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Evaluating
Beige Book
Nathan S. Balke and Mtne K. yaal

Is There a Persistence Problem?
Part 2: Maybe Not
Evan F Koenig

Reliance, Composition, and Inflation
joydeep Bhattacharya and joseph H. Haslag

This publication was digitized and made available by the Federal Reserve Bank of Dallas' Historical Library (FedHistory@dal.frb.org)

[conomic and
financial Review
Federal Reserve Bank of Dallas

Robert D. McTeer, Jr.
President and Chief Executive Officer

Helen E. Holcomb
First Vice President and
Chief Operating Officer

Robert D. Hankins
Senior Vice President, Banking Supervision

Harvey Rosenblum
Senior Vice President and Director ofResearch

W. Michael Cox
Senior Vice President and Chiefeconomist

Editors
Stephen P. A. Brown
Senior Economist and Assistant Vice President

Jeffery W. Gunther
Research Officer

Mark A. Wynne
Research Officer

Director of Publications
Kay Champagne
Associate Editors
Jennifer Afflerbach
Monica Reeves
Design and Production
Gene Autry
Laura J. Bell

Economic and Financial Review (ISSN 1526-3940),
published quarterly by the Federal Reserve Bank of
Dallas, presents in-depth information and analysis
on monetary, financial, banking, and other economic
policy topics. Articles are developed by economists in
the Bank's Economic Research and Financial Industry
Studies departments The views expressed are those of
the authors and do not necessarily reflect the positions
of the Federal Reserve Bank of Dallas or the Federal
Reserve System.
Articles may be reprinted on the condition that the
source is credited and the Public Affairs Department is
provided with a copy of the publication containing the
reprinted material
Subscriptions are available free of charge. Please
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address changes to the Public Affairs Department,
Federal Reserve Bank of Dallas, P.O. Box 655906,
Dallas, TX 75265-5906; call 214-922-5254; or subscribe
via the Internet at www.dallasfed.org. Economic and
Financial Review and other Bank publications are
available on the Bank's web site, www.dallasfed,org,

Contents
fvaluatin~ the fleventh
DiHrict'~ Bei~e Boo~
Nathan S. Balke and Mine K. YOcel
Page 2

I~ There aPeni~tence Pro~lem?
Part 2: may~e not
Evan F. Koenig

In this study Nathan Balke and Mine Yucel ask whether the
Eleventh Federal Reserve District's Beige Book description contains
timely information about economic activity within the District. They
examine whether the Beige Book description tracks current Texas
real gross state product (GSP) growth and current Texas employment growth. They also study whether the Beige Book has information about growth not present in other regional indicators that
would have been available to analysts at the time of the Beige
Book's release. They find that both the Beige Book summary and
the average across sectors reflect Texas GSP and employment
growth very well. These two measures of the Beige Book also have
predictive content for one quarter ahead GSP growth. Balke and
Yucel also find that the Eleventh District's Beige Book has information content for Texas economic activity over and above other
state economic indicators such as Texas employment growth, personal income, or sectoral employment growth. Because the Beige
Book is released at least one month earlier than employment data
and at least two years before GSP data, its timeliness makes it a
good tool for current regional economic analysis.

In Part 1 of this two-part series, Evan Koenig explains why
some economists are skeptical that staggered price adjustment can
account for monetary policy's sustained effects on aggregate economic activity. In Part 2, Koenig looks at labor-market imperfections as a possible source of persistence. He concludes that persistence is much easier to obtain if either labor cannot move freely
from firm to firm or wages are set in overlapping wage contracts.

Page 11

Reliance, (ompo~ition,
and Inflation
Joydeep Bhattacharya and
Joseph H. Haslag
Page 20

In this article Joydeep Bhattacharya and Joseph Haslag explore the effect of fiscal policy actions on long-run prices and the
inflation rate. They study a model economy in which the central
bank is not independent. Indeed, the government explicitly relies
on the central bank for a predetermined amount of its revenue. Despite the absence of independence, the central bank does
unilaterally control the composition of government paper. Bhattacharya and Haslag show that changes in reliance and composition
have long-run impacts on prices and inflation. They conduct two
separate policy experiments that suggest how a subservient central
bank can retain substantial control over the inflation rate and still
meet its revenue requirements set by the government.

In formulating policy, the Federal Reserve’s
Federal Open Market Committee (FOMC) relies
on information about not only national but also
regional economic conditions. In fact, former
Federal Reserve Governor George Mitchell once
testified that the regional information “brings the
committee qualitative judgments and insights
that aggregative statistics will always lack.” However, up-to-date regional statistics are not readily available at the time of the FOMC meeting.
The most timely data —state and metropolitan
employment statistics—are released with at
least a month lag and provide direct information
about only one dimension of the economy.
Gross state product (GSP) data, which give a
more comprehensive measure of economic
activity, are released with at least a two-year lag.
As a result, an important potential source of
regional information is the Federal Reserve’s
Beige Book, an anecdotal report on economic
conditions drawn mainly from surveys of businesses in the twelve Federal Reserve Districts
and released approximately two weeks before
each FOMC meeting.
Several recent papers have studied the
information about aggregate economic activity
contained in the Beige Book. Balke and
Petersen (1998) give numerical scores to various dimensions of the Beige Book discussion
and find that several Beige Book indexes have
significant predictive content for current- and
next-quarter real gross domestic product
(GDP) growth. Furthermore, the Beige Book
has information about current quarter real
GDP growth not present in other indicators,
such as the Blue Chip consensus forecast or
time series models that use real-time data.
Payne (1998) uses a different methodology to
quantify the Beige Book but also finds it
strongly correlates with aggregate economic
activity. Fettig, Rolnick, and Runkle (1999),
using not only the publicly available Beige
Book but also its previously unreleased predecessor, the Red Book, find that the Beige Book
predicts current-quarter real GDP growth and
explains about 30 percent of the uncertainty in
current-quarter real growth. However, Fettig,
Rolnick, and Runkle conclude that the Beige
Book provides little additional information
about current-quarter real GDP growth once
the private sector forecasts have been taken
into account.1
We examine whether the Eleventh District
Beige Book description tracks current Texas
real GSP growth and current Texas employment growth.2 We also study whether the Beige
Book contains information about growth not

Evaluating the Eleventh
District’s Beige Book
Nathan S. Balke and Mine K. Yücel

n this article, we examine how

well the Beige Book corresponds
to the growth rate of real
Texas gross state product
and employment.

Nathan S. Balke is a research associate for the
Federal Reserve Bank of Dallas and an associate
professor of economics at Southern Methodist University.
Mine K. Yücel is a senior economist and
research officer in the Research Department of the
Federal Reserve Bank of Dallas.

FEDERAL RESERVE BANK OF DALLAS

Examples of Eleventh District Beige Book Summary
1. Eleventh District summary paragraph from
January 18, 1995, Beige Book.

2. Eleventh District summary paragraph from
March 15, 1995, Beige Book.

“The Eleventh District economy
continued to grow at a solid pace in
late November and December. Increasing strength was reported in the
service sector, and manufacturing
orders continued to rise at a steady
rate. Strong commercial construction
activity offset a further decline in the
single-family sector. Retail sales
growth slowed after the Thanksgiving
holiday and Christmas sales were
lower than expected. Growth in loan
demand continued at a strong pace,
but competition between banks for
customers squeezed margins. District
energy activity remained unchanged
but was slightly below last year’s
levels.”

“The Eleventh District economy
continued to expand in late January
and February but at a slightly slower
pace. Manufacturing orders rose, and
activity at business service firms
remained very strong. Retail sales
slowed, however, and some contacts
said that Texas sales were among the
weakest in the nation. Construction
activity was steady as an increase
in commercial construction offset a
decline in homebuilding. Loan demand
continued to rise. Energy activity declined seasonally and remained below
last year’s levels. Agricultural production was better than expected. Despite
growth in the district economy, respondents in several industries said expectations of a slowdown in the U.S. economy and uncertainty over the effects
of the Mexican peso devaluation had
reduced their optimism.”

The Balke and Petersen readers both scored the
summary as 1.0. Note that while this Beige Book
was released in mid-January, it really contains
information about December’s economic activity.

One reader scored the summary as 0.5, while the
other scored it as 1.0, for an overall score of 0.75.

present in other regional indicators available
to analysts at the time of the Beige Book’s
release. If the Beige Book is a good predictor
of regional economic activity, it can provide
timely information on employment and GSP
growth and help us understand the state’s current economic climate.

information from statistical releases and newspapers may be reported in the Beige Book.
NUMERICAL BEIGE BOOK INDEXES
To evaluate the Eleventh District Beige
Book, we must assign numerical values to
various aspects of the Beige Book description.
We use the Beige Book scoring of Balke
and Petersen (1998) for the Eleventh District.
They read and scored each Beige Book from
July 1983 through January 1997. Along with
national and district summaries, Balke and
Petersen graded the Eleventh District sectoral discussions for retail, manufacturing,
finance or banking, construction, and mining
sectors (which typically reflects the oil and
gas industry).
Balke and Petersen gave the Beige Book
descriptions numerical values ranging from –2
to 2. Typically, if the Beige Book description
appeared to suggest “moderate” or “normal”
economic growth, it was scored a 0.5, while a
description implying “strong” economic growth
was given a score of 1.0 or 1.5. Keywords could
be helpful in scoring but were not relied on
exclusively. (See the box above for examples of
summary paragraphs from the Eleventh District
Beige Book and how they were scored.) The

ELEVENTH DISTRICT BEIGE BOOK SURVEY
Each of the twelve Federal Reserve Banks
is responsible for reporting on economic conditions within its district. The district Banks are
free to emphasize the sectors or aspects of economic activity they deem important for that particular Beige Book cycle. In the Dallas District,
we contact about 100 businesses by telephone
to obtain information on current conditions.3
To get a clear industry picture, we gather a
minimum of three responses for each industry
we cover. An analyst writes a summary for each
sector surveyed. An economist reviews these
sectoral reports, then writes a regional economic summary and a more detailed sectoral
description.
In recent years, the Beige Books have
also included descriptions of price and wage
pressures in the districts, and very recently,
e-commerce activity. In addition to the surveys,

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

Figure 1

Phillips’ quarterly GSP estimates, which are the
sum of the sectoral GSP estimates.5
Texas employment growth data are released monthly. Preliminary estimates are available with a one-month delay, revisions come
out the next month, and the final revision is
released in March of the following year. For
both employment and GSP growth, we use the
final, revised estimates, which we take to be the
best measure of economic activity during the
period in question. Of course, these data are
released many months or, in the case of GSP,
many years after the fact.
Figure 1 plots the numerical scores for the
Eleventh District Beige Book summary against
quarterly GSP growth. The Beige Book index
tracks the general cyclical movements in GSP
growth well, capturing the Texas economy’s
boom in the early 1980s and the oil bust of the
mid-1980s. It also reflects the relatively strong
economic growth Texas experienced during the
mid-1990s. Recall that the Beige Book is
released nearly two years before the GSP numbers are finally released.
In Table 1, we examine the information
in the Eleventh District Beige Book by regressing various Beige Book indexes against real
GSP and against Texas employment growth.
In addition to the District summary, we also
examine an average of the Eleventh District’s
five sectoral Beige Book indexes.
The table shows that the Beige Book
Eleventh District summary and the averageacross-sectors scores (sectoral average) reflect
the Texas economy quite well, with large and
significant coefficients in both the real GSP and
employment regressions.6 Although the Beige
Book was not scored for its outlook, we find
that it also has predictive content for nextquarter real GSP. Again, both the District summary and the sectoral average have large and
significant coefficients. The sectoral average explains real GSP slightly better than the District
summary does. This suggests that the individual
sectoral discussions in the Beige Book contain
information not entirely reflected in the Beige
Book summary paragraph. Note also that the
R2s of the next-quarter GSP regressions are
about half those of the current GSP regressions,
reflecting the difficulty of forecasting one quarter ahead.
We also examine whether the individual
Beige Book sectoral summaries have any predictive power in explaining Texas real GSP and
employment growth (Table 1 ). We find that the
Beige Book descriptions of the manufacturing
and mining sectors have predictive content for

GSP Versus Beige Book Index
Real GSP growth

Beige Book summary index

4
Gross state product

0
Beige Book

–5

–1

–10

–2
’83

’85

’87

’89

’91

’93

’95

’97

SOURCES: Balke and Petersen (1998); Berger and Phillips
GSP data.

Beige Books were read in random order and
with references to the calendar year removed to
lessen the likelihood that hindsight would color
scoring. Both readers scored all the Beige
Books, and their grades were averaged to
obtain the final score. Unlike traditional time
series data — such as GDP, which refers to a
specific quarter, or employment growth, which
refers to a specific month — the Beige Book,
compiled eight times a year, does not correspond exactly to a particular quarter or month.
As a result, Balke and Petersen attempted to
match the period for which the Beige Book was
relevant with the period for the more traditional
indicators of economic activity.4
TRACKING ELEVENTH DISTRICT
ECONOMIC ACTIVITY
To evaluate how well the Beige Book
tracks Eleventh District economic activity, we
need some measure of District economic activity with which to compare the Beige Book. In
this article, we examine how well the Beige
Book corresponds to the growth rate of real
Texas GSP and employment. The GSP data from
the Bureau of Economic Analysis are available
only on an annual basis and with at least a twoyear delay. As of May 2000, the latest GSP data
available are from 1997. Berger and Phillips
(1995) estimate quarterly GSP for each standard
industrial classification for the available GSP:
“…industry-specific (real) GSP is measured so
that the sum of GSP across all industries equals
to total real output. That is, each industry’s GSP
is a measure of value-added and is different
from the total number of units produced or the
total sales of the industry.” We use Berger and

FEDERAL RESERVE BANK OF DALLAS

Table 1

The Beige Book versus Texas Gross State Product and Texas Employment Growth

Independent variable
Model
Constant
Beige Book Eleventh District summary
Simple average of individual sectors
Retail Beige Book Index
Manufacturing Beige Book Index
Finance Beige Book Index
Construction Beige Book Index
Mining Beige Book Index
Sum of individual sector coefficients
χ2 statistic for jointly excluding
individual sectors (p-value)
Adjusted R2
SEE
Ljung–Box Q statistic

Dependent variable
Texas Gross State Product
Current quarter Texas
Next quarter Texas
real GSP growth
real GSP growth
1
2
3
4
5
6
1.39
1.70
1.26
1.86
2.15
1.98
(.84)
(.81)*
(.72)
(.98)
(.99)
(.68)**
3.79
3.16
(1.01)**
(1.11)**
4.45
3.65
(1.29)**
(1.49)**
.41
–.36
(.64)
(.85)
3.07
2.69
(.91)**
(1.19)**
.63
.05
(.61)
(.69)
.14
.23
(.55)
(.74)
.71
1.24
(.36)*
(.63)*
4.96
3.85
(1.05)**
(1.11)**
31.4
17.7
(.00)
(.00)
.26
.29
.36
.14
.15
.22
3.21
3.13
2.97
3.83
3.81
3.67
91.0
108.6
66.5
113.7
131.2
65.8
(.00)
(.00)
(.00)
(.00)
(.00)
(.00)

Texas Employment Growth
Current month of
Texas employment growth
7
8
9
.77
1.00
.74
(.64)
(.58)
(.56)
3.18
(.76)**
3.85
(.94)**
.93
(.49)
1.51
(.66)*
.01
(.45)
.79
(.47)
.69
(.38)*
3.94
(.82)**
24.0
(.00)
.25
.30
.30
2.76
2.67
2.67
32.8
34.65
66.5
(.20)
(.15)
(.00)

** Significant at the 5 percent level.
** Significant at the 1 percent level.
NOTES: Standard errors in parentheses for the coefficients. Standard errors derived from heteroskedastic, autocorrelation-consistent covariance matrix.

overall Texas economic activity but the Beige
Book descriptions of retail, finance, and construction sectors generally do not. The manufacturing and mining indexes are also significant in explaining changes in next-quarter GSP.
Nonetheless, the sum of the coefficients of the
sectoral summaries is statistically significant,
and the coefficients of the sectoral summaries
are also jointly significant for both current and
next-quarter Texas real GSP. We see a similar
pattern for Texas employment growth. The
Beige Book mining and manufacturing sectors
closely track changes in total employment, but
retail, construction, and finance do not. In the
employment growth regressions, as with GSP,
the sum of coefficients of the five sectoral
summaries is statistically significant, and the
hypothesis that all five coefficients are equal to
zero is strongly rejected.

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

The fact that the mining and manufacturing sector descriptions generally have predictive
content for Eleventh District economic activity
may be a function of their coverage in our Beige
Book survey. The manufacturing and mining
sectors are surveyed heavily, while the retail
and finance sectors are not covered as extensively. Moreover, retail, finance, and construction are relatively small sectors compared with
mining and manufacturing. The share of manufacturing in GSP has been relatively constant at
around 16 percent in the 1980s and 1990s.
Although mining is only 7 percent of GSP today,
it was 20 percent in the early 1980s. Currently,
retail, construction, and finance are 7.2 percent,
4.4 percent, and 2.8 percent, respectively. Another
reason some Beige Book sectors don’t explain
GSP growth could be that these sectors are not
in sync with the state’s economy in general. For

Table 2

Texas GSP Regressions with Beige Book Indexes and the
Four Most Recent Months of Texas Employment Growth

Independent variable
Model
Constant
Beige Book Eleventh District summary
Simple average of individual sectors
Retail Beige Book Index
Manufacturing Beige Book Index
Finance Beige Book Index
Construction Beige Book Index
Mining Beige Book Index
P-value for jointly excluding
individual sectors
P-value for exclusion of the four most
recent months of Texas employment
growth data
Adjusted R2
SEE
Ljung–Box Q statistic

Dependent variable
Current quarter Texas
Next quarter Texas
real GSP growth
real GSP growth
1
2
3
4
5
6
1.76
1.86
1.48
2.22
2.43
2.39
(.61)**
(.69)**
(.53)**
(.94)*
(.96)**
(.60)**
2.69
1.96
(.67)**
(1.20)
3.58
2.18
(1.12)**
(1.73)
.32
–.77
(.63)
(.81)
2.64
2.22
(.80)**
(.88)**
–.01
–.65
(.57)
(.66)
.16
.03
(.49)
(.62)
.77
1.14
(.34)*
(.58)
.000
.001
.002

.007

.001

.010

.055

.023

.33
3.05
90.8
(.00)

.38
2.93
108.2
(.00)

.44
2.78
58.1
(.00)

.22
3.64
121.3
(.00)

.23
3.64
139.3
(.00)

.31
3.44
56.7
(.00)

Tables 2 through 4 summarize our findings. Table 2 compares the Beige Book’s predictive content with that of the four most recent months of (real-time) Texas employment
growth data. As before, we consider the Beige
Book summary, the sectoral average, and the
five disaggregated sectoral scores. Four lags of
employment growth are included as regressors
in each model. We find that the Beige Book has
predictive content beyond that in the employment growth data. Both the summary and sectoral average variables continue to be highly
significant and only slightly smaller in magnitude than in the model without the employment data (Table 1 ). Similarly, in the model
with the disaggregated sectors, the Beige Book
manufacturing and mining sectors continue to

example, previous work by Petersen, Phillips,
and Yücel (1994) shows that in the 1980s the
construction sector peaked much later than the
oil sector or the regional economy in general.
DOES BEIGE BOOK GO BEYOND
OTHER ECONOMIC INDICATORS?
We now examine whether the Beige Book
summaries contain information not in other real
time economic indicators, such as state employment and personal income. To gather these
series, we went back to the original statistical
releases and compiled the employment growth
and personal income data that analysts had
available at the time they were reading the
Beige Book.

FEDERAL RESERVE BANK OF DALLAS

Table 3

Texas GSP Regressions with Beige Book Indexes and the
Four Most Recent Quarters of Real Texas Personal Income

Independent variable
Model
Constant
Beige Book Eleventh District summary
Simple average of individual sectors
Retail Beige Book Index
Manufacturing Beige Book Index
Finance Beige Book Index
Construction Beige Book Index
Mining Beige Book Index
P-value for jointly excluding
individual sectors
P-value for exclusion of the four most
recent quarters of real personal
income growth
Adjusted R2
SEE
Ljung–Box Q statistic

Dependent variable
Current quarter Texas
Next quarter Texas
real GSP growth
real GSP growth
1
2
3
4
5
6
1.53
1.85
1.15
3.07
3.45
3.16
(1.06)
(1.07)
(.89)
(.98)**
(.99)**
(.86)**
3.63
4.13
(.97)**
(1.04)**
4.30
4.71
(1.18)**
(1.28)
.30
–.13
(.63)
(.76)
3.09
2.38
(.93)**
(.91)**
.47
.84
(.61)
(.77)
.12
.50
(.57)
(.60)
.63
1.15
(.32)*
(.58)*
.000
.002
.166

.086

.073

.176

.205

.265

.28
3.16
103.9
(.00)

.29
3.08
121.9
(.00)

.38
2.92
79.7
(.00)

.27
3.57
63.9
(.00)

.27
3.53
65.7
(.00)

.29
3.50
45.0
(.02)

be significant, and the sum of coefficients
for individual Beige Book sectors is significant.
For all three models, the sum of the coefficients
of lagged Texas employment is also significant.
The hypotheses that the coefficients are zero
were rejected both for the lags of employment
and for the Beige Book sectoral summaries.
When real-time, real personal income
is included rather than total Texas employment,
the Beige Book coefficients become larger
as real personal income does not add much to
the regression. As can be seen in Table 3, the
lags of personal income are not significant at the
5 percent level in the Texas GSP equation.
We see a similar pattern in next-quarter
GSP results. When the four most recent months
of employment growth are added to the model,

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

both the Beige Book summary and sectoral
averages continue to be significant, albeit with
slightly smaller coefficients. Again, the Beige
Book has predictive content for real GSP data
that is not contained in the four most recent
months of Texas employment growth data. For
the Beige Book sectoral summaries, manufacturing and mining continue to be significant,
and retail, finance, and construction remain insignificant.
In Table 4, we examine whether the Beige
Book has predictive content for Texas employment growth after taking into account the information of other economic indicators. Again, we
find that the Beige Book summaries continue to
have predictive content above and beyond the
information in past values of (real-time) Texas

Table 4

Texas Employment Growth Regressions with
Beige Book Indexes and the Four Most Recent
Months of Employment Growth Data

Table 5 shows that Beige Book sectoral
summaries of the retail, construction, and mining sectors are significant at the 1 percent level,
while finance and manufacturing are significant
at the 5 percent level. Furthermore, the four
most recent months of sectoral employment
growth are significant in only the FIRE and mining value-added regressions. When sectoral employment is the dependent variable (Table 6 ),
the mining and manufacturing Beige Book indexes continue to explain sectoral employment
well, even when lags of sectoral employment
are included in the regressions. The lags do not
generally have much predictive power for sectoral employment itself; only in the construction
and mining regressions are the lags significant.
Thus, overall, the Beige Book contains information about Texas economic activity at the
sectoral level not completely reflected by past
values of employment growth in those sectors.

Dependent variable
Current month of
Texas employment growth
1
2
3
1.03
1.12
.94
(.53)*
(.51)*
(.44)
2.37
(.61)**
3.15
(.83)**
.80
(.48)
1.21
(.59)*
–.53
(.38)
.79
(.44)
.70
(.34)*
2.96
(.66)**
26.7
(.00)
13.6
16.4
19.8
(.00)
(.00)
(.00)
.28
2.70
35.0
(.14)

.33
2.60
32.46
(.22)

CONCLUSION
In this study, we analyze how well the
Eleventh District Beige Book descriptions of
regional economic activity track the Texas economy. We find that both the summary and the
average across sectors reflect GSP and employment growth very well. These two measures of
the Beige Book also have predictive content for
GSP growth one quarter ahead. We also find that
the Eleventh District’s Beige Book has information for Texas economic activity over and above
other state economic indicators, such as Texas
employment growth, personal income, or sectoral employment growth. The Beige Book sectoral summaries also have predictive content for
total GSP and employment growth. Furthermore,
they typically contain information about economic activity in their own sectors not reflected
in past values of sectoral employment growth.
We have shown that the Beige Book,
although anecdotal in nature, tracks the regional
economy well and has predictive content over
and above other economic indicators. Because
the Beige Book is released at least one month
earlier than employment and two years before
GSP data, its timeliness makes it a good tool
for current regional economic analysis. Alan
Blinder (1997) refers to the Fed’s use of anecdotal evidence as the “ask your uncle” method
of gathering information about the economy.
However, this study suggests that the ask your
uncle method can provide timely information
about economic activity in the region. To paraphrase Nobel Prize-winning economist George
Stigler, data are the plural of anecdote.

.35
2.57
24.4
(.61)

** Significant at the 5 percent level.
** Significant at the 1 percent level.
NOTES: Standard errors in parentheses for the coefficients. Standard errors derived
from heteroskedastic, autocorrelation-consistent covariance matrix.

employment growth. However, past values of employment growth also have predictive content
for employment growth. Nonetheless, it appears
that the Beige Book has additional predictive
content for final Texas employment growth
above that in employment data available to analysts at the time of the Beige Book’s release.
BEIGE BOOK SECTORAL INDEXES AND
SECTORAL ECONOMIC ACTIVITY
Finally, we analyzed whether the sectoral
summaries explained movements in sectoral
Texas GSP or sectoral employment. We also
included the four most recent months of sectoral employment growth data in both the real
sectoral GSP and the sectoral employment
growth regressions to determine whether the
Beige Book sectoral summaries had predictive
content over and above the sectoral employment growth data.

FEDERAL RESERVE BANK OF DALLAS

Table 5

Sectoral Value-Added Regressions with Sectoral Beige Book Indexes
and the Four Most Recent Months of Sectoral Employment Growth

Independent variable
Model
Constant
Retail Beige Book Index
Manufacturing Beige Book Index
Finance Beige Book Index
Construction Beige Book Index
Mining Beige Book Index
P-value for exclusion of the four most
recent months of Texas sectoral
employment growth data
Adjusted R2
SEE
Ljung–Box Q statistic

Dependent variable: Texas sectoral value-added growth
Wholesale
Manuand retail
facturing
FIRE
Construction
Mining
1
2
3
4
5
1.06
.80
3.50
–.56
–2.50
(.77)
(1.59)**
(1.84)
(1.42)
(2.78)
2.95
(1.03)**
5.28
(2.10)*
4.99
(2.25)*
4.54
(1.22)**
9.98
(2.64)**
.438
.069
.001
.053
.000

.10
5.61
64.5
(.00)

.27
9.26
98.0
(.00)

.12
13.24
32.4
(.22)

.29
9.18
46.0
(.01)

.53
17.5
129.8
(.00)

** Significant at the 5 percent level.
** Significant at the 1 percent level.
NOTES: FIRE is the acronym for finance, insurance, and real estate. Standard errors in parentheses for the coefficients.
Standard errors derived from heteroskedastic, autocorrelation-consistent covariance matrix.

Table 6

Sectoral Employment Growth Regressions with Sectoral Beige Book Indexes
and the Four Most Recent Months of Real-Time Sectoral Employment Growth

Independent variable
Model
Constant
Retail Beige Book Index
Manufacturing Beige Book Index
Finance Beige Book Index
Construction Beige Book Index
Mining Beige Book Index
P-value for exclusion of the four most
recent months of real-time Texas
sectoral employment growth data
Adjusted R2
SEE
Ljung–Box Q statistic

Dependent variable: Texas sectoral employment growth
Wholesale
Manuand retail
facturing
FIRE
Construction
Mining
1
2
3
4
5
–.48
–.40
–.14
–.45
–.62
(.62)
(.64)
(.29)
(1.07)
(.63)
.60
(.55)
1.65
(.76)*
.22
(.31)
1.62
(1.07)
2.50
(.91)**
.071
.438
.058
.000
.000

–.04
6.12
6.3
(.99)

.04
4.55
15.2
(.97)

.00
3.15
28.4
(.39)

.15
7.77
45.4
(.01)

.47
7.37
27.2
(.45)

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

NOTES
1

REFERENCES

The apparently conflicting results of Balke and
Petersen (1998) and Fettig, Rolnick, and Runkle (1999)
are due to the timing difference of the private forecasts
used. Fettig, Rolnick, and Runkle compare the quarterly American Statistical Association/National Bureau
of Economic Research (ASA/NBER) consensus
forecast, which is released at the end of the second
month of the quarter, with the Beige Book released
earlier in the quarter. Given that the ASA/NBER survey
participants are likely to have had access to the Beige
Book reports at the time of their survey, it is perhaps
not surprising that the Beige Book has no additional
explanatory power. When the ASA/NBER surveys are
compared with Beige Books released later in the
quarter, the Beige Book does contain additional
predictive content.
The Eleventh District consists of Texas and parts of
Louisiana and New Mexico. However, because Texas
accounts for 95 percent of economic activity in the
District, the Eleventh District Beige Book only covers
Texas.
Industries surveyed are retail sales; auto sales;
agriculture; construction; real estate; legal, accounting,
consulting, temporary, finance, and transportation
services; petroleum refining; lumber and wood;
chemicals; oil field machinery; apparel; electrical and
electronic equipment; paper; primary metals; fabricated metals; stone, clay, and glass; food and kindred
products; and telecommunications manufacturing.
See Balke and Petersen (1998) for a more detailed
discussion of the issues associated with quantifying
the Beige Book and with the timing of the quantified
Beige Book series.
We deflate nominal sectoral GSP by the Consumer
Price Index to correct for inflation. We believe that the
overall price level rather than a sector-specific one is
the relevant deflator for Beige Book respondents
because their main concern is real profits, that is, the
buying power of their nominal profits.
We used the “robust errors” option in RATS to compute
a heteroskedastic, autocorrelation-consistent covariance matrix. The number of moving average terms
was set to four.

Balke, Nathan, and D’Ann Petersen (1998), “How Well
Does the Beige Book Reflect Economic Activity?
Evaluating Qualitative Information Quantitatively,” Federal
Reserve Bank of Dallas Research Paper no. 9802
(Dallas, June). Also forthcoming in Journal of Money,
Credit, and Banking.
Berger, Franklin D., and Keith R. Phillips (1995), “A New
Quarterly Output Measure for Texas,” Federal Reserve
Bank of Dallas Economic Review, Third Quarter, 16 – 23.
Blinder, Alan S. (1997), “What Central Bankers Could
Learn From Academics — and Vice Versa,” Distinguished
Lecture on Economics in Government, Journal of
Economic Perspectives 11 (Spring): 3 –19.
Fettig, David, Arthur J. Rolnick, and David E. Runkle
(1999), “The Federal Reserve’s Beige Book: A Better
Mirror Than Crystal Ball,” Federal Reserve Bank of
Minneapolis The Region, March, 10 –13, 28 – 32.
Payne, David R. (1998), “Two Versions of a Beige Book
Index,” mimeograph, Economics and Statistics
Administration, U.S. Department of Commerce.
Petersen, D’Ann M., Keith R. Phillips, and Mine K. Yücel
(1994), “The Texas Construction Sector: The Tail That
Wagged the Dog,” Federal Reserve Bank of Dallas
Economic Review, Second Quarter, 23 – 33.

FEDERAL RESERVE BANK OF DALLAS

Empirical studies suggest that monetary
policy shocks have real economic effects that
continue for many quarters after a policy
change is implemented.1 These persistent real
effects have sometimes been attributed to price
contracts that are staggered across firms. In
principle, staggered price setting can substantially delay the aggregate price level’s response
to policy shocks even if each individual price is
fixed for only a short period. However, this
result depends on the assumption that each firm
seeks to keep its price close to the prices others
charge. Recently, Chari, Kehoe, and McGrattan
(2000)—hereafter CKM—have questioned the
validity of this assumption. For a wide range of
technology and taste specifications, CKM
demonstrate that staggered price adjustment
speeds up — rather than slows down — the
economy’s response to policy shocks.
Part 1 in this series of two articles develops the intuition underlying the CKM result
(Koenig 1999). It runs as follows: The prices its
competitors charge are relevant to the pricing
decisions of a profit-maximizing firm only indirectly, through their impact on the firm’s unit
labor costs. If, say, the money stock has unexpectedly increased, unit labor costs will rise for
two reasons. First, since most firms’ prices are
preset, the policy surprise will lead to an
increase in real cash balances that stimulates
aggregate sales and, hence, the demand for
labor. Second, households, feeling wealthier,
will be less inclined to work. For reasonable
values of the wage and wealth elasticities of the
labor supply, these two forces exert such a
strong upward pressure on the market-clearing
wage rate that any firm with the chance to
adjust its price will increase it more than proportionately to the change in the money
stock—not less than proportionately, as required to generate persistence.
This discussion suggests that what occurs
in the labor market is critical for determining
whether output prices adjust slowly toward longrun equilibrium following a monetary policy
shock. If a labor-market friction were to shortcircuit the wage increase that accompanies a
monetary expansion in the CKM analysis, firms
would feel less immediate pressure to raise their
prices and monetary policy might have longer
lasting effects on the real economy. This article
uses a simple model to illustrate that labormarket frictions are, indeed, a potentially important part of the solution to the persistence
problem.
The model economy developed here can
be interpreted in two ways. Under one inter-

Is There a Persistence Problem?
Part 2: Maybe Not
Evan F. Koenig

xplaining persistence may

not be that difficult after all.
If there are labor-market
frictions, monetary policy can
be expected to have longlasting real effects even if
final-goods prices are
completely flexible.

Evan Koenig is a senior economist and
vice president in the Research Department
at the Federal Reserve Bank of Dallas.

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

(1)

pretation, hours of labor supplied by different
households (or groups of households) are
imperfect substitutes in production. This imperfect substitutability gives workers a measure of
monopoly power. Each worker (or worker
group) acts as a wage setter, announcing a time
path for the wage at which he is willing to supply labor.2 This path is periodically revised to
reflect new information on demand and supply
conditions. The timing of the wage revisions is
staggered across workers. Essentially, the staggered price setting of Part 1 is replaced by
staggered wage setting.
An alternative interpretation of the model
is that each household acts as an independent
intermediate-goods producer. The intermediate
goods different households produce are imperfect substitutes for one another. Price adjustment in the intermediate-goods market is staggered. Under this interpretation of the model,
the key difference from the previous analysis is
that intermediate-goods producers do not compete with one another for labor.3
Under either interpretation, the model captures important aspects of reality. Wage rates are
commonly specified well in advance—by as
much as three years in union labor contracts.4 At
the same time, transportation costs, imperfect
information, and workers’ investments in firmspecific skills limit employee mobility.
The article’s bottom line is that explaining
persistence may not be that difficult after all.
Indeed, if there are labor-market frictions, monetary policy can reasonably be expected to have
long-lasting real effects even if final-goods prices
are completely flexible.5 If final-goods prices
are set in overlapping contracts, persistence is
further enhanced.

U (Ci , L i ) = (C i1 – σ – 1)/(1 – σ)
– L i1 + 1/ξ/(1 + 1/ ξ )

each period, where Ci and L i are the levels
of output consumed and labor supplied, respectively, and where σ and ξ are positive constants. The first of these parameters is the
inverse of the elasticity of intertemporal substitution, which measures households’ willingness
to shift consumption over time. The second
parameter would be the wage elasticity of the
labor supply if the labor market were competitive. Realistically, σ ≥ ½ and ξ < 1.8
A wage-taking, utility-maximizing household would supply labor up to the point where
the marginal rate of substitution between leisure
and consumption equals the real wage: –UL /UC
= W/P. However, I assume each household faces
a downward-sloping demand curve for its labor:
(2)

li = l – (wi – w)/(1 – E ),

where l and w are the (logarithms of the) average aggregate employment level and money
wage, respectively, wi is the (logarithm of the)
wage charged by household i, and 0 < E < 1 is
a parameter that is an inverse measure of the
household’s monopoly power.9 (Throughout
this article, lowercase characters denote logarithms of the corresponding uppercase variables.) Confronting a labor demand schedule
like that in Equation 2, household i will want to
be paid a premium over the competitive wage.
In particular, taking l and w as given, household
i will want to charge a wage rate that satisfies
the equation
(3)

Wi /P = –(UL /UC )/E .

Taking logarithms,
(3′ )

THE MODEL ECONOMY

wi – p = (1/ ξ)li + σci – ,

where ≡ ln(E ). The desired wage exceeds the
competitive wage to the extent that E is less
than 1.
My objective is to see whether staggered
wage setting can help explain the persistent
real effects of monetary policy. Accordingly, I
assume each household must specify in
advance a path for its wage rate. The length of
time for which the wage path is preset is the
same for every household, but the timing of
their decisions differs. As a practical matter, to
assume that households prespecify their wages
means Equations 3 and 3′ will not hold for
every household at every instant. However,
whenever it has a chance to reset its wage path,
household i will choose a path that it expects
will satisfy Equations 3 and 3′ at each point in

This section describes a simple, log-linear
economy with labor-market frictions. I arbitrarily
emphasize the sticky-wage interpretation of the
model rather than the immobile-labor interpretation. As in Part 1 of this series, several simplifying assumptions are convenient. For example, I ignore capital investment. Labor contracts
specify a path for the nominal wage rather than
a fixed wage level.6 Also, most of the analysis is
limited to the case in which output prices are
completely flexible.7
Household Decisionmaking
As in my earlier analysis, I assume that a
typical household —call it household i —has a
utility function of the form

FEDERAL RESERVE BANK OF DALLAS

put prices are perfectly flexible, so that
Equation 7 holds at every instant for every firm.
(This assumption is relaxed in the box that
accompanies this article.) If the price level
responds sluggishly to monetary policy shocks,
it is only because the average aggregate wage
responds sluggishly to such shocks.

the future. Firms decide how much of household i ’s labor is hired at the specified wage.
Households will be content to cede short-run
control of hours to firms as long as the real
wage continues to exceed the marginal rate of
substitution between leisure and consumption.10
As in Part 1, I assume households’ desired
money balances are determined by their consumption expenditures:
(4)

Short-Run and Long-Run Equilibrium Conditions
For notational convenience, I assume there
is one household per firm. Then y denotes both
the output each firm produces and average
household income. The variable l denotes both
the amount of labor each firm hires and the
average amount of labor each household supplies. At every instant, l = y = c = m – p, where
(recall) the variables c and m are the amounts
of output consumed by and money held by
each household, respectively. It follows that if
we can determine how the price level moves
over time in response to a monetary policy
shock, we will also know how employment, output, and consumption move over time. Monetary policy shocks have persistent real effects
only to the extent that the price level reacts
sluggishly to changes in the money supply.
Once every household has adjusted its
wage path in response to a policy shock, all
households will charge the same wage and
work the same number of hours. If we use
an asterisk to denote the value each endogenous variable takes on in this long-run, marketclearing equilibrium,

mi – p = ci .

It greatly simplifies the analysis to assume
households are able to fully insure consumption
against idiosyncratic differences in the timing of
wage decisions. In other words, it is convenient
to assume all households end up with the same
level of consumption and, hence, the same level
of real money balances, regardless of when they
are able to reset their wage paths. Accordingly,
I henceforth drop the subscripts from c and m
in Equations 3′ and 4.
Firm Decisionmaking
Firms use the labor of a cross section of
households to produce output, which is then
sold back to households. I use the same, simple,
linear production technology as in Part 1:
(5)

yf = lf ,

where yf is the amount of output firm f produces using lf units of labor. It follows that the
firm’s marginal cost schedule is horizontal and
that its height equals the prevailing average
wage rate, w.
In general, the products of different firms
are imperfect substitutes, so that each firm has
some monopoly power in the output market.
In particular, I assume the demand for firm f ’s
output is given by
(6)

(9)

w* = m + θ – (θ + )ξ/(1 + σξ),

(10)

yf = y – (pf – p)/(1 – Θ ),

p* = m – (θ + )ξ/(1 + σξ).

Money is neutral in the long run. An increase
in the money stock eventually drives up the
nominal wage and the price level and leaves
real variables unchanged.
SHORT-RUN WAGE AND PRICE ADJUSTMENT
Equation 7 implies that the average wage
and the price level always move together. Thus,
whether the price level reacts sluggishly to policy shocks is determined by how the average
wage moves over time in response to unexpected changes in the stock of money. How the
average wage moves over time is, in turn, determined by how aggressively households that are
able to adjust their wages do so. Do these
households have an incentive to keep their

pf = w – θ.

In contrast to CKM (and my earlier article), out-

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

y * = c * = l * = (θ + )ξ/(1 + σξ),

and

where y and p are the average aggregate output level and price level, respectively, pf is the
price charged by firm f, and 0 < Θ < 1. Equation
6 says the higher firm f ’s price is relative to
the economywide average, the lower the firm’s
sales will be relative to economywide-average
sales.11 Perfect competition is obtained in the
limit as Θ → 1. The firm is assumed to be small
enough that it takes y and p as given. It follows
that the firm’s marginal revenue is pf + θ, where
θ ≡ ln(Θ) < 0.
Profit is maximized when marginal revenue equals marginal cost:
(7)

(8)

Table 1

Overshooting Unlikely with Overlapping Wage Contracts
a wage that exceeds the market-clearing wage
rate. Below, I refer to ω′ ≡ α(1/ξ + σ) as the
overshooting parameter for an economy with
staggered wage contracts.

Possible values of the overshooting parameter in an economy with flexible prices and
overlapping wage contracts (ω ′) and in an otherwise identical economy with flexible
wages and overlapping price contracts (ω ).
A. The case in which σ = 1.
ω
ξ = 1/5
ξ = 1/4
ξ = 1/3
ξ = 1/2

6
5
4
3

ω′
E = .99

E = .95

E = .90

E = .85

E = .80

.01
.01
.01
.01

.06
.06
.07
.07

.12
.12
.13
.14

.17
.18
.19
.21

.23
.24
.25
.27

A Comparison with Price Adjustment
in the CKM Model
In the simple version of the CKM model
developed in Part 1 of this series, price adjustment is governed by an equation very similar to
the wage-adjustment equation derived above. In
particular,

B. The case in which σ = 2.
ω
ξ = 1/5
ξ = 1/4
ξ = 1/3
ξ = 1/2

7
6
5
4

ω′
E = .99

E = .95

E = .90

E = .85

E = .80

.01
.01
.02
.02

.07
.07
.08
.10

.14
.15
.16
.19

.20
.22
.24
.28

.27
.29
.31
.36

(13)

where pf is the price chosen by a firm able to
respond to the policy shock, p * is the marketclearing price level, and p is the average current
price level. The key difference between
Equations 12′ and 13 is the α parameter, which
appears in the former equation but is absent
from the latter. This parameter acts unambiguously to make wage (and hence, price) adjustment in the staggered-wage-contract model
slower than price adjustment in the CKM staggered-price-contract model. In the staggeredprice economy, the overshooting parameter is
ω ≡ 1/ξ + σ. In the staggered-wage economy,
the overshooting parameter is ω′ = αω < ω.
Is the contribution of staggered wage setting to persistence likely to be quantitatively
significant? Table 1 compares the values of ω
and ω′ implied by a range of reasonable values
for the inverse of the elasticity of intertemporal
substitution (σ), the wage elasticity of the labor
supply (ξ), and the ratio of the competitive to
the monopolistically competitive wage (E ).12
The table suggests that ω can reasonably be
expected to fall somewhere between 3 (when
σ = 1 and ξ = 1/2) and 7 (when σ = 2 and
ξ = 1/5). (Note that the competitiveness of the
labor market is irrelevant for ω.) In any event,
the overshooting parameter in an economy with
flexible wages and overlapping price contracts
is well above 1—a result consistent with CKM.
In sharp contrast, the overshooting parameter in
an economy with flexible prices and overlapping wage contracts ranges from a low of 0.01
(when the labor supply is highly inelastic and
the labor market is nearly competitive) to a high
of only about 1/3 (when ξ = 1/2 and E = .8). In
other words, the overshooting parameter is at
least an order of magnitude smaller in an economy with staggered wage setting than it is in
an economy with staggered price setting. If
workers don’t have much bargaining leverage, it
may well be several orders of magnitude
smaller. The implication is that staggered wage

wages close to the average wage? If so, the
average wage will move slowly toward its market-clearing level and policy shocks will have
long-lasting real effects.
An Individual Household’s Wage Demands
Consider a household (i ) that is updating its wage demands in response to the latest
economic data. Using Equation 2 to eliminate
li from Equation 3′, and using the fact that l = c
= m – p:
(11)

wi = w + α[(1/ξ + σ)(m – p) – (θ + )],

where α ≡ ξ(1 – E )/[1 + ξ(1 – E )] < 1. This equation becomes
(11′)

0 = α[(1/ξ + σ)(m – p * ) – (θ + )]

in long-run, market-clearing equilibrium. By
subtracting Equation 11′ from Equation 11, we
obtain
(12)

wi = w + α(1/ξ + σ)(p * – p),

or (recalling that Equation 7 holds for every firm
at every instant)
(12′)

pf = p + (1/ξ + σ)(p * – p),

wi = w + α(1/ξ + σ)(w * – w).

Equation 12′ is the key formula relating the
wage demands of household i to the current
average wage and the market-clearing wage. If
α(1/ξ + σ) < 1, households with a chance to
respond to a policy shock choose a wage partway between the market-clearing wage and the
average wage; they don’t want their wages to
move too far from the wages others charge. If,
on the other hand, α(1/ξ + σ) > 1, households
with a chance to respond to a policy shock pick

FEDERAL RESERVE BANK OF DALLAS

Figure 1

contracts are far more likely to generate persistence than are staggered price contracts of the
same length.

Response to a Monetary Policy Shock
Panel 1: Assumed Path of Money Growth
(deviation from the initial equilibrium)

Tracking the Economy Over Time
In this section, I use a series of figures to
illustrate the impact labor-market imperfections
can have on the economy’s response to a monetary policy shock. (For a more general treatment, see the box entitled “The Short-Run
Dynamics of an Economy with Labor-Market
Frictions.”) These figures assume that ω′ =
.25—an overshooting parameter that is toward
the upper end of the range in Table 1 and that,
accordingly, may understate persistence. For
comparison, the figures also show the policy
responses of an economy with flexible wages
and overlapping price contracts. For this economy, I assume ω = 4.5 —the same value my earlier article uses and near the middle of the range
in Table 1.
The policy shock I consider is a surprise,
temporary increase in the money growth rate
that permanently raises the level of the money
stock 1 percent above what the public had
expected. I arbitrarily assume the moneygrowth surge lasts one-twelfth as long as contracts do. So if contracts specify the wage path
for a year at a time, money growth remains elevated for only one month.13 (See Panel 1 of
Figure 1.) The market-clearing price, p *, rises
with the money stock, reaching a new, permanently higher level in one month (Panel 2).
Panels 2 and 3 show the paths of the average price level and rate of production in the
economy with overlapping wage contracts
(assuming ω′ = .25) and the economy with
overlapping price contracts (assuming ω = 4.5).
Clearly, price and output adjustment take substantially longer in the staggered-wage economy
than in the staggered-price economy. (As the
box discusses, price and output adjustment are
even further delayed if staggered wage and
staggered price setting are combined.) With
staggered wages, it takes 9.6 months for the
price level to move halfway to its long-run, market-clearing level, compared with 2.2 months
with staggered prices.14 Similarly, the output
response is larger and longer lasting in the staggered wage economy than in the staggeredprice economy. These results are consistent
with the view that persistent real monetary
policy effects are much easier to obtain in an
economy with labor-market imperfections than
in an economy without such imperfections.
It is important to note that the differences
between the staggered-price and staggered-

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

Percent
14
12
10
8
6
4
2
0
0

Time (years)

Panel 2: Implied Paths of the Market-Clearing
and Average Price Levels
(deviations from the initial equilibrium)
Percent
p*

p
(staggered prices)

p
(staggered wages)

0
0

Time (years)

Panel 3: Implied Paths of Output
(deviations from the initial equilibrium)
Percent
1
y
(staggered wages)

y
(staggered prices)

0
0

Time (years)

wage economies seen in Figure 1 are not due to
any difference in contract length between the
two economies: in both, contract length is one
year. Price adjustment and output adjustment
are slower in the staggered-wage economy than
in the staggered-price economy solely because
households’ incentive to keep their wages close
to the average wage in the former economy is
stronger than firms’ incentive to keep their
prices close to the average price in the latter

The Short-Run Dynamics of an Economy with Labor-Market Frictions
Consider an economy that is initially in long-run, marketclearing equilibrium, with (for notational convenience) a constant money stock. Suddenly, at t = 0, a change in the money
stock’s path is announced. The announcement is a complete
surprise but fully credible. Without any loss of generality, we
can define the unit time interval to equal the length of a labor
contract. Then, by t = 1 every household will have had a
chance to reset its wage path, and the economy will be back
in market-clearing equilibrium. This box derives the formulas
that govern the behavior of output, wages, and the price level
over the interval from t = 0 to t = 1. I begin with the case in
which final-goods prices are completely flexible, then briefly
discuss how the analysis would differ in an economy with
overlapping price contracts.
Flexible Final-Goods Prices. The basic building blocks
for the analysis are the equations
(B.1)

w *(t ) = m(t ) + θ – (θ + )ξ/(1 + σξ),

(B.2)

wi (t ) = w (t ) + ω′[w *(t ) – w(t )],

and
(B.3)

w(t ) = twi (t ) + (1 – t )w (0).

Equation B.1 gives the market-clearing wage as a function of
the current money stock. It restates Equation 9 from the main
text. Similarly, Equation B.2 is a restatement of Equation 12′.
It gives the wage rate that will be chosen at time t by any
household that has had a chance to react to the new monetary policy. Finally, Equation B.3 is a formula for the average
wage that follows from the assumption that wage adjustment
is evenly staggered over the unit interval. At any given time t,
0 < t < 1, the fraction t of households will have had a chance
to reset their wage paths and will be charging wi (t ). The
fraction 1 – t of households will be charging the wage that
prevailed in the initial market-clearing equilibrium, w (0).1
Together, Equations B.2 and B.3 imply that
(B.4)


 ∗
ω ′t
w (t ) = w (0) + 
[w (t ) − w (0)].
t
+
(
1
−
t
)
ω
′



Since every firm sets its price as a markup over the average
wage (compare Equation 7), we also have

 ∗
ω ′t
p(t ) = p(0) + 
 [p (t ) − p(0)],
t
+
(
1
−
t
)
ω
′


where the market-clearing price level is proportional to the
current money stock (Equation 10 ). This equation is the
same as that governing price adjustment in an economy with
staggered price setting, except ω′ has replaced ω. (Compare
Equation B.5, above, with Equation B.4 in Part 1 of this series.)
Price adjustment is one-half complete when ω′t /[ω′t + (1 – t )]
= 1/2, or t = 1/(1 + ω′). So the smaller the overshooting
parameter, ω′, the slower the aggregate price adjustment.
Recall that our units of measurement are chosen so
that average employment and output both equal real money
balances at every instant: l (t ) = y (t ) = m(t ) – p(t ). Using
Equations 10 and B.5, it follows that
(B.5)

(B.6)

l (t ) = y (t ) = m (t ) − p(t ) = [m (0) − p(0)]
 1− t

+
 [m (t ) − m (0)].
 ω ′t + (1− t ) 

Equations B.5 and B.6 are the basis for Panels 2 and 3 of
Figure 1 in the main text.
Staggered Final-Goods Prices. Staggered price
setting adds to persistence when present in an economy with
labor-market frictions. It also causes the real wage to vary
procyclically. I illustrate these facts in the special case where
price contracts have the same length as wage contracts.

When there are staggered final-goods price contracts,
Equation 7 applies only to firms that have had a chance to
reset their price paths following the monetary shock. While
Equation 12 remains valid, Equation 12′, in general, does not.
Hence, we must go back a step and replace Equation B.2 with
pf (t ) = w(t ) – θ

(B.7)
and

wi (t ) = w (t ) + ω′[p *(t ) – p (t )],

(B.8)

which are simply restatements of Equations 7 and 12, respectively, in the main text. While previously we had p (t ) = pf (t ),
now
(B.9)

p (t ) = tpf (t ) + (1 – t )p (0).

Equation B.9 governs the evolution of the average price level
in much the same way that Equation B.3 governs the evolution of the average wage.2
Equations B.3 and B.7– B.9 can be solved for the paths
of the wage rate and price level:
(B.10)


 *
ω ′t
w (t ) = w (0) +  2
 [w (t ) − w (0)];
t
+
(
1
−
t
)
ω
′



(B.11)



ω ′t 2
p(t ) = p(0) + 
 [p*(t ) − p(0)].
2
 ω ′t + (1− t ) 

From Equations 9 and 10, w (0) – p (0) = w *(t ) – p *(t ) =
θ. Hence, subtracting B.11 from B.10,
 ω ′t (1 − t ) 
w (t ) − p(t ) = θ +  2
 [m(t ) − m(0)].
 ω ′t + (1 − t ) 

(B.12)

It follows that the real wage is procyclical to the extent that
the business cycle is driven by monetary policy shocks.
Straightforward algebraic manipulations establish that
l (t ) = y (t ) = m(t ) − p(t ) = [m(0) − p(0)]

(B.13)



1− t
+ 2
 [m(t ) − m(0)].
t
t
ω
+
(
1
−
)
′


Since t 2 < t for 0 < t < 1, output and employment are more
sensitive to monetary shocks in this economy than they are
in an economy with flexible final-goods prices. (Compare
Equations B.6 and B.13.)
What of persistence? According to Equation B.11, price
adjustment is half completed when ω′t 2 = 1 – t in the economy
examined here. With flexible final-goods prices, the corresponding condition is ω′t = 1 – t. The left-hand side of each
of these equations is an increasing function of t, but since
t 2 < t for 0 < t < 1, it takes a larger t to satisfy the first equation
than the second. In other words, monetary shocks have more
persistent real effects in an economy where both wages and
prices are preset in overlapping contracts than in an otherwise identical economy in which only wages are preset.

NOTES
1

Equation B.3 is an approximation of the exact formula, which can be
found using the definition of W given in Note 9 to the main text:
w (t ) = [(E – 1)/E ]ln{t • exp[wi (t )E /(E – 1)]
+ (1 – t )• exp[w (0)E /(E – 1)]}.

The approximation will be good as long as wi (t ) is not too different
from w (0).
Like Equation B.3, Equation B.9 is a log-linear approximation.

FEDERAL RESERVE BANK OF DALLAS

market frictions than in a similar economy with
staggered price setting, flexible wages, and
mobile labor. The effect is to increase the
amount of time required for the price level to
complete half its adjustment by a factor of four
or more.

economy. The staggered-wage economy would
generate even more persistence than is displayed in Figure 1 if our analysis recognized
that some real-world labor contracts are renegotiated only once every three years.15
SUMMARY AND CONCLUSION

NOTES

If the labor market is frictionless — if
wages are flexible and workers can move freely
from one employer to another —it is difficult to
understand how monetary policy changes can
have long-lasting effects on output and employment. The problem is that any policy that stimulates real activity will also drive the wage rate
sharply higher in such an economy. This higher
wage rate gives firms that are free to adjust their
prices a powerful incentive to raise them. Consequently, for realistic contract lengths the average price level moves quickly toward its marketclearing level, and the stimulus to aggregate
output and employment is short-lived.
Staggered wage contracts are a possible
solution to this persistence problem. Workers—
fearful of pricing themselves out of the market
—will not press their wage demands aggressively in response to stimulatory monetary
policy. Consequently, the average wage level
adjusts slowly. Since cost pressures are muted,
firms feel little need to raise their prices and the
stimulus to aggregate output and employment
persists. This argument applies even if finalgoods prices are completely flexible. (If they are
sticky, persistence is further enhanced.)
Labor immobility across employers is
another possible explanation for persistence.
With immobile labor, the wage a firm must pay
is tied as much to its own labor demand as to
the economywide employment level.16 A firm
that is able to raise its price relative to others’
following monetary stimulus will find that its
marginal labor costs tend to decline along with
the demand for its output. Consequently, a
smaller price increase is chosen than would
be optimal in an otherwise identical economy
with mobile labor. Since firms with an opportunity to adjust their prices choose to stay fairly
close to the average price, the average price
moves slowly and output and employment
effects persist.
The results this article reports suggest that
labor-market frictions are potentially significant
quantitatively as well as qualitatively. A key
parameter that measures the speed with which
the price level moves toward its market-clearing
level is likely between one and three orders of
magnitude smaller in an economy with labor-

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

3
4

For example, see Leeper, Sims, and Zha (1996). The
evidence is not definitive. There is always a danger
that such studies attribute to monetary policy real
fluctuations that are, in fact, caused by unobserved
changes in tastes and technology to which policymakers are reacting — a point Sims (1992) emphasizes.
Blanchard and Kiyotaki (1987) develop the basic
framework. An alternative approach would be to model
the bargaining that takes place between workers and
their employers. For an example, see Benabou and
Bismut (1988).
Gust (1997) and Ascari (2000) take this approach.
See Taylor (1983) for a detailed look at the length of
union labor contracts and the timing of negotiations.
Even in the nonunion sector, evidence suggests that
wage rates are typically prespecified for a year or
more. For a nice summary of the empirical evidence,
see Taylor (1999).
See Koenig (1997) and Andersen (1998) for early
developments of this argument. Ascari (2000) reaches
a superficially different conclusion with regard to
persistence. He is interested in whether labor-market
imperfections similar to those examined here are able
to generate a near-random walk in output in response
to monetary policy shocks — a very high degree of
persistence indeed. A near-random walk in response
to money shocks is required only if one wants to claim
that changes in the money stock are the principal
source of output variation in the economy. These days,
few economists would take so extreme a position.
Hence, the analysis presented here is more closely related to that of Fischer (1977) than to that of Taylor (1980).
If anything, relaxing these assumptions would make it
easier to obtain persistent real monetary effects. For
example, it is well known that when contracts specify
a wage path, real monetary effects cannot last longer
than the longest contract, whereas when contracts
specify a fixed wage, policy shocks are propagated
beyond the longest contract (Taylor 1980). Similarly,
Erceg’s (1997) analysis suggests that making investment endogenous contributes to persistence, provided
the demand for money is linked to consumption rather
than to income. That moving from a world of sticky
wages and flexible prices to a world of sticky wages
and prices tends to add to persistence is discussed
in the box that accompanies this article.
Empirical estimates Pencavel (1986) reviews suggest
ξ ≈ .25. It is often assumed utility is logarithmic in

consumption (σ = 1) — an approximation consistent
with estimates Beaudry and van Wincoop (1996)
obtain. On the other hand, Attanasio and Weber
(1994) and Ogaki and Reinhart (1998) report σ ≈ 2.
A labor demand curve of this form is consistent with
profit maximization by firms if the labor variable that
enters firm f ’s production function is a composite of
the labor different households supply. In particular,
if there is a continuum of households indexed by
i [0, 1], Equation 2 is obtained if
E

1/E

Lf = (∫Lfi di )

price level to adjust halfway toward its new marketclearing level.
To generate a realistically persistent economic response
to monetary shocks, it is sufficient that only a small
fraction of labor contracts be renegotiated infrequently
(Koenig 1997).
Recall that I assume households are able to insure
their consumption against idiosyncratic shocks.
Consequently, a higher average level of economic
activity raises everyone’s standard of living and,
through the resultant wealth effect, tends to lower
everyone’s willingness to work.

and
W ≡ (∫W i

E/(E – 1)

REFERENCES

(E – 1)/E

di )

where Lfi is the amount of household i ’s labor used by
firm f (Blanchard and Kiyotaki 1987).
Erceg (1997) takes another approach. In his analysis,
monetary policy is non-neutral because of staggered
price contracts, as in CKM. Labor contracts preset
wages — short-circuiting the rise in unit labor costs that
is responsible for rapid price adjustment in CKM — but
hours of employment vary as if wages were perfectly
flexible.
A demand curve of this form is consistent with household utility maximization if the output variable, Ci , that
enters household i ’s utility function is a composite of
the goods different firms produce. In particular, if there
is a continuum of firms indexed by f [0, 1], Equation
6 is obtained if
Θ

Andersen, Torben M. (1998), “Persistency in Sticky Price
Models,” European Economic Review 42 (May): 593 – 603.
Ascari, Guido (2000), “Optimising Agents, Staggered
Wages and Persistence in the Real Effects of Money
Shocks,” Economic Journal 110 (July): 664 – 86.
Attanasio, Orazio P., and Guglielmo Weber (1994), “Is
Consumption Growth Consistent with Intertemporal
Optimization? Evidence from the Consumer Expenditure
Survey,” NBER Working Paper Series, no. 4795
(Cambridge, Mass.: National Bureau of Economic
Research, July).
Benabou, Roland, and Claude Bismut (1988), “Wage
Bargaining and Staggered Contracts: Theory and Estimation,” CEPREMAP Working Paper no. 8810 (Paris, June).

1/ Θ

Ci = (∫C fi df )
and
Θ/(Θ – 1)

P ≡ (∫Pf

Beaudry, Paul, and Eric van Wincoop (1996), “The
Intertemporal Elasticity of Substitution: An Exploration
Using a U.S. Panel of State Data,” Economica 63
(August): 495 – 512.

(Θ – 1)/ Θ

df )

where Cfi is the amount of firm f ’s output consumed
by household i.
As Note 8 mentions, recent studies suggest σ = 1 or 2
and ξ ≈ .25. Unfortunately, empirical evidence concerning E is almost nonexistent. Studies that examine the
substitutability of one type of labor for another usually
divide workers into only a few broad classes, such as
skilled and unskilled. In the present context, however,
the relevant elasticity of substitution [1/(1 – E )] is that
between the labor supplied by different individual
bargaining units. One would expect this elasticity to
be much greater than that between skilled laborers
as a group and unskilled laborers as a group. A high
elasticity of substitution means a low monopoly wage
premium (a value of E close to 1).

Blanchard, Olivier Jean, and Nobuhiro Kiyotaki (1987),
“Monopolistic Competition and the Effects of Aggregate
Demand,” American Economic Review 77 (September):
647– 66.
Chari, V. V., Patrick J. Kehoe, and Ellen R. McGrattan
(2000), “Sticky Price Models of the Business Cycle: Can
the Contract Multiplier Solve the Persistence Problem?”
Econometrica 68 (September): 1151– 75.
Erceg, Christopher (1997), “Nominal Wage Rigidities and
the Propagation of Aggregate Demand Disturbances,”
Federal Reserve Board of Governors International
Finance Discussion Paper no. 590 (Washington, D.C.,
September).

While three-year contracts are typical in unionized industries, currently only about 10 percent of workers are
union members. Moreover, CKM examine one-year price
contracts and it seems desirable to compare like with
like. The reader is free to reinterpret the unit time interval.
When both wage adjustment and price adjustment are
staggered, 9.9 months are required for the average

Fischer, Stanley (1977), “Long-Term Contracts, Rational
Expectations, and the Optimal Money Supply Rule,”
Journal of Political Economy 85 (February): 191– 205.

FEDERAL RESERVE BANK OF DALLAS

Gust, Christopher J. (1997), “Staggered Price Contracts
and Factor Immobilities: The Persistence Problem
Revisited” (unpublished working paper, Northwestern
University, November).

Pencavel, John H. (1986), “Labor Supply of Men: A
Survey” in Handbook of Labor Economics, Vol. 1,
ed. Orley Ashenfelter and Richard Layard (Amsterdam:
North-Holland), 3 –102.

Koenig, Evan F. (1999), “Is There a Persistence Problem?
Part 1: Maybe,” Federal Reserve Bank of Dallas
Economic and Financial Review, Fourth Quarter, 10 –17.

Sims, Christopher A. (1992), “Interpreting the Macroeconomic Time Series Facts: The Effects of Monetary Policy,”
European Economic Review 36 (June): 975 –1000.

——— (1997), “Aggregate Price Adjustment: The
Fischerian Alternative” (unpublished working paper,
Federal Reserve Bank of Dallas, January).

Taylor, John B. (1999), “Staggered Price and Wage Setting
in Macroeconomics,” in Handbook of Macroeconomics,
Vol. 1B, ed. John B. Taylor and Michael Woodford
(Amsterdam: Elsevier Science, North-Holland), 1009 – 50.

Leeper, Eric M., Christopher A. Sims, and Tao Zha
(1996), “What Does Monetary Policy Do?” Brookings
Papers on Economic Activity no. 2: 1– 63.

——— (1983), “Union Wage Settlements During a Disinflation,” American Economic Review 73 (December):
981– 93.

Ogaki, Masao, and Carmen M. Reinhart (1998),
“Measuring Intertemporal Substitution: The Role of
Durable Goods,” Journal of Political Economy 106
(October): 1078 – 98.

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

——— (1980), “Aggregate Dynamics and Staggered
Contracts,” Journal of Political Economy 88 (February):
1– 23.

To pay for their spending, governments use
one or more of the following: taxes, sale of debt
to the public, and money creation. Taxes and
debt issuance are typically under the purview of
the treasury (the government’s fiscal side), and
money creation is under the control of the central
bank (the government’s monetary side). This split
seems natural since most central banks are
required to maintain price stability and, hence,
ought to have complete control over the money
supply. In recent years, however, based on the
work of Christ (1968) and Sargent and Wallace
(1981), economists have noted that a single, forward-looking budget constraint unifies these two
government branches. As a direct consequence
of this constraint, every fiscal action potentially
has a monetary component to it, and vice versa.
As such, it becomes hard to pinpoint whether the
central bank really has complete control over
money creation or whether it is passively creating
money at the treasury’s beck and call. If the latter
is true, the central bank is severely constrained in
performing its task of maintaining price stability.
Or is it? This article presents a model in which the
central bank retains substantial control over the
inflation rate despite being subservient to the
treasury in a very precise sense.
We consider a situation in which the government explicitly relies on the central bank to
meet a portion of the government’s revenue
needs. More precisely, our measure of this reliance captures the extent to which the central
bank is required to raise revenue from money
creation (seigniorage) to pay for the interest
expenses on the debt floated by the treasury.
Greater reliance implies that seigniorage accounts for a larger fraction of the treasury’s revenue requirements brought on by its outstanding interest obligations. This notion of reliance
stems from the idea of “economic independence” as
described by Grilli, Masciandaro, and Tabellini
(1991), Alesina and Summers (1993), and Capie
et al. (1994). Capie et al., for instance, differentiate between goal independence and instrument
independence. Goal independence exists when
the central bank can choose what it wants monetary policy to accomplish without regard to the
treasury’s or other policymakers’ desires.1 Instrument independence is present when the central
bank can choose how to use the instrument of monetary policy without regard to the treasury’s wishes.2
In contrast, our measure of reliance has
little connection with the idea of goal independence. Interestingly, as Grilli, Masciandaro, and
Tabellini (1991) point out, goal independence and
instrument independence are not always positively correlated.3

Reliance, Composition,
and Inflation
Joydeep Bhattacharya and Joseph H. Haslag

his article explores the effect
of fiscal policy actions on
long-run prices and
the inflation rate.

Joydeep Bhattacharya is an assistant professor
of economics at Iowa State University.
Joseph Haslag is a former senior economist
and policy advisor in the Research Department
at the Federal Reserve Bank of Dallas.
He is currently an associate professor of economics
at the University of Missouri.

FEDERAL RESERVE BANK OF DALLAS

bank to raise a fraction of its interest expenses
on outstanding debt (henceforth the reliance
parameter).
First, we analyze the long-run relationship
between this reliance parameter and the price
level, the inflation rate, and the nominal interest
rate. In other words, we attempt to answer the
question: Do countries that rely heavily on
seigniorage endure higher long-run inflation
rates in comparison with countries with less
seigniorage? Second, we examine the relationship between the composition of government
paper—bonds versus money—and the effects
on the price level, the inflation rate, and the
nominal interest rate. This inquiry may be of
topical interest in that more and more governments are realizing primary surpluses and paying off some outstanding debt. Insofar as these
surpluses translate into permanent changes in
the composition of government paper, we ask
how such a change would affect the long-run
values of these economic variables.
The two main results are easily summarized. First, we show that the price level is positively related to the stock of government debt as
long as the government relies on the central
bank to raise some revenue. This reliance requires the central bank to monetize some of the
outstanding debt. Consequently, the treasury’s
debt decisions affect the price level. In short, the
price level has a “fiscal” aspect. Viewed another
way, the effective stock of money in the economy consists of the actual quantity of money
and the fraction of bonds backed by money.
Second, we derive the impact of permanent changes in both the reliance and the composition parameters on the long-run inflation
rate. We show that the inflation is positively related to the government’s reliance on seigniorage and is inversely related to the composition
of government paper. When the latter shifts
toward money, government debt falls, implying that the government’s expenses are smaller.
Hence, less seigniorage is required.
The chief policy lesson is that an economically dependent central bank, via its ability to
control the composition of government paper,
may be quite successful in controlling the inflation rate.5
We begin by laying out the details of the
model economy.

In this article, the central bank is (possibly) goal independent although it is not instrument independent because it has to raise a certain amount of revenue for the government. As
such, it is constrained in its choice of, say, the
money growth rate. It does, however, have control over the composition of government liabilities, namely debt versus money. Our question,
then, is: Does the control over the composition
of government “paper” translate into control
over the inflation rate even when the central
bank is not instrument independent in the sense
of Capie et al. (1994)?
To get a sense of some of the issues
involved, consider the case of a government
that floats some debt on the market to, partly,
finance its expenditures. The government must
credibly demonstrate the presence of enough
funds to cover the principal and interest payments on all debt held by the public. Using the
government’s long-run budget constraint, it is
possible to show that having a current outstanding debt requires the government to run
surpluses in the future. These surpluses may be
generated by cutting expenditures, implementing taxes, or altering the revenue from money
creation, or seigniorage.4
We are particularly interested in seigniorage. The central bank may print money to pay
for the treasury’s interest expenses or exchange
new money for existing government bonds. In
the case of an open market purchase, in which
the central bank buys government bonds and
gives money to the public, the stock of money
in the economy goes up but the interest expense of the debt goes down. Because money
does not pay interest, future taxes may go
down. This may reduce the government’s revenue needs, such that the central bank has more
control over the inflation rate. Thus, the central
bank, even though it is not independent, can,
via open market operations, control the composition of government paper, thereby affecting
the government’s de facto reliance on seigniorage (and indirectly the inflation rate).
This article illustrates some of these basic
ideas within the context of a well-specified general equilibrium model in the tradition of
Sidrauski (1967). In our model, a large number
of infinitely lived households with 20/20 foresight derive utility from the consumption of a
single nonproduced perishable good and from
liquidity services (money). The government
sells bonds and prints money to cover its interest obligations on these bonds. The central
bank is not economically independent; in fact,
the government explicitly relies on the central

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

THE MODEL ECONOMY
The economy is populated by a large
number of dynastic (infinitely lived) households. Time is discrete and is indexed by t = 1,

2, 3…. There is a single, perishable consumption good. At each date t ≥ 1, a household
receives a fixed endowment of y units of the
single consumption good; it does not have to
exert any effort to produce or receive this good.
Households may hold their wealth two
ways: government bonds and fiat money. Both
assets are nominally denominated (in, say, dollars). Government bonds mature one period
after they are issued. If the household pays $1
for a unit of government debt at date t, it
receives $I at date t + 1. In contrast, no interest
is paid on money. At date t = 1, each household
is endowed with $B 0 and $M0.
At the start of any period, a representative
household’s wealth comprises three entities: the
proceeds from the sale of its endowment of y
goods, its money holdings from the previous
period (whose value, as we will see, may have
gone up or down depending on inflation), and
the interest (plus principal) payments on its
bond holdings from the previous period. The
household may use this wealth to provide for its
consumption during that period, buy new
bonds and money, and pay a lump-sum tax to
the government.
The household’s budget constraint, therefore, is
(1)

where m denotes the real value of money balances and b the real value of government
bonds. Equation 2 states the household’s budget
constraint —both sources of income and expenditures —measured in units of the consumption
good. Note that b can be either positive or negative. With b > 0, the government is borrowing
from the household. With b < 0, the government
is loaning resources to households.
The left side of Equation 2 represents the
resources the household has available to spend
at date t. Given these resources, how much consumption can this household afford at the market price? How much money and bonds should
it hold? We now turn to a determination of the
household’s demand for consumption, money,
and bonds. We study an equilibrium in which
the demands for all three are positive. A problem we face in this environment is that money
is dominated in rate of return by government
bonds, and, hence, households will not hold
money unless we build into the model some
rationale for money to be demanded.
Possibly the simplest way to achieve our
purpose is to assume the household has preferences defined over the consumption good and
real money balances. In other words, households value liquidity directly and are willing to
alter their consumption to get the desired
amount of liquidity. We are not arguing that
households derive happiness from holding intrinsically worthless pieces of paper. Rather, the
fact that money facilitates market exchange
makes it relatively more attractive than bonds
and accounts for why the latter are not also in
the utility function. We do not explicitly model
how and why money is more liquid than bonds.
Suffice it to say that money-in-the-utility-function is a general formulation that encompasses
many deeper reasons why fiat money is valued
in the real world despite being dominated in
rate of return.6
For expositional convenience, the representative household’s preferences at date t are
represented as

pt y + Mt –1 + It –1Bt –1 = pt ct + Mt + Bt + pt τt ,

where p is the price level measuring the number of dollars traded for one unit of the consumption good, M is the quantity of money, B
is the quantity of government bonds, τ is the
lump-sum tax, and c is consumption. Equation
1 stipulates that the dollar value of the household’s after-tax resources must equal the dollar
value of its expenditures, including savings.
It is possible, and instructive, to convert
the household’s budget constraint (written in
dollar terms in Equation 1) to its goods value.
To do this, let
pt
and Rt − 1 = 1 + rt − 1
pt − 1
1 + it − 1
I
= t −1 =
.
1 + πt
1 + πt

1 + πt =

(3)

U (ct ,mt ) = lnct + θlnmt ,

where θ is the rate at which a household will substitute money for consumption. Equation 3 specifies that the household’s utility is characterized
in a log-separable form. Three properties of the
function U (.) are worth noting. First, the household’s utility increases when either consumption
or real money balances increase. In other words,
marginal utility is positive with respect to each
variable. Second, an increase in consumption
results in declining marginal utility. Third, separa-

Here, π stands for the rate of change in the price
level over time, or the inflation rate; i is the net
nominal interest rate; r is the net real interest
rate; and R is the gross real interest rate (principal plus interest). Divide both sides of Equation
1 by pt to obtain
m
(2) y + (1 + rt − 1 )bt − 1 + t − 1 − τt = ct + mt + bt ,
1 + πt

FEDERAL RESERVE BANK OF DALLAS

The Long-Run Government Budget Constraint
In this box we formally derive the government’s long-run budget constraint.
There are principal and interest expenses associated with outstanding government
debt. These expenses are backed by the revenues from taxes and seigniorage.
We begin with the period-by-period expression of the government budget
constraint; that is, at date t

bility means a household’s marginal utility of consumption is invariant to changes in real money
balances, and vice versa.
The government consists of two separate
entities bound by a single budget constraint.
The fiscal authority, or treasury, collects the
lump-sum taxes and sells and redeems bonds.
It has no other expenditures. Simultaneously,
the monetary authority, or central bank, potentially controls the nominal quantity of money
over time. It can alter the quantity of money
by directly handing money over to each household; alternatively, it could trade money for an
equal dollar value of government bonds—an
open market operation. Changes in the nominal
money stock allow the government to buy goods
with the extra money printed. Each authority
operates in such a way that the following budget
constraint is satisfied period by period:
(4)

At date t + 1, Equation B.1 is written as

Thus, the date t level of government debt is
bt =

τt +1 + bt +1 + st +1
.
(1+ rt )

Substitute for bt in Equation B.1, yielding
(1 + rt −1)bt −1 = τt +

(B.3)

τt +1 + bt +1 + st +1
+ st .
(1 + rt )

Next, update Equation B.1 two periods, solving for bt +1 and substituting in Equation
B.3, yielding

(1 + rt –1)bt –1 = τt + bt + st ,

(1+ rt −1)bt −1 = τt +

τt +1 + bt +1 + st +1 τt + 2 + bt + 2 + st + 2
+
+ st .
(1+ rt )
(1+ rt +1)(1+ rt )

By repeating this process, we get the following expression
(1+ rt −1)bt −1 = Tt + St + limt →∞

(B.4)

bt + j
(1+ rt + j −1)…(1+ rt )

Tt = τt +


τt +1
τt + 2
τt + 2
1 
+
+ K = τt +
+ K ,
τt +1 +
(1+ rt ) (1+ rt +1)(1+ rt )
(1 + rt ) 
(1 + rt +1)


St = st +


st +1
st + 2
1 
st + 2
+ K .
+
+ K = st +
st +1 +
(1+ rt +1)
(1+ rt ) (1+ rt +1)(1+ rt )
(1 + rt ) 


Equation B.4 states that the government’s principal and interest expense is equal to
the sum of the present value of its tax revenues, its seigniorage and its long-run debt
position. We impose the condition that the treasury cannot roll over its debt (or loans)
forever. The standard no-Ponzi condition is represented by the following expression:
(B.5)

limt →∞

bt + j
(1+ rt + j −1)K(1+ rt )

= 0.

Thus, the no-Ponzi condition implies that the government’s date t principal and
interest expenses are backed completely by tax revenues and seigniorage.
Now that we have defined our notion of backing, we can articulate our notion of
reliance. Suppose the government decrees that a fraction φ of its date t debt obligations will be met by tax revenues. Thus,
Tt = φ(1+ rt −1)bt −1.

(B.6)

The government’s long-run budget constraint, Equation B.4, together with Equations
B.5 and B.6, implies that
St = (1 − φ)(1 + rt −1)bt −1.

(B.7)

How should current taxes be set, given Equations B.6 and B.7? Recall that
Tt = τt +

PV (τt ) = (1 – φ)(1 + rt –1)bt –1 ,

1
1
Tt +1 = τt +
[φ(1+ rt )bt ] = τt + φbt .
(1+ rt )
(1+ rt )

Since τt = Tt – φbt , current taxes must satisfy

PV (st ) = φ(1 + rt –1)bt –1 ,

(B.8)

where PV stands for the present value of the
term in parentheses. In other words, the present

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

where

and
(6)

(1 + rt )bt = τt +1 + bt +1 + st +1.

(B.2)

where s denotes the seigniorage raised by the
central bank.
Conceivably, the treasury could keep issuing new debt to pay for the interest obligations
on outstanding debt but never really retire the
debt, thus rolling it over forever. Forward-looking agents will understand this and refuse to
lend to the treasury. Hence, we must impose an
additional long-run restriction on the treasury’s
debt issuance. Specifically, as we show in the
box entitled “The Long-Run Government Budget
Constraint,” the present value of government
revenues must be equal to the initial stock of
the treasury’s real bond payments. More concretely, the present value of the treasury’s debt
must equal the present value of government
revenues (that is, future debt obligations must
be fully backed by future revenues of the
treasury and the central bank). Thus, the treasury is restricted to be neither a lender nor a borrower, at least in terms of the present value of
its debt obligations. This policy is sometimes
referred to as a no-Ponzi condition.
We now introduce the notion of reliance.
Since each authority contributes to the present
value of revenues, we can assign the contribution from each. Reliance, therefore, represents
the portion of the present value of revenues that
must come from each authority:
(5)

(1 + rt –1)bt –1 = τt + bt + st .

(B.1)

τt = φ(1+ rt −1)bt −1 − φbt = φ[(1+ rt −1)bt −1 − bt ].

value of lump-sum taxes and seigniorage is
equal to the principal and interest expenses of
the initial stock of real government bonds. It is
possible (see Equation B.8 in the box) to write
(7)

In equilibrium, since the good is perishable, the
household will consume all its endowment; that
is, ct = y for all t.7 Substituting for c in Equation 8 and using Equation 7 to substitute for
τ, the household’s date t budget constraint
(Equation 2 ) can be written as

τt = (1 – φ)[(1 + rt –1)bt –1 – bt ].

Thus, another way to think of our notion of
reliance is that current taxes are responsible for
(1 – φ) percent of the current interest expenses
on the outstanding debt or that the central bank
is responsible for φ percent of the current interest expenses. Hereafter, we refer to φ as the
seigniorage-reliance parameter.
A few remarks about measurement and
realism are in order. First, reliance is difficult to
measure because it is quite hard to isolate those
changes in the stock of high-powered money
that the central bank engineered exclusively to
finance government deficits. This is because
high-powered money could change for reasons
other than to finance deficits. Second, we have
taken a particular stand with respect to the institutional structure linking the fiscal authority and
the central bank. It is difficult to find examples
of countries that fit our environment perfectly.
As discussed in the introduction, we like to
think of φ as a continuous version of instrument
independence as postulated by Capie et al.
(1994). One could be agnostic about all this,
simply follow Aiyagari and Gertler (1985), and
refer to φ as the portion of government bonds
eventually backed by money.
In the next section, we turn our attention
to the equilibrium relationship between the
reliance parameter and the price level in our
economy.

(9 )

Thus, the household’s budget constraint is characterized by the size of the endowment, the
path of government bonds, the real interest rate,
the inflation rate, and the government’s longrun reliance on taxes.
In this article, we focus only on steadystate, or long-run, equilibria, that is, equilibrium
allocations—consumption, real money holdings,
and real bond holdings—that are time invariant.
With consumption constant across time, the
price of date t + 1 consumption measured in
units of date t consumption is constant (see
Equation 8′ ). This price is the gross real interest
rate, (1 + r ). In steady state, therefore, we know
that
1
(1 + r ) = .
β
Using this, we can rewrite the household’s budget constraint as
θy π(1 + r )
(10 )
φrb =
.
i
Next, solve Equation 10 for real government
bonds:

A FISCAL THEORY OF PRICES

(11)

The household’s utility maximization
problem can be stated as
∞

(

max ∑ βt ln ct + θ ln mt
t =0

b =θ

(1 + r )πy
.
i φr

Note that Equation 11 is the quantity of real
government bonds that people will hold in
equilibrium. Thus, Equations 8, 11, and c = y
completely describe the household’s steady-state
allocations.
We conduct the following experiment to
demonstrate how fiscal policy directly affects
the price level. Suppose the nominal stocks of
money and government bonds are set at their
initial levels. It is straightforward to derive the
relationship between the equilibrium steadystate price level and seigniorage reliance.8 We
substitute the steady-state expressions for bonds,
money, and consumption into the household’s
budget constraint (Equation 9 ), and after some
rearrangement, the steady-state price level is expressed as

)

subject to Equation 2. β is a positive fraction
that measures the rate at which the household
discounts future utility. In equilibrium, the household’s maximization problem yields the following decision rule for real money balances and
consumption:
 1 + it 
(8 )
mt = θ
 ct
 it 
and
(8 ′ )

 1 + it − 1  y
y + φ(1 + rt − 1 )bt − 1 + θ

 it − 1  1 + πt
 1 + it 
= y + θ
 y + φbt .
 it 

1 β(1 + rt )
=
.
ct
ct + 1

FEDERAL RESERVE BANK OF DALLAS

(12)

(

)

rβ
M + φB .
θy

 i 
m = θ
 y.
1 + i

To understand the deeper implications of
Equation 12, consider an increase in the central
bank’s revenue generation responsibility, φ. With
the central bank raising more revenue, the treasury can reduce the household’s taxes and retire
some outstanding debt using the funds the central bank raised. Retiring debt means that B falls.
It follows that households now have a smaller
stock of assets available. In contrast, with lower
lump-sum taxes, the household’s disposable
income rises. If φ < 1, it can be shown that the
former effect dominates. The bottom line is that
an increase in the central bank’s revenue generation responsibility raises the quantity of
resources available for the household to spend.
More resources chase the same amount of
goods. The price level rises as a consequence.
Equation 12 says the long-run price level
is proportional to the “monetized” portion of the
government’s liabilities. Note that φ represents
the long-run fraction of government bonds
backed by money. In the minds of forwardlooking agents, then, the actual amount of
money in the economy is not only the money
stock M but also the fraction of bonds backed
by money. When the latter goes up, agents see
this as an increase in the amount of money in
the economy; consequently, the price level
rises. With φ > 0, in addition to the central bank,
the treasury plays a role in determining the
price level through the quantity of government
bonds outstanding.
Equation 12 captures an idea in contrast to
the standard textbook version of the quantity
theory of money, which postulates that only
changes in the money stock affect the price
level. Here, fiscal policy actions (such as a permanent increase in the treasury’s stock of debt)
can easily affect the price level as long as φ < 1
holds, even though the stock of money is held
constant. Thus, when considering correlations
between the price level and money, the appropriate definition of money should include the
stock of debt, a point long recognized by proponents of the real bills doctrine.9
To finance the government’s interest
expenses, the money stock will change over
time. We turn our attention to the effect that
changes in reliance and composition have on
the steady-state inflation rate and the nominal
interest rate. To that end, with c = y, the equilibrium expression for real money demand
using Equation 8 is given by

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

Set this equal to real money supply M /p, where
p is computed from Equation 12.10 After some
rearrangement, it is possible to show that
(13)

(1 − β)(M + φB )
,
M − (1 − β)(M + φB )

and
(1 − β)φB
.
M − (1 − β)(M + φB )
We now can answer our initial question:
Does increased reliance on seigniorage increase
the inflation rate? Recall that the seigniorage
reliance parameter is denoted by φ. Then, an
increase in this parameter raises the numerator
of Equation 14 and reduces the denominator,
thereby increasing π. Simply stated, an increase
in the central bank’s revenue-raising responsibility precipitates an increase in the inflation
rate. Analogously, we can show (using Equation
13) that such an action increases the nominal
interest rate.11
Note that money demand is interestinelastic (Equation 8 ). This point is important in
deriving the relationship between reliance and
both the inflation rate and the nominal interest
rate. To illustrate, suppose money demand is
interest-elastic. Money demand decreases, in percentage terms, more than nominal interest rises.
In steady state, nominal interest rate movements
reflect movements in the inflation rate; recall that
the steady-state real interest rate is 1/β, a constant. In the interest-elastic case, the economy
could be on the wrong side of the Laffer curve.
In other words, seigniorage would decrease
because the tax base (money demand) falls by
more than the tax rate. Interest-inelastic money
demand assures that this does not occur.12
Evidence supports the conclusion that
greater reliance is correlated with higher inflation. Grilli, Masciandaro, and Tabellini (1991)
examine the period 1950–89. They construct an
“economic independence indicator” for a group
of European nations and for each of the four
decades in their sample. (See Table 14 in their
paper.) They estimate the correlation coefficient
between each country’s decade-average inflation rate and the economic independence measure, finding that countries with more economically dependent central banks (such as Greece,
Portugal, and Spain) have consistently higher
inflation rates and the highest levels of seigniorage.
(14 )

π=

inversely related to movements in α.14 So, the
composition of government liabilities does matter. This result has an unpleasant monetarist
arithmetic feel to it.15 An open market purchase
lowers the eventual interest expenses associated
with interest-bearing government bonds. Consequently, less inflation is needed to fund the
smaller expenses. Hence, inflation declines as
the composition shifts toward money and away
from bonds.

What effect would a change in each type
of government paper have on the long-run inflation rate? To answer this, rewrite Equation 14 as
1
(14′ )
π=
.
 β • M • 1
−1
1 − β B φ


Then an increase in M reduces the inflation rate,
whereas an increase in B increases the inflation
rate. The intuition is clear: money is a cheaper
way to pay off the government’s interest obligations because the government does not pay
interest on money. On the other hand, an
increase in the stock of bonds requires the central bank to eventually raise more revenue, for
a given seigniorage reliance, to meet the increased interest obligations on this debt, thereby
increasing the inflation rate.

CONCLUDING REMARKS
In this article, we investigate the effects of
monetary policy decisions that are explicitly
linked to fiscal policy decisions and vice versa.
More important, the nature of the linkage —
here, the government stipulates how much it
will rely on seigniorage to back its long-run
expenses—has direct consequences for the
inflation rate. Our model economy produces the
following prediction: controlling for other factors, if a country’s reliance on seigniorage
increases, the country’s inflation rate will increase. We go on to show that a permanent
open market purchase (one in which a country
reduces its stock of government bonds and
increases the quantity of money) results in a
decline in the long-run inflation rate.
Our analysis has implications for a classic
question in monetary economics: How much
control can a central bank have over the value of
its currency? (Sargent 1987, 139). We consider
cases in which the central bank is not instrument
independent. These central banks can—via open
market operations—switch the composition of
government liabilities toward non-interest-bearing money and away from debt. We show that
the open market operation lowers debt expenses
and reduces the government’s effective reliance
on seigniorage. This way, it can retain substantial
control over the value of its currency.
In light of our results, we close with two
important questions for future research. First
and foremost, how should φ and α be measured? This is a difficult issue because φ represents the fraction of money created to meet
the government’s financing needs. Governments
typically do not preannounce how much they
will rely on the seigniorage. Consequently, one
must infer how much money is created for
financing needs and how much is created to
meet other central bank activities. Second, what
is the relationship between φ and α? That is,
is there a relationship between a country’s
reliance on seigniorage and its composition of
government liabilities?

COMPOSITION OF GOVERNMENT LIABILITIES
We can use our setup to answer yet
another important question: Does the composition of government liabilities (interest-bearing
debt, like bonds, versus non-interest-bearing
debt, like money) matter? The answer seems
particularly relevant as more and more countries, including the United States, realize budget
surpluses and pay down their debt.
Define α = M /(M + B ). Then it is possible
to rewrite Equation 12 as

{[

](

)}

rβ
1 − (1 − φ)(1 − α ) M + B .
θy
Consider a one-for-one exchange in which government bonds are permanently traded for
money. This changes the composition of the
government’s liabilities but not their total value,
M + B. With 0 < φ < 1, an increase in α, for
instance, results in a higher price level.
We next analyze how a change in the
composition of government liabilities affects the
inflation rate. An increase (decrease) in α may
be thought of as representing a less restrictive
(tight) monetary policy.13 Suppose the government initiates a permanent open market purchase of bonds in exchange for money. This
open market operation results in more money
and fewer bonds, that is, α increases. To see the
effect of this on the inflation rate, rewrite
Equation 14 as
(15)

(16 )

π=

(1 − β)φ
.
 α 
β
 − (1 − β)φ
 1 − α

Then, Equation 16 indicates that inflation is

FEDERAL RESERVE BANK OF DALLAS

NOTES
6

Chapter 4 in Walsh (1998) stimulated many of the
ideas presented here. Part of the work was done when
Bhattacharya visited the Federal Reserve Bank of
Dallas’ Research Department in the summer of 1999.
We gratefully acknowledge the department’s hospitality and helpful comments from Mark Wynne, Mark
1

Guzman, and Jim Dolmas.
Though they adopt different terminology, Grilli,
Masciandaro, and Tabellini (1991) focus on a similar
concept. To borrow from their definition, goal independence “is the capacity to choose the final goal of
monetary policy, such as inflation or the level of
economic activity.”
Alesina and Summers (1993) use slightly different
terminology. Specifically, they assert, “Economic
independence is defined as the ability [of the central
bank] to use instruments of monetary policy without
restrictions. The most common constraint imposed
upon the conduct of monetary policy is the extent to
which the central bank is required to finance government deficits. This index of economic independence
essentially measures how easy it is for the government
to finance its deficits by direct access to credit from
the central bank.”
Grilli, Masciandaro, and Tabellini (1991) in Table 13
of their paper provide some evidence on the Alesina –
Summers instrument-independence indicator. According to them, instrument independence of the central
bank is high in West Germany, Switzerland, the United
States, Austria, and Belgium. Conversely, central
banks in Italy, New Zealand, Portugal, Greece, and
Spain have very little instrument independence.
Take the example of India. The Reserve Bank of India
(RBI) is definitely politically independent. Nonetheless,
during 1998 – 99, the net lending by the RBI to the
Indian government was about 10 percent of the gross
fiscal deficit for that year, precipitating an 18 percent
increase in M1.
Using data from a large group of countries over
many years, Fischer (1982) shows that governments
do generate revenue from money creation more often
than not. Click (1998) documents that between 1971
and 1990, in a wide cross section of countries,
currency seigniorage as percent of GDP ranged
from 0.3 percent to 14 percent, and seigniorage as
percent of government spending ranged from 1 percent to 148 percent.
One implication of our findings is that prohibition of
deficit financing is redundant. For instance, in the
membership requirements put forward by the European Union, there is an upper bound on the debt-toGDP ratios. What really matters, and what the central

ECONOMIC AND FINANCIAL REVIEW FOURTH QUARTER 2000

bank can achieve, is the mandate for price stability.
See Feenstra (1986) for a more formal description of
the functional equivalence between models with explicit
transaction costs and those with money-in-the-utilityfunction. It is important to mention here that functional
equivalence does not mean that the intuition or
interpretation of the results is model invariant.
One may wonder why people hold money here since
they end up consuming only their endowment anyway.
The answer lies in the notion of equilibrium. When
agents solve their individual problems to determine
how much money to hold, they perceive the possibility
of trade in the good and do not know that, in equilibrium, they will all simply consume their endowment.
For the interested reader, the notion of a steady-state
price level is more fully developed in Walsh (1998),
143 – 46.
Sargent and Wallace (1982) and Smith (1988) contain
good discussions of the doctrine.
Alternatively, one could equate bond demand (see
Equation 11) to real bond supply and arrive at the same
expressions for i and π as in Equations 13 and 14.
For the interested reader, the optimal policy (one that
maximizes steady-state welfare of agents) would be to
set φ = 0. In words, the household’s welfare is highest
when the government relies solely on lump-sum taxes
to pay for its interest expense. The general flavor of
this result extends to several cases in which distorting
taxes are present. See Chari, Christiano, and Kehoe
(1996) and Correia and Teles (1999).
See Lucas (2000) for an excellent discussion on the
elasticity of money demand. He provides an overview
of the empirical support for the position that money
demand is interest inelastic.
Greenwood (1998), for instance, focuses on tight
money policies. As the recent crisis in Japan unfolds,
many commentators are suggesting that the blame
should be placed on the Japanese central bank for
following tight money policies over the last decade,
thereby “strangling’’ the economy. The central bank
argues that its tight money policies have kept
Japanese inflation in check.
To verify this, differentiate Equation 16 with respect to
α. The sign of the resulting expression is negative.
Sargent (1987) discusses the effect a permanent open
market sale of bonds has on the inflation rate. Given a
fixed deficit, such a sale “bequeaths” a larger stock of
interest-bearing debt to the future; eventually inflation
would have to rise to pay for the outstanding interest
obligations. Sargent and Wallace (1981) called this
paradoxical phenomenon (tight money policies
increase the eventual inflation rate) the “unpleasant
monetarist arithmetic.” See Bhattacharya and Haslag
(1999) for a survey.

Fischer, Stanley (1982), “Seigniorage and the Case for
a National Money,” Journal of Political Economy 90
(April): 295 – 313.

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Greenwood, John (1998), “Tight Money Strangles
Japan’s Recovery,” The Wall Street Journal, July 16, A18.

Alesina, Alberto, and Lawrence H. Summers (1993),
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Performance: Some Comparative Evidence,” Journal of
Money, Credit, and Banking 25 (May): 151– 63.

Grilli, V., D. Masciandaro, and G. Tabellini (1991),
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Bhattacharya, Joydeep, and Joseph H. Haslag (1999),
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Federal Reserve Bank of Dallas Economic and Financial
Review, Third Quarter, 26 – 36.

Lucas Jr., Robert E. (2000), “Inflation and Welfare,”
Econometrica 68 (March): 247– 74.
Sargent, Thomas J. (1987), Dynamic Macroeconomic
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Capie, Forrest, Charles Goodhart, Stanley Fischer, and
Norbert Schnadt (1994), The Future of Central Banking:
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Sargent, Thomas J., and Neil Wallace (1981), “Some
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of Minneapolis Quarterly Review, Fall, 1–17.

Chari, V. V., Lawrence J. Christiano, and Patrick J. Kehoe
(1996), “Optimality of the Friedman Rule in Economies
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37 (April): 203 – 23.

——— (1982), “The Real-Bills Doctrine Versus the
Quantity Theory: A Reconsideration,” Journal of Political
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Christ, Carl F. (1968), “A Simple Macroeconomic Model
with a Government Budget Restraint,” Journal of Political
Economy 76 (January/February): 53 – 67.

Sidrauski, Miguel (1967), “Rational Choice and Patterns
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Click, Reid W. (1998), “Seigniorage in a Cross-Section
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Smith, Bruce D. (1988), “Legal Restrictions, ‘Sunspots,’
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Correia, Isabel, and Pedro Teles (1999), “The Optimal
Inflation Tax,” Review of Economic Dynamics 2 (April):
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(Cambridge: MIT Press).

Feenstra, Robert C. (1986), “Functional Equivalence
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Journal of Monetary Economics 17 (March): 271– 91.

FEDERAL RESERVE BANK OF DALLAS

Full text of Review (Federal Reserve Bank of Dallas) : Fourth Quarter 2000

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