.
Under the assumption of competitive capital markets, the investor breaks even, which implies that
the investor’s participation constraint is fulfilled at
equality. For the investor to break even, the entrepreneur has to issue the outside equity at a discount:
x̃ = x (1 + r ) .
Because the investor does not do better than break
even, the entrepreneur reaps the whole (positive)
NPV, which implies that the entrepreneur’s participation constraint is satisfied.
Equivalence of Legal Forms. In summary, the
public corporation model is equivalent to the
partnership model when the constraint x∼ >1/2 is
added and the outside equity constraint is allowed
to hold at equality:

w
K

≥

r
.
1+ r

In contrast to the limited partnership, the wealth of
the entrepreneur in the corporation may adopt a
value of zero.
For the constraint x∼ >1/2, which demands the
outsider to hold the majority of votes, we obtain the
following after rearranging terms:
w
K

1
+r
< 2
.
1+ r

This constraint never binds, because the entrepreneur can choose to invest only the amount e ≤ w of
his wealth.
The outside equity constraints of all three legal
forms are summarized in Table 1.

CONCLUSION
In this article we analyzed outside equity financing of the entrepreneurial firm when cash flows
are non-verifiable. The study covered three legal
forms: the limited partnership, the private corporation, and the public corporation. We showed that
the limited partnership and the public corporation
are equivalent with regard to the outside investor’s
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bargaining power once he is invested. Of the three
analyzed legal forms, the private corporation renders
the most ex post bargaining power to the outside
investor. Consequently, when organizing the project
into a private corporation, the entrepreneur faces
the least restrictive outside equity constraint. This
is because the outside investors in the private corporation are block holders whose costs of collective
action are low. The block holders have the power to
remove the entrepreneur from his post (or, equivalently, liquidate the firm). Clearly, this presupposes
that the outsiders hold the majority of votes. If outside equity holds a minority interest in the corporation, the insider has no incentive to pay dividends
and will divert all free cash flow for personal use.
The article underlines the importance of venture
capital financing. Venture capital allows positive-NPV
projects that are organized into private corporations
to be financed even when the entrepreneur is
strongly wealth-constrained. For less wealthconstrained entrepreneurs, the three legal types are
equivalent. If the entrepreneur’s wealth is sufficiently low, however, positive-NPV projects cannot
be financed in either legal form. This is because of
the entrepreneur’s inability to commit to a level of
dividend payments that allows the outside investor
to break even.

REFERENCES
Dagan, Nir; Volij, Oscar and Winter, Eyal. “A Characterization
of the Nash Bargaining Solution.” Unpublished manuscript,
Brown University, Washington University, and Hebrew
University, 2000, <http://www.nirdagan.com/research/>.
Grossman, Sanford J. and Hart, Oliver D. “One Share–One
Vote and the Market for Corporate Control.” Journal of
Financial Economics, January/March 1988, 20(1/2), pp.
175-202.

26

N OV E M B E R / D E C E M B E R 2 0 0 1

Harris, Milton and Raviv, Artur. “Corporate Governance:
Voting Rights and Majority Rules.” Journal of Financial
Economics, January/March 1988, 20(1/2), pp. 203-35.
Hart, Oliver. Firms, Contracts, and Financial Structure. New
York: Clarendon Press, 1995.
Jensen, Michael C. A Theory of the Firm: Governance,
Residual Claims, and Organizational Forms. Cambridge,
MA: Harvard University Press, 2000.
___________ and Meckling, William H. “Theory of the
Firm: Managerial Behavior, Agency Costs, and Capital
Structure.” Journal of Financial Economics, October 1976,
3(4), pp. 305-60.
Kirilenko, Andrei A. “Valuation and Control in Venture
Finance.” Journal of Finance, April 2001, 56(2), pp. 565-87.
McConnell, John J. and Servaes, Henri. “Additional Evidence
on Equity Ownership and Corporate Value.” Journal of
Financial Economics, October 1990, 27(2), pp. 595-612.
Milgrom, Paul and Roberts, John. Economics, Organization,
and Management. Englewood Cliffs, NJ: Prentice-Hall, 1992.
Morck, Randall; Shleifer, Andrei and Vishny, Robert.
“Management Ownership and Market Valuation: An
Empirical Analysis.” Journal of Financial Economics,
January/March 1988, 20(1/2), pp. 293-315.
Myers, Stewart C. “Outside Equity.” Journal of Finance, June
2000, 55(3), pp. 1005-37.
Zingales, Luigi. “In Search of New Foundations.” Journal of
Finance, August 2000, 55(4), pp. 1623-53.
Zwiebel, Jeffrey. “Dynamic Capital Structure Under
Managerial Entrenchment.” American Economic Review,
December 1996, 86(5), pp. 1197-215.

FEDERAL RESERVE BANK OF ST. LOUIS

Appendix

Is the partnership contract renegotiation-proof,
or does the investor have an incentive to demand
renegotiation of the contract by threatening to
withdraw his funds?
If at the end of the first fiscal year the investor
threatens to withdraw his funds, the entrepreneur
has the option of not making the last dividend
payment and substituting (renegotiation-free) debt
for equity by issuing an infinitely lived bond, a
console. The console would have a par value equal
∼ K– and sell for xK– . The periodic, annual interest
to x
∼d . If the entrepreneur
payment would amount to x
defaults on servicing the console, the assets transfer

to the debt holder either entirely (total liquidation,
undertaken by the investor) or partially (partial
liquidation, undertaken by the entrepreneur).
Because the operating assets are worth more in
the project than outside, the entrepreneur has an
incentive to make the agreed-upon payments. On
the other hand, the entrepreneur's ability to substitute a console for outside equity implies that the
limited partner has no bargaining power when
trying to renegotiate the partnership contract.
Thus the partnership contract is renegotiationfree, which in turn implies that outside equity is
equivalent to debt.

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FEDERAL RESERVE BANK OF ST. LOUIS

Dollarization as a
Monetary Arrangement
for Emerging Market
Economies
Gaetano Antinolfi and Todd Keister
cuador and El Salvador have recently adopted
the U.S. dollar as legal tender, replacing their
own national currencies.1 This same move
has received serious attention in policy debates
in both Argentina and Mexico. Abandoning the
national currency is a decision with far-reaching
economic and political implications that are not
well understood. In response to this phenomenon,
a growing literature has aimed at evaluating the
economic costs and benefits of “dollarizing.” In
this article, we provide an overview of the emerging literature and point out some issues that we
feel warrant further research.2
Throughout, we focus on official dollarization,
where the U.S. dollar (or some other currency)
replaces the national currency as legal tender.
Unofficial dollarization, where private agents use
a foreign currency as a substitute for the domestic
currency, is already widespread in Latin America
and elsewhere. We focus on Latin America and the
U.S. dollar because of the recent events and policy
debates mentioned above. Most of the issues we
discuss, however, would apply to any country considering the official adoption of a foreign currency.
Discussions of the optimal monetary and
exchange rate arrangements for an emerging market
economy have traditionally centered on fixed or
flexible exchange rates or (most often) some hybrid
of the two, perhaps combined with capital controls
or other regulatory measures. We begin our discussion by examining the causes of the current surge
of interest in official dollarization. We then turn to

E

Gaetano Antinolfi is an assistant professor of economics in the
Department of Economics, Washington University, and a visiting
scholar at the Federal Reserve Bank of St. Louis. Todd Keister is an
assistant professor of economics in the Departamento de Economía
and Centro de Investigación Económica, Instituto Technológico
Autónomo de México (ITAM) and a visiting assistant professor in the
Department of Economics, University of Texas at Austin. The authors
would like to thank James Morley, Patricia Pollard, Bob Rasche, Mika
Saito, and Frank Schmid for helpful comments. William Bock provided research assistance.

© 2001,

T H E F E D E R A L R E S E R V E B A N K O F S T. L O U I S

the details of the issues that we feel are most important in analyzing the potential costs and benefits of
dollarizing.

WHY CONSIDER DOLLARIZATION?
Financial Crises
The current interest in official dollarization is
largely a reaction to the recent string of currency
crises. In the past decade, these crises have affected
numerous countries, both industrialized (Italy and
the United Kingdom in 1992) and emerging markets
(Mexico in 1994, and East Asia and Brazil in 1997).
Comparing the crises in industrialized countries
with those in emerging markets reveals an important
difference: although these crises are not costly in
terms of lost output for industrialized economies,
they are extremely costly for emerging market
economies.3 For example, in 1995 Mexican gross
domestic product (GDP) declined by 7 percent in real
per capita terms. (In the years before the crisis, for
comparison, real per capita growth ranged between
3 percent and 10 percent.) Moreover, when one
emerging economy suffers a crisis, others are often
hit by interest rate increases and a recession, as
happened in Argentina following the Mexican crisis.
This phenomenon is known as contagion.
The events in emerging market economies share
certain characteristics that allow us to identify a
typical “anatomy” of a crisis.4 Beforehand, there is
an incipient capital inflow and a corresponding
current account deficit. The onset of the crisis is
marked by a sudden capital outflow and a large
devaluation of the exchange rate. There is often a
crisis in the banking system at about the same time.5
The result is a sharp and painful fall in output. Much
of the current interest in dollarization stems from
a strong desire to avoid such crises in the future.
Before discussing the potential costs and benefits of
1

Guatemala has also recently adopted the U.S. dollar as legal tender,
but it has decided to maintain its own currency in circulation, without fixing a parity with the dollar.

2

The interested reader can find a good, basic introduction to the topic
of dollarization in Chang (2000).

3

This reflects the general finding that an exchange rate devaluation is
usually contractionary for emerging markets, whereas it is typically
expansionary for industrialized countries. See, for example, Edwards
(1989).

4

For a detailed discussion, see Calvo (2000).

5

Kaminsky and Reinhart (1999) empirically show that banking crises
tend to precede exchange rate crises.

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dollarizing, we look at some of the more traditional
approaches to these problems and why they seem
to be falling out of favor.

The Fear of Floating
One approach that naturally comes to mind
(to an economist, at least) is to allow prices and
quantities to be determined by supply and demand
in markets. The definition of a flexible exchange
rate system is exactly this: the price of one currency
relative to another is determined by the market without any intervention by central banks. That is to
say, any current account deficit has to be financed
entirely by capital inflows (a financial account
surplus) and vice versa, without any change in
official reserves.
In reality, however, we do not observe many
countries with truly flexible exchange rate systems.
Rapid growth in world capital markets has led to
a substantial increase in the size of international
capital flows. At times, these flows become very
volatile; indeed, as we mentioned above, a sudden
reversal in capital flows is the typical “spark” of a
crisis. Under a pure flexible exchange rate system,
such volatility in capital flows causes corresponding
volatility in the exchange rate. A volatile exchange
rate, in turn, means that relative prices in the economy are volatile, which can be very disruptive to
real economic activity.
Calvo and Reinhart (2000) have termed the
unwillingness to let exchange rates be completely
determined in markets “the fear of floating.” They
also point out several additional reasons why emerging market economies seem to be averse to floating
exchange rates. These include high levels of dollardenominated debt, high-exchange-rate pass through
(reflected in domestic inflation), and in general an
adverse effect of currency instability on credit market
access. In support of their argument, they conduct
an empirical analysis comparing the announced
exchange rate regime of countries to the actual
exchange rate behavior. Their findings indicate
that countries classified as letting their exchange
rate float, in general, do not. Hence it seems that
very few, if any, countries are willing to take this
approach.

The Costs of Capital Controls
Sudden reversals in the flow of capital have been
an important and particularly damaging aspect of
currency crises. If capital market volatility is the
30

N OV E M B E R / D E C E M B E R 2 0 0 1

problem, one way of avoiding it is to introduce capital controls. Clearly the aim of such a policy would
not be to stop capital inflows, because emerging
market economies rely on them for investment,
but to diminish their volatility. There is evidence
indicating that capital controls involving taxes and
reserve requirements can change the composition
of capital inflows in favor of long-term investment,
and thereby decrease the likelihood of large, sudden
outflows. Calvo and Reinhart (1999), however, caution that these results may depend on the accounting classifications of capital flows. In addition,
Edwards (1999) argues that, when analyzing the
maturity of a country’s foreign debt, the relevant
concept is residual maturity6 rather than contractual
maturity. Using data from Chile, Edwards shows
that short-term capital controls had a limited effect
on Chile’s residual maturity of foreign debt and that
Chile had higher residual maturity than Mexico (a
country without capital controls) at the end of 1996.
More generally, capital controls are typically
not considered sound economic policy because
they limit the ability of a country to borrow and
invest, they hinder international risk sharing and
technology transfer, and they prolong the survival
of unsustainable domestic policies. The main practical objection to capital controls, however, is that
they create a strong incentive for tax evasion and
require a costly enforcement apparatus. These problems make them poor candidates for permanent
solutions.7

The Vanishing Intermediate Regime
The unwillingness to let exchange rates float
and to use direct capital controls has pushed countries toward “intermediate” exchange rate regimes
in which official intervention is used to keep the
exchange rate within predetermined bounds. This
move, however, has been accompanied by the recent
crises mentioned previously. This association has led
many observers to claim that intermediate exchange
rate regimes are no longer viable for emerging market economies. These observers claim that only
extreme (totally fixed or totally flexible) exchange
rate regimes are viable for emerging market economies. Eichengreen (forthcoming) colorfully likens
6

Residual maturity is measured by the value of a country’s liabilities
that are held by foreigners and mature within a year.

7

See De Grauwe (1996, Chapter 11) and Neely (1999) for an extensive
assessment of capital controls. Calvo and Reinhart (1999) provide a
discussion related to the context of dollarization.

FEDERAL RESERVE BANK OF ST. LOUIS

adopting an intermediate regime to “painting a bull’s
eye on the forehead of the central bank governor
and telling speculators to ‘shoot here’.”8 There are, of
course, situations for which some authors are willing to defend intermediate regimes as appropriate,
but they are generally viewed as temporary remedies.9 Fischer (2001) presents empirical evidence
that the proportion of emerging market economies
using intermediate regimes has indeed declined
over the past decade.
An important question is how extreme a policy
must be in order to avoid the problems associated
with the middle ground. Even a currency board has
proven not to be extreme enough in some ways.
Under this arrangement, the central bank commits
to back its monetary base entirely with foreign
reserves at all times; thus, a unit of domestic currency can be introduced into the economy only if
an equivalent amount of foreign reserves is obtained.
In principle, this system is equivalent to dollarization. However, even though Argentina has been
operating under a currency board since 1991, the
interest rate differentials between peso-denominated
and dollar-denominated debt remain and have
widened during periods of financial turmoil, as with
the Brazilian and Mexican crises (see Figure 1). This
indicates that financial markets believe there to be
a significant probability that the currency board
will be abandoned under such circumstances, and
the Argentine economy has suffered as a result.

THE KEY ISSUES
We now turn to what we see as the key issues
in evaluating the costs and benefits of dollarization.
Two of the primary benefits of dollarization are
straightforward: exchange rate volatility (against the
dollar) and exchange rate crises would be eliminated,
and in most cases the inflation rate would be lowered
substantially. One of the costs is also fairly straightforward, although occasionally misunderstood: the
loss of seignorage revenue. We begin our discussion
with this issue.
There are other costs and benefits that are more
subtle and difficult to measure. Dollarization implies
the loss of monetary policy, but, if it enhances the
credibility of economic policy, dollarization could
lower interest rates and substantially decrease the
likelihood of future financial crises. If it increases
economic integration with the United States, dollarization could yield substantial benefits in both
product and financial markets. An important con-

cern, however, is that dollarization would limit the
ability of the central bank to act as a lender of last
resort. We discuss these issues in turn below. Finally,
a discussion of dollarization would not be complete
without looking at the “initial conditions” in which
many emerging market economies currently find
themselves and approaching the issue from the
perspective of the United States.

Seignorage Revenue
An obvious cost of dollarization is the loss of
the seignorage revenue that comes with the power
to print fiat currency. The size of the flow of seignorage revenue depends on both the rate of growth of
output and the rate of inflation. For some emerging
market economies, it constitutes a substantial fraction of government revenues. With any other fixedexchange-rate arrangement, seignorage revenues
are present in some form. In particular, under a
currency board, newly printed domestic money is
used to buy interest-bearing foreign reserves. Dollarization entails losing this interest. It also entails buying back the domestic monetary base using foreign
reserves and, therefore, losing the interest on this
stock of reserves as well. Velde and Veracierto (1999)
calculate this latter number for Argentina to be $658
million, or 0.2 percent of GDP, per year.
Note that computing the present level of seignorage revenue and calling that a “cost” of dollarization
is clearly a mistake in most cases. Chang and Velasco
(2000b) make this point: If a country dollarizes in
order to lower its inflation rate, this reflects a decision that the benefits of lower inflation outweigh
the value of the revenue that higher inflation brings.
Instead, one should focus on the seignorage revenue
that would have been earned at the new, lower
inflation rate. This is the “loss” in seignorage revenue
relative to the (ideal) case where the inflation rate
is (somehow) lowered without dollarizing.
There are two reasons to believe that this amount
may still overestimate the true revenue loss from
dollarizing. First, a dollarizing country may be able
to negotiate a deal with the United States under
which it receives some of the increased U.S. seignorage revenue (which could equal the “loss” calcu8

See also Obstfeld and Rogoff (1995) and Summers (1999; 2000, p.8).
For a classification of different exchange rate regimes, see Frankel
(1999).

9

See Mussa et al. (2000), who argue that an unsustainable policy need
not be undesirable in the short run, and Frankel (1999), from whom
we borrowed the title of this section.

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Figure 1
Interest Rates on Loans Given to Prime Companies
40
35
30
25
20
15
10
5
0
Jan-1994 Jul-1994 Jan-1995 Jul-1995 Jan-1996 Jul-1996 Jan-1997 Jul-1997 Jan-1998 Jul-1998 Jan-1999 Jul-1999 Jan-2000 Jul-2000 Jan-2001
Pesos

Dollars

Difference

SOURCE: Central Bank of Argentina.

Interest Rates on Deposits (30- to 59-Day Term)
25

20

15

10

5

0
Jan-1994 Jul-1994 Jan-1995 Jul-1995 Jan-1996 Jul-1996 Jan-1997 Jul-1997 Jan-1998 Jul-1998 Jan-1999 Jul-1999 Jan-2000 Jul-2000 Jan-2001
Pesos

Dollars

Difference

SOURCE: Central Bank of Argentina.

lated above).10 Second, a large part of the reason
for dollarizing is to create a more stable economic
environment that will encourage investment and
growth. While it is extremely difficult to make quantitative predictions about the size of this effect, it is
clear that the increase in tax revenue from increased
economic activity should at least partially offset
the loss of seignorage revenue.
Regarding this last point, however, it is important to note that the increase in tax revenue would
take time to develop. In the meantime, a government
32

N OV E M B E R / D E C E M B E R 2 0 0 1

with lower revenues would have to decrease expenditures, increase taxes, or increase the public debt.
To the extent that the loss of seignorage revenue is
compensated by an increase in government borrowing, it may not be the case that a stable currency
necessarily provides more macroeconomic stability.
This is an indication that the fiscal plan accompanying a dollarization would be critical to its success.
10

Such a plan was actually proposed as part of the International
Monetary Stability Act, introduced by then Senator Connie Mack of
Florida. Details can be found in Mack (2000).

FEDERAL RESERVE BANK OF ST. LOUIS

Fiscal Consequences
Because dollarization entails a loss of both
seignorage revenue and independent monetary
policy, it is likely to have important consequences
for the conduct of fiscal policy. Sims (2001) argues
against dollarization for precisely this reason. He
argues that the option value of issuing fiat debt
(which can be defaulted on through inflation) is too
high to surrender because inflation is part of an
optimal taxation scheme. In support of his argument,
Sims computes the unexpected component of U.S.
government debt yields and shows that it is substantial. His calculations show that fiat debt worked to
relax the government budget constraint in times
of high economic turmoil (such as the oil crisis of
1973). One possible interpretation of this fact is that,
without fluctuations in the unexpected component
of government bond yields, more variability would
have been observed in taxation and government
expenditure, which may have been very costly. More
research (as Sims acknowledges) is needed to evaluate (i) how much of the variability in the unexpected
component of government bond yields actually
reflects inefficient variation in monetary and fiscal
policy that is better avoided and (ii) how much of it
reflects an “optimal” response to real shocks.
Similarly, Chang and Velasco (2000b) argue that
an optimal taxation plan would always entail surprise inflation (or devaluation) because this acts as
a lump-sum tax and therefore is non-distortionary.
Dollarization removes the ability of the government
to use this tax. The contributions of Sims (2000) and
Chang and Velasco (2000b) in this way stress the
potentially high costs of losing flexibility in economic policy. Surprise inflations, however, cannot
be repeatedly engineered, and anticipated inflation
is typically not part of an optimal taxation plan.
Hence the government has a time-consistency
problem; it wants to convince people that it will
not engineer an inflation increase, but once people
are convinced, it wants to surprise them. Because
people know this, the economy can end up in a
situation of anticipated inflation. If this problem is
very costly to the economy, then the benefit of using
dollarization to solve it may easily outweigh the
cost of the lost flexibility.11
Chang and Velasco (2000b) go on to point out
that dollarization might decrease the incentives for
fiscal discipline. Lack of fiscal discipline, in turn,
may mean that crises due to high sovereign default
risk would persist and the economy would not benefit from lower interest rates. Would the adoption of

the dollar imply more or less fiscal discipline? Chang
(2000) argues that, under alternative arrangements,
changes in exchange rates or interest rates make
the costs of a lack of fiscal discipline immediate.
Dollarization would take those incentives away by
allowing the costs of present fiscal looseness to be
shifted to the future (in terms of higher future taxes,
for example). Hence the incentives for fiscal discipline would decrease.
Although these incentive problems are real, it is
important to recognize that there are other factors
working in the opposite direction. First, as noted
above, emerging markets depend heavily on foreign
capital, and capital outflows could serve to make the
cost of a lack of fiscal discipline immediate. Second,
the incentive for domestic investors to monitor and
put political pressure on the government for fiscal
discipline would be higher. Heavy government borrowing would be perceived to induce macroeconomic instability and would cause interest rates for
all domestic borrowers to increase. Through these
channels, market discipline would be present for a
dollarized government.
If dollarization does undermine the incentives
for fiscal responsibility, does that mean it should
be accompanied by legal restrictions on the government budget deficit? In part, this was the route taken
by the European Monetary Union (EMU) in tying
the Stability Pact to the launch of the euro. It is
important to notice, however, that a unilateral dollarization is very different from the EMU’s in this regard.
In the latter case, members relinquished control to
a common central bank for the conduct of monetary
policy. The decision to dollarize, in contrast, entails
total loss of monetary authority. As such, legal
restrictions on the government budget would constrain an already shrunken set of policy alternatives,
which could prove very costly in an economic
downturn.12

Economic Integration
A potential benefit of dollarization is that it
could increase the level of integration of the dollarizing economy with the U.S. economy. This may
come about for several reasons, including reduced
transactions costs and the elimination of uncertainty
11

On the optimal-tax property of inflation, see Calvo and Guidotti
(1993). For the analysis of time-consistency problems, see Kidland
and Precott (1977) and Calvo (1978).

12

Also, see Ghiglino and Shell (2000) for a discussion of when deficit
restrictions do not really constrain the government and hence have
no real effects.

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about exchange rates. Frankel and Rose (2000)
present evidence that currency unions lead to large
increases in trade flows between member countries.13 Furthermore, Frankel and Rose argue that
these increases do not come from the diversion of
trade away from non-member countries; rather,
currency union membership leads to a higher ratio
of total foreign trade to GDP. In fact, they interpret
their results as indicating that increased trade is
the primary benefit of joining a currency union (or
dollarizing).
In addition to increased trade, dollarization
could increase the level of financial integration
between the dollarizing country and the United
States. Stockman (2001) focuses on the “central bank
area” that would result from dollarization. He argues
that this would be the most important effect of
dollarization in Mexico—the Federal Reserve System
would become Mexico’s central bank.
This scenario would lead to changes in monetary policy (which Stockman defines broadly to
include supervisory and regulatory policies) that
would affect the incentives of financial intermediaries and thereby affect the levels of investment
and financial integration. This change is important
because the level of financial development is
strongly related to economic growth and is shown
in some studies to cause growth14; thus, the potential benefits are indeed large.
Other studies, however, indicate that integration
should come before dollarization. For example,
Bencivenga, Huybens, and Smith (2001) show that
dollarization has a different impact depending on
the extent of the integration between the two
economies’ financial markets. They show that dollarization is beneficial when capital markets are
well integrated; otherwise, dollarization may be a
source of volatility and indeterminacy in the economy. Hence in their model, it is the ex ante level of
integration of capital markets that determines the
benefits of dollarization.
Bencivenga, Huybens, and Smith (2001) complement and extend the traditional optimal currency
literature, where it is the integration of real markets
that determines the boundaries of the optimal currency area. This theory is based on the work of
Mundell (1961) and specifically addresses the issue
of when two economies should use the same currency. According to the theory, the key issue in determining whether two economies fall in the same
optimal currency area is whether or not there is a
substantial benefit of having independent monetary
34

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policy to accommodate asymmetric shocks to the
economies. An optimal currency area in general is
one where: (i) asymmetric shocks are not substantial, (ii) there is high mobility of factors of production, and (iii) prices are flexible. It is important to
keep in mind, however, that these considerations
have not been the motivation behind the current
interest in dollarization.
Using the criteria of the literature on the traditional optimal currency area, it is hard to imagine
Argentina being in the same optimal currency area
as the United States. Even neighboring Mexico is
far from perfectly integrated with the U.S. economy.
The interest on dollarization fundamentally stems
from the desire to bring about financial stability.
The involvement of the banking sector in the recent
crises underlined the importance of this issue, which
is beyond the scope of the traditional optimalcurrency-area model.

The Lender of Last Resort Function
A common argument against dollarization is
that it would severely limit the ability of the central
bank to act as a lender of last resort when the banking sector is in distress. One of the crucial roles that
banks perform is maturity transformation: taking
in short-term deposits and making long-term loans.
This naturally puts a bank at risk if, for whatever
reason, depositors have a sudden increase in their
demand for liquidity and want to withdraw their
money. When there is a domestic currency that
can be printed freely, the central bank always has
the ability to meet this liquidity demand by lending
cash to the banking sector. Banks can then repay
the loans when the crisis passes. In a dollarized
economy, the central bank would not have unlimited
resources to lend. The fear, therefore, is that giving
up the ability to print currency will make these types
of crises more frequent and/or more severe.
The emerging literature has shown that this
concern is likely overstated for several reasons. First,
the ability of the central bank to act as a lender of
last resort is equally limited under fixed exchange
rates and currency boards. Nevertheless, Argentina
has developed several other mechanisms to deal
13

For a critique of their result and a review of the literature in contrast
with it, see Pakko and Wall (2001).

14

King and Levine (1993) show that financial development predicts
subsequent growth, and Rajan and Zingales (1998) provide evidence
of causation. See also Levine (1997). Levine and Carkovic (2001) argue
that the positive effects of dollarization would be indirect, working
through financial development.

FEDERAL RESERVE BANK OF ST. LOUIS

with liquidity crises. These include holding excess
foreign reserves (above those required to back the
currency in circulation), having banks contribute
to a deposit insurance fund, and contracting a type
of contingent credit line with foreign banks. Velde
and Veracierto (1999) calculate that, together, these
mechanisms cover 40 percent of total deposits.
Second, as Calvo (2001) points out, central banks
in industrialized countries do not generally perform
their lender-of-last-resort function by printing currency; they borrow instead. This was the case, for
example, in the banking crises in Sweden and
Finland in 1992. Third, as proposed by Calvo (2001)
and others, a “special fund” or a credit line guarantee from an international lender of last resort could
be set up to guard against a large crisis that would
overwhelm domestic resources. One potential
source of revenue for the fund is the increase in
seignorage revenue that the United States would
receive when a country dollarizes. Since the fund
would likely increase the stability of dollarizedcountry financial markets, this could be a productive
(and politically acceptable) use of the funds from
the U.S. point of view.15
Finally, several studies have identified the
domestic lender of last resort as a cause of both
excess volatility in emerging economies’ financial
markets and currency crises.16 This is largely related
to the moral hazard problem that such a lender can
create when the supervisory and regulatory aspects
of the banking system are underdeveloped. This
problem was particularly severe in East Asia and is
now thought to be one of the primary causes of
that crisis.17 A related problem is that the lender
of last resort might not be able to take the “right”
action in times of crisis because of heavy political
pressure. Ennis (2000), for example, shows how
such pressure may prevent the lender of last resort
from implementing the optimal policy and, instead,
force the use of a suboptimal inflation tax to bail
out a banking sector in distress. In this context,
dollarization works as an ex ante commitment not
to surrender to political pressure in the event of a
liquidity crisis. Antinolfi and Keister (2000) show
how dollarization can be seen as a way of committing to charge a (perhaps unpopular) “penalty rate”
on discount window loans during a crisis—exactly
the policy advocated by Bagehot (1873). These
studies indicate that dollarization can actually be
seen as fixing some of the problems created by a
lender of last resort.18 Such political-economy issues
have received relatively little emphasis in the litera-

ture on dollarization, and in our opinion they
deserve further research.

Existing Liability Dollarization
The set of initial conditions on which dollarization would be implemented is also crucial for understanding dollarization proposals. Our analysis would
be incomplete without a discussion of the current
state of an economy considering dollarizing, particularly with respect to existing liability dollarization.
Liability dollarization refers to domestic borrowing
denominated in or indexed to a foreign currency.
Both sovereign debt and private debt in emergingmarket economies are often dollarized.
Our main concern in this section is private
sector dollar-denominated debt, which has been
growing rapidly in emerging-market economies.
This includes both direct borrowing by individual
firms and borrowing by the domestic banking sector.
Is widespread liability dollarization an indication
that an economy should officially dollarize? The
answer to this question must depend on what is
causing the liability dollarization to occur. Why
are firms willing to borrow in a foreign currency
when this creates a balance-sheet mismatch that
greatly increases their vulnerability to unexpected
devaluations?
Two types of explanations have been offered in
the literature. The first (see, for example, Burnside,
Eichenbaum, and Rebelo, 2001) is based on (implicit
or explicit) government guarantees of the liabilities,
especially those of the banking system. Under a fixed
exchange rate regime, the interest rate on dollar
loans will be lower than the domestic interest rate,
the difference reflecting the possibility of devaluation. This condition leads banks to borrow in dollars.
In addition, because the government guarantee
implies that it will act as a residual claimant on bank
15

Clearly, any such contribution of seignorage would be a matter for
the Congress and executive branch to decide.

16

See, for example, Chang and Velasco (2000a), Mishkin (1999), and
Fischer (1999). See also Antinolfi, Huybens, and Keister (2001), which
shows how a lender of last resort having the ability to print money
can allow inflationary beliefs to become self-fulfilling.

17

See Corsetti, Pesenti, and Roubini (1999) and Mishkin (1999) on this
topic.

18

But would dollarization itself find the necessary political support to
be implemented? Ennis (2000) goes on to show that this is possible if
the economy has a large population of international banks (i.e., banks
that operate in several countries). It is interesting to note that this is,
in essence, a form of financial-market integration, which we saw
above (in a different context) to be a factor that is likely to increase
the probability of success with dollarization.

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assets in bad states of the world (in which banks go
bankrupt), banks face no ex ante incentives to purchase insurance against bad states of the world.
Hence, they do not hedge (sufficiently) against
foreign exchange risk. In other words, the guarantee creates a moral hazard problem that leads to a
fragile banking system that is overexposed to currency risk. The reason the government would provide
this guarantee is that it reduces the interest rate that
domestic firms pay when financing working capital
from domestic banks and, therefore, has positive
effects on economic growth. This benefit the government obtains is sufficient to overcome the cost of
increasing the probability of a banking crisis when
the exchange rate is devalued. This is an indication
that official dollarization may be warranted, as it
would bring this benefit without the cost.
The second type of explanation claims that liability dollarization is a result of underdeveloped
domestic financial markets (see Caballero and
Krishnamurthy, 2000). The underdevelopment
means that firms cannot pledge their entire return
to foreign investors. As a result, assets that can be
used as international collateral become essential.
In such an environment, individual firms choose
between borrowing in local currency (which is
immune to changes in the exchange rate) and borrowing in dollars (which is cheaper). Caballero
and Krishnamurthy (2000) interpret borrowing in
domestic currency as purchasing insurance against
exchange rate fluctuations. They go on to show how
competitive markets mis-price this insurance. This
problem happens because, at the firm level, there
are two types of collateral—internationally accepted
and domestically accepted assets. At the economywide level, however, only internationally accepted
assets are net collateral. Because firms “overestimate” the amount of collateral that they have available, they tend to purchase less insurance than would
otherwise be optimal. If this is the reason for the
observed liability dollarization, it is less clear that
officially dollarizing would help matters. The problem of scarce internationally accepted collateral
may still arise. In this case, the benefit of official
dollarization is likely to be indirect—through the
development of domestic financial markets and
their integration with international markets.

viewpoint of the economy considering dollarizing.
The view of dollarization from the perspective of
the United States is also important. When Ecuador
and El Salvador adopted the dollar, the impact on
the United States was clearly minimal. It is doubtful
that the same could be said about Argentina or,
especially, Mexico. Two areas where a large dollarization could have an important impact on the
United States are seignorage revenue and the conduct of monetary policy.
We have discussed above how dollarization
entails a transfer of seignorage revenue from the
dollarizing government to the United States. We have
also discussed how the dollarizing country might
like to either receive a share of this money or have
it set aside in a fund for lender-of-last-resort functions. The second plan might receive more support
in the United States, since otherwise the United
States would possibly be directly involved in trying
to alleviate banking crises. This possibility introduces interesting questions about the relationship
between the United States and the dollarized economies that the literature has yet to explore. To the
extent that the United States perceives there to be
costs to having the dollar used widely, it may be
reluctant to give up the benefit of the extra revenue.
The financial integration with the United States
that could follow a dollarization is commonly considered to be a major benefit of dollarizing. Arguably,
financial integration can prove to be a major benefit
also for the U.S. economy. In addition, however, U.S.
monetary policy will have stronger effects abroad,
and the United States might have to take these
effects into account. As an example, suppose there
is a recession in a dollarized Mexico that calls for a
looser policy while events in the United States call
for a tighter policy. Although the United States would
have the option of ignoring events in Mexico, doing
so would likely cause a significant increase in the
flow of illegal immigrants into the United States.
Hence the optimal policy (from a selfish point of
view) would likely be looser than it would have been
had Mexico kept the peso.19 In this way, it is not only
the dollarizing economy that is losing monetary
independence; the United States might lose some
as well.

The Effects from the Perspective of the
United States

19

Our discussion so far has focused on the potential costs and benefits of dollarization from the
36

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For an analysis of the potential relation between dollarization and
Mexican migration to the United States see Borjas and O’N. Fisher
(2001). Their results indicate that the flow of illegal immigrants is
more volatile when Mexican authorities adopt a fixed exchange rate,
whereas the flow of legal immigrants remains unaffected.

FEDERAL RESERVE BANK OF ST. LOUIS

As a final (and highly speculative) note, we
observe that, if the United States benefits from the
increase in seignorage revenue, widespread dollarization would give an incentive to generate a higher
steady-state level of inflation. Although it seems
unlikely that this incentive would influence U.S.
policy, it is interesting to report how Fischer (1982)
concludes his paper:
Use of a foreign money also implies that the
domestic government is relying on the foreign government to maintain better control
over the inflation rate than it does itself—
an admission that most governments would
be reluctant to make. And besides, Who is to
guard the guardians?

FURTHER READING
We have discussed some of the key issues that
are important for a country considering official
dollarization, including some of the likely costs and
benefits. A crucial issue that we have not discussed,
however, is how large these costs and benefits would
be. There is little historical evidence that can be used
as guidance on this question. There are many inherent difficulties in quantifying the effects of dollarization, and these are reflected in a wide range of
predictions that are obtained from different models
that focus on different aspects of the problem. An
example of this disparity can be found in the results
of Cooley and Quadrini (2001), Del Negro and
Obiols-Homs (2001), Mendoza (2001), and SchmittGrohé and Uribe (2001), all of which are quantitative
studies related to dollarization in Mexico. Some of
these papers conclude that the overall benefits
would be very large, while others conclude they
would be small or even negative.
All four of these papers, along with some others
we have referenced and some we have not, are
gathered together in a special issue of the Journal
of Money, Credit, and Banking (May 2001). We encourage the interested reader to consult this source
directly for a more extensive discussion of the
issues related to dollarization than is possible here.
In addition, Spanish-speaking readers are encouraged to consult La Dolarización como Alternativa
Monetaria para México (Del Negro et al., forthcoming). This volume consists largely of papers presented
at a conference on dollarization sponsored by the
Instituto Technológico Autónomo de México (ITAM)
in December 2000.

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Persistence, Excess
Volatility, and Volatility
Clusters in Inflation
Michael T. Owyang
hree key features of the U.S. inflation time
series have been identified by empirical
studies. First, innovations in the level are
persistent—that is, changes in the inflation rate
generally endure. Second, volatility appears in
clusters directly after changes in inflation. Following an innovation in the inflation rate, short periods
of increased volatility are indicated by the presence
of autoregressive conditional heteroskedasticity
(ARCH) in the regression residuals. Third, periods
with high mean inflation have a correspondingly
high variance of inflation, and vice versa. Likewise,
periods with low levels of inflation tend to be associated with low variability.
This paper presents a model in a single, integrated framework that offers one possible explanation for these facts about the U.S. inflation time
series. In this model, the policymaker faces a tradeoff between inflation and unemployment in the
form of an expectations-augmented Phillips curve.1
The Phillips curve is subject to two shocks: a persistent shock that follows a Markov process and a white
noise shock. The magnitudes of both shocks are
unobservable, forcing the policymaker to employ
an ordinary least-squares (OLS) learning technology
to determine the policy target. Agents have the same
information set as the policymaker and form rational
expectations of monetary policy. In addition to the
Phillips curve shocks, an independent Markov process governs the policymaker’s preferences; agents
form their expectations after observing current
policymaker preferences.
Learning and the interaction between the

T

Michael T. Owyang is an economist at the Federal Reserve Bank of
St. Louis. A previous version of this paper was written at the University
of California, San Diego, and appears in Owyang (2000). The author
thanks Jim Hamilton, Garey Ramey, and Valerie Ramey for their input,
as well as Takeo Hoshi, Neal Beck, Thomas Sargent, Robert Shimer,
Leora Freidberg, Kevin Lansang, Glenn Rudebusch, and seminar
participants at the Federal Reserve Banks of Dallas, St. Louis, and San
Francisco, the Board of Governors of the Federal Reserve System,
and Emory University for useful comments. The author also thanks
Chang-Jin Kim and Charles Nelson for assistance with the program.
Abbigail J. Chiodo provided research assistance.

© 2001,

T H E F E D E R A L R E S E R V E B A N K O F S T. L O U I S

Markov processes governing the position of the
Phillips curve and the policymaker’s preferences
provide one possible explanation for the three
stylized facts about the U.S. inflation time series.
Changes in the variable that determines the position
of the Phillips curve (henceforth called the structural
variable) are persistent and directly determine the
policymaker’s target. Thus, regime shifts in the
structural variable induce persistent shifts in inflation—the first of three stylized facts. The second,
volatility clustering, is driven by the policymaker’s
learning mechanism. Once the economic fundamentals change, the policymaker resets the learning
algorithm to determine the magnitude of the new
shock. As the policymaker learns, new information
each period does not lead to as large of an update
of his estimate of the position of the Phillips curve.
Thus, periods of volatility follow the shock, then
drop off.
The third fact, the relationship between mean
and variance, is a result of the process governing the
policymaker’s preferences. In addition to persistence
effects, uncertainty in the policymaker’s estimate
of the position of the Phillips curve produces variability in the policy target. When the policymaker is
accommodative, i.e., inflation is high, this uncertainty
is amplified. However, when the policymaker is in
an inflation-intolerant regime, uncertainty about
fluctuations in the Phillips curve are not amplified,
as the policymaker is less willing to trade off inflation for small gains in unemployment.
The model is estimated using Gibbs sampling.
The estimation procedure will generate both a
parameter vector for the model and posterior densities for each Markov process. Monte Carlo simulations using the estimated parameters reveal that
three-state versions of both Markov processes
(governing the Phillips curve and the policymaker’s
preferences) produce artificial data that exhibit the
three characteristics described above.

FEATURES OF THE U.S. DATA
Figure 1 shows the U.S. monthly annualized
inflation rate for the period 1947:01–1998:05.2
The inflation data over this period exhibit three
particular time-series characteristics:
1

This literature stems from the seminal work of Kydland and Prescott
(1977) and Barro and Gordon (1983). Models possessing policymaker
preferences of similar form include Barro (1986), Cukierman and
Meltzer (1986), and Ball (1992, 1995).

2

The data are seasonally adjusted CPI data taken from Citibase.

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Figure 1
U.S. Inflation
25%

20%

15%

10%

5%

0%

-5%

-10%
1947

1952

1957

1962

1967

1972

1. Changes in inflation are persistent.
2. Inflation series have volatility clusters and
can be modeled as some form of ARCH series.
3. High/low levels of inflation are associated with
relatively high/low variance and uncertainty.
The first of these phenomena has been considered
in the empirical literature by Barsky (1987) and
Fuhrer and Moore (1995). They find that innovations
in the rate of inflation are largely permanent, causing persistent shifts in trend; in the presence of an
aggregate shock, the inflation rate rises and stays
high for an extended period. Consider the subperiod
1968-73, for example; here, an innovation in the
inflation rate is associated with a largely permanent
shift in trend.3
Table 1 shows the results from an analysis of the
autocorrelations for monthly data over the sample
period 1947:01–1998:05. Autocorrelations for the
first eight lags range between approximately 0.4
and 0.6, providing strong evidence of the presence
of serial correlation. Results indicate that inflation
is largely persistent with lagged coefficients that
are clearly significant, indicating that innovations
that occur in any period spill over into subsequent
periods.
42

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1977

1982

1987

1992

1997

Following Engle’s (1982) original analysis of
the U.K. inflation data, a number of papers have
attempted to fit the U.S. inflation data to an ARCH
model to test for the presence of volatility clusters.
Kim (1993) tests ARCH against alternate specifications and finds that ARCH does not perform as
well as an unobserved-component time series with
Markov-switching heteroskedasticity. However,
Baillie, Chung, and Tieslau (1996) employ an alternate specification to model the inflation process,
using an autoregressive, fractionally integrated,
moving-average version of a generalized autoregressive conditional heteroskedasticity model (ARFIMAGARCH). They find evidence of persistence and
mean reversion, as well as heteroskedasticity, in
the inflation time series.
In light of this evidence, consider a GARCH(1,1)
model for the variance of the form

σ t2 = κ + χet2−1 + δσ t2−1 ,
in which the current conditional variance depends
3

This period coincides with the beginning of the two-tiered system
for gold coverage in 1968, the closing of the gold window in 1971,
and the end of the adjustable peg in 1973.

FEDERAL RESERVE BANK OF ST. LOUIS

Table 1
Autocorrelations and AR(4) Regression for U.S. Time Series Inflation 1947:01–1998:05
Autocorrelations
Lag 1

0.611

Lag 5

0.473

Lag 2

0.575

Lag 6

0.465

Lag 3

0.501

Lag 7

0.463

Lag 4

0.466

Lag 8

0.475

Variable

Coefficient

Standard error

t Statistic

∆CPIt–1

0.392983

0.044755

8.780743

∆CPIt–2

0.217638

0.053232

8.780741

∆CPIt–3

0.153694

0.048365

3.177771

∆CPIt–4

0.180432

0.044039

4.097130

C

0.334763

0.114108

2.933746

ARCH(1)

0.141611

0.017654

8.021489

GARCH(1)

0.830818

0.020444

40.63829

Mean inflation

4.099219

0.376006

SD inflation

4.511847

3.564057

Akaike info criterion

2.553171

Summary statistics
R2
Adjusted R

0.382133
2

SE of regression

LM test
F Statistic

62.33962

Probability

0.00000

Obs R2

56.66900

Probability

0.00000

Variable

Coefficient

Standard error

t Statistic

C

6.959891

1.016461

6.847182

RESID^2(–1)

0.302882

0.038361

7.895545

on the lagged conditional variance and the lagged
squared residual. A test for ARCH by employing a
Lagrange multiplier (LM) test indicates that the null
hypothesis of ARCH cannot be rejected. Table 1
contains the results from the LM test of an AR(4)
model and the variance results of the GARCH(1,1)
regression of the U.S. inflation time series. Both the
ARCH and GARCH components of the variance
equations are significant.
Ball and Cecchetti (1990) cite a relationship
between the level of inflation and its variance,
noting that an increase in the level of inflation is
not only persistent but often associated with a
corresponding increase in the variance and/or
uncertainty of future inflation.4 Explanations for

this phenomenon have focused on three primary
areas: changes in the expectations-augmented
Phillips curve, temporary and permanent aggregate
shocks, and idiosyncratic policy.
Using the U.S. quarterly gross national product
(GNP) deflator and consumer price index (CPI) data
divided into subperiods of various lengths, Ball and
Cecchetti (1990) test the hypothesis that the level
and variability of inflation are related. Their result
is that the correlation between level and variance
rises for the first few years and then begins to fall.
4

Logue and Willet (1976), Cosimano and Jansen (1988), Devereux
(1989), and Evans (1991) also test this relationship. Evans pays particular attention to estimating inflationary uncertainty. Ball (1992) provides
a theoretical model that attempts to explain this correlation.

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REVIEW

• a monetary policymaker with Markovswitching preferences for low inflation
relative to low unemployment, and
• policymaker learning.

Figure 2
Correlation Between Mean and Variance
for Five-Year Subperiods
9

The policymaker faces a short-run tradeoff
between inflation and unemployment embodied in
the Phillips curve.5 Mankiw (2000) argues for the
inclusion of both expectations and supply shocks
to provide a complete and stable view of the economy. This model incorporates these features but
assumes that the magnitude of these supply shocks
is unobservable and must be learned.6 This model
focuses on the actions of a policymaker under uncertainty and subject to shifts in preferences. During
each period, events occur in the following order:

8
7
6
5
4
3
2
1

ρ =0.23

• The policymaker’s preferences are determined
and revealed to the public.
• Agents and the policymaker simultaneously
set expectations and the policy target,
respectively.
• The economic shocks then occur, and the
policymaker and agents observe the realized
inflation and unemployment rates.
• The policymaker’s and agents’ information
sets are updated.

0
0

1

2

3

4
5
Mean Inflation

6

7

8

9

Ball and Cecchetti decompose inflation into a series
of permanent shocks and temporary shocks—a
trend stationary component and a white noise component. They show that permanent shocks have
increasing variance with level and thus cause a rise
in uncertainty when trend rises.
Consider the mean and uncertainty of inflation
over five-year, non-overlapping subperiods and the
correlation between sample means and standard
deviations across these subperiods. The results are
plotted in Figure 2. Examination of the results
reveals a relationship between mean and standard
deviation, with a correlation of about 0.23. Figure 3
plots the inflation means and standard deviations
for each subsample. The magnitude of these increases in mean and variance varies with the sample
period, but this indicates a relationship that might
not be completely revealed using a simple correlation test. Note that only for the period 1975-79 does
the variance fall when the subsample mean rises.

Consider an economy in which a monetary
policymaker sets an inflation target and private
agents form expectations about the realized inflation
rate.7 Suppose that the policymaker faces an expectations-augmented Phillips curve of the form
(1)

where ut is the unemployment rate; πt is the inflation rate; πte are the period t inflation expectations;
ηt is a persistent unemployment shock that follows
5

In order to abstract from interest rate properties, this paper does not
consider directly the policymaker’s instrument. In addition, I do not
include smoothing as a policymaker objective. If interest rates were
added as the policymaker’s instrument, the paper could be nested as
a special case of the model found, for example, in Clarida, Gali, and
Gertler (1999). The backward-looking nature of this model, driven by
the learning process in agent expectations, is similar to that proposed
originally by Taylor (1981) and later by Fuhrer and Moore (1995) and
Rudebusch and Svenson (1998).

6

A number of academic papers consider the effect of the Fed learning
about the world. Sargent (1999) considers a model in which uncertainty
generates paths between economic equilibria. Kasa (1999), Lansang
(2001), Sack (1998), and Wieland (1998, 2000) also consider models
in which the policymaker faces some degree of parameter or model
uncertainty.

7

Owyang and Ramey (2001) use a similar model with adaptive expectations to measure monetary policy.

Model
To formulate an integrated model that provides
one possible explanation for the previously mentioned time-series characteristics of U.S. inflation
data, I propose a reduced-form macroeconomic
model with the following features:
• a neoclassical rational expectations–
augmented Phillips curve subject to a Markov
shock to the natural rate of unemployment,
44

N OV E M B E R / D E C E M B E R 2 0 0 1

ut = k (π te − π t ) + ηt + ε t ,

FEDERAL RESERVE BANK OF ST. LOUIS

Figure 3
Mean and Variance of Five-Year Periods Over Time
Percent
9
8

Inflation

7
6
5
4

S.D. Inflation

3
2
1
1947-1949

1950-1954

1955-1959

1960-1964

1965-1969

1970-1974

a three-state Markov-switching process with a vector
of possible structural states h=(h1,h2,h3), a transition
kernel Tη , and period t state indicator vector St ; and
εt~N(0,σε2 ) is a white noise shock that occurs each
period.
Shifts in ηt represent dramatic, persistent
changes in the current economic environment.
These shifts can be viewed as unexpected but
highly visible events, such as wars or oil crises, in
which the timing of the event is clearly observed.8
However, the new value of ηt that arises following
a switch cannot be observed, but rather must be
learned by the policymaker and agents.9 Let
η̂t=Et [ηt|Ω t] denote the policymaker’s period t
estimate of ηt conditional on his information set
Ω t=(u1,u2,…,ut,π1,π 2,…,π t).
The policymaker has preferences over inflation
and unemployment, Lt=α t u 2t+π 2t, with the relative
weight on unemployment, α t, governed by a Markov
process with transition kernel T α and possible states
α=(a1,a2,a3). A high α t policymaker attaches more
weight to output and sets a higher inflation target,
conditional on the estimated state of the world, η̂t.
The low α t policymaker is an inflation hawk and
sets a lower conditional inflation target. It can be
shown that a policymaker who minimizes the
current period value of his quadratic loss will form
a short-run, discretionary inflation target that can
be given by
ˆt )
(kπ te + η
π t = kα t
(2)
,
2
1 + k αt
where η̂ t is the policymaker’s estimate of the
magnitude of the unemployment shock.10 Although
the policymaker can set an inflation target, the

1975-1979

1980-1984

1985-1989

1990-1994

1995-1998

realized inflation rate is subject to some normally
distributed noise, υt.11
For exposition, assume that agents form expectations rationally and with the same information
set, Ω t, as the policymaker. Agent expectations are
then
(3)

π te = π t .

Combining equations (2) and (3) gives
(2′)

π t = kα t ηˆ t .

Equation (2′) can be interpreted in terms of
current and historical policy. Assuming that α t ≠ 0,
the policymaker’s short-run target moves as a function of his belief about the state of the economy. As
the balance of risks shifts toward higher perceived
8

It is convenient but not necessary to assume that the policymaker
observes the timing of the event. Similar results obtain if the event is
unobserved. If there is a switch but the policymaker believes there is
none, the policymaker’s inflation target will induce a poor unemployment outcome. If this persists for a number of periods, the policymaker
can conclude that a switch has occurred. On the other hand, if the
policymaker believes a switch occurred when it in fact had not, the
policymaker resets the gain sequence. New information does not
change the target on average but does induce more volatility.

9

Agents in the model, including the policymaker, are not assumed to
know the structure of the underlying process. They are assumed to
believe that the economy can take on a continuum of possible states.

10

Note that this formulation assumes the policymaker is optimizing
over the current period only. A more forward-looking policymaker
complicates the learning via feedback from the economy and is left
as an extension. This formulation, however, does not presuppose a
lack of a consistent long-run inflation target.

11

This can be interpreted as the policymaker setting an intermediate
interest rate target and realizing an inflation target with some error.
For this application, I suppress the interest rate target and consider
only the effect on inflation.

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unemployment (i.e., higher η̂ t ), the policymaker
will allow the inflation rate to wander while focusing
attention on achieving a higher growth rate (and,
thus, lower unemployment) and vice versa.
The effect of the switching process α t on the
inflation target can be historically exemplified by
changes in Federal Reserve chairman, although the
model does not restrict it to be so. Clarida, Gali, and
Gertler (2000), among others, recognize the fundamental change in Fed objectives at the onset of the
Volcker regime in October 1979.
Finally, since the magnitude of the unemployment shock is unknown, the policymaker must infer
the state of the economy from the data. Since the
timing of the shock is known, the policymaker can
employ an OLS learning technology of the form

ηˆ t =

(4)

g −1
1
ut −1 + t
ηˆ t −1 ,
gt
gt

where gt is the number of periods since the last
switch in ηt. The sequence is g1, g2,…, gt referred to
as the gain sequence. The policymaker resets the
gain sequence when a switch occurs. This is synonymous with discarding previous (and now useless)
information gathered before the shock and attaching more weight to incoming information. As the
policymaker accumulates more information, new
information becomes less valuable and the weight
attached falls.

Inflation Dynamics
The model specified by equations (1) through
(4) simplifies into two time-series equations governing unemployment and inflation: the Phillips curve
(equation (1)) and
(5)

πt =

gt − 1
kα
π t −1 + t (ηt −1 + ε t −1 − υt −1 ) + υt ,
gt
gt

where υt is normally distributed inflation noise
that occurs after the policymaker sets the inflation
target and can be interpreted as control error.12
Equation (5) embodies the aforementioned
time-series characteristics of the inflation time
series. First, the autoregressive nature of equation
(5) and the Markov structure of the shocks indicate
that shocks to the inflation rate in the form of preference shocks to α t or structural shocks to ηt are
persistent, i.e., shifts in the inflation rate are lasting.
This can be verified if the diagonal elements of the
transition kernel sum to greater than 1. Second, a
Markov shock to the Phillips curve in the form of
46

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a shift in ηt will induce periods of volatility while
the policymaker learns. Third, an accommodative
policymaker (i.e., high α t ) will tend to induce more
volatility in the inflation rate than the relatively
hawkish (i.e., low α t ) policymaker.13
The first property implies that the equilibrium
inflation path exhibits persistence whenever α t >0,
as a direct result of persistence in the processes
determining α t and ηt and indirectly through the
effect of the learning rule on the policy choices. The
second property is demonstrated in the following
thought experiment. Consider an aggregate shock
at time t=0 that shifts the Phillips curve out through
an increase in the parameter ηt. The policymaker
would react to the shock by raising his inflation
target and raising the mean level of inflation, thus
causing a persistent change in the inflation rate.
The policymaker, however, does not know the exact
value of the target and cannot infer the magnitude
of the shock because of unemployment noise, ε t ,
and inflation noise, υt. He must therefore implement
a policy based on estimates of the new Phillips curve
parameters, which he constructs using the learning
technology. In the short term, the policymaker’s
estimate—and thus the inflation rate—is greatly
affected by new information in the form of new
observations. This result stems from the policymaker resetting the gain sequence, gt, in equation
(4). The weight on new information is increased
because information prior to the incidence of the
new shock is no longer valuable. Over time, the
policymaker collects inflation-unemployment data
and updates his estimate of the shock magnitude,
causing the accuracy of his prediction to increase.
Also, the accumulation of information allows the
policymaker to decrease the weight of new information, and inflation becomes less variable.14
Suppose now that the policymaker’s preferences
change, switching from an accommodating regime
to an anti-inflationary regime. The policymaker
attaches more emphasis to minimizing the level of
inflation and subsequently reduces the inflation
12

Equation (5) elucidates a time-series path for inflation. A similar
equation could be written for unemployment. However, the timeseries characteristics for unemployment are less well documented,
and I leave discussion of them to another paper. It is sufficient to say
that, in this formulation, the unemployment time series would follow
a Markov process with noise.

13

A formal presentation of these results is given in Appendix A.

14

This paper assumes a particular learning specification. However,
these results are robust to permutations of the policymaker’s learning
technology provided that the learning mechanism implemented
converges (see Marcet and Sargent, 1989).

FEDERAL RESERVE BANK OF ST. LOUIS

Table 2
Estimated Parameters
Parameter

Estimated value

Parameter

Estimated value

a3

1.2130 (0.3681)

h3

6.1817 (1.2968)

a2

0.4856 (0.2468)

h2

5.3110 (0.9644)

a1

0.0929 (0.1516)

h1

4.3160 (0.9168)

συ

2.7434 (1.1105)

σε

2.4194 (1.0503)

Pr[α t = a3|α t– 1 = a3]

0.9663 (0.0191)

Pr[ηt = h3|ηt– 1 = h3]

0.9908 (0.0398)

Pr[α t = a2|α t– 1 = a2]

0.9706 (0.0189)

Pr[ηt = h2|ηt– 1 = h2]

0.7645 (0.2057)

Pr[α t = a1|α t– 1 = a1]

0.9058 (0.0768)

Pr[ηt = h1|ηt– 1 = h1]

0.6874 (0.2133)

NOTE: Standard deviations across iterations are given in parentheses.

target for a given estimate, η̂t. Additionally, because
the policymaker’s preferences enter multiplicatively
instead of additively, the adjustments made during
the learning process become smaller. Thus, the
policymaker sets a lower target with less variability—
the third property.

ESTIMATION
The preceding model of inflation and unemployment is estimated using Gibbs sampling. Gibbs
sampling uses an iterative filtering algorithm and
a Monte Carlo algorithm to generate the ergodic
density for the parameter vector conditional on the
data. An outline of the sampling procedure appears
in Appendix B. Seasonally adjusted monthly data
for both series are taken from Citibase for the sample
period 1947:01–1998:05. The inflation rate is taken
as the annualized rate of change of the CPI.15 The
parameter estimates are given in Table 2.
Here, α=(a1,a2,a3) reflects the policymaker’s
preferences and h=(h1,h2,h3) describes unemployment shocks to the Phillips curve. The combination
(ai and Pr[α t=ai|α t –1=a j ] for i, j=1,2,3) defines the
Markov process that determines the policymaker’s
preferences. Recall that α directly affects the policymaker’s inflation target. The high value for the
preference parameter, a3, indicates the most accommodative policymaker, while the low value, a1, represents a policymaker less willing to trade high inflation
for lower unemployment; a1 defines a regime in
which the policymaker sets a nearly zero inflation
target that does not respond much to changes in
the state of the economy. On the other hand, a2 and
a3 correspond to policymakers who are increasingly
responsive to shocks to the structural variable.

Suppose a shock hits the economy in the form of
an increase in the natural rate ηt. The accommodative policymaker (αt=a3 ) responds to the shock by
increasing his inflation target. A 1 percent increase
in the natural rate, ηt, when the policymaker is in
the a3 state implies a 1.3 percent increase in the
inflation target. Similarly, a 1 percent increase in
the natural rate when the policymaker is in the a1
state implies a 0.5 percent increase in the inflation
target.
The parameters (Pr[α t=ai|α t–1=a i ] for i=1,2,3)
are the on-diagonal transition probabilities that
determine the duration of the policymaker’s preference regime. They also determine the expected
number of regime changes over the sample period.
The number of regime shifts predicted by the estimated transition probabilities are similar to the predictions in Romer and Romer (1989).16
Now consider the three-state process for the
structural variable ηt. The process (hi, Pr[ηt=hi|ηt –1
=h j ] for i, j=1,2,3) represents three shocks to the
natural rate of unemployment and their transition
probabilities. One interpretation of this process is
that the state ηt=h2 represents the “normal” state
of the economy, while the other two states are the
product of exogenous shocks. The low value, h1, can
be interpreted as the natural rate of unemployment
in an unusually productive state of the economy,
15

Results using the monthly personal consumption expenditures (PCE)
index are not appreciably different. Postwar quarterly GDP deflator
data are of insufficient length to run this type of estimation.

16

Romer and Romer find seven instances during this sample when the
Fed reacted to explicitly reduce inflation. For a more detailed comparison of the type of model presented here and the Romer dates, see
Owyang and Ramey (2001).

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Table 3
Three-State Monte Carlo Results
Simulated*

U.S. time series†

AR(1)

0.3114 (0.0454)

0.3841 (0.0438)

AR(2)

0.2326 (0.0401)

0.2238 (0.0517)

AR(3)

0.1886 (0.0436)

0.1604 (0.0468)

AR(4)

0.1720 (0.0389)

0.1739 (0.0436)

Constant

3.2497 (2.883)

0.2554 (0.1053)

ARCH

0.0400 (0.0488)

0.1410 (0.0170)

GARCH

0.6753 (0.2754)

0.8406 (0.0195)

Five-year
correlation‡

0.2453 (0.3660)

0.3155

Sample mean

3.89 (0.21)

3.99

Variance

4.30 (0.61)

4.40

Skewness

0.92 (0.15)

0.85

Kurtosis

2.70 (0.21)

5.02

NOTE: Simulated data statistics are taken from 1000 iterations
of 608 period samples. The first column contains results from
the regression of inflation on four lags. GARCH(1,1) parameters are taken from the following model of the variance σ t2=
κ+χut2– 1+δσ t2– 1 ,χ ,δ >0.
*Standard deviations across samples are given in parentheses.
†Standard errors for the AR(4) regression are given in
parentheses.

Indicates the correlation between mean and variance of fiveyear intervals.
‡

perhaps caused by a positive technology shock.
The high value, h3, represents the innovation to the
natural rate after an adverse event such as an oil
shock.17

Simulations
To evaluate how well the proposed model fits
the data, the estimated parameters from the previous
section are used in Monte Carlo simulations. The
goal is to determine whether the model replicates
the moment and variability characteristics of the
U.S. inflation time series. Artificial data series are
created according to equation (5), and AR(4) regressions are performed for comparison with the U.S.
time series.18 The residuals are then tested for
GARCH(1,1). Results of the simulations and subsequent statistical tests are shown in Table 3.
The coefficients on the autoregressive terms
and variability characteristics taken from the regres48

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sions on the artificial data are statistically consistent
with those obtained from the U.S. time series. However, both the ARCH and GARCH parameters are
comparatively low and more variable. This can be
explained by the manner in which the simulations
are generated. The estimated variability characteristics show dependency on the average duration of
the regime. Short-lived regimes in ηt will reduce
the variability characteristics of the artificial data,
as the policymaker is unable to carry out the learning process. The policymaker resets the gain at the
onset of each switch; however, if regimes tend to
be of short duration, the policymaker never has a
chance to reduce the gain. Variability characteristics
are driven by the switches in the regime rather than
the learning process. Long regimes in the ηt variable
can cause similar problems. When there are few
switches, the policymaker’s gain remains at low
levels, reducing the amount of variability induced by
learning. Analysis of individual simulations reveals
that, in iterations in which the policymaker reverts
to an anti-inflationary regime for unusually long
periods, the GARCH coefficient is near zero. Essentially, the variability parameters are biased downward in both cases of extremely high numbers of
switches and extremely low numbers of switches.
Incorporating switching processes into Monte
Carlo experiments of this kind makes these results
unavoidable, as some samples are bound to be
outliers.
The artificial data also exhibit the meanvariability relationship found in the U.S. time series.
The correlation between mean and variance for fiveyear intervals is highly variable in the simulated
data, however. This correlation is also caused by
the incorporation of Markov processes into Monte
Carlo experiments. Recall that the mean-variability
relationship depends on switches in the preference
process. Thus, the statistic will be biased downward
if the changes in the inflation level are driven primarily by switches in the structural process. If no
switches in the α t process occur, the mean-variance
correlation can actually be negative. A similar result
is true if there is a large number of preference
switches, which can also have a tendency to understate the relationship or cause a negative correlation.
17

An alternate explanation for shifts in the natural rate involves the
change in demographics over time. Shimer (1999) attributes recent
changes in the natural rate to the “baby-boomers” phenomenon.

18

Series lengths are 750 observations. The first 142 observations are
discarded to avoid issues associated with initial conditions.

FEDERAL RESERVE BANK OF ST. LOUIS

CONCLUSION
The above model combines a reduced-form
model of monetary policy with a Marcet-Sargent
(1989) policymaker OLS learning formulation to
provide one possible explanation for the three stylized facts about U.S. inflation. Results indicate that
a bivariate, three-state Markov-switching model can
generate these characteristics of the U.S. inflation
time series. The model is able to produce inflation
persistence, volatility clusters, and a correlation
between level and variance and the parameter estimates that are similar to those of the actual U.S.
inflation time series.
These inflation characteristics are generated
by the interaction among the unobserved shock to
the Phillips curve, policymaker learning, and the
switches in the policymaker’s preferences. Persistent
shocks to either preferences or the Phillips curve
translate, through the policymaker’s decision rule,
into persistent changes in the inflation target. Additionally, more inflation-tolerant policymakers tend
to allow shocks to the economy to have a greater
effect on the inflation target, causing the inflation
target to become more variable when it is relatively
high. Finally, clusters of volatility are a reflection of
the policymaker’s learning process. The uncertainty
generated by the onset of a new shock makes the
target more variable; however, as the policymaker
learns, the target settles down.
What might this model, if correct, imply for
the future of the U.S. economy? Has the economy
entered a new technological regime? Can the economy sustain a low level of unemployment? Is a
slowdown inevitable? Forecasters move rapidly to
change their opinions at the onset of new information. Fluctuations in economic indicators can quickly
alter the tenor of expectations. The Fed scrambles
to adjust rates; economists on Wall Street adjust
expectations. The result: more volatility while we
all figure out the real state of the economy.

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FEDERAL RESERVE BANK OF ST. LOUIS

Appendix A

PROPOSITIONS AND PROOFS
Proposition 1. A shift in either α t or ηt results in
a persistent change in the inflation target π–t.
Proposition 2. A one-time switch in the structural
parameter causes the inflation variance to rise in
periods following the switch.
Proof. Given equation (5) and the fact that the
shocks are uncorrelated, write the variance of
inflation, conditional on gt, as

(A1) Var (π t | gt ) =
2

2

 gt − 1
 kα 
2
2
2

 var (π t −1 | gt ) +   (σ υ + σ ε ) + σ υ .
g
g
 t 
 t
Further
ˆ t | gt ) =
Var (η

σ ε2
.
gt − 1

Combining yields

For t<t′, the economy is in a steady state with
gt=∞, and Var(π t|gt )=σ υ2. Further, (A2) implies that
Var(π t|gt ) is strictly decreasing in gt , from which
follows that the variance of inflation rises following t′. Q.E.D.
Proposition 3. The mean level of inflation is
increasing in α. Additionally, when α is larger, the
switch in ηt causes the variance of inflation to rise
by a greater amount.
Proof. The first statement follows directly from (5).
When α rises, the expected value of the second
term on the right-hand side of (5) rises and the
expected value of the next period target rises. In
period t, the expected value of the second term is
again larger than it was before the regime shift.
The first term has also risen because the target
rose that period. The conclusion follows by induction. Consider again (A1). It is easy to verify that
the variance of inflation rises with α, which implies
the latter result. Q.E.D.

2

(kα t )2 2  kα t  2
2
σε + 
(A2) Var (π t | gt ) =
 συ + συ .
gt
 gt 

Appendix B

THE GIBBS SAMPLER
The goal of the sampling routine is to estimate
∼ ∼ ∼
the conditional posterior distribution p( β T, S T, Z T ,
∼
∼
ω |yT ), where yT =( y1, y2,…, yT ) is the vector of
observables through time T and ω is the vector of
parameters governing both Markov processes and
the variances of the white noise shocks to the
Phillips curve and the inflation rate.19 The Markov
processes make the direct estimation of this distri∼ ∼
bution impractical. However, draws from p ( β T, S T,
∼
∼
Z T,ω |yT) can be made from an ergodic distribution
of Markov simulations generated iteratively from
the following conditional densities:

(B1)




p(˜βT ,˜ST ,˜ZT ,ω | ˜yT ) 




p(˜βT | ˜yT ,˜ST ,˜ZT ,ω )
p(˜ST | ˜yT ,˜βT ,˜ZT ,ω )
.
p(˜ZT |˜yT ,˜βT ,˜ST ,ω )
p(ω |˜yT ,˜βT ,˜ST ,˜ZT )

The process of drawing from each of the
above marginal distributions is accomplished by

a version of Carter and Kohn’s (1994) multi-move
algorithm, with one exception. The conditional
∼ ∼
∼
distribution p ( S T |y∼T, β T, Z T,ω ) differs from the
∼
others in (B1) in that St depends on St–1 because of
the policymaker’s gain sequence. The multi-move
∼
algorithm generates the entire vector S T simultaneously. However, given St’s dependence on previous states, it cannot be generated in this manner.
∼
Thus, S T will be drawn from sequential sampling
from
(B2)

˜ T ,ω ) ,
p( St | ˜S −t ,˜yT ,˜βT , Z

∼
where S –t=(S1,S2,…,St –1,St+1,…,ST ). The joint den∼ ∼ ∼
sity p ( β T, S T, Z T,ω |y∼T) can then be estimated using
the marginal densities (B1) and (B2).

19

More detailed analyses of the Gibbs sampler are available in Cassela
and George (1992) and Kim and Nelson (1999).

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