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PERIODICALS

• p* in the Short Run
Identifying a simple long-term relationship between p* and the price level is
justified on empirical grounds because
other variables, particularly nominal interest rates, do not seem to affect the
long-term equilibrium value of M2
velocity. While interest rates trended
upward over most of the postwar
period, there is no clear evidence of
any effect on the trend in M2 velocity.
On the other hand, evidence strongly
suggests that interest rates are important for identifying a short-run relationship between M2 and nominal GNP.
Recent research indicates that money
demand may be more interest-rate sensitive than previously thought. Figure 4
reveals a close linkage between movements in interest rates and the velocity
of M2. Thus, it would appear that interactions among money, nominal income, and interest rates matter in the
short-run relationship between P" and
the price level.

policy. This seems evident in the fact
that one of the best predictors of inflation is previous inflation. Including
lagged inflation in models designed to
predict inflation can be justified if
lagged inflation is a reasonable proxy
for inflationary expectations.
This characterization of the short-run
inflation process is troubling because

the empirical research supporting the con-

difficult to justify sluggish price adjustment on theoretical grounds, most
economists find Iittle evidence that
prices of goods and services respond
immediately to changes in monetary

1. A more complete description of P" and
cept are found in Jeffrey J. Hallman, Richard
D. Porter, and David H. Small. "M2 per Unit
of Potential GNP as an Anchor for the Price
nors of the Federal Reserve System. April
1989.

choosing among alternative models.
Thus, it is difficult to know whether

Monetary Policy in an Era of Change, Proceedings from the American Enterprise In-

short-run inflation control based on the
P" indicator would lead to excessive
economic volatility.

stitute's Conference of November 16-17,

cal evidence supports the view that P"
can be a useful indicator in this regard.

by John B. Carlson

Level," Staff Study No. 157, Board of Gover-

tion from targets and goals is discussed by

some Federal Reserve officials may
have begun to use P" as an indicator
for clues concerning the achievement
of the price-stability objective. Statisti-

The Indicator P-Star:
Just What Does It Indicate?

Footnotes

policy? While there may be plausible
economic models that do not display
these cyclical effects of monetary
policy, there is no sound basis for

• Conclusion
Recent public statements suggest that

Federal Reserve Bank of Cleveland

longer perspective to avoid the possibility that short-term policy considerations might interfere with the longerterrn goal of price stability.

policy changes to induce business
cycles. Indeed, simple models linking

Identification of a short-run relationship between P" and the price level is
further complicated by the problem
that prices often adjust slowly to changing economic conditions. Although it is

useful in helping policymakers assess
the longer-term consequences of policy
actions. It is essential to maintain some

•

changes in inflation to the difference
between P" and the price level-the
price gap-indicate
a significant potential for cyclical effects of monetary

eCONOMIC
COMMeNTORY

While p* is not without some potential
shortcomings, it is likely to be most

in any economic model with lagged effects, there is a potential for monetary

2. This notion of an indicator and its distinc-

Financial
markets pay a great deal of
attention to the Federal Reserve System
and, in particular, to the deliberations of
its key policymaking arm, the Federal
Open Market Committee (FOMC).
This "Fed watching" focuses largely on
anticipating how the FOMC is likely to
react to unfolding events in the

Bennett T. McCallum in "Targets, Instruments, and Indicators of Monetary Policy,"

1988.

-

3. See Hallman et al., op. cit.

economy, and how such actions become
translated into changes in the cost and
availability of money and credit.

John B. Carlson is an economist at the
Federal Reserve Bank of Cleveland. The
author wishes to thank Christine Dingledine

Specifically, markets are interested in
knowing which variables the FOMC
considers in assessing whether it is ac-

for excellent research assistance.
The views stated herein are those of the
author and nat necessarily those of the

complishing its objectives. These variables are often referred to as indicators.
In recent years, Federal Reserve offi-

Federal Reserve Bank of Cleveland or of the
Board of Governors of the Federal Reserve
System.

cials have proposed a variety of new
monetary indicators, including commodity prices, the trade-weighted value
of the dollar, and the yield curve. Most
recently, however, the Federal Reserve

BULK RATE
Postage Paid
Cleveland,OH
Permit No. 385

u.s.

Federal Reserve Bank of Cleveland
Research Department
P.O. Box 6387
Cleveland, OH 44101

Address Correction

has unveiled P-Star (P*) , an indicator
of potential inflation. 1
• What Is an Indicator?
An indicator is neither an ultimate objective to be achieved (a goal), nor a
stand-in objective to be aimed at (a target). Rather, an indicator is a variable

Requested:

Please send corrected mailing label to
the above address.

QUV13t\31Q .:10
)lH\'B )i, '. S ::I1V~303':!

68. HV SO Ot 51

that provides information about
whether policy instrument settings are
likely to accomplish their specified objectives, which are observed only

d3S

after a lag. An indicator essentially

Material may be reprinted provided that
the source is credited. Please send copies

September 15, 1989

provides information concerning the
current state of the econorny.f
If an indicator value is unusually high
(or low) on the basis of some historical
standard, it could indicate that goal or
target variables are likely to miss their
marks. A policymaker might then
reconsider policy instrument settings to
attempt to avoid undesired outcomes.
However, policymakers are under no
commitment to react in any specified
way to changes in the value of an indicator; nor are they committed to seek
a specified value.
Because policymakers typically look at
a variety of indicators, they often observe conflicting signals. Moreover, different policymakers give different
weights to different indicators. Thus, it
is often difficult to predict how a group
of policymakers will react to substantial changes in indicator values.
• What Is P*?
Simply put, P" is the eventual price
level implied by the current level of the
M2 monetary aggregate. It is calculated as p* = (M2 x V*)/Q*, where V*
is an estimate of the long-run value of
the GNP velocity of M2-the mean
value from 1955:Q I to I988:Q4-and
Q* is a Federal Reserve Board staff
measure of potential output. Recent advances in understanding long-term
statistical relationships indicate that P"

AlPH1811 HOHV3S3H

of reprinted materials to the editor.
ISSN 0428·1276

Monetary

indicators can help

policymakers to evaluate the likely
success or failure of policy instrument settings. The recently unveiled
P-Star indicator can be useful as an
indicator of potential inflation and,

more broadly, as a method of assessing the Federal Reserve's long-term
goal of price stability.

and the current price level probably
share a common trend.
The indicator property, of P" is revealed in figure I. The vertical dotted
lines denote the quarters when the current price level (implicit price deflator)
and P" cross (top panel). Periods after
which P" begins to persistently exceed
the current price level are ultimately
characterized by rising inflation (bottom panel) .
Conversely, periods after which P"
begins to persistently remain below the
current price level are followed by
periods of disinflation. There is a
noteworthy variation, however, in the
lag between the time the two series
cross and the point when inflation
changes direction.

FIGURE

Presently, the level of M2 appears ap-

1 p* AS AN INDICATOR

proximately consistent with the current
price level. In the first half of 1989, P"

OF INFLATION

Natural log of price

fell slightly, so that p* and the price
level are about equal. Given the recent

0.5 p* vs, Implicit Price Deflator

12 Inflation"
10 .
•

6

•

2

•

o .
1955
a. Inflation is the percentage change in the implicit price deflator from four quarters earlier.

-

NOTE:

The vertical lines in the top and bottom panels mark the quarters when P and P' cross.

SOURCES:
Board of Governors
of Economic Analysis.

FIGURE

acceleration in M2 in early 1989:Q3
and current money-market interest
rates, it is unlikely that P" will continue to fall. Nevertheless, if p* moves

3,800

below the current price level and
remains there persistently, then the inflation rate would be expected to fall.

2,300

the money supply ultimately determines the level of prices. Moreover,
the P" relationship implies that any particular trend in M2 will be associated

of the Federal Reserve System: and U.S. Department of Commerce,

Bureau

2,800

Ratio
1.85r---------------------------------------~

1.80

rently no consensus on a method for assessing ex ante changes in trend output
growth: at any time, an estimate of

1,800

potential output may be inappropriate .
1,300~ ...•....•
'-!-::~...•....•
'-!-::~...•....•
~~
1955

...•....•
~~..L..I~~..L..I~~..L..I~

1990

Percent change, annual rate
4. 0

r-------------------------------------------.

2.52.0'::+
.•...•.
~1~'-'-~1~1"-&...~~
1955
1960
1965

-

SOURCE:

What distinguishes p* from.other characterizations of the quantity theory is

FIGURE

I..L..II~I~

1970

••.•.••
...L::_II~'-'-~I,_!_I"-&...~

1975

1980

1985

1990

Board of Governors of the Federal Reserve System.

4 M2 VELOCITY

AND INTEREST

are long and variable lags between
money growth rates, it is difficult to
find a simple measure of money
growth that would reliably indicate the
future inflation rate. Differing conclusions may result from choosing different periods over which to calculate
money growth rates. P*, on the other

Percent
18
16

1.80

14

1.75

independent of both economic factors
and the money-supply level. Also, p*

12

is based on a particular estimate of the
level of potential output, which is as-

10
1.65

sumed to be independent of policy in
the long run.

Despite these problems, p* has some
advantages over other inflation indicators. For example, because there

hand, provides an absolute reference
point for the price level.

RATES

Velocity
1.85r----------------------------------------.,

measure of money is based on evidence that, over sufficiently long
periods, M2 velocity retums to some
mean value (see figure 2), and hence is

2 M2 VELOCITY

tom panel), however, illustrates how
the estimate of potential output growth
has changed discretely at different
times. These changes have been recognized only after the fact. There is cur-

3,300

with its own unique path for the longrun equilibrium price level.

the extent to which it is specified in
practical terms, making it somewhat
more applicable to real-world policies.
For example, the choice of M2 as the

OUTPUT

Billions of 1982 dollars (log scale)
4,300

• Isn't This Just the Quantity
Theory?
Economists will recognize P" as a characterization of the quantity theory of
money, which states that the level of

Percent

8

-

FIGURE 3 POTENTIAL

ficulty in using such estimates. In
terms of levels (top panel), it would appear that the measure of potential output grows rather smoothly. Expressing
the measure in growth-rate terms (bot-

8

• p* as a Nominal Anchor
It is useful to clarify the distinction between the short-run and long-run implications of P*. By the nature of its
construction, p* indicates only the
long-run equilibrium level of prices,
not what the price level will be in any
near-term month or quarter, Such an indicator is particularly useful in a framework within which to evaluate policies
for achieving the Federal Reserve's
long-term goal of price stability.

1.60
1

• Two Key Assumptions
Specification of values for the long-run
level of M2 velocity and for potential
output is a matter of judgment. Some

6

,

1'\ I
t \f3-month
Treasury

analysts have argued that it is unlikely
that M2 velocity was not in some way

SOURCES:
Board of Governors of the Federal Reserve System: and U.S. Department of Commerce,
of Economic Analysis.

Bureau

4

bill
1984

1989

affected permanently by deregulation
in the early 1980s. They believe that
deregulation removed constraints on

SOURCE:

banks, allowing them to compete more
successfully for funds.

(not counted as M2) to M2 instruments, including checking accounts

velocity estimate is more accurate, then
any particular path for the eventual

Consequently, one might expect that
deregulation led to a portfolio shift of

and savings and time deposits. As
evidence of such a shift, analysts point
to the mean value of M2 velocity in the
recent period from 1982:Q4 to

price level, P*, would be compatible
with a higher path for M2.

funds from nondepository

instruments

Board of Governors of the Federal Reserve System.

1988:Q4, which is somewhat below the
longer-term average. If the lower

Often the focus of policy is concentrated on immediate real economic conditions. Policymakers naturally seek to
avoid economic downturns. However,
if policies do not take into account intermediate- and long-term consequences for the price level, even more
severe policy restraint may be required
later. Having a simple empirical guidepost like P" could serve to anchor nominal spending, limiting its longer-term
variability. This, in turn, could limit the
potential for policy mistakes and hence
the severity of the business cycle.

Similarly, some analysts question the
measure of potential output used in calculating P*. Figure 3 illustrates the dif-

FIGURE

Presently, the level of M2 appears ap-

1 p* AS AN INDICATOR

proximately consistent with the current
price level. In the first half of 1989, P"

OF INFLATION

Natural log of price

fell slightly, so that p* and the price
level are about equal. Given the recent

0.5 p* vs, Implicit Price Deflator

12 Inflation"
10 .
•

6

•

2

•

o .
1955
a. Inflation is the percentage change in the implicit price deflator from four quarters earlier.

-

NOTE:

The vertical lines in the top and bottom panels mark the quarters when P and P' cross.

SOURCES:
Board of Governors
of Economic Analysis.

FIGURE

acceleration in M2 in early 1989:Q3
and current money-market interest
rates, it is unlikely that P" will continue to fall. Nevertheless, if p* moves

3,800

below the current price level and
remains there persistently, then the inflation rate would be expected to fall.

2,300

the money supply ultimately determines the level of prices. Moreover,
the P" relationship implies that any particular trend in M2 will be associated

of the Federal Reserve System: and U.S. Department of Commerce,

Bureau

2,800

Ratio
1.85r---------------------------------------~

1.80

rently no consensus on a method for assessing ex ante changes in trend output
growth: at any time, an estimate of

1,800

potential output may be inappropriate .
1,300~ ...•....•
'-!-::~...•....•
'-!-::~...•....•
~~
1955

...•....•
~~..L..I~~..L..I~~..L..I~

1990

Percent change, annual rate
4. 0

r-------------------------------------------.

2.52.0'::+
.•...•.
~1~'-'-~1~1"-&...~~
1955
1960
1965

-

SOURCE:

What distinguishes p* from.other characterizations of the quantity theory is

FIGURE

I..L..II~I~

1970

••.•.••
...L::_II~'-'-~I,_!_I"-&...~

1975

1980

1985

1990

Board of Governors of the Federal Reserve System.

4 M2 VELOCITY

AND INTEREST

are long and variable lags between
money growth rates, it is difficult to
find a simple measure of money
growth that would reliably indicate the
future inflation rate. Differing conclusions may result from choosing different periods over which to calculate
money growth rates. P*, on the other

Percent
18
16

1.80

14

1.75

independent of both economic factors
and the money-supply level. Also, p*

12

is based on a particular estimate of the
level of potential output, which is as-

10
1.65

sumed to be independent of policy in
the long run.

Despite these problems, p* has some
advantages over other inflation indicators. For example, because there

hand, provides an absolute reference
point for the price level.

RATES

Velocity
1.85r----------------------------------------.,

measure of money is based on evidence that, over sufficiently long
periods, M2 velocity retums to some
mean value (see figure 2), and hence is

2 M2 VELOCITY

tom panel), however, illustrates how
the estimate of potential output growth
has changed discretely at different
times. These changes have been recognized only after the fact. There is cur-

3,300

with its own unique path for the longrun equilibrium price level.

the extent to which it is specified in
practical terms, making it somewhat
more applicable to real-world policies.
For example, the choice of M2 as the

OUTPUT

Billions of 1982 dollars (log scale)
4,300

• Isn't This Just the Quantity
Theory?
Economists will recognize P" as a characterization of the quantity theory of
money, which states that the level of

Percent

8

-

FIGURE 3 POTENTIAL

ficulty in using such estimates. In
terms of levels (top panel), it would appear that the measure of potential output grows rather smoothly. Expressing
the measure in growth-rate terms (bot-

8

• p* as a Nominal Anchor
It is useful to clarify the distinction between the short-run and long-run implications of P*. By the nature of its
construction, p* indicates only the
long-run equilibrium level of prices,
not what the price level will be in any
near-term month or quarter, Such an indicator is particularly useful in a framework within which to evaluate policies
for achieving the Federal Reserve's
long-term goal of price stability.

1.60
1

• Two Key Assumptions
Specification of values for the long-run
level of M2 velocity and for potential
output is a matter of judgment. Some

6

,

1'\ I
t \f3-month
Treasury

analysts have argued that it is unlikely
that M2 velocity was not in some way

SOURCES:
Board of Governors of the Federal Reserve System: and U.S. Department of Commerce,
of Economic Analysis.

Bureau

4

bill
1984

1989

affected permanently by deregulation
in the early 1980s. They believe that
deregulation removed constraints on

SOURCE:

banks, allowing them to compete more
successfully for funds.

(not counted as M2) to M2 instruments, including checking accounts

velocity estimate is more accurate, then
any particular path for the eventual

Consequently, one might expect that
deregulation led to a portfolio shift of

and savings and time deposits. As
evidence of such a shift, analysts point
to the mean value of M2 velocity in the
recent period from 1982:Q4 to

price level, P*, would be compatible
with a higher path for M2.

funds from nondepository

instruments

Board of Governors of the Federal Reserve System.

1988:Q4, which is somewhat below the
longer-term average. If the lower

Often the focus of policy is concentrated on immediate real economic conditions. Policymakers naturally seek to
avoid economic downturns. However,
if policies do not take into account intermediate- and long-term consequences for the price level, even more
severe policy restraint may be required
later. Having a simple empirical guidepost like P" could serve to anchor nominal spending, limiting its longer-term
variability. This, in turn, could limit the
potential for policy mistakes and hence
the severity of the business cycle.

Similarly, some analysts question the
measure of potential output used in calculating P*. Figure 3 illustrates the dif-

PERIODICALS

• p* in the Short Run
Identifying a simple long-term relationship between p* and the price level is
justified on empirical grounds because
other variables, particularly nominal interest rates, do not seem to affect the
long-term equilibrium value of M2
velocity. While interest rates trended
upward over most of the postwar
period, there is no clear evidence of
any effect on the trend in M2 velocity.
On the other hand, evidence strongly
suggests that interest rates are important for identifying a short-run relationship between M2 and nominal GNP.
Recent research indicates that money
demand may be more interest-rate sensitive than previously thought. Figure 4
reveals a close linkage between movements in interest rates and the velocity
of M2. Thus, it would appear that interactions among money, nominal income, and interest rates matter in the
short-run relationship between P" and
the price level.

policy. This seems evident in the fact
that one of the best predictors of inflation is previous inflation. Including
lagged inflation in models designed to
predict inflation can be justified if
lagged inflation is a reasonable proxy
for inflationary expectations.
This characterization of the short-run
inflation process is troubling because

the empirical research supporting the con-

difficult to justify sluggish price adjustment on theoretical grounds, most
economists find Iittle evidence that
prices of goods and services respond
immediately to changes in monetary

1. A more complete description of P" and
cept are found in Jeffrey J. Hallman, Richard
D. Porter, and David H. Small. "M2 per Unit
of Potential GNP as an Anchor for the Price
nors of the Federal Reserve System. April
1989.

choosing among alternative models.
Thus, it is difficult to know whether

Monetary Policy in an Era of Change, Proceedings from the American Enterprise In-

short-run inflation control based on the
P" indicator would lead to excessive
economic volatility.

stitute's Conference of November 16-17,

cal evidence supports the view that P"
can be a useful indicator in this regard.

by John B. Carlson

Level," Staff Study No. 157, Board of Gover-

tion from targets and goals is discussed by

some Federal Reserve officials may
have begun to use P" as an indicator
for clues concerning the achievement
of the price-stability objective. Statisti-

The Indicator P-Star:
Just What Does It Indicate?

Footnotes

policy? While there may be plausible
economic models that do not display
these cyclical effects of monetary
policy, there is no sound basis for

• Conclusion
Recent public statements suggest that

Federal Reserve Bank of Cleveland

longer perspective to avoid the possibility that short-term policy considerations might interfere with the longerterrn goal of price stability.

policy changes to induce business
cycles. Indeed, simple models linking

Identification of a short-run relationship between P" and the price level is
further complicated by the problem
that prices often adjust slowly to changing economic conditions. Although it is

useful in helping policymakers assess
the longer-term consequences of policy
actions. It is essential to maintain some

•

changes in inflation to the difference
between P" and the price level-the
price gap-indicate
a significant potential for cyclical effects of monetary

eCONOMIC
COMMeNTORY

While p* is not without some potential
shortcomings, it is likely to be most

in any economic model with lagged effects, there is a potential for monetary

2. This notion of an indicator and its distinc-

Financial
markets pay a great deal of
attention to the Federal Reserve System
and, in particular, to the deliberations of
its key policymaking arm, the Federal
Open Market Committee (FOMC).
This "Fed watching" focuses largely on
anticipating how the FOMC is likely to
react to unfolding events in the

Bennett T. McCallum in "Targets, Instruments, and Indicators of Monetary Policy,"

1988.

-

3. See Hallman et al., op. cit.

economy, and how such actions become
translated into changes in the cost and
availability of money and credit.

John B. Carlson is an economist at the
Federal Reserve Bank of Cleveland. The
author wishes to thank Christine Dingledine

Specifically, markets are interested in
knowing which variables the FOMC
considers in assessing whether it is ac-

for excellent research assistance.
The views stated herein are those of the
author and nat necessarily those of the

complishing its objectives. These variables are often referred to as indicators.
In recent years, Federal Reserve offi-

Federal Reserve Bank of Cleveland or of the
Board of Governors of the Federal Reserve
System.

cials have proposed a variety of new
monetary indicators, including commodity prices, the trade-weighted value
of the dollar, and the yield curve. Most
recently, however, the Federal Reserve

BULK RATE
Postage Paid
Cleveland,OH
Permit No. 385

u.s.

Federal Reserve Bank of Cleveland
Research Department
P.O. Box 6387
Cleveland, OH 44101

Address Correction

has unveiled P-Star (P*) , an indicator
of potential inflation. 1
• What Is an Indicator?
An indicator is neither an ultimate objective to be achieved (a goal), nor a
stand-in objective to be aimed at (a target). Rather, an indicator is a variable

Requested:

Please send corrected mailing label to
the above address.

QUV13t\31Q .:10
)lH\'B )i, '. S ::I1V~303':!

68. HV SO Ot 51

that provides information about
whether policy instrument settings are
likely to accomplish their specified objectives, which are observed only

d3S

after a lag. An indicator essentially

Material may be reprinted provided that
the source is credited. Please send copies

September 15, 1989

provides information concerning the
current state of the econorny.f
If an indicator value is unusually high
(or low) on the basis of some historical
standard, it could indicate that goal or
target variables are likely to miss their
marks. A policymaker might then
reconsider policy instrument settings to
attempt to avoid undesired outcomes.
However, policymakers are under no
commitment to react in any specified
way to changes in the value of an indicator; nor are they committed to seek
a specified value.
Because policymakers typically look at
a variety of indicators, they often observe conflicting signals. Moreover, different policymakers give different
weights to different indicators. Thus, it
is often difficult to predict how a group
of policymakers will react to substantial changes in indicator values.
• What Is P*?
Simply put, P" is the eventual price
level implied by the current level of the
M2 monetary aggregate. It is calculated as p* = (M2 x V*)/Q*, where V*
is an estimate of the long-run value of
the GNP velocity of M2-the mean
value from 1955:Q I to I988:Q4-and
Q* is a Federal Reserve Board staff
measure of potential output. Recent advances in understanding long-term
statistical relationships indicate that P"

AlPH1811 HOHV3S3H

of reprinted materials to the editor.
ISSN 0428·1276

Monetary

indicators can help

policymakers to evaluate the likely
success or failure of policy instrument settings. The recently unveiled
P-Star indicator can be useful as an
indicator of potential inflation and,

more broadly, as a method of assessing the Federal Reserve's long-term
goal of price stability.

and the current price level probably
share a common trend.
The indicator property, of P" is revealed in figure I. The vertical dotted
lines denote the quarters when the current price level (implicit price deflator)
and P" cross (top panel). Periods after
which P" begins to persistently exceed
the current price level are ultimately
characterized by rising inflation (bottom panel) .
Conversely, periods after which P"
begins to persistently remain below the
current price level are followed by
periods of disinflation. There is a
noteworthy variation, however, in the
lag between the time the two series
cross and the point when inflation
changes direction.