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Money Stock
Measurement
History, Theory
and Implications
Proceedings of the
Eighteenth Annual Economic Policy Conference o f the
Federal Reserve Bank o f St. Louis
THE
FEDERAL
J RESERVE
BANK of
A r ST.IiH LS
i
Federal R eserve Bank o f St. Louis
R e v ie w
March/April 1994
In This Issue . . .
iii
v
vii
1
Contributing Authors
President’s Message
Thomas C. Melzer
Editor's Introduction
Richard G. Anderson
A H istorical P erspective on the Federal R eserve’s M onetary A ggregates:
Definition, C onstruction and Targetin g
Richard G. Anderson and Kenneth A. Kavajecz
32
The E volution o f the F ederal R eserve’s M onetary Aggregates: A Tim eline
Kenneth A. Kavajecz
67
Commentary
Charles W. Calomiris
73
E m pirical Evidence on the Recent B eh avior and U sefuln ess of
Sim ple-Sum and W eighted M easures o f the M oney Stock
K. Alec Chrystal and Ronald MacDonald
110
Commentary
Charles R. Nelson
117
M oney D em and in a Flexible D ynam ic F o u rie r E xpenditure System
Douglas Fisher and Adrian Fleissig
129
Commentary
James L. Swofford
133
Financial F irm s’ P ro d u c tio n and Supply-Side M onetary A ggregation
U n d e r Dynam ic Uncertainty
William A. Barnett and Ge Zhou
166
Commentary
William C. Brainard
169
Response to Commentary
William A. Barnett and Ge Zhou
MARCH/APRIL 1994
175
Can the Central Bank A chieve Price Stability?
Jerome L. Stein
205
Commentary
Frederic S. Mishkin
209
A Conference P an el D iscussion
Michael J. Boskin, Philip H. Dybvig and Bennett T. McCallum
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FEDERAL RESERVE
Federal Reserve Bank of St. Louis BANK OF ST. LOUIS
iii
Contributing Authors
R ichard G. A n d e rso n
Research & Public
Information Department
Federal Reserve Bank o f St. Louis
St. Louis, MO 63102
W illiam A. Barnett
Department of Economics
Washington University
St. Louis, MO 63130
M ichael J. B osk in
American Enterprise Institute
Washington, D.C. 20036
W illiam C. B ra in ard
Department of Economics
Yale University
New Haven, CT 06520
Ch arles W. Calom iris
Department of Finance
University o f Illinois
Urbana, IL 61820-6271
K. Alec Chrystal
Centre for Banking
The City University of London
London EC2
England
P h ilip H. D y b v ig
Graduate School of Business
Washington University
St. Louis, MO 63130
D o u glas Fisher
Department of Economics
North Carolina State University
Raleigh, NC 27695-8109
Kenneth A. Kavajecz
Kellogg Graduate School of Management
Northwestern University
Evanston, IL 60201
R onald M acDonald
Department of Economics
University o f Strathclyde
Glasgow G4 OLN
Scotland
Bennett T. M cCallum
Graduate School of
Industrial Administration
Carnegie-Mellon University
Pittsburgh, PA 15213
Federic S. M ishkin
Graduate School o f Business
Columbia University
New York, NY 10027
Charles R. Nelson
Department of Economics
University of Washington
Seattle, W A 98105
Jerom e L. Stein
Department o f Economics
Brown University
Providence RI 02912
James L. S w o ffo rd
Department of Economics
and Finance
University o f South Alabama
Mobile, AL 36688
A d ria n Fleissig
Department of Economics
North Carolina State University
Raleigh, NC 27695-8109
MARCH/APRIL 1994
V
President’s Message
The Federal Reserve Bank o f St. Louis has
long emphasized the central role o f monetary
aggregates in the conduct of monetary policy.
Appropriate long-run growth of the supply of
money is essential to attaining the principal goal
of monetary policy—price stability—which, in
turn, is necessary to maximize sustainable
growth in the economy. And the monetary ag
gregates have, in fact, played important roles as
indicators of monetary policy in connection
with the actions leading to the deceleration of
U.S. inflation over the last several years.
Translating the abstract scientific concept of
"money” into a measurable empirical counter
part has often been controversial. Obviously, a
monetary aggregate must include the exchange
medium of the economy, including currency
and checkable deposits. The spending plans of
households and firms are also affected by and
reflected in the quantities of other liquid assets
that they hold. How many of these should be
included in a monetary aggregate? And, by
what criteria should they be selected?
Studies o f the measurement o f money tell us
that the answers to these questions change
through time. Financial innovation changes in
stitutional arrangements and practices, forcing
us to revise our measures o f money. In some
cases, new financial instruments such as money
market mutual funds are added to the monetary
aggregates. In other cases, increasing similarity
among financial institutions may require a
major change in the institutional coverage of
the aggregates. W e experienced both of these
phenomena in the 1970s. Technological progress
continues to cloud our measures of money by
reducing the transaction costs of quickly ex
changing one asset for another.
in the Federal Reserve Bulletin. Twenty-five
years ago, the St. Louis adjusted monetary base
first appeared in this Bank’s Review. Through
widely circulated publications such as Monetary
Trends and U.S. Financial Data, Homer Jones and
his successors have disseminated monetary ag
gregates data to a worldwide audience of
analysts and researchers.
Research at St. Louis has also examined the
policy implications of linkages between various
monetary aggregates and nominal economic
variables. This year, for example, marks the
25th anniversary of publication in the St. Louis
Fed’s Review o f Leonall Andersen and Jerry Jor
dan’s seminal research linking the growth of
nominal income to the growth o f the M l mone
tary aggregate.
Today, some suggest that the monetary ag
gregates may no longer be useful guides for
monetary policy. The weaker-than-anticipated
growth of M2 during the recent economic
recovery and expansion has brought to the fore
front once again issues regarding the measure
ment, modeling, and continued policy usefulness
of monetary aggregates. I am hopeful that the
presentations and discussions presented at this
conference will improve our understanding of
the issues involved in measuring money and the
implications of alternative measures for the con
duct of monetary policy.
Thomas C. Melzer
President and Chief Executive Officer
Federal Reserve Bank o f St. Louis
Our staff in St. Louis has contributed in a
number o f ways to the measurement o f mone
tary aggregates. Thirty-three years ago, William
Abbott's revised M l monetary aggregate appeared
MARCH/APRIL 1994
vii
Editor’s Introduction
Monetary aggregates have played a prominent
role in policy research at the Federal Reserve
Bank of St. Louis for more than 25 years. The
Bank’s 18th annual Economic Policy Conference
in October 1993 brought together a variety of
evidence on the interaction between the use of
monetary aggregates in policymaking and mea
surement o f the money stock.
The first session of the conference addressed
issues in the construction o f monetary aggregates.
Milton Friedman and Anna Schwartz have noted
that measurement of the stock of money in the
United States is an activity almost as old as the
republic itself. Their well-known histories of
these data, however, largely precede both the
first modern monetary aggregates published by
the Federal Reserve in 1960 and the aggregates
used today in macroeconomic research. In the
first paper presented at the conference, Richard
Anderson and Kenneth Kavajecz review the his
tory and construction of the Federal Reserve’s
monetary aggregates.
Following a broad introductory discussion of
definitional and statistical issues, Anderson and
Kavajecz trace the history of the Federal Reserve’s
m o n eta ry aggregates since 1943. T h e y describe
in detail the sources of data used in bu ildin g
the current aggregates, cautioning the reader
that a wide variety o f data are received and in
corporated into the aggregates throughout the
year. Because various Federal Reserve publica
tions are released at different times, observations
on a monetary aggregate in one publication may
differ significantly from observations in another.
Moreover, data in different issues of the same
publication more than a year apart may not be
comparable since the monetary aggregates are
benchmarked each year to incorporate addition
al incoming data and new seasonal adjustment
factors. The authors find that these annual
benchmarks often significantly change published
growth rates for the monetary aggregates,
although the size of the revisions is small except
for the most recent years. The authors conclude
with a summary of the Federal Reserve’s use of
monetary aggregates as monetary targets.
The article is followed by a unique timeline
compiled by Kenneth Kavajecz that traces the
history of the Federal Reserve’s monetary ag
gregates from 1960-93. The date of each change
in definition and benchmark revision is included,
as well as descriptions o f many special events
that affected the monetary aggregates. Of general
interest to all readers, the chronology will be in
valuable to researchers working with highfrequency data on the monetary aggregates.
In his commentary, Charles Calomiris proposes
a number o f reasons why empirical economists
should be concerned about the construction of
the monetary aggregates data that they use in
their research. Since tests of many hypotheses
in modern macroeconomics require long time
series of data, researchers may be at risk by
ignoring issues such as changes in sampling and
seasonal adjustment procedures used by the
data constructors. Further, the construction of
long time series is complicated by the Fed’s fre
quent retrospective revisions and redefinitions
of the monetary aggregates. Calomiris also notes
that the redefinitions discussed by Anderson
and Kavajecz call into question the usefulness of
the monetary aggregates for testing many pro
positions in macroeconomics. If the redefinitions
are motivated by a desire to make the new
aggregate better track economic activity, then
the redefined aggregates may not be suitable
for tests o f the structural stability of macroeco
nomic relationships, including money demand.
A number of economists have argued over
the last 15 years that simple-sum monetary
aggregates of the type published by the Federal
Reserve Board are not defensible in terms of
either economic aggregation or statistical index
number theory. These researchers have suggested
a number o f alternative measures of the money
stock including the Divisia monetary aggregate
MARCH/APRIL 1994
viii
proposed by Barnett and the currency-equivalent
aggregate suggested by Rotemberg. In the con
ference’s second paper on the policy implica
tions of differing measures of the money stock,
K. Alec Chrystal and Ronald MacDonald com
pare the indicator properties o f simple-sum
aggregates to those o f alternative measures of
money in seven industrialized countries.
The authors' first set o f tests is based on a
variant of the classic St. Louis reduced-form
equation for nominal output. Perhaps as might
be expected, the results show little difference
between the indicator properties of narrow
simple-sum and Divisia aggregates. For broader
aggregates, however, the Divisia aggregates are
generally found to be preferable to simple-sum
aggregates. Next, the authors conduct a series of
sophisticated multivariate causality tests based on
estimated error-correction models. These tests
also suggest that Divisia aggregates are preferred
to simple-sum aggregates, although the results
are not so strong as to find that a Divisia ag
gregate has significant indicator value when a
simple-sum aggregate does not. In a test on U.S.
data since 1980—a period of extensive financial
innovation—the authors find particularly strong
support for the superior indicator properties of
a Divisia M2 index relative to the simple-sum
M2 aggregate.
In his commentary, Charles Nelson notes that
the authors' specification of the St. Louis equa
tion for the U.S. is not comparable to that for
their other countries, with the form er better
seen as a structural demand equation and the
latter as reduced-form equations. For the U.S.,
although differences between results based on
alternative various M l and M2 aggregates may
be reasonable, he finds puzzling the sharp differ
ences among results for M l and Divisia M l and
M IA when one might have expected the three
aggregates to closely resemble each other.
Nelson also questions the authors’ causality
inferences drawn from their estimated errorcorrection models. Emphasizing that monetary
aggregates enter the error-correction models
through both the first differences of their growth
rates and the error-correction terms (which are
specified in growth rates rather than levels), he
suggests that Chrystal and MacDonald’s emphasis
solely on the significance o f the coefficients on
the first differences o f growth rates may be
misplaced. Strong significance of the errorcorrection terms in some equations suggests
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more o f a role for monetary aggregates than
the authors perhaps recognize.
The papers presented in the second session ad
dressed a pair of econometric issues in measure
ment o f monetary aggregates. Financial assets,
like other goods, are demanded by households
because they yield a flow o f services. This simple
insight suggests the potential value o f analyzing
the demand for money in the context of a multi
variate expenditure system, rather than as a sin
gle isolated demand equation. Despite its intuitive
appeal, the expenditure system approach has
had limited acceptance due to a number o f short
comings. Most prominent perhaps has been un
certainty regarding the correct functional form.
This uncertainty has led to widespread use of
flexible functional forms able to furnish (at least)
a second-order approximation to the true un
known function at (at least) one point.
The Fourier flexible functional form proposed
by Gallant solves the approximation problem by
providing an arbitrarily accurate global approxi
mation to any unknown function and its partial
derivatives. Expenditure systems based on this
functional form typically have been static, how
ever, limiting their usefulness with economic
time series data. Douglas Fisher and Adrian
Fleissig propose and compare two dynamic ex
tensions of the Fourier functional form. Their
estimates o f dynamic expenditure systems that
include monetary assets suggest that the dynamic
models are more consistent with the data than
the Fourier static model. In particular, the
dynamic models seem to provide much sharper
estimates o f the elasticities o f substitution be
tween the various types of monetary assets held
by households.
No econometric model can be all things, but
James Swofford concludes in his commentary
that Fisher and Fleissig have done a commenda
ble job of achieving the goals they set forth for
their model. Their dynamic extension of the
Fourier functional form is an important contri
bution, likely of value to many future research
ers. He notes, however, that although their
elasticity estimates are plausible, many readers
may find them difficult to interpret. The reader
who is primarily interested in understanding
household money demand may miss entirely the
importance o f estimating expenditure systems if
authors, including Fisher and Fleissig, fail to
provide a thorough discussion o f their findings.
Swofford also concludes that Fisher and Fleissig’s
ix
model fares laudably well against the very
demanding criteria proposed by Carl Christ at
last year’s St. Louis economic policy conference.
The next paper addresses the relatively new
topic of supply-side monetary aggregation. Meas
ured money stocks in most economies are pri
marily composed o f inside money or, in other
words, of the liabilities of profit-maximizing
firms. The supply-side aggregation conditions
applicable to the monetary services produced by
these liabilities differ from those more commonly
studied in the demand-side monetary aggrega
tion literature. Recognition o f the risk and un
certainty facing these intermediaries further
complicates aggregation, since existing economic
aggregation conditions and index number theory
(such as that for Divisia monetary aggregates)
have usually considered only cases of perfect
certainty. William Barnett and Ge Zhou introduce
to the literature a stochastic model of monetary
services production by banks under uncertainty.
In the model, banks are treated as neoclassical
competitive firms that maximize the present
value o f expected utility. The banks contract for
deposits and real factor inputs (labor, for exam
ple) at the beginning o f each period. During the
period, three variables—the economy’s average
price level, reserve requirement ratios for each
deposit type, and the ex post realized rate of
return on loans—are determined by random
processes not controllable by the firm. The em
pirical results support the hypothesis that the
banks' deposit liabilities are weakly separable
from purchased real factor inputs such as labor.
A comparison o f the Divisia, simple-sum, and
currency-equivalent monetary aggregates to the
model’s estimated exact monetary aggregate sug
gests that the ability o f the Divisia index to
track the exact aggregate is little diminished un
der uncertainty. This conclusion is invariant to
whether the exact aggregate is constructed
from model estimates based on alternative as
sumptions of risk neutrality and risk aversion.
In his commentary, William Brainard notes
the increasing importance o f studies of the sup
ply of monetary assets. Unlike simpler times,
when the money stock could be well measured
by summing currency and demand deposits, to
day’s relatively low costs of substituting among
a wide variety of financial assets makes less cer
tain both the measurement and control of
monetary aggregates. Brainard notes, however,
that the dynamic structure of the model may
not be as rich as the authors suggest. In partic
ular, the period-by-period balance sheet con
straint imposed by Barnett and Zhou as equation
2 prevents the model firm from carrying re
tained earnings (or losses) forward. Each period,
the firm’s available resources include only the
deposits and real inputs contracted for at the
beginning o f that period plus a fixed amount of
capital; in turn, all earnings must be paid out to
the owners o f the firm at the end of the period
since the balance sheet constraint prevents any
from being carried forward into the next. He
suggests that the apparent dynamic structure of
the profit function in their equation 3 arises be
cause Hancock’s profit function, equation 1 in
Barnett and Zhou, differs from the cash flow
that the firm will in fact receive in each period,
conditional on its decisions and the stochastic
nature o f the economy. This reservation aside,
the richness o f Barnett and Zhou’s paper is
reflected in the numerous extensions proposed
by Brainard for future researchers.
In a response to Brainard, Barnett and Zhou
present additional results clarifying the dynam
ics of their model. The model requires some
type of temporal separability restriction on
either the discounted profit stream or the inter
temporal utility function to avoid the intractable
problem of estimating a system of simultaneous
Euler equations. The formulation employed by
Barnett in previous work, and preferred by
Brainard, appears as but one o f a number of al
ternative separability hypotheses. The relative
plausibility o f the hypotheses remains a subject
for further empirical research.
Papers at the conference’s final session once
again turned to the implications of alternative
measures o f the money stock for the conduct of
monetary policy. Monetary policymakers often
rank price stability first among their goals. Dur
ing the 1970s, central banks worldwide adopted
growth targets for monetary aggregates that
they hoped would guide them toward price sta
bility. In many countries, however, initial opti
mism became disappointment as Goodhart’s law—
that the behavior of a monetary aggregate will
change when the central bank targets its growth
—seemed to prevail. Jerome Stein studies
whether Goodhart’s law has applied with equal
force in the United States to all measures of the
money stock. Working with the dynamic model
he developed with Infante in the 1980s, Stein
demonstrates that the short-run stability o f the
linkage between inflation and money growth is
MARCH/APRIL 1994
X
apparent only when the model includes a varia
ble representing the state of the economy,
measured in his model by the difference be
tween the current and long-run equilibrium un
employment rates. In that case, the growth of
M2 arises as a good indicator of movements in
both inflation and unemployment. Further, M2’s
indicator properties appear superior to those of
statistical index number monetary aggregates,
including Divisia M2, the currency-equivalent
aggregate CE, and a Divisia CE aggregate.
Regardless of its indicator value, a monetary ag
gregate must be controllable before it can be
chosen as a policy target. Stein concludes that
none of the broad monetary aggregates are
sufficiently controllable to be used as targets.
He finds, however, that adjusted bank reserves
appear to be an acceptable target for control of
the inflation rate.
Although monetary aggregates may be valua
ble indicators of the stance of monetary policy,
they are not necessary for central banks to
achieve price stability. Agreeing with Stein that
the long-run inflation rate is largely determined
by growth o f the money stock, Frederic Mishkin
notes that Federal Reserve policy has supported
a relatively low, steady inflation rate during the
last decade without strict adherence to any
monetary target. He suggests that the highly dy
namic nature of Stein’s model might help ex
plain the relatively poor showing of M2 per se
as an indicator for individual variables such as
inflation and real output while being a valuable
indicator for nominal GDP. Since real output
growth accelerates more quickly following a
monetary shock than inflation and later tends to
slow while inflation accelerates, cyclical move
ments in M2 may be more closely correlated
with both short- and long-run movements in
nominal GDP than with either inflation or real
output separately. At the same time, Mishkin
finds troubling the poor fit of the model to
quarterly data which may indicate that Stein’s
empirical surrogate model is not capturing well
the dynamic interactions prominent in the SM
theoretical model. Also puzzling are the very
different conclusions reached by Stein and by
Chrystal and MacDonald regarding the relative
indicator properties of simple-sum and Divisia
M2. Finally, Mishkin emphasizes that the omis
sion o f rational expectations from Stein’s model
prevents him from analyzing the importance of
credibility in policymaking. Announced targets
for monetary aggregates might help prevent
sharp jumps in inflationary expectations by sig
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nalling the public that the central bank is serious
about achieving its inflation targets. In this
event, monetary aggregate targets might help
the central bank stabilize the inflation rate even
when measurement of the monetary aggregate
is uncertain or monetary aggregates are not
highly controllable.
The conference concluded with a panel dis
cussion o f the role of monetary aggregates in
feedback rules for the conduct of monetary
policy. Monetary aggregates have historically
been constructed to guide monetary policy. The
introduction of rational expectations into macroeconomic models emphasized that the feedback
rules by which policymakers adjust growth of
monetary aggregates are an important part of
the structure o f the economy.
In the panel discussion, Michael Boskin sug
gests that Federal Reserve actions under Alan
Greenspan, and to some lesser extent under
Paul Volcker, should be viewed as a rules-based
policy. He sees the Fed as setting out a strategy
whereby its actions in most periods are
governed by pursuit of its goal of long-run price
stability, rather than by a feedback rule based
on a monetary aggregate. Temporary deviations
from pursuit o f the goal are permitted for ex
igencies that are well understood by the public.
Further, in his view, the Federal Reserve will
never find satisfactory any policy rule that in
cludes only a small set of monetary aggregates
or similar indicacor variables.
Behavioral rules arise naturally as solutions in
decision-theoretic models. Could a monetary
policy rule based on monetary aggregates arise
as the solution to a decision problem? The se
cond panelist, Philip Dybvig, proposes a com
plete prototypical decision framework for the
Fed, including an objective function, control
variables, constraints and a well-defined infor
mation set. Although too much of the structure
remains unknown to obtain explicit solutions,
he concludes that future research on the value
of monetary policy rules and the role of mone
tary aggregates might usefully be guided by
such a framework.
Some researchers have argued that monetary
aggregates have little value as either policy tar
gets or indicators. If so, discussion of their
measurement seems vacuous. The third panelist,
Bennett McCallum, concludes the conference by
suggesting that monetary aggregates are indeed
irrelevant to the conduct of monetary policy. In
xi
his framework, the central bank’s main job is to
keep nominal GDP growing smoothly at a noninflationary rate. Even when the penultimate goal
is price stability rather than stable growth of
nominal output, he argues that we know much
better what growth rate for nominal GDP is likely
to be consistent with long-run price stability
than we do the appropriate long-run growth
rates for M l or M2. McCallum’s research sug
gests that directly targeting the growth of nomi
nal GDP through control of the monetary base
is preferable to targeting any monetary ag
gregate, no matter how measured.
Richard G. Anderson
St. Louis, Missouri
April 8, 1994
MARCH/APRIL 1994
1
Richard G. Anderson and Kenneth A. Kavajecz,
Richard G. Anderson is a research officer at the Federal
Reserve Bank of St. Louis. Kenneth A. Kavajecz is a Ph.D.
candidate in finance at Northwestern University. An earlier
version of this paper was completed while the authors were in
the Division of Monetary Affairs at the Federal Reserve Board.
We wish to thank numerous former colleagues at the Board for
their generous assistance and access to their unpublished
writings, without which this study would not have been
possible, including Sean Collins, Dennis Farley, David Lindsey,
Leigh Ribble and Jack Walton. We thank Richard Kopcke for
stressing the importance of regarding changes in Regulation Q
as equivalent to redefinitions of the monetary aggregates. We
also thank Heather Deaton and Christoph Hinkelmann for
research assistance.
A Historical Perspective on the
Federal Reserve’s Monetary
Aggregates: Definition,
Construction and Targeting
"...the Federal Reserve should use as an intermediate target that monetary total (aggregate), or those to
tals, through which it can most reliably affect the behavior o f its ultimate objectives — the price level,
employment, output, and the like. Which total or totals best satisfy that requirement depends in turn on
(1) how accurately the total can be measured; and (2) how precisely, and at what costs including unwant
ed side effects, the Fed can control the total; and (3) how closely and reliably changes in the total are
related to the ultimate policy objectives.
“In general, though by no means uniformly, the broader the concept, the greater the problems o f
measurement and control."
Improving the Monetary Aggregates (Report of the Advisory
Committee on Monetary Statistics), 1976, p. 7.
D
TA ON THE MONETARY AGGREGATES
A
are the fundamental raw material of research in
many facets of economics and finance. Money
demand modelling, measurement o f money
stock announcement effects, tests of the ration
ality of preliminary money stock forecasts and
financial market efficiency, and comparison of
alternative seasonal adjustment procedures are
just a few such areas. Monetary aggregates also
are used by Federal Reserve System staff in for
mulating policy alternatives for the Federal
Open Market Committee (FOMC). Perhaps no
government data are more important or more
widely used in economic and financial research
MARCH/APRIL 1994
2
than the monetary aggregates. Often unap
preciated by researchers, however, is the extent
to which the appropriate use of monetary ag
gregates data is intimately connected with
changes through time in the data's definitions,
construction, revision and publication. A failure
to appreciate the interdependence of time, data,
definitions and procedures may adversely affect
or vitiate research and policy conclusions.
This paper discusses the construction, publica
tion and evolution of monetary aggregates data
since the inception o f the Federal Reserve Sys
tem in 1914. In opening their seminal volume on
U.S. monetary data, Friedman and Schwartz
(1970) set a similar objective:
This book attempts to provide a comprehensive
survey o f the construction o f estimates o f the
quantity o f money in the United States — an ac
tivity that dates back almost to the beginnings of
the Republic. The survey covers sources, methods
o f construction, and the end product, (p. 1)
Friedman and Schwartz present a consistent
time series of monetary aggregates based on
their own data for 1867-1946 and Federal
Reserve data through the mid-1960s. This paper
and the companion timeline (Kavajecz, 1994)
extend Friedman and Schwartz by reviewing the
construction and publication of the Federal
Reserve’s monetary aggregates from 1960
through 1993. We focus on the years since 1960,
the period for which the Federal Reserve Board
staff currently publishes official monetary ag
gregates. The interested reader will find few (if
any) available descriptions o f the Federal
Reserve’s monetary aggregates comparable to
Friedman and Schwartz’s narrative.
The evolution of the monetary aggregates as
economic statistics has been influenced by both
economic thought and statistical practice.1 Struc
tural change in financial markets and the in
troduction of new financial instruments require
periodic redefinition of the monetary aggregates
to accurately reflect the portfolio choices availa
ble to households and firms. Never defined nor
constructed in the abstract, however, monetary
aggregates exist largely as indicators and/or tar
gets of monetary policy. Thus, to an unknown
but perhaps considerable extent, selection of the
1We do not discuss in this paper the work on aggregation
theory and related monetary aggregates such as the
Divisia and MQ aggregates. These were consistently
labelled by Board staff as experimental and not adopted for
policy analysis. The interested reader is referred to Barnett
(1980) and Spindt (1985).
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definitions of the monetary aggregates has been
based on the relative ability o f alternate ag
gregates to predict economic activity. Prior to
1980, commercial banks furnished most transac
tion deposits and their nontransaction deposits
seemed to be the closest substitutes for money.
In turn, the Federal Reserve’s monetary ag
gregates emphasized both the distinctions
between types o f deposits and between commer
cial banks and thrift institutions. The narrower
M l and M2 aggregates first published in 1971,
for example, included only deposits at banks,
while thrifts were included in M3. These distinc
tions were preserved in 1975 when M3 was re
vised and M4 and M5 were introduced.
Perceived breakdowns in the historical rela
tionship between a monetary aggregate and eco
nomic activity, reflected, say, in a putative
permanent shift in its velocity, may lead to calls
for redefinition o f the aggregate. Such pressures
on M l and M2 (as initially defined in 1971) were
apparent throughout the 1970s. Reinforced by
accelerations in inflation and a shift by some
macroeconomists toward increased emphasis on
the monetary aggregates, these pressures led in
early 1974 to the appointment of the Advisory
Committee on Monetary Statistics, chaired by
professor George Bach o f Stanford. By 1980,
the Depository Institution Deregulation and
Monetary Control Act (DIDMCA) permitted a
redefined set of monetary aggregates to be con
structed from a greatly expanded, much richer
and much more costly flow of data than had
ever previously been available. The new ag
gregates also seemed to have more stable re
lationships to economic activity. Published
analyses at the time o f the 1980 redefinition cit
ed with approval the lack of trend in the veloci
ty of the new M2 relative to the old measure,
although they stopped short of proposing a less
variable long-run velocity as a choice criterion.2
Although such pragmatic redefinition seems
clearly to be in the spirit of Friedman and
Schwartz3 it may account for at least some part
,
of the ex post stationarity of the GNP velocity of
M2 (as currently defined) identified by Hallman,
Porter and Small (1991).
The ideal monetary aggregate would be com
posed o f assets that are capital-certain (or
2Simpson (1979, 1980). Other descriptions of the construc
tion of the Federal Reserve’s monetary aggregates include
Broaddus (1975), Duprey (1982), Lawler (1977) and Walter
(1989).
3See especially chapter 4.
3
nearly so), highly liquid and closely related to
economic activity. Narrow monetary aggregates
composed primarily o f medium of exchange seem
to satisfy at least the first two criteria acceptably
well, while broader aggregates do so somewhat
less well. Broader aggregates often include assets
that are capital-uncertain or, in other words, as
sets whose market values vary with market in
terest rates, the pace o f economic activity, or
expectations of such variables. Broad monetary
aggregates are uniformly defined to include the
nominal (face) value of capital-uncertain assets
rather than the market value, however. Small
time deposits included in the non-Ml compo
nent of M2, for example, may be taken to be
capital-uncertain when there are penalties for
withdrawal before maturity.4 Money market
mutual fund (MMMF) shares, also included in
the non-Ml component o f M2, appear capitalcertain to their holders even though the market
value o f the funds’ assets varies inversely with
market interest rates. So long as the MMMFs
satisfy a variety of Securities and Exchange
Commission rules (including restrictions on the
maturity of the funds’ assets) and short-term
market interest rates don’t move too rapidly the
funds need not pass through changes in the
market value of their assets to shareholders.
The market values of money market instruments
included in very broad aggregates such as M3
and (the seldom used) L vary considerably more,
however. Such instruments include negotiable
large time deposits included in the non-M2 com
ponent o f M3, and most items included in the
non-M3 component of L. Monetary aggregates
defined to include the nominal rather than mar
ket value of these assets necessarily omit some
actual portfolio constraints faced by firms and
households, who must necessarily substitute
among financial assets at market rather than
nominal values. Including these assets in mone
tary aggregates at market values, however, would
cause the measured size of the aggregate to vary
with market rates. This might reduce the useful
ness of the aggregate as an indicator of the im
pact of policy actions. A policy action that
reduced reserve availability could reduce not
only the quantity of money demanded as mar
4Under Regulation Q, depositories were required to impose
early withdrawal penalties. Many institutions have chosen
to continue such penalties even in the absence of Regula
tion Q. On the demise of Regulation Q, see Gilbert (1986).
The liquidity of time deposits has varied through time. Pri
or to Reg Q, some time deposits were indistinguishable
from modern savings and transaction deposits; see Fried
man and Schwartz (1970), p. 76-7.
ket interest rates increased, but also the appar
ent quantity "supplied” as prices of the included
money market instruments fell. The indicator
properties o f movements in such capital-uncertain
monetary aggregates for economic activity have
not been established.5
The statistical issues in building monetary ag
gregates also are formidable. If cost were no ob
ject, an ideal monetary aggregate would be built
from daily observations on all its components at
all financial intermediaries. In fact, cost/benefit
tradeoffs figure prominently in both data collec
tion and the definition of the aggregates. The
Congress has mandated that a cost/benefit analy
sis be part of each application for renewal of
major deposit reports, typically required every
three years. Reporting burden is generally to be
kept as low as possible while obtaining adequate
data for the conduct o f monetary policy. This
position has led to deposit reporting strategies
based on survey sampling wherein deposit
coverage and reporting frequency vary by size
o f institution.
Most of these issues have largely been omitted
from the literature on money demand. As fine a
work as Laidler’s (1993) classic text on money
demand fails to discuss the definition, construc
tion or revision of monetary aggregates, except
to acknowledge Friedman and Schwartz’s re
search. Nowhere is the reader warned of the
potential pitfalls in monetary aggregates data
awaiting the unwary. This problem arises largely
from the difficulty and high cost to researchers
of locating relevant institutional details. This
paper attempts to reduce that cost.
SOURCES OF MONETARY
AGGREGATES DATA
Throughout U.S. history, every definition of
money has been composed primarily of the lia
bilities of private financial institutions, both
notes and deposits. During most periods, these
financial institutions have been subject to
government regulation. In turn, the primary
sources of current and historical monetary ag
gregates data are government reports filed by
these financial institutions.
5The difficulties of interpreting monetary aggregates that in
clude capital-uncertain instruments are prominent in
proposals to include bond and equity mutual funds in a
redefined M2. See, for example, Collins and Edwards
(1994) and Orphanides, Reid and Small (1993).
MARCH/APRIL 1994
4
The Federal Reserve's first published monetary
aggregate appeared in 1943 in Table 9 of Bank
ing and Monetary Statistics. The table showed
currency demand deposits and time deposits for
June call dates from 1892 to 1922 and for June
and December call dates from 1923-41. The sum
of currency and demand deposits was defined
as "the supply o f money” or "means of pay
ment" although it was noted that time deposits
often were used for current payments "...during
the 1920s.” Subsequent data were published in
the Federal Reserve Bulletin.6 Later, Copeland and
Brill (1948) presented a series based on the lastday-of-the-month consolidated condition state
ment of the banking system. In 1949, the Board
began monthly publication of this series.
The first modern monetary aggregate based
on averages of daily data, labelled M l, was con
structed by William Abbott and Marie Wahlig of
the Federal Reserve Bank o f St. Louis and ap
peared in the Federal Reserve Bulletin in 1960
(Abbot, 1960); a revision was published in 1962
(Abbot, 1962). Building monetary aggregates
from daily data is important because seasonal
patterns within a month may cause data for in
dividual days to be unrepresentative of both the
month’s average level and the aggregate’s trend
growth rate. Abbott and Wahlig’s data, which
began in 1947, reflected available deposit reports
and were shown at half-monthly and monthly
frequencies. Member banks had begun report
ing in 1944 averages of daily data at the middle
and end of each month. Data for nonmember
banks and mutual savings banks (MSBs) were es
timated from Federal Deposit Insurance Corpo
ration (FDIC) call reports, although the precise
interpolation method is not stated.
Monetary aggregates data subsequently were
published on the Board’s statistical release,
known as the J.3 and entitled Demand Deposits,
Currency, and Related Items, twice a month from
November 1960 through July 1965. The release
included averages of daily data at half-monthly
and monthly frequencies, seasonally adjusted,
and at weekly, half-monthly and monthly fre
quencies, not seasonally adjusted.7 The most re
cent data included on the release predated the
publication date by two weeks.
6For details, see the introductory notes to section 1 in Bank
ing and Monetary Statistics and the notes to chapters 1-4 in
Banking and Monetary Statistics 1941-1970.
7Member banks began reporting daily data each week in
December 1959. For years after 1959, the weekly data
were prorated to obtain monthly and half-monthly
frequencies.
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
The J.3 was succeeded by the current release,
known as the H.6 and entitled Money Stock,
Liquid Assets, and Debt Measures, on July 30,
1965. It shows averages of daily figures at week
ly and monthly frequencies. A revised monetary
aggregates series based on weekly averages of
daily data beginning in 1959 was later presented
by Fry, Beck and Weaver (1970).8 The current
definitions o f the monetary aggregates were
largely established in 1980; see Kavajecz (1994)
and Simpson (1979, 1980). At the time of the
redefinition, monetary aggregates based on the
new definitions were constructed back to 1959.
Details o f their construction are discussed in the
appendix.
For researchers, monetary data extracted from
individual issues of the J.3 and H.6 releases pro
vide contemporaneous estimates of the mone
tary aggregates based on a well-defined infor
mation set: the data available to Board staff as
of the publication date. These statistical releases
allow a researcher interested in announcement
effects or the policy formation process o f the
FOMC to observe Federal Reserve Board staff es
timates o f the level o f the money stock at each
point in time, or permit a researcher interested
in market efficiency or the “rationality” o f initial
money stock estimates to study the timing and
extent o f revisions to initially published data.
The statistical releases are not very useful for
longer-run studies, however, because the infor
mation set underlying the release changes each
week as Board staff receives both new data and
revisions to previously reported data. Further,
the definitions of the monetary aggregates have
changed through time.
While the Federal Reserve Board has published
a number of historical volumes, each with unique
features making it a valuable source of data, use
of these data also is complicated by varying defi
nitions and observational frequencies. Ideal his
torical data would be computed at similar frequen
cies under consistent definitions. The two most
comprehensive volumes, Banking and Monetary
Statistics and Banking and Monetary Statistics
1941-1970, were published by the Federal
Reserve in November 1943 and September 1976,
8Some independent researchers have attempted to build
monetary aggregates data for earlier periods using current
definitions. For a careful discussion of the issues, see
Rasche (1987, 1990).
5
respectively.9 Observational frequency differs
across data series, with various data at monthly,
weekly or daily frequencies. There are also im
portant conceptual distinctions through time in
the data, such as the difference between mem
ber and nonmember banks and the difference
between thrifts and commercial banks. When
using data from other sources in conjunction
with the Banking and Monetary Statistics
volumes, researchers should appreciate that data
published subsequently are not strictly compara
ble, since more recent publications incorporate
further revisions to the data.
A closely related publication, and the yearly
counterpart to the Banking and Monetary Statistics
volumes, is the Annual Statistical Digest. The
Digest is released at the end o f each year and
contains data for the previous year. The Board’s
Annual Report also contains information about
the monetary aggregates, but the information
tends to be more descriptive than numerical.
These publications provide a long-run, consis
tent perspective o f the monetary aggregates
over their respective published date ranges,
since within each issue of each publication the
observations are based on a single, consistent in
formation set. They perhaps are less appropri
ate, however, for lines of research where the
hypotheses depend on the information set
used in constructing the money stock estimate,
since the date the estimate was formulated is
not explicitly given.
Similar concerns suggest that data sets con
structed from various issues of the Federal
Reserve Bulletin may not be suitable for a variety
of research. Board staff have published compo
nents of the monetary aggregates, such as de
mand deposits and currency, in the Bulletin
since its inception in May 1915. In February
1944, the staff first showed demand deposits
and currency in the same table, foreshadowing
the later M l monetary aggregate. While the
Bulletin’s current T&ble 1.10 (first published in its
present form in January 1977) descends from
the 1944 table, the data published in this table
through the years are not a consistent time ser
ies due to definition changes, reporting changes,
9The 1943 edition of Banking and Monetary Statistics was
reprinted in August 1976. See also the Board’s corrected
1959 reprint of All-Bank Statistics.
,0The title of this publication has changed somewhat through
time. It currently is produced by the Money and Reserves
Projections Section of the Division of Monetary Affairs. Pri
or to 1988, it was produced by the Banking Section of the
Division of Research and Statistics. Prior to 1993, the print
ed publication was offered to the public as a supplement
annual benchmark revisions, and reestimation of
seasonal adjustment factors. At the same time,
the Bulletin is an excellent resource for tracking
the various changes that have occurred in the
definitions and construction of the monetary ag
gregates through time. Due to its somewhat
longer time span, data extracted from various is
sues of the Bulletin illustrate how the monetary
aggregates have evolved; occasional articles have
presented detailed information on changes in
the monetary aggregates. Unfortunately, like
many other Federal Reserve historical publica
tions, the Bulletin does not specify the date at
which the estimates were made, that is, the
time-indexed information set on which they
were based. In general, data in the Bulletin pre
cede by two months the Bulletin’s publication
date, but at times it has been longer. Since
monetary aggregates data appear with differing
lags in various System publications (for example,
10 days on the H.6), data from different sources
may be based on quite different information
sets even when the dates that they first appear
in print are close together. This suggests that, in
general, a database built from one Federal
Reserve source or publication should not be up
dated from another.
Finally, a publication that presents compre
hensive, consistent time series is Money Stock
Revisions. 0 This publication is offered to the
1
public early in each year as a supplement to the
issue of the H.6 release that incorporates the
Board staff’s annual benchmark revisions, in
cluding reestimated seasonal adjustment factors.
The publication presents a comprehensive set of
monetary aggregates data, beginning in 1959 for
monthly data and in about 1975 for weekly
data.1 Unlike other Board staff publications, the
1
information set and definitions used in con
structing the data are well-defined, making the
data ideal for longer-run studies. Note, however,
that since each year’s publication uses that
year's current definitions — and the definitions
of the monetary aggregates and their compo
nents have changed through time — the data
may differ significantly from previously pub
lished data.
to the issue of the H.6 release that contained the newly
benchmarked monetary aggregates data; data in machine
readable form were sold by the National Technical Informa
tion Service of Springfield, Virginia. In 1993, the publica
tion and associated data were first offered for sale by
Publications Services at the Board of Governors.
"Subject to the availability of the particular series. See Table
2 for the availability of specific series.
MARCH/APRIL 1994
6
DATA COLLECTION
The data collection process is the foundation
of the construction of monetary aggregates data.
The collection o f data useful for the monetary
aggregates has changed (and improved) dramati
cally during the last eight decades. We present
here a brief outline of the principal data inflows
to the Federal Reserve during a small number of
distinct periods over which data collection and
publication practices differed significantly.
1915-43
The data collected during this period have
been extensively documented by Friedman and
Schwartz (1970), chapters 12-15. Beginning in
1923, data for all member banks are available.
From April 1923-December 1928, the Federal
Reserve collected and published deposits as o f a
single day each month; from January 1929March 1944, monthly averages of daily data; af
ter March 1944, averages o f daily data were col
lected twice a month. Data also continued to be
reported each week on Wednesday by a sample
of several hundred weekly reporting banks that
held a majority of bank deposits. Data for non
member banks and for MSBs were available on
call reports.
1944-80
Averages of daily member bank deposit data
were collected twice a month through Decem
ber 1, 1959, when weekly averages began to
be collected. Regular publication beginning
in November 1960 of monthly money stock
figures on the J.3 release necessitated estimates
o f the monetary liabilities o f nonmember banks.
Nonmember bank data continued to be collected
on call reports, typically two per year until
1960, when thereafter four per year were
required.
1980-Present
Perhaps the least appreciated aspect of the
Monetary Control Act of 1980 was a significant
12ln particular, thrift institutions and nonmember banks be
gan reporting deposits weekly to the Federal Reserve.
13A zero reserve requirement ratio applies to the reserve ex
emption amount of deposits. The reserve exemption
amount is not to be confused with the low reserve tranche.
The tranche allows a lower 3 percent reserve requirement
ratio to be applied to some portion of deposits, while a
higher ratio (currently 10 percent) applies to the balance.
Both the reserve exemption amount and the low reserve
tranche are indexed. For 1993, the reserve exemption and
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
improvement in the quantity and quality of
data flowing to the Federal Reserve. A water
shed in data collection, the act empowered
the Federal Reserve System to impose reporting
requirements on all depository institutions
with reservable liabilities above a prescribed
minimal amount. The act significantly eased
estimation of the money stock, as deposit re
porting by financial institutions became nearly
universal and was no longer a function of mem
bership status or charter type.1 'IWo years later,
2
in the Garn-St. Germain Act, Congress mandated
that the Federal Reserve establish guidelines
to ease reporting burden borne by financial in
stitutions while maintaining adequate coverage
o f the outstanding monetary liabilities o f the
banking system. In response, a system o f report
ing categories was established wherein the
reporting burden — measured by frequency of
reporting and number of items reported —
depends upon both total deposits and reservable
liabilities.
Under this system, the Federal Reserve Board
staff each year establishes a cutoff level o f total
deposits and an exemption level o f reservable
liabilities. Increases in both levels are indexed
to the year-over-year increase in aggregate
deposits at all depository institutions as calculat
ed from second quarter (June 30th) call
reports.1 Tible 1 summarizes the System’s
3
reporting categories and the type/frequency of
report submitted by financial institutions in
each category for 1992, 1993 and 1994.1 The
4
deposit cutoff and reserve exemption levels were
established at $25.0 and $2.4 million, respective
ly, beginning January 1985. These have subse
quently been indexed each year, based on 80
percent of the growth in aggregate deposits,
except in 1988. In that year, Board staff research
suggested that little accuracy would be sacrificed,
and a significant reporting burden reduced for
smaller institutions, by increasing the deposit
cutoff more rapidly. The deposit cutoff, which
had automatically increased in January to $30
million from the previous year’s $28.6 million,
low reserve tranche amounts are $3.8 and $46.8 million,
respectively. For 1994, the amounts are $4.0 and $51.9 mil
lion, respectively.
' “Values for each year are typically published in the respec
tive January issues of Federal Reserve Bulletin. Values for
1992, 1993 and 1994, for example, appear on pp. 36-7, 18
and 23-4 of the January 1992, 1993 and 1994 issues,
respectively.
7
Table 1
Depository Institution Reporting Categories 1992-94
by Deposit Cutoff and Reserve Exemption Amount
Reserve Exemption Amount
reservable liabilities
Deposit Cutoff
total deposits
if more than
$3.6
($3.8)
[$4.0]
if less than
$3.6
($3.8)
[$4.0]
if more than
$44.8
($44.8)
[$44.8]
the institution must file the
FR2900 report weekly
the institution must file the
FR2910Q report quarterly
if less than
$44.8
($44.8)
[$44.8]
effective
as of January
1992
(1993)
[1994]
the institution must file the
FR2900 report quarterly
the institution might be
exempt from reporting
Note: All figures are in millions of dollars.
was raised in September to $40.0 million. Sever
al thousand smaller banks were exempted from
weekly reporting by this change.
ed), or, including nondeposit liabilities, about 80
percent o f the aggregate liabilities o f financial
institutions included in the monetary aggregates.
Institutions that file the FR2900 at a weekly
frequency (Table 1, the upper left-hand box)
report daily levels for about a dozen deposit and
nondeposit liabilities. Institutions falling in the
other boxes have a sharply reduced reporting
burden. Institutions that file the FR2900 at a
quarterly frequency (the lower left-hand box) re
port the same items but only for a single week
each quarter (the week that contains the third
Thursday in the last month of the quarter). Insti
tutions that file the FR2910Q (upper right-hand
box) report weekly average data on fewer items
for one week each quarter. Institutions in the
lower right-hand box of 'Fable 1 are exempt from
filing reports with the Federal Reserve if and only
if Federal Reserve staff are able to accurately
obtain required data from other sources, such as
call reports.1 For institutions other than weekly
5
reporters (all categories except those in the up
per left-hand box), Federal Reserve Board staff
must estimate their deposits during the periods
between reports. In 1992, daily data were re
ceived each week from approximately 9,100
financial institutions, about 30 percent of all
depositories. These data comprised about 90 per
cent o f the aggregate deposits included in the
monetary aggregates (the balance being estimat
Construction of weekly values of broad mone
tary aggregates such as M2 and M3 also relies
on a variety o f weekly reports o f data for non
deposit liabilities such as repurchase agreements
(RPs), Eurodollar deposits, and reports from non
bank financial institutions such as MMMFs. The
numerous sources and reports used by Board
staff in the construction of the monetary ag
gregates are shown in Table 2. In general,
broader aggregates such as M2 and M3 are less
precisely measured than M l because a larger
proportion o f the data included in the aggregate
is either not reported directly to the Federal
Reserve, and/or is reported less frequently than
the data included in M l. In addition, a larger
number of various nonmoney stock items are
netted out of the broader aggregates.
In the non-Ml components of M2 and M3,
MMMF shares have been among the more com
plex items. A dynamic industry characterized by
rapid growth, new funds have frequently ap
peared and old ones vanished. In addition,
funds may merge, change names or change in
vestment objective by, say, lengthening the
maturity of their assets to become a short-term
bond fund. All these events complicate accurate
15lf not, the institution is required to file an annual report.
MARCH/APRIL 1994
FEDERAL RESERVE
Table 2
Information about the Definition, Availability and Source Data for the Monetary Aggregates________________
BANK O ST. LOUIS
F
This table provides information on the construction of the monetary aggregates M1, M2, M3 and L as of October 1993. Readers are cautioned that some definitions and
data sources may differ in earlier periods. Each aggregate reflects the amounts of the designated assets held by the nonbank public, which includes households, business
es and government entities other than the U.S. Treasury. Assets issued in the U.S. are included whether they are held by foreign or domestic residents. Certain dollardenominated assets issued abroad and held by U.S. residents also are included. The aggregates are constructed by consolidation rather than aggregation, such that the
liabilities of one money stock issuer that are held by another issuer within the same aggregate cancel each other. For example, the amount of large time deposits held by
money market mutual funds is subtracted from gross large time deposits in building M3, because these deposits are both a liability of one money stock issuer (banks) and
an asset of another (money market mutual funds).
Monetary aggregates published by the staff of the Board of Governors as of October 1993 were:
M1
M2
M3
L
=
=
=
=
currency + checkable deposits;
M1 + certain nontransaction deposits and other liquid assets;
M2 + certain assets that are either less liquid and/or issued in large denominations; and
M3 + certain money market instruments.
Federal Reserve System reports are referred to below by the prefix FR and reports of the interagency Federal Financial Institutions Examination Council by the prefix FFIEC. Call
reports are administered by the FFIEC, a joint agency including the Federal Reserve, the Federal Deposit Insurance Corporation (FDIC), the Treasury Department and the
National Credit Union Administration (NCUA). Complete report titles and reporting frequency are shown only the first time a report is cited; references thereafter are
abbreviated.
NSA published data begin
Money Stock Component
M1 =
( + ) Money stock currency =
Currency held by the nonbank
public (in other words, held out
side the U.S. Treasury, Federal
Reserve Banks and the vaults of
depository institutions).
monthly
weekly
1/59
Definition
1/6/75
1/59
Source of Information
1/6/75
Federal Reserve Board staff have judged that adequate data are not
available before these dates to construct monetary aggregates based
on current definitions.
( + ) Currency in circulation
Currency held outside the U.S.
Treasury and Federal Reserve
Banks.
Federal Reserve Statement of Condition (internal Fed balance sheet)
(FR34), daily; Treasury and Mint Reports on currency and coin in
circulation.
( - ) Vault cash
Cash held by depository institu
tions (including cash in automatic
teller machines).
Report of Transaction Accounts, Other Deposits and Vault Cash
(FR2900), from weekly and quarterly reporters; Quarterly Report of
Selected Deposits, Vault Cash and Reservable Liabilities (FR2910Q);
Annual Report of Total Deposits and Reservable Liabilities
(FR2910A); Consolidated Reports of Condition and Income (call
reports) (FFIEC 031, 032, 033, 034), quarterly, last business day of
the quarter. The FR2900 is the core report for the monetary ag
gregates. More than 9,000 financial institutions file the FR2900
report weekly following their Monday close of business, each report
containing daily deposit data for the preceeding week. Some smaller
institutions file the FR2900 report only for one week each quarter.
See the text for discussion.
co
■■■■
NSA published data begin
Money Stock Component
monthly
weekly
( + ) Travelers checks
Outstanding amount of U.S.
dollar-denominated travelers
checks issued by nonbanks
(checks issued by banks are in
cluded in demand deposits).
1/59
1/6/75
( + ) Demand deposits adj usted =
Demand deposits at all depository
institutions in the U.S. other than
those due to other depositories
(including money market mutual
funds [MMMFs]), the U.S.
government, and foreign banks
and official institutions, less cash
items in the process of collection
(CIPC) and Federal Reserve float.
1/59
1/6/75
( + ) Gross demand deposits
Definition
Source of Information
Monthly Report of Travelers Checks Outstanding (FR2054), last
business day of the month; weekly data are interpolated from
seasonally adjusted monthly data.
FR2900; FR2910Q/A; call reports
Deposit liabilities of banks payable
on demand; time deposits with
original maturity of less than
seven days; travelers checks and
money orders that are the primary
obligation of the issuing deposi
tory institution.
( - ) Demand deposits due to
depository institutions, for
eign banks and official insti
tutions, and the U.S. Treasury
Weekly Report of Assets and Liabilities for Large Banks (FR2416),
includes about 160 large banks, weekly, close of business Wed
nesday; call reports for other depositories, quarterly, last business
day of quarter.
( + ) Other money orders
Money orders and official checks
issued by nonbank subsidiaries
or bank holding companies.
Weekly Report of Money Orders and Similar Payments Instruments
issued by Nonbank Subsidiaries of Bank Holding Companies
(FR2053), close of business Monday.
( - ) Cash items in process of
collection
Third-party payment instruments
(checks) redeemable in immedi
ately available funds if presented
today.
Same as gross demand deposits; all checks being collected are
deducted from demand deposits regardless of the type of account
wherein the deposit was made.
FR34
( - ) Float on the Federal
Reserve
( + ) Other checkable deposits
MARCH/APRIL 1994
NOW and automatic transfer
service (ATS) accounts at com
mercial banks, U.S. branches and
agencies of foreign banks, and
Edge Act corporations; NOW and
ATS accounts at thrifts; credit
union share draft balances; and
demand deposits at thrifts.
1/63
1/6/75
FR2900; FR2910Q/A; call reports, quarterly
FEDERAL
NSA published data begin
Money Stock Component
RESERVE
( + ) Savings deposits, net =
BANK O ST. LOUIS
F
( + ) savings and MMDA
deposits at banks and thrifts
Passbook and statement savings
deposits plus money market de
posit accounts (MMDA) other
than those due to general
purpose and broker/dealer
money market funds, foreign
banks and official institutions and
the U.S. government. MMDAs
are a special type of savings ac
count that permits a small num
ber of third-party payments per
month.
weekly
1/5/81
Adequate weekly thrift data are not available before 1981; see Appen
dix 1 for discussion of monthly thrift data for 1959-80.
1/59
12/82*
(*MMDAs)
11/3/80
12/20/82*
MMDAs were first authorized in December 1982; separate savings
and MMDA data were collected until September 1991. Thereafter,
only a single combined series has been collected.
FR2900; FR2910Q/A; call reports
Deposit or account in which the
depositor is not currently, but
may be at any time, required by
the financial institution to give
written notice of intent not less
than seven days prior to with
drawal.
FR2416; call reports
( - ) savings and MMDA
deposits due to foreign banks,
foreign official institutions and
the U.S. Treasury
( + ) Adjusted small time deposits =
Deposits, including retail repur
chase agreements (RPs), issued
in amounts of less than $100,000
with original maturities of seven
days or more, less all IRA/Keogh
retirement account balances at
banks and thrifts.
1/59
11/3/80
FR2900; FR2910Q/A; call reports
( + ) gross small time deposits
( + ) retail RPs at commercial
banks and mutual savings
banks (MSBs)
Source of Information
monthly
1/59
Definition
Non-M1 component of M2 =
Retail RPs are issued in small
denominations most often to
households and small businesses.
Monthly Survey of Selected Deposits (FR2042), last Wednesday of
the month.
( + ) retail RPs at savings and
loan associations
Office of Thrift Supervision, quarterly thrift balance sheet
( - ) IRA/Keogh balances at
commercial banks and MSBs
FR2042
( - ) IRA/Keogh balances at
savings and loan associations
Office of Thrift Supervision, quarterly thrift balance sheet
NSA published data begin
Money Stock Component_________ Definition__________________________ monthly
weekly______ Source of Information
Non-M1 component of M2 =
(continued)
( + ) Share balances in general
purpose and broker/dealer
MMMFs
MMMFs are certain types of
investment companies that agree
to abide by the SEC’s Rule 2a-7
and a variety of other regulations
regarding the types and maturi
ties of allowable assets. Shares
in these funds may be held by
households, businesses and vari
ous institutions.
1/74
2/4/80
( + ) Overnight RPs, net =
One-day and continuing-contract
RPs issued by all depository in
stitutions to other than depository
institutions, MMMFs and foreign
official institutions.
11/69
1/6/75
( + ) gross overnight RPs
RPs as of close business, one
day each week
Report of Selected Borrowings (FR2415), for commercial banks,
weekly, close-of-business Monday; Weekly Report of Repurchase
Agreements on U.S. Government and Federal Agency Securities
with Specified Holders (FR2415t), for thrifts, close of business
Monday
( - ) overnight RPs held by
MMMFs
( + ) Overnight Eurodollars, net =
The Investment Company Institute (ICI) voluntarily collects informa
tion for the Federal Reserve. Weekly and monthly reports cover both
the funds’ liabilities (shares) and assets. The amounts of individual
assets held by MMMFs are important because most assets—
including RPs, Eurodollars, large time deposits and Treasury bills
—are netted from the monetary aggregates during the consolidation
of M2, M3 or L. Data are labeled by Federal Reserve staff as the
Weekly (Monthly) Report of Assets of Money Market Mutual Funds
[FR2051a (FR2051 b)]; Weekly Report of Assets for Selected Money
Market Mutual Funds (FR2051 c); or the Weekly Report of Overnight
Eurodollars for Selected Money Market Mutual Funds (FR2051d).
The ICI data are as of close of business on Wednesday. The Wed
nesday level is included in the aggregate for the week ending the
following Monday. For example, M2 and M3 for the week of January
10, 1994, contained data on MMMF shares as of Wednesday,
January 5.
FR2051a, c
MARCH/APRIL 1994
Eurodollar deposits with original
maturity of one day issued by
foreign branches of U.S. banks
worldwide to U.S. nonbanks
(U.S. addresses other than
depository institutions and
MMMFs)
2/77
12/31/79
( + ) gross overnight Eurodollars
Report of Selected Deposits in Foreign Branches held by U.S. Ad
dresses (FR2050), weekly reporting of daily data, close of business
Monday; Monthly (Quarterly) Report on Foreign Branch Assets and
Liabilities [FR2502, (FR2502s)], last business day of the period
( - ) overnight Eurodollars held
by MMMFs
FR2051a, c
FEDERAL
NSA published data begin
Money Stock Component
RESERVE
( + ) Large time deposits, net =
BANK O ST. LOUIS
F
Deposits issued by banks and
thrifts in amounts of $100,000 or
more with initial maturities of
seven days or more, other than
those held by MMMFs, other
depository institutions, and for
eign banks and official insti
tutions
monthly
weekly
1/59
Definition
Non-M2 component of M3 =
1/5/81
1/59
Source of Information
11/3/80
( + ) gross large time deposits
FR2900; FR2910Q/A; call reports
( - ) large time deposits due to
foreign banks and official insti
tutions, and the U.S. Treasury
FR2416; call reports, quarterly
( - ) large time deposits held
by MMMFs
FR2051a, c
( - ) mortgage-backed bonds at
savings and loan associations
ro
10/69
( + ) Term RPS, net =
( + ) gross term RPs
Office of Thrift Supervision, Statement of Condition (call report),
quarterly
Mortgage-backed bonds are
reported as a reservable liability
on the FR2900. They are not
deposits, however, and, hence,
are subtracted from the monetary
aggregates.
1/6/75
FR2415
RPs issued by all depositories
with original maturities greater
than one day, other than continu
ing contract and retail RPs and
RPs issued to other depositories
and foreign banks and official in
stitutions.
FR2051a, c
( - ) term RPs held by MMMFs
1/59
( + ) Term Eurodollars, net =
( + ) gross term Eurodollars
{ - ) term Eurodollars held by
MMMFs
Eurodollar deposits due to U.S.
nonbank addresses with maturity
longer than one day at all foreign
branches of U.S. banks and at
offices of non-U.S. banks in the
U.K. and Canada
12/31/79
FR2050; FR2502; data furnished by the Bank of England and
Bank of Canada.
FR2051a, c
NSA published data begin
Money Stock Component
Definition
monthly
weekly
4/74
2/4/80
Source of Information
Non-M2 component of M3 =
(continued)
( + ) Shares in institution-only
(l-O) MMMFs, net =
( + ) shares in l-O MMMFs,
gross
MMMFs that under SEC guide
lines require large minimum in
vestments (typically $50,000 + )
and sell shares only to sophisti
cated investors and institutions,
thereby gaining exemption from
certain SEC accounting rules.
These shares may be held by
households, businesses or insti
tutions.
FR2051a, c
( - ) overnight RPs and Euro
dollars held by l-O MMMFs
Note that term RPs and Eurodol
lars held by MMMFs were netted
above.
FR2415 for banks; FR2415t for thrifts
Non-M3 component of L =
( + ) Bankers acceptances, net =
1/59
Bankers acceptances held by the
nonbank public other than ac
cepting banks, Federal Reserve
Banks, foreign official institutions,
Federal Home Loan Banks and
MMMFs.
NA
1/59
NA
CO
(+ ) gross bankers acceptances
Monthly Survey of Eligible Bankers Acceptances (FR2006), month
ly, last day of the month; call reports, quarterly
( - ) acceptances held by
Federal Reserve Banks
FR34
( - ) acceptances held by
MMMFs
( + ) Commercial paper, net =
FR2051a, c
Commercial paper held by the
nonbank public other than
MMMFs.
1/59
NA
MARCH/APRIL
( + ) gross commercial paper
Report of Commercial Paper Outstanding Placed by Brokers and
Dealers (FR2957a), weekly, Wednesday; Report of Commercial
Paper Outstanding Placed Directly by Issuers (FR2957b), weekly,
Wednesday and last day of the month
( - ) commercial paper held by
MMMFs
FR2051a, c
1994
FEDERAL RESERVE
NSA published data begin
Money Stock Component
( + ) Short-term U.S. Treasury
securities, net =
Definition
BANK O ST. LOUIS
F
Treasury bills and coupons with
remaining maturities of less than
12 months held by the nonbank
public other than depositories,
Federal Reserve Banks, MMMFs,
and foreign banks and official
institutions.
monthly
weekly
1/59
NA
Source of Information
( + ) gross short-term Treasuries
Monthly Statement of Public Debt, U.S. Treasury Department
( - ) Federal Reserve Bank
holdings of short-term
Treasuries
FR34
FR2051a, c
( - ) MMMF holdings of short
term Treasuries
( + ) U.S. savings bonds
U.S. government savings bonds
held by the nonbank public.
1/59
N.A.
SOURCE: Compiled by the authors from published and unpublished Federal Reserve documents.
Monthly Statement of Public Debt, U.S. Treasury Department
15
measurement of the aggregate amount of
MMMF shares held by the nonbank public.
Retirement accounts (IRA/Keogh) at banks,
thrifts and MMMFs also have sometimes been
nettlesome. These deposits, netted from the
monetary aggregates, are not collected in the
same manner as other deposit data included in
the aggregates. As shown in Tkble 2, retirement
balances at banks are collected in the FR2042
report. This report surveys fewer banks less fre
quently than the FR2900 report that provides
most deposit data. Retirement balances at
MMMFs are collected by the Investment Compa
ny Institute from member mutual funds and,
like data for commercial banks and thrifts, lags
somewhat behind the reporting of deposits and
other liabilities included in the aggregates.
Measurement problems also arise regarding
Eurodollars and RPs. High-quality timely data
are available on the overnight Eurodollar com
ponent of M2 because these deposits are largely
held at Caribbean branches of U.S. banks.1
6
Tferm Eurodollars held in foreign branches of
U.S. banks are reported on approximately the
same basis. Term Eurodollars, however, also are
held extensively at non-U.S. banks in England
and Canada, not subject to Federal Reserve
reporting. The Bank of England and the Bank of
Canada collect quarterly data for U.S.-dollar
denominated deposits due to U.S. nonbank ad
dresses. Although aggregate totals are given to
Federal Reserve staff, data for individual banks
are confidential and, hence, can neither be
checked nor edited by Federal Reserve staff.1
7
For RPs, the problem is more a conceptual is
sue than a matter of data reporting. Overnight
RPs are included in the non-Ml component of
M2 because, at least in part, they are an attrac
tive alternative to holding transaction balances.
RPs with maturity o f more than one day also, of
course, may serve the same purpose. RPs with a
maturity longer than one day however, are
reported as term RPs and included in the nonM2 component of M3. An investor who accepts
a two-day RP contract rather than a sequence of
two, one-day contracts may reduce the size of
16ln fact, these deposits are recorded in New York while be
ing legally booked through “ nameplate” branches in the
Caribbean (so-called because the office largely consists of
a brass nameplate).
M2 without any economic significance. It seems
likely that much of the predictable part of such
switches, say, due to holiday weekends, is cap
tured in the seasonal adjustment factors. The
balance remains as statistical noise.
Overall, weekly first-published values of M2
and M3 shown on the current H.6 release are
based about 80 percent on data that are report
ed weekly, with the balance estimated from
lesser frequency reports.1
8
MAJOR OPERATIONS RY ROARD
STAFF THAT AFFECT THE
MONETARY AGGREGATES
In addition to the principal sources o f data,
well-informed researchers should be aware of
the more important revision practices and
schedules used by Federal Reserve Board staff
that affect the continuity of the data. Bench
marks, seasonal factor reestimation and defini
tion changes may have significant impacts on
the monetary aggregates and, correspondingly,
on research employing that data.
B en ch m a rk R evision s
All monetary aggregates data are subject to a
“benchmark” revision annually. In its most
general form, a benchmark of the monetary ag
gregates by Board staff would be (ideally) a
measurement of the universe o f money stock is
suers and their holdings of monetary liabilities.
A benchmark serves three main purposes. First,
it allows Board staff to incorporate deposit data
on institutions that are exempt from reporting
directly to the Federal Reserve. These data are
obtained either from bank and thrift call
reports or from other annual reports filed by
the institutions. Second, it allows the incorpora
tion o f corrected/revised data submitted by
depository institutions throughout the year.
Third, it allows staff to update estimates of
some nondeposit components of the aggregates.
Depository institutions generally submit re
vised deposit data throughout the year. Such
18Detailed estimates of such coverage ratios are prepared
about every three years and furnished to the Office of
Management and Budget as part of the reauthorization
process for the report. See Walton and others (1991).
17ln addition, few statistics are available for coverage ratios,
error rates, and so on.
MARCH/APRIL 1994
16
data from weekly reporting institutions are in
corporated into the monetary aggregates pub
lished on the H.6 release only during the first
three weeks following the week in which the
report was due, that is, the four most recent
weeks shown on the H.6 release. Deposit data
submitted after that time are held in abeyance
and incorporated at the annual benchmark,
along with data received from institutions that
report only once per year. (Deposit data received
from quarterly reporting institutions are incor
porated when received during the year, as are
nondeposit data received from many sources.
See Table 2.) This three-step process begins with
aggregation of all deposit data reported by
financial institutions during the past six or
seven years. Next, data are matched to call
reports for all depository financial institutions
to identify missing institutions (if any) and ob
tain deposit levels at the call dates for those in
stitutions exempt from filing deposit reports
with the Federal Reserve. Finally, miscellaneous
data collected during the year regarding items
not covered by deposit reports are incorporated.
Benchmarks constitute a clear break-in-series
for monetary aggregates data, changing signifi
cantly not only past data but altering the base
upon which new estimates will be published
during the coming year. Since 1964, a bench
mark of the monetary aggregates has been done
at least annually In recent years, Board staff
have published the benchmark data prior to the
February Humphrey-Hawkins testimony of the
Federal Reserve Chairman before Congress.
From 1974 through 1980, however, benchmark
revisions of the monetary aggregates were con
ducted approximately every quarter. The in
creased frequency of benchmarks addressed a
concern, raised by the Bach Commission, that
the methods used at the time to estimate nonmember bank deposits could introduce a bias
into the monetary aggregates. It was felt that
more timely benchmarks would serve to keep
the Federal Reserve’s estimates more closely
aligned with the true, unobserved figures. This
was not a new concern, however, and in fact all
benchmarks prior to the Monetary Control Act
had focused heavily on nonmember bank
deposits, since these institutions were not re
quired to report to the Federal Reserve.1 The
9
power to enforce near-universal reporting that
19The quarterly deposit data reported on the call reports by
nonmember banks also were not without problems. The
definitions of “deposits” differ somewhat between the Fed’s
Regulation D and the call report instructions, making the
FEDERAL
http://fraser.stlouisfed.org/RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
was endowed on the Federal Reserve by the
Monetary Control Act obviated the need for fre
quent benchmarks after 1980. Tbday, bench
marks focus on special items not covered on
deposit reports.
The effects o f these revisions on quarterly
growth rates o f the monetary aggregates are
shown in the first page of Table 3. The columns
of the table correspond to the annual bench
marks published in early 1986-93. Each entry in
the table is the change in the annualized growth
rate o f the corresponding monetary aggregate
during that quarter due to revisions of the un
derlying source data. The largest revisions due
to any benchmark occur in the most recently
completed year, shown as the shaded areas in
the table. Revisions for prior years, not shaded,
are smaller. While not following a consistent
pattern, the data suggest that any particular
quarter may be revised significantly especially
for the broader aggregates. In part, the latter
are related to the higher percentage of non
deposit components in those aggregates.
Seasonal Adjustm ent
Seasonal adjustment o f the monetary ag
gregates has long been an important area of
research. The FOMC formulates its monetary
policy in terms of seasonally adjusted data, and
both the public and policymakers often take re
cent movements in adjusted data as indicating
the underlying trend growth rate of the mone
tary aggregates.
Seasonal adjustment methods attempt to
separate recurring calendar-related patterns in
data (due to, say, calendar dating, payroll sched
ules, tax filing deadlines, and so on) from ran
dom shocks and the underlying trend. In general
terms, the data generating process for the
monetary aggregates is assumed to be well
represented as the product of three compo
nents: a time-varying trend, a time-varying
seasonal and an irregular.
Each year, Board staff publish revised seasonal
factors for most historical periods and projected
seasonal factors for the upcoming year. With
few exceptions, these seasonal factors are based
on, and published simultaneously with, the andata not fully comparable. For earlier analyses of the effect
of benchmark revisions, see Lang (1978) and Simpson
and Williams (1981).
Table 3
Page 1: Revisions to Previously Published Quarterly Growth Rates of the Monetary Aggregates (s.a.) Due to
Benchmark Data Revisions
Year of annual benchmark (usually published in February; see Kavajecz, 1994)
1986
1987
1988
1989
1990
Periods
M1
M2
M3
M1
M2
1984 Q4
0.4
0.6 -0 .2
0.4
0.5
-0 .6 -1 .2
1985 Q1
Q2
Q3
Q4
0.1 - 0 . 4 -1 .0
0.1
0.3 -0 .3
0.1
0.0 0.0
0.6 -0 .1 -0 .6
-0 .2 -0 .3
0.2 0.0
0.1
0.2
0.5 0.8
-0 .4 -0 .1
-0 .1
0.2
0.0 0.2
0.2 -0 .1
0.0 0.0
0.0 0.0
0.1
0.1
-0 .1 -0 .1
0.1
0.7
0.5 0.6
0.4 0.5
-0 .1 -0 .1 - 0 .5
0.0 - 0 .5
0.1
0.1
-0 .1
0.0
0.0 -0 .1
0.0
0.0
0.0
0.0
-0 .1 - 0 .2 - 0 .4
0.4 0.1
0.3
0.0 0.0 0.0
0.2 0.0 0.1
0.3
- 0 .2
0.1
0.1
0.0
0.0
0.0
0.0
1991
0.0
0.0
0.0
0.1
1986 Q1
Q2
Q3
Q4
1987 Q1
Q2
Q3
Q4
1988 Q1
Q2
Q3
Q4
1989 Q1
Q2
Q3
Q4
1990 Q1
Q2
Q3
Q4
M3
0.5
0.1
0.0 0.0
-0 .1 - 0 .7 - 0 .4
-0 .1 - 0 .2 -0 .1
-0 .1 -0 .1
0.1
M1
M2
M3
M1
M2
0.1
0.0
0.1
0.0
0.3
0.3
M1
M2
-0 .1
M3
0.2
M3
0.0 0.1
0.1
0.2 - 0 .2
0.0
0.2 - 0 .3 - 0 .3
0.0 -0 .1 -0 .1
MARCH/APRIL 1994
0.0
0.1
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.1
0.1
0.0
0.0 -0 .1
0.0 -0 .1
0.0
0.0
0.0 0.0
0.0
0.0
0.0
0.0
0.0 -0 .1
0.0
0.0
0.0
0.0
0.0
0.0
0.1
0.0
0.0
0.1
0.0
0.1
0.3
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.1
0.1 -0 .1
-0 .1
0.0
0.0 - 0 .3
0.0
0.3
0.4
0.0
0.0
0.0
0.0
0.0
0.0
0.1
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.1
0.0
0.0
0.0
0.0
0.0
0.3
-0 .1
0.1
0.1
0.0
0.1
0.1
0.0
0.0
-0 .1
0.1
-0 .1
0.2
0.1
0.1
0.1
0.4
0.0
0.0
0.0
0.0
0.0
0.1
0.1
0.1
0.0 -0 .1
0.0
0.0
0.0 -0 .1
0.0 -0 .1
0.3
0.3
0.0
0.0
0.0
0.4
0.2
0.1
0.1
0.4
0.2
0.0
-0 .1
-0 .1
0.1
0.2
0.0
0.1
0.3
0.1
0.0 -0 .1
0.0 -0 .1
-0 .1
0.1
0.0 0.0
-0 .1
0.2
0.1
-0 .1
0.1 -0 .1
0.0 0.2
0.5 0.2
0.7 - 0 .2
0.1
0.0
0.3
0.3
M3
0.0
-0 .1
0.0
-0 .1
0.0
0.0
0.0
0.0
-0 .1
-0 .2
-0 .2
-0 .1
1992 Q1
Q2
Q3
Q4
Note: These revisions do not include effects due to revisions in seasonal adjustment factors and/or changes in definitions.
M2
0.0
0.0 -0 .1
M1
1993
M2
1991 Q1
Q2
Q3
Q4
1992
M1
0.0
0.0
0.1 -0 .1
-0 .1 -0 .1
0.0
0.0
0.2
M2
M1
M3
M3
0.0 0.0
0.0 0.0
-0 .1 -0 .1
0.1
0.1
0.0
0.1
0.0
0.1
0.0
0.2 0.1
-0 .1 -0 .2
-0 .1 -0 .1
-0 .2 -0 .1 -0 .1
0.2 - 0 .4
0.0
0.2 0.1
0.7
-0 .1 -0 .2 -0 .3
0.0 -0 .1 - 0 .2
FEDERAL RESERVE
Table 3 (cont.)
Page 2: Revisions to Previously Published Quarterly Growth Rates of the Monetary Aggregates (s.a.) Due to
Revisions to Seasonal Adjustment Factors
Year of annual seasonal review (usually published in February, along with benchmark data revisions)
1987
1986
0.9
0.0 - 0 .3
-0 .6
0.0
0.4
0.2
0.7
0.6
- 0 . 6 - 0 . 7 - 0 .6
1.1
0.1 - 0 . 4
1986 Q1
Q2
Q3
Q4
1987 Q1
Q2
Q3
Q4
1988 Q1
Q2
Q3
Q4
1989 Q1
Q2
Q3
Q4
M1
M2
0.8 0.6
- 0 . 3 -0 .3
- 0 . 4 -0 .2
- 0 . 3 -0 .3
1.0
1.0 0.1
- 0 . 2 - 0 .4
0.1
- 0 . 7 - 0 .3 -0 .4
-0 .1 - 0 .2
0.1
-0 .1 -0 .1
-0 .1
0.0
- 0 .2
0.0
0.0
0.1
- 0 .2 -0 .1
0.1 -0 .1
0.0 0.1
0.1
0.1
0.0 -0 .1
-0 .1 -0 .1
- 0 .3
0.1
0.2
0.0
0.0
0.0
0.0
0.0
0.3
-0 .2
-0 .2
0.1
0.0
0.0
0.0
0.0
-0 .3 -0 .3
0.0 - 0 .4
-0 .1
0.3
0.6 0.6
- 0 .2
0.0
0.4
0.3
0.0
0.1
- 0 .5 -0 .3
0.0 0.0
0.1
0.2
0.0 -0 .1
- 0 .2
0.0
-0 .3 -0 .1
0.0 0.0
0.2 0.0
0.1
0.0
0.2
-0 .1
-0 .1
0.1
0.0
0.0
0.0
0.0
-0 .5 - 0 .4
0.0 - 0 .5
- 0 .3
0.3
1.0 0.7
-0 .1
0.2
0.7 0.4
0.1 - 0 .2
- 0 .9 -0 .5
0.0 -0 .1
0.3 0.2
- 0 .2 -0 .2
-0 .1
0.0
-0 .2
-0 .1
0.2
0.1
0.0
0.0
0.1
0.0
0.1
-0 .1
-0 .1
0.1
0.0
0.0
0.0
0.0
-0 .1
0.3
1.1
0.5
0.1 - 0 .3
-1 .3 -0 .6 -0 .6
0.0 -0 .1
0.4 0.3
- 0 .3 -0 .2
-0 .1
0.0
-0 .2 -0 .1
- 0 .2 -0 .1
0.4 0.2
0.1
0.0
0.0
0.0
-0 .1
0.1
0.0
0.0
0.1
0.0
0.0 0.4 0.2
1.3 0.5 0.6
0.2 - 0 .3 -0 .1
- 1 . 6 - 0 . 8 - 0 .6
0.0 -0 .1
0.4 0.4
- 0 .4 -0 .3
0.0 0.0 - 0 .5
- 0 .3 -0 .1
- 0 .3 - 0 .2
0.5 0.3
0.0 0.0
-0 .2 -0 .1
0.0 0.0
0.1
0.2
0.0 0.0
0.1 - 0 .2 -0 .1
0.4
0.5 -0 .1
- 0 .4 - 0 .3 -0 .3
-0 .1
0.0 0.6
- 0 .4
0.0
- 0 .3 - 0 .4
0.6 0.4
0.2 0.0
-0 .4 -0 .3
0.1
0.1
0.7 0.4
-0 .3 -0 .1
0.7
0.1
0.0 -0 .1
0.0 - 0 .3
0.0 0.2
0.3 0.4
0.1
0.2
-0 .4
0.2
0.4 -0 .3
-0 .1 -0 .2 - 0 .2
0.1
0.3 0.4
-0 .6
0.2
0.1
0.6 - 0 .2 -0 .3
-0 .2 - 0 .2 -0 .2
0.1
0.0
M2
M2
M2
M3
0.0
0.0 0.1
-0 .1
0.2
0.1 -0 .3
-0 .1 -0.1
M1
M2
0.0
M3
0.2
0.7
- 0 .6 - 0 .7 -0 .3
-0 .1 - 0 . 6 -0 .5
- 0 .2
0.5 0.1
1.1
0.9 0.6
M3
1990 Q1
Q2
Q3
Q4
1991 Q1
Q2
Q3
Q4
1992 Q1
Q2
Q3
Q4
Note: These revisions shown do not include effects of benchmark data revisions to and/or changes in definition.
M1
M2
M3
1993
M1
M1
M1
1992
1991
1990
1989
1988
M3
CO
1984 Q4
1985 Q1
Q2
Q3
Q4
M3
o
I
M2
CD
M1
o
I
BANK O ST. LOUIS
F
Periods
M3
M1
M2
M3
0.1 -0 .1
0.2
- 0 .6
0.0 -0 .6
- 0 .2 - 0 .4 -0 .2
0.6 0.6 0.6
0.2 0.0 0.2
-0 .8 -0 .4
0.3 0.1
1.1
0.6
- 0 .4 - 0 .2 - 0 .3
- 1 .2 - 0 .5 -0 .2
0.6 0.1
0.3
1.4 0.7 0.4
- 0 .7 - 0 .5 -0 .3
oo
Table 3 (cont.)
Page 3: Revisions to Previously Published Quarterly Growth Rates of the Monetary Aggregates (s.a.) Due to
Changes in Definition_______________________________________________________________________________
Year of redefinition (published at time of benchmark and seasonal review)
1986
Quarters
M1
M2
1987
M3
M1
M2
1988
M3
1989
M1
M2
M3
1986 Q1
Q2
Q3
Q4
0.4
0.0
0.1
0.4
0.3
0.2
0.0
0.0
0.0
0.0
M2
1990
M3
M1
M2
1991
M3
M1
M2
1992
M3
M1
M2
1993
0.0
1987 Q1
Q2
Q3
Q4
M1
M3
M1
0.0
0.0
0.0
0.0
M2
M3
1984 Q4
1985 Q1
Q2
Q3
Q4
CO
1988 Q1
Q2
Q3
Q4
0.0
1989 Q1
Q2
Q3
Q4
0.0
0.0
0.0
0.0
-
-
0.1
0.0
0.1
0.1
0.2
0.1
0.0
0.0
0.0
0.0
1990 Q1
Q2
Q3
Q4
MARCH/APRIL 1994
1991 Q1
Q2
Q3
Q4
Note: These revisions shown do not include effects due to benchmark data revisions and changes in seasonal adjustment factors.
Source: Data shown in shaded areas are taken from the issues of the Federal Reserve Board’s H.6 statistical release, published after the annual benchmark. See
Kavajecz (1994) for exact dates. Other data shown are the authors’ calculations from annual issues of Money Stock Revisions.
20
nual benchmark data.2 Monthly seasonal factors
0
are estimated by a variant of the Statistics Cana
da Xll-ARIMA method.2 In the first step of this
1
method, the observed data are extended by the
addition of one or two years of forecasts. The
forecasts are obtained via an ARIMA model that
includes exogenous intervention variables for
each month and, in some cases, a small number
of special events.2 In recent years, intervention
2
variables have been included for events such as
the impact of the 1986 Tax Reform Act on the
levels of liquid deposits in early 1987 and the
dramatic surge in M l that occurred during
Hurricane Gloria’s sweep up the east coast of
the United States in September 1985. Seasonal
factors are then obtained by applying standard
X ll algorithms to the lengthened series.
Weekly seasonal factors are estimated via a
two-step process. In the first, initial estimates of
weekly seasonal factors are obtained from an
unobserved-components time series model.2 In
3
the second, these initial estimates are modified
via a quadratic programming model such that
averages of a particular path o f seasonally ad
justed weekly data equal the previously estimat
ed monthly seasonal pattern.2 Projected weekly
4
seasonal factors are obtained in a similar man
ner, subject to judgmental adjustment by Board
staff for events such as unusual calendar dating
and holiday effects that are not captured by the
statistical models.
Like other aspects of the monetary aggregates,
the methods used for seasonal adjustment have
evolved over time. From 1955 — when the first
seasonally adjusted numbers were published —
through 1981, seasonal adjustment was done us
ing the classic Census X ll procedure.2 In 1982,
5
the Xll-ARIMA procedure proposed by Dagum
was adopted to reduce well-known potential
problems due to the use of truncated moving20The very few exceptions in which the seasonal review was
completed and published after the benchmark are noted in
Kavajecz (1994).
21See Farley and O’Brien (1987).
22See Box and Tiao (1975).
23The statistical model has been developed over a number of
years; see Cleveland and Grupe (1983), Pierce, Grupe and
Cleveland (1984), and Cleveland (1986). The model allows
for a noninteger number of weeks during the year and
other effects. Statistically, it seeks to estimate trend,
seasonal and irregular components of a time series that is
sampled at a frequency which differs from the fundamental
frequencies of the data generating processes for its com
ponents.
24See the appendix to Farley and O'Brien (1987) for details
of the algorithm.
25See Pierce and Cleveland (1981).
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average filters near the ends of the sample.2
6
Other features that have been added to improve
the estimation include trading day effects, pay
ment schedules and holiday dating.
Following recommendations of the Advisory
Committee on Monetary Statistics, the Federal
Reserve publishes both seasonally adjusted and
unadjusted data. The weekly H.6 release, for ex
ample, currently includes adjusted data for four
monetary aggregates and 25 components, and
unadjusted data for the four aggregates, 26 com
ponents and 11 related miscellaneous series.
Most of the adjusted components are furnished
for ease of analysis, however, and are not used
in construction o f the monetary aggregates.
Seasonally adjusted M l is constructed as the
sum of four separately adjusted components:
currency, travelers checks, demand deposits and
other checkable deposits (OCDs). The non-Ml
component of M2 and the non-M2 component
of M3 are adjusted as a whole, with adjusted
M2 equal to the sum of adjusted M l and the
non-Ml component of M2; M3 similarly is
formed by summing M2 and the adjusted nonM2 component of M3.
Early each year, Board staff forecast seasonal
adjustment factors for the monetary aggregates
during the coming year. These projected factors
are published on the H.6 release at the same
time as the benchmark data, and are not re
vised during the year on the basis o f incoming
data.2 Hence, published monetary growth rates
7
throughout the year are based on ex ante fixed
seasonal factors that incorporate no information
received during the current year. Thus, it
perhaps is not surprising that revised seasonal
factors for the most recently completed year
may differ significantly from those that were
forecast a year earlier. Revisions to the mone
tary aggregates due to revisions to seasonal fac26While X11 uses two-sided moving-average filters for most
observations, the filters must be truncated near the ends of
the time series. This effect tends to increase the size of
the revisions to the most recent year’s seasonal factors
when they are reestimated the following year. Further, it
also tends to underestimate the degree of seasonality near
the end of the sample. Extending the sample via ARIMA
model forecasts seems to attenuate both problems. See
Dagum (1983).
27Experimental estimates of concurrent seasonal factors, up
dated using incoming data, were published as an appendix
to the H.6 for several years but never incorporated into any
official monetary aggregate. The Board’s committee of ex
perts on seasonal adjustment had recommended explora
tion of concurrent factors; see Pierce and Cleveland (1981).
A similar recent review at the Bank of England (1992) sug
gested that concurrent adjustment might reduce the size of
subsequent revisions.
21
tors, shown on the second page of Table 3,
often have exceeded those due to either revi
sions to underlying source data (shown on the
first page of the table) or to changes in defini
tions (the third page of Table 3).
mation about the stance of monetary policy
with respect to economic activity. The Federal
Reserve responded by creating the monetary ag
gregates M2 and M3 in 1971, and M4 and M5 in
1975.
Although the concept of seasonal movements
in data may be fairly straightforward, there is
no generally accepted statistical definition of
seasonality. ‘"Ii'ue” seasonal factors are never ob
served nor measured, even with error. Thus,
seasonally adjusted monetary aggregates neces
sarily retain a significant subjective component,
even in the long run. Lindsey and others (1981)
notes that the adjusted monetary aggregates
have tended to become somewhat smoother
through time as their seasonal adjustment fac
tors have been subjected to successive annual
revisions. Although he attributes this to in
creases in our knowledge about, and precision
in, estimation of the seasonal adjustment factors,
an alternative hypothesis is that the seasonal
component is absorbing more of the irregular
component, leaving an adjusted time series that
more closely resembles its trend component.
Despite the increasing attention focused on
near-moneys, the multiple definitions of the
monetary aggregates during the 1970s continued
to reflect legislative distinctions between the as
set and liability powers of banks and thrifts.
These distinctions faded after passage o f the
Monetary Control and Garn-St. Germain Acts,
permitting a new set of nested definitions such
that M l became a subset of M2, and M2 a sub
set of M3.2 By internalizing within M2
9
opportunity-cost-induced shifts of funds be
tween medium-of-exchange and liquid near
moneys for all intermediaries, this design en
hanced the usefulness of M2 as an intermediate
policy target through better estimates of a
(nominally) stable demand curve for M2.3
0
Changes In D efinitions
Although financial innovation has been an im
portant factor, the evolution of the Federal
Reserve Board staff’s definitions o f monetary ag
gregates primarily has been governed by econo
mists' changing empirical perceptions of the
appropriate concept of money.2 In the 1960s,
8
economists’ focus on the medium o f exchange
function of money made M l the principal ag
gregate. As empirical relationships for M l ap
peared to break down in the 1970s and attention
turned once again to the role of liquid near
moneys, some suggested that multiple monetary
aggregates might collectively reveal more infor
28Our view is that many of the theoretical arguments for the
inclusion and/or exclusion of specific assets are ex post ra
tionalizations of workable empirical definitions. The same
argument is, of course, made by Friedman and Schwartz
(1970).
29There are a few qualifications to this characterization. From
1980-87, a portion of the vault cash and demand deposits
held by thrifts had been included in M1 (but not in M2 and
M3), while the balance was excluded (none of the vault
cash and interbank deposits held by commercial banks
were included in the aggregates). In 1988, the treatment of
these items for thrifts was changed to be comparable to
that for banks. Similarly, in constructing M3, a variety of
netting items are deducted, such as large time deposits at
commercial banks held by M2-type money market funds. In
general, in moving from narrower to broader aggregates,
any asset held by a money stock issuer (say, a money
market fund) that was issued by another money stock
Since monetary aggregates data first appeared
on the J.3 statistical release in 1960, the broad
monetary aggregates (roughly corresponding to
M l, M2, M3) have been redefined about a dozen
times. Changes have ranged in magnitude from
the massive redefinition in February 1980 to
small additions and subtractions such as the in
clusion of nonbank travelers checks in June
1981. Whenever a definition change is put in
place, Board staff recompute all historical data
for the monetary aggregates and components
under the most recent definitions.3 Available
1
Federal Reserve publications, including Money
Stock Revisions, show monetary aggregates data
solely in terms of current definitions. For re
searchers studying Federal Reserve behavior,
"knowing what money was" at a particular time
is complicated by changes in definitions as well
issuer (say, a commercial bank) is netted out of the broad
er consolidated monetary aggregate.
30For discussion, see Simpson and Porter (1980).
3,The 1980 redefinition, for example, required Board staff to
“ rebuild” M2 for years prior to 1980 with an expanded set
of thrift deposit data. Some details are discussed in the
appendix.
MARCH/APRIL 1994
22
as by the annual benchmark and seasonal
review process.
Definitional changes perhaps are usefully sum
marized in three categories. First, there is the
inclusion (or, less often, exclusion) of an existing
money market instrument or depository liabili
ty.3 A prominent example is the addition in
2
1980 of general purpose and broker/dealer
MMMFs to the M2 aggregate.3 While M2 was
3
recomputed on a consistent basis for all prior
periods following the redefinition, conceptually
this is a nontrivial change. During the 1970s,
when the first surge in money market fund
growth occurred, the contemporaneous M2 ag
gregate excluded money market funds; shifts by
households into the funds were (in principal)
embedded in the elasticity o f M2 with respect to
its opportunity cost and reflected in shifts in the
income velocity of M2. Researchers using the
redefined M2, however, see an aggregate that in
ternalizes these shifts, has a smaller interest
elasticity, and different velocity behavior. Of
course, the importance of this change in defini
tion for analysis o f Fed behavior is mitigated by
the FOMC’s emphasis on M l during the period.
Other examples are the inclusion in M2 o f retail
RPs (which were basically uninsured small time
deposits exempt from Reg Q) in 1982, the exclu
sion of retirement accounts from the monetary
aggregates in 1983, and the addition o f term Eu
rodollar deposits to M3 in 1984. While the last
had been discussed earlier, inclusion of the
deposits had to await a reliable source of data.
The second type of definition change is the in
clusion of a new money market instrument or
depository institution liability. In some cases,
the new instrument or deposit may simply
reflect the removal o f a prohibition against that
type of deposit or of a ceiling on a deposit
offering rate (Regulation Q ceilings). To the ex
32The precise definition of M1 has changed several times
due to changes in the treatment of demand deposits due
to foreign commercial banks and official institutions. Includ
ed in M1 prior to 1980 (see Kavajecz, 1994), these deposits
were excluded thereafter following recommendations of the
Advisory Committee on Monetary Statistics. See Advisory
Committee on Monetary Statistics (1976), p. 4, or Farr and
others (1978). These changes also complicate building M1
based on current definitions for years prior to 1959; see
Rasche (1987).
33Tax-exempt general purpose and broker/dealer MMMFs, ex
cluded in 1980, were added in February 1983.
34See Kavajecz (1994) for details. More obscure examples in
clude certain assets sold by depositories with recourse,
bank investment contracts (BICs), and bank deposit notes
(the latter classified as a deposit under Federal Reserve
Regulation D but not by the FDIC). Brokered deposits pro
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FEDERAL
Federal Reserve Bank of St. Louis
tent that deregulation or the authorization of
new instruments permanently changes the be
havior of depositories, its affect on the monetary
aggregates is similar to a change in definition.
Examples include the authorization of NOW ac
counts nationwide in 1980, the introduction of
money market deposit accounts (MMDAs) in
1983, and the major discrete steps in the
phaseout of Regulation Q that occurred in 1982,
1983 and 1986.3 In many cases, this type of
4
deposit account was already included in the ag
gregates (both OCDs and MMDAs are types of
savings deposits). The authorization o f these
new instruments, largely born of deposit in
terest rate controls, likely induced unusual tran
sitory volatility in published data during the
period when money may be shifting between
components and may also have permanently
changed the income and interest elasticities of
the monetary aggregate.3
5
The third type o f definition change is reclas
sification o f the liabilities o f different types of
financial institutions. Prior to the 1980 redefini
tion, deposits at banks and thrift were included
in separate monetary aggregates. Deposits at
thrifts were included in M3 and M5 while com
parable deposits at banks were included in M2
and M4. The 1980 redefinition restructured the
monetary aggregates to combine similar types of
deposits at commercial banks and thrifts. Al
though strongly motivated by the increasing
similarity of the deposits offered by banks and
thrifts during the 1970s, some economists coun
selled against the pooling of bank and thrift lia
bilities in the new aggregates. Their arguments
were based largely on the joint product nature
of depositories. To the extent that firms and
households tend to purchase a bundle o f serv
ices from a single institution rather than
separate products from a number o f institutions,
there may be value to aggregation by institutionvide another example. Although a bank or thrift might
receive a deposit of a million dollars (or more) from a
broker, the amount of the deposit is included in M2 as a
small time deposit if the deposit is placed entirely for the
benefit of individuals. In this manner, the development of
the brokered retail CD market could potentially have affect
ed the apparent interest elasticity of M2 by altering the be
havior of its small time deposit component.
35There is no doubt this was the case in 1983, when the
FOMC decided to rebase its target growth rate ranges for
the year following the introduction of MMDAs. The implica
tions of deregulation during the 1980s, including the
demise of Reg Q, for money demand models are dis
cussed by Moore, Porter and Small (1990).
23
al type rather than by product. In response, the
Board adopted the recommendation that, to ev
ery extent feasible, data for banks and thrifts
should be published separately so as to permit
such analysis. This argument is similar to Fried
man and Schwartz’s position that financial assets
may appropriately be aggregated if they are
sufficiently close substitutes in either demand or
supply.
Overall, annual revisions to the monetary
aggregates due to revisions to source data, sea
sonal factors and definitions render treacherous
any attempt by a researcher to update or extend
previous studies by mixing differing vintages of
monetary aggregates data. One recent empirical
study (Dewald, Thursby and Anderson, 1986)
found in an extensive computer simulation ex
periment that empirical results may be highly
sensitive to the mixing o f different vintages of
data, including data on the monetary aggregates.
A complete chronology of revisions and redefini
tions of the monetary aggregates is shown in
Kavajecz (1994).
CONCLUSION: THE MONETARY
AGGREGATES AS MONETARY
TARGETS
We conclude our historical examination of the
Federal Reserve’s monetary aggregates with a
summary of their use as monetary policy tar
gets. The FOMC’s target and monitoring ranges
for the aggregates are shown in T&ble 4.3
G
Targeting of monetary aggregates began with
House Concurrent Resolution 133 in 1975, later
formalized in the Humphrey-Hawkins Act of
1978 as an amendment to the Federal Reserve
Act. From 1975 through 1978, the committee rebased each quarter its annual four-quarter tar
get range for the monetary aggregates. The
resulting base drift in the committee’s targets
has been controversial.3 Since 1978, the com
7
mittee has set one, fourth-quarter-to-fourthquarter range each year except 1983. Authoriza
tion of MMDAs in late 1982 led to a surge in M2
growth as aggressive bidding by depositories
against money market funds apparently drew
nonmonetary balances into M2. (Recall that taxa
ble general purpose and broker/dealer MMMFs
had been included in M2 in 1980 and that
MMDAs, a type of savings deposit, were always
included in M2. M2 was redefined slightly in
February 1983 to include tax-exempt general
purpose and broker/dealer money market funds.)
The committee subsequently reset its 1983 tar
get ranges using a February-March base.
While relatively narrow through the early
1980s, target ranges widened during the decade
as an accelerating pace of innovation in financial
markets apparently complicated money demand
forecasting and money stock control. The range
for M l was widened to 4 percentage points in
1983 and to 5 points in 1985. Citing uncertainty
regarding the demand for M l and its relation
ship to economic activity, the committee did not
set a target range for M l in 1987 or beyond.3
8
The target range for M2 similarly was widened
over this interval, although it has remained at
its current width of 4 percentage points since
1988. In part, the widening of the range in 1988
reflects the increased difficulty of forecasting
the demand for M2 during an era o f turmoil in
financial markets, including the restructuring of
the thrift industry, capital and earnings difficul
ties at commercial banks, and a restructuring
(deleveraging) o f household and firm balance
sheets.
The monetary aggregates during most years
have grown within their target ranges, as shown
in Figures 1 and 2. Growth often has run well
toward the upper or lower bounds of the cones,
however, suggesting that the midpoint of the
committee’s target range may not always be the
best forecast o f an aggregate’s growth.
36Target and monitoring ranges differ in terms of the strength
of the implied policy reaction function. In general, deviation
of an aggregate from a target range suggests a somewhat
stronger policy response than deviation from a monitoring
range, ceteris paribus.
37For contrasting views, see for example Axilrod (1982),
Broaddus and Goodfriend (1984) and Walsh (1986).
“ “ Monetary Policy Report to the Congress,” Federal Reserve
Bulletin, April 1987.
MARCH/APRIL 1994
24
Table 4
Growth Cones for the Monetary and Credit Aggregates
(percent annual rate)_______________________________
Target and monitoring ranges
Date
established
Apr.75
Jun.75
Jul.75
Oct.75
Jan.76
Apr. 76
Jul.76
Nov.76
Jan.77
Apr. 77
Base
period
Mar. 75
Jun.75
7502
75Q3
7504
7601
7602
76Q3
7604
7701
Span
Mar.75-Mar.76
Jun.75-Jun.76
75Q2 - 7602
7503 - 7603
7504 - 7604
7601 - 7701
7602 - 7702
7603 - 7703
7604 - 7704
7701 - 7801
M1
5.0
5.0
5.0
5.0
4.5
4.5
4.5
4.5
4.5
4.5
-
M2
7.5
7.5
7.5
7.5
7.5
7.0
7.0
6.5
6.5
6.5
8.5
8.5
8.5
7.5
7.5
7.5
7.5
7.5
7.0
7.0
-
Bank credit
proxy
M3
10.5
10.5
10.5
10.5
10.5
10.0
9.5
10.0
10.0
9.5
10.0
10.0
10.0
9.0
9.0
9.0
9.0
9.0
8.5
8.5
-
12.0
12.0
12.0
12.0
12.0
12.0
11.0
11.5
11.5
11.0
6 . 5 - 9.5
6.5 - 9.5
6 . 5 - 9.5
6 . 0 - 9.0
6.0 - 9.0
6 . 0 - 9.0
5.0 - 8.0
5 . 0 - 8.0
7.0 - 10.0
7.0 - 10.0
Bank credit
Jul.77
Oct.77
Feb.78
Apr.78
Jul.78
Oct.78
Feb. 79
Feb.80
Feb.81
Feb.82
7702
77Q3
7704
7801
7802
7803
7804
7904
8004
8104
7702
7703
7704
7801
78Q2
7803
7804
7904
8004
8104
-
7802
7803
7804
7901
79Q2
7903
7904
8004
8104
8204
4.0
4.0
4.0
4.0
4.0
2.0
1.5
4.0
3.5
2.5
-
6.5
6.5
6.5
6.5
6.5
6.0
4.5
6.5(M1B)
6.0{M1B)
5.5
7.0
6.5
6.5
6.5
6.5
6.5
5.0
6.0
6.0
6.0
-
9.5
9.0
9.0
9.0
9.0
9.0
8.0
9.0
9.0
9.0
8.5 8.0 7.5 7.5 7.5 7.5 6.0 6.5 6.5 6 .5 -
11.0
10.5
10.0
10.0
10.0
10.0
9.0
9.5
9.5
9.5
7.0 7.0 7.0 7.5 8.5 8.5 7.5 6 .0 6.0 6 .0 -
10.0
10.0
10.0
10.5
11.5
11.5
10.5
9.0
9.0
9.0
Debt
Feb.83
Feb.83
Jul.83
Jan.84
Feb. 85
Jul.85
Feb.86
Feb.87
Feb.88
Feb.89
Feb. 90
Jul.90
Feb.91
Feb.92
Feb.93
Jul.93
83Feb/Mar
8204
8302
8304
8404
85Q2
85Q4
86Q4
87Q4
8804
8904
89Q4
90Q4
9104
9204
9204
83Feb/Mar-83Q4
8204 - 8304
8302 - 8304
83Q4 - 84Q4
84Q4 - 85Q4
85Q2 - 85Q4
8504 - 86Q4
86Q4 - 87Q4
87Q4 - 88Q4
8804 - 8904
8904 - 9004
8904 - 90Q4
9004 - 9104
9104 - 92Q4
9204 - 9304
9204 - 9304
_
4.0
5.0
4.0
4.0
3.0
3.0
-
8.0
9.0
8.0
7.0
8.0
8.0
NS
NS
NS
NS
NS
NS
NS
NS
NS
7.0 - 10.0
_
_
NC
6.0 - 9.0
6.0 - 9.0
NC
6.0 - 9.0
5.5 - 8.5
4.0 - 8.0
3.0 - 7.0
3.0 - 7.0
NC
2.5 - 6.5
2.5 - 6.5
2.0 - 6.0
1.0 - 5.0
6.5 - 9.5
NC
6 . 0 - 9.0
6 . 0 - 9.5
NC
6 . 0 - 9.0
5 . 5 - 8.5
4.0 - 8.0
3 . 5 - 7.5
2.5 - 6.5
1 . 0 - 5.0
1 . 0 - 5.0
1 . 0 - 5.0
0 . 5 - 4.5
0 . 0 - 4.0
8.5 - 11.5
NC
8.0 - 11.0
9.0 - 12.0
NC
8.0 - 11.0
8.0 - 11.0
7.0 - 11.0
6.5 - 10.5
5.0 - 9.0
NC
4.5 - 8.5
4.5 - 8.5
4.5 - 8.5
4.0 - 8.0
The FOMC first set desired longer-run growth targets for M1, M2, M3 and the bank credit proxy at its meeting on April
14-15, 1975. On February 15, 1977, ranges for the monetary aggregates were added to the Domestic Policy Directive sent
to the Open Market Desk at the Federal Reserve Bank of New York. On April 18, 1978, the range for bank credit was
added to the Domestic Policy Directive.
NC: Not Changed
NS: None Specified
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
25
Figure 1
M2 Historical Target Ranges
Billions of dollars
Quarterly data
Figure 2
M3 Historical Target Ranges
Billions of dollars
Quarterly data
MARCH/APRIL 1994
26
REFERENCES
Abbott, William J. “ Revision of Money Supply Series,” Feder
al Reserve Bulletin (August 1962), pp. 941-51.
________“A New Measure of the Money Supply,” Federal
Reserve Bulletin (October 1960), pp. 1102-23.
Advisory Committee on Monetary Statistics. Improving the
Monetary Aggregates: Report of the Advisory Committee on
Monetary Statistics. Board of Governors of the Federal
Reserve System, 1976.
Axilrod, Stephen. “ Comments in ‘Is the Federal Reserve’s
Monetary Control Policy Misdirected? Resolved: That the
Federal Reserve’s Current Operating Procedures for Con
trolling Money Should be Replaced,’ ” Journal of Money,
Credit and Banking (February 1982), pp. 119-47.
Bank of England. Report of the Seasonal Adjustment Working
Party, Occasional Paper no. 2 (October 1992).
Barnett, William A. “ Economic Monetary Aggregates: An
Application of Index Number and Aggregation Theory,”
Journal of Econometrics, Annals of Applied Econometrics
1980-3, a supplement (1980), pp. 11-48.
Beck, Darwin L. “Sources of Data and Methods of Construc
tion of the Monetary Aggregates,” in Improving the Mone
tary Aggregates: Staff Papers. Board of Governors of the
Federal Reserve System, 1978, pp. 117-33.
Board of Governors of the Federal Reserve System. All-Bank
Statistics 1896-1955. Board of Governors of the Federal
Reserve System, 1959.
________Annual Report.
_______ . Annual Statistical Digest.
_______ . Banking and Monetary Statistics 1941-1970. Board of
Governors of the Federal Reserve System, 1976.
________Banking and Monetary Statistics. Board of Gover
nors of the Federal Reserve System, 1943.
_______ . Demand Deposits, Currency, and Related Items (J.3).
_______ . Federal Reserve Bulletin.
________Money Stock, Liquid Assets, and Debt Measures
(H.6).
________Money Stock Revisions, annual supplement to the
H.6.
Box, G.E.P., and G.C. Tiao. “ Intervention Analysis With
Applications to Economic and Environmental Problems,”
Journal of American Statistical Association (March 1975),
pp. 70-9.
Broaddus, Alfred. “Aggregating the Monetary Aggregates:
Concepts and Issues,” Federal Reserve Bank of Richmond
Economic Review (November/December 1975), pp. 3-12.
_______ , and Marvin Goodfriend. “ Base Drift and the
Longer Run Growth of M1: Experience from a Decade of
Monetary Targeting,” Federal Reserve Bank of Richmond
Economic Review (November/December 1984), pp. 3-14.
Cleveland, William P. “ Calendar Adjustment and Time Ser
ies,” Board of Governors of the Federal Reserve System
Special Studies Paper, Division of Research and Statistics,
no. 198 (October 1986).
Copeland, Morris A., and Daniel H. Brill. “ Banking Assets
and the Money Supply Since 1929,” Federal Reserve Bulle
tin (January 1948), pp. 24-32.
Dagum, Estella Bell. The X-11-ARIMA Seasonal Adjustment
Method. Statistics Canada, 1983.
Dewald, William G., Jerry G. Thursby, and Richard G.
Anderson. “ Replication in Empirical Economics: The Jour
nal of Money, Credit and Banking Project,” The American
Economic Review (September 1986), pp. 587-603.
Duprey, James N. “ How the Fed Defines and Measures
Money,” Federal Reserve Bank of Minneapolis Quarterly
Review (Spring-Summer 1982), pp. 10-9.
Farley, Dennis E., and Yueh-Yun C. O’Brien. “ Seasonal Ad
justment of the Money Stock in the United States,” Journal
of Official Statistics (1987, vol. 3, no. 3), pp. 223-33.
Farr, Helen T., Lance Girton, Henry S. Terrell, and Thomas H.
Turner. “ Foreign Demand Deposits at Commercial Banks in
the United States,” in Improving Monetary Aggregates: Staff
Papers. Board of Governors of the Federal Reserve Sys
tem, 1978, pp. 35-54.
Friedman, Milton, and Anna J. Schwartz. Monetary Statistics
of the United States. Columbia University Press, 1970.
Fry, Edward R., Darwin Beck, and Mary F. Weaver. “ Revision
of the Money Stock,” Federal Reserve Bulletin (December
1970), pp. 887-909.
Gilbert, R. Alton. “ Requiem for Regulation Q: What it Did
and Why It Passed Away,” this Review (February 1986), pp.
22-37.
Hallman, Jeffrey J., Richard D. Porter, and David H. Small.
“ Is the Price Level Tied to the M2 Monetary Aggregate in
the Long Run?” The American Economic Review (Septem
ber 1991), pp. 841-58.
Kavajecz, Kenneth A. “The Evolution of the Federal Reserve’s
Monetary Aggregates: A Timeline,” this Review (March/April
1994).
Laidler, David W. The Demand for Money: Theories, Evidence,
and Problems, 4th edition. Harper and Row, 1993.
Lang, Richard W. “ Benchmark Revisions of the Money Stock
and Ranges of Money Stock Growth,” this Review (June
1 9 7 8 ), pp. 11 -9 .
Lawler, Thomas A. “ Seasonal Adjustment of the Money
Stock: Problems and Policy Implications,” Federal Reserve
Bank of Richmond Economic Review (November/December
1977), pp. 19-27.
Lindsey, David, and others. “ Monetary Control Experience
Under the New Operating Procedures,” in New Monetary
Control Procedures. Board of Governors of the Federal
Reserve System, 1981.
Moore, George R., Richard D. Porter, and David H. Small.
“ Modeling the Disaggregated Demands for M2 and M1:
The U.S. Experience in the 1980s,” in Peter Hooper and
others, eds., Financial Sectors in Open Economies: Empiri
cal Analysis and Policy Issues. Board of Governors of the
Federal Reserve System, 1990, pp. 21-105.
National Credit Union Association. Annual Report.
_______ , and Michael R. Grupe. “ Modeling Time Series
When Calendar Effects Are Present,” in Arnold Zellner,
ed., Conference on Applied Time Series Analysis of
Economics Data. U.S. Department of Commerce, 1983,
pp. 57-67.
Orphanides, Athanasios, Brian Reid, and David Small. “The
Empirical Properties of a Monetary Aggregate That Adds
Bond and Equity Mutual Funds to M2.” Board of Gover
nors of the Federal Reserve System Financial and Eco
nomics Discussion Paper no. 93-42, Division of Monetary
Affairs (December 1993).
Collins, Sean, and Cheryl L. Edwards. “ Redefining M2 to
Include Bond and Equity Mutual Funds,” mimeo. Board
of Governors of the Federal Reserve System, 1994.
Pierce, David A., and William P. Cleveland. “ Seasonal Adjust
ment Methods for the Monetary Aggregates,” Federal
Reserve Bulletin (December 1981), pp. 875-87.
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
27
_______ , Michael R. Grupe, and William P Cleveland.
.
“ Seasonal Adjustment of the Weekly Monetary Aggregates:
A Model-Based Approach,” Journal of Business and Eco
nomic Statistics (July 1984), pp. 260-70.
_______ , and John R. Williams. “ Recent Revisions in the
Money Stock: Benchmark, Seasonal Adjustment, and Cal
culation of Shift-Adjusted M1-B,” Federal Reserve Bulletin
(July 1981), pp. 539-42.
Rasche, Robert H. “ Demand Functions for Measures of U.S.
Money and Debt,” in Peter Hooper and others, eds., Finan
cial Sectors in Open Economies: Empirical Analysis and
Policy Issues. Board of Governors of the Federal Reserve
System, 1990, pp. 113-61.
Spindt, Paul A. “ Money Is What Money Does: Monetary
Aggregation and the Equation of Exchange,” Journal of Po
litical Economy (1985), pp. 175-204.
_______ . “M1-Velocity and Money-Demand Functions: Do
Stable Relationships Exist?” Carnegie-Rochester Confer
ence Series on Public Policy (autumn 1987), pp. 9-88.
Simpson, Thomas D. “The Redefined Monetary Aggregates,”
Federal Reserve Bulletin (February 1980), pp. 97-114.
________“A Proposal for Redefining the Monetary Aggre
gates,” Federal Reserve Bulletin (January 1979), pp. 13-33.
_______ , and Richard Porter. “ Some Issues Involving the
Definition and Interpretation of the Monetary Aggregates,”
Controlling Monetary Aggregates III, Federal Reserve Bank
of Boston Conference Series no. 23 (October 1980),
pp. 161-234.
Van Peski, Neva. “Appendix: Data Sources and Construction
of the Proposed Monetary Aggregates,” Federal Reserve
Bulletin (January 1979), pp. 33-42.
Walsh, Carl. “ In Defense of Base Drift,” The American Eco
nomic Review (September 1986), pp. 692-700.
Walter, John R. “ Monetary Aggregates: A User’s Guide,” Fed
eral Reserve Bank of Richmond Economic Review (Janu
ary/February 1989), pp. 20-8.
Walton, Jack, and others. “ Performance Evaluation of Money
Stock, Liquid Assets, and Debt Measures (H.6) Statistical
Release,” unpublished memorandum. Board of Governors
of the Federal Reserve System, Division of Monetary
Affairs, 1991.
MARCH/APRIL 1994
28
Appendix
Building Historical Monetary Aggregates 1959-80
The 1980 redefinition of the monetary ag
gregates confronted Board staff with the daunt
ing task of building comparable historical data.
In some cases, large amounts o f additional data
needed to be collected. In others, various esti
mates and approximations had to be made since
required historical data had not been collected
in the needed detail, at the desired frequency,
or on the basis of consistent definitions. Although
the data sources available as o f 1977 have been
described elsewhere, little has been written
about the earlier data.1 This appendix, based on
published and unpublished material, summarizes
available information about the data sources and
methods used to construct monetary aggregates
for years prior to 1980.
Monetary aggregates are built by consolidation
of data, not addition. Consolidation requires not
only data on the types and amounts of outstand
ing liabilities of financial intermediaries but also
data on the ownership of such liabilities by
other money-stock-issuing institutions, the latter
being netted from the aggregate during consoli
dation. So far as possible, the discussion below
reviews available data on both items.
DEPOSITS INCLUDED IN M l
Most commercial bank deposit items were
available at least twice a year from call reports.
Demand deposits had been reported by member
banks since well before 1959. Call report data
were available quarterly from all banks begin
ning in 1961, when quarterly call reports be
came required by law.
Daily data on OCD accounts were available for
member banks. End-of-month data begin
ning in September 1972 for other New England
financial institutions were obtained from the
Federal Reserve Bank of Boston.
MSBs issued two types of demand deposits.
One was used for regular third-party payments,
'Beck (1978) describes data available in 1977 and refers to
unpublished memoranda for earlier sources and methods.
Our discussion here draws from unpublished Federal
Reserve Board memoranda by Neva Van Peski and Darwin
Beck, and from Van Peski (1979). We thank them for help
ful comments while absolving them of responsibility for
remaining errors or omissions.
2The report form filed by weekly reporting banks had been
revised in 1961 and 1966 to improve coverage of these
http://fraser.stlouisfed.org/
FEDERAL
Federal Reserve Bank RESERVE BANK OF ST. LOUIS
of St. Louis
that is, it was checkable. The other consisted
mainly of escrow balances, not used for regular
payments. Only the first is included in the
monetary aggregates. Separation of the two
types of deposits prior to 1980 was based on
month-end data collected by the FDIC during an
18-month survey conducted from July 1975 to
December 1976. The survey data themselves
were included in M l for the 18 months they
were available. Before and after this period, data
on total demand deposits reported on semi
annual or quarterly call reports were multiplied
by the average ratio of checkable to total de
mand deposits during the survey period. Month
ly data were obtained by interpolation.
Share draft balances at federal credit unions
were obtained from the National Credit Union
Administration (NCUA) as o f month-end for MaySeptember 1976. Thereafter, only end-of-quarter
data were available. No data were available on
share drafts at state credit unions. For total
credit union savings deposits, as o f July 1977,
federal credit unions held 55 percent o f savings
deposits; their share o f share draft accounts is
unknown.
Under the 1980 definition o f the monetary ag
gregates, demand deposits at commercial banks
due to thrifts, foreign banks and foreign official
institutions are subtracted from total demand
deposits in building M l (see Table 2). Demand
deposits at U.S. commercial banks due to foreign
commercial banks and official institutions were
available weekly (on Wednesday) for weekly
reporting banks since May 1961, and quarterly
or twice a year from call reports for all banks
since (at least) 1959.2 Ml-type deposits at
foreign-related institutions were available as of
the last Wednesday of the month since Novem
ber 1972 (beginning in 1977, Edge Act corpora
tions reported only quarterly, but other
institutions continue to report monthly). For
earlier years, estimates were based on data
items; see the introduction to chapter 4 in Banking and
Monetary Statistics 1941-1970. Ironically, these data were
originally collected from weekly reporting banks so that
they could be added back into the monetary aggregates
after being removed during earlier adjustments. Following
the 1980 redefinitions, these reported data were used to
remove the same items from the new aggregates.
29
taken from the Annual Report of the Superin
tendent of Banks in New York and for Edge
Act corporations from call reports submitted
twice a year to the Federal Reserve Bank of
New York.
Deposits due to thrifts were handled in vari
ous ways. For MSBs, demand deposits at weekly
reporting (commercial) banks (FR2416 reporters)
due to MSBs were available for each Wednesday
since May 1961. Quarterly or semiannual data
for all commercial banks also were available on
call reports since before 1959. These deposits
were netted out of Ml. For credit unions, de
mand deposits at all commercial banks due to
credit unions were estimated to equal 0.03 per
cent of total year-end credit union assets for
each year through 1974. After 1974, they were
taken to equal the "cash” item in the annual
reports o f the NCUA. (No adjustment was made
for credit union vault cash, also included in this
item.) For savings and loan associations (S&Ls),
demand deposits at commercial banks before
1973 were assumed to be a constant fraction of
the item “cash on hand and in banks” reported
annually in condition statements issued by the
Federal Home Loan Bank Board (FHLBB); we do
not know the value of the fraction used. Begin
ning September 1973, semiannual call reports
are available in March and September from the
FHLBB.
DEPOSITS INCLUDED IN THE
NON-MI COMPONENT OF M2
Savings D eposits
The savings deposit component o f M2 includes
deposits at commercial banks, MSBs, S&Ls and
credit unions. As usual, construction o f mone
tary aggregates requires both gross deposit
amounts and, as a netting item, the amounts of
deposits held by other money stock issuers.
Monthly savings deposit data generally were
available beginning in 1968. For prior years, sav
ings deposits often were estimated as a constant
share of total deposits, the share itself being es
timated from data available circa 1968. The fol
lowing paragraphs discuss estimates for each
type of depositary.
For commercial banks from June 1961 through
June 1966, total savings deposits were taken
from semiannual and quarterly call reports;
monthly values were obtained by interpolation.
For July 1966 through January 1968, savings
deposits at member banks were estimated from
monthly summary reports submitted by the Fed
eral Reserve Banks (FR422). Beginning January
1968, member banks reported daily savings
deposits each week. Monthly nonmember bank
data were obtained by interpolation of quarterly
call reports.3 The number of data items required
as netting items in consolidation is small since
commercial banks were not permitted to offer
savings accounts to profit-making businesses
(including other depositories) prior to November
1975. Thereafter, data regarding savings deposits
due to domestic and foreign banks and foreign
official institutions were available on Wednes
days for weekly reporting banks and for all
banks on quarterly call reports since March
1976. (Note that this corresponds to current
practices shown in T&ble 2.)
We have been unable to clarify precisely which
data were used from 1959-67 for MSBs. From
1959-67, total deposits were available on a
month-end basis from the National Association
of Mutual Savings Banks (NAMSB), but no
separate savings deposit series was available. For
1968-71, savings deposits were estimated using
total deposit data and a deposit breakdown col
lected in a quarterly survey by the FDIC.4 Begin
ning in December 1971, month-end savings
deposits were published by the NAMSB. Monthaverage data (to correspond to averages of daily
data, so far as possible) were constructed by
averaging month-end data.
3The discussion in this appendix is somewhat more precise
than what we have been able to document. From July 1966
through January 1968, for example, Board staff wrote that
“ nonmember bank data were estimated using ratios gener
ated from call report data...,” but they do not say precisely
how this was done or which ratios were used. The staff
memos do note that nonmember bank data continued to
be taken from call reports after January 1968, and that
monthly values were obtained by interpolation of quarterly
call report data.
4Unfortunately, we have been unable to locate a description
of the estimation procedure.
MARCH/APRIL 1994
30
T\vo netting items were needed for MSBs: sav
ings deposits at MSBs due to the U.S. Treasury,
and savings deposits held by MSBs at commer
cial banks. Both series were available on call
reports beginning in March 1976. Different ap
proximations were used to generate data for pri
or dates. U.S. Treasury deposits were in fact
zero for all months prior to November 1974, the
first month MSBs were permitted to offer
interest-bearing savings deposits to governments.
Government deposits were assumed to be $1
million in November 1974 and all intermediate
months were obtained by linear interpolation.
Similarly, savings accounts held by MSBs at com
mercial banks were assumed to be $1 million in
November 1975 and intermediate months
through March 1976 were obtained by interpo
lation.
For S&Ls, total deposits for all operating S&Ls
from 1959 to June 1968 were obtained from the
Federal Savings and Loan Insurance Corporation
(FSLIC).5 Beginning in July 1968, month-end sav
ings deposits at all federally-insured S&Ls be
came available from the FSLIC. For the earlier
period (1959 to June 1968), savings deposits
were assumed to equal total deposits multiplied
by the July 1968 ratio of savings to total deposits.
Month-average data were obtained by averaging
month-end data.
Savings deposits held by S&Ls at other deposi
tories, netted out in consolidating M2, were
available semiannually beginning in September
1973 from the March-September reporting sys
tem release published by the FHLBB (essentially
a semiannual call report). Values for prior
months were obtained by linear interpolation
between an assumed zero in December 1967
and the September 1973 value of $19 million.
Credit union shares were obtained on a
month-end basis from NCUA.6 Month-average
data are constructed by averaging month-end
data. Deposits of credit unions at other credit
5Conversations with former FHLBB staff during the course
of this research suggest that these data never, in fact, co
vered all operating S&Ls. Some data for non-FSLIC institu
tions were apparently estimated rather than obtained
directly. Other sources report that federally insured S&Ls
likely held as much as 95 percent or more of total S&L
deposits. Recall that state-insured thrifts in Massachusetts
and New York were chartered as MSBs.
6lt isn’t clear whether these data covered all credit unions
or only federally insured institutions. Our guess is the lat
ter. If so, other credit union deposits would be excluded
from the aggregates, perhaps one-half of total credit union
deposits.
http://fraser.stlouisfed.org/
FEDERAL RESERVE
Federal Reserve Bank of St. Louis BANK OF ST. LOUIS
unions, netted out in consolidation, are available
annually for federal credit unions from the
year-end report o f the NCUA beginning in De
cember 1968; values for prior years are as
sumed to be zero.7 Similar data for state credit
unions were estimated by multiplying total as
sets at state-chartered credit unions by the ratio
of such inter-credit-union shares to total assets
at federal credit unions.
Small Tim e D ep osits
The small time deposit component of M2 in
cludes bank and thrift deposits under $100,000
with an original maturity of seven days or more.
U.S. Treasury deposits and deposits of thrifts
with commercial banks and other thrifts are
netted out in consolidation.
For commercial banks, small time deposits
were computed as a residual by subtracting two
series, savings deposits and time deposits of
more than $100,000, from reported data on total
time and savings deposits. Total time and savings
deposits at member banks had been reported
weekly since 1959. Small time deposits at nonmember banks were estimated by multiplying
small time deposits at small member banks by
the ratio o f small time deposits at nonmember
banks to small time deposits at small member
banks on call report dates.8
Time deposits due to the U.S. Treasury and
due to MSBs were netted from the non-Ml
component of M2 in consolidation. For weekly
reporting member banks, these data were availa
ble on Wednesday since 1959 and 1961, re
spectively (however, see Banking and Monetary
Statistics 1941-1970, chapter 4, for a discussion
of changes in items reported). For other banks,
semiannual and quarterly call report data were
available since before 1959.
For MSBs, month-end time deposits beginning
in December 1971 were obtained from NAMSB.
For prior periods, time deposits were estimated
7Smaller credit unions often hold, as a significant part of
their assets, shares in large “corporate central” credit un
ions. Although the latter have some retail business, they
primarily act as an investor of excess funds deposited with
them by other credit unions.
8As in some other cases, this is a somewhat more specific
statement of what we believe was done than we have, in
fact, been able to locate.
31
by Board staff from data on total deposits at
MSBs (available at least from 1959) and from
time deposit data collected on quarterly FDIC
surveys (available at least since 1966). We have
no description of what was done for 1959-65,
but it is likely that the 1966 ratio of time
deposits to total deposits was simply maintained
over this period. (Precisely what was done may
be of little importance, since time deposits at
MSBs were only 1 percent of total deposits in
1966.)
Time deposits of S&Ls at banks are netted
from M2 in consolidation. Beginning in Septem
ber 1973, time deposits of S&Ls at commercial
banks were taken from a semiannual FHLBB
publication, referred to in unpublished Board
memoranda as the FHLBB March-September
reporting system. For all dates prior to Septem
ber 1973, it was assumed that S&Ls kept the
same proportion of their cash assets in bank
time deposits as they had in September 1973. In
other words, S&L time deposits at banks from
1959-72 were assumed to be a constant fraction
of the amount of "cash on hand and in banks”
reported by S&Ls in annual condition state
ments to the FHLBB. The value o f that fraction
was the ratio o f bank time deposits to cash as
sets shown in the September 1973 report in the
FHLBB March-September reporting system.
Time deposits of credit unions at banks and
S&Ls also are netted from M2. Deposits of
credit unions at S&Ls (assumed to be time
deposits) were reported at year-end by federal
credit unions, and were available from the
NCUA Annual Report since before 1959. The ra
tio of these assets to total assets was used to es
timate these items for state-chartered credit
unions. Annual reports issued by the NCUA and
its predecessor were available since before 1959.
Time deposits o f credit unions at commercial
banks were estimated at year-end; until 1974,
they were treated as a residual, the difference
between “cash” reported in the annual reports
and estimated demand deposits. After 1974, the
cash item excluded time deposits, which were
then estimated by applying the ratio o f time
deposits to total assets in 1974 to total assets in
later years. Year-end cash figures were available
since before 1959 for federal credit unions, and
since December 1964 for state-chartered credit
unions from the annual reports.
Large Tim e D ep osits in M 3
The large time deposit component of the
monetary aggregate M3 consists of time deposits
over $100,000 at all depositories less domestic
interbank time deposits and time deposits due
to other depositories, foreign commercial banks
and foreign governments. The distinction be
tween large and small time deposits essentially
begins in 1961. Construction of large time
deposit data beginning in 1961 is discussed by
both Friedman and Schwartz (1970) and Beck
(1978).
MARCH/APRIL 1994
32
Kenneth Kavajecz
The Evolution of the Federal Reserve’s Monetary Aggregates: A Timeline
This timeline follows the history of the monetary aggregates published by the staff o f the Fed
eral Reserve’s Board of Governors. The chronology is based on the Board’s J.3 and H.6 statistical
releases as well as material from the Federal Reserve Bulletin, Money Stock Revisions, and other
publications.
The timeline includes descriptions of all definition changes and benchmark revisions, the basis
on which data were published (monthly, bimonthly, weekly), and the day of the week and time
of day that the money stock data were released to the public. The last are o f particular impor
tance for financial researchers using high frequency data. Additional miscellaneous items related
to the monetary aggregates are included, selected by the author on the basis of their likely im
portance to the evolution of the monetary aggregates and/or the role o f monetary aggregates in
monetary policy.
Note the following in the timeline:
• Each page gives information on events that occurred during a single year.
• The lines at the top of the pages trace the life of every official monetary aggregate published
by the Board staff between 1959 and 1993 (experimental aggregates are excluded). The names
of monetary aggregates that were defined and being published during a year are shown in
bold face on that page, and the period over which they were being published is shown as a
solid line.
• Each event of interest is shown as a vertical line with a parallelogram attached. Each event is
also dated in the upper left corner of the parallelogram.
• Definitional changes are distingished from other events by having a solid vertical line with a
three-dimensional rectangle attached.
Key:
M1A
<
- ........................• ---------------------- >
Undefined
Defined
i
i
i
i
r
/
Definition Change
http://fraser.stlouisfed.org/
FEDERAL RESERVE
Federal Reserve Bank of St. Louis BANK OF ST. LOUIS
/
Other Event
33
1960
,
J , F , M ,
A
M,
J,
J , A , S , O
N,
D,
MI A
M1/M1B
M1+
M1 - shift adjusted
M2
M3
M4
M5
L
z
N ovem ber 14,1960
The first Federal Reserve statistical release on the money supply was published. The J.3
release entitled Demand Deposits, Currency, and Related Items was thereafter published
twice a month. The reported figures were averages o f daily figures rather than the on eday figures reported in the Federal Reserve Bulletin. The money stock was called ’’the
money supply.” It measured a concept that would later be called M I A , namely currency
plus demand deposits adjusted. The currency component included currency held outside
the Treasury, the Federal Reserve, and the vaults o f all commercial banks. The demand
deposit component consisted o f demand deposits other than those due to commercial
banks and the U.S. Government, less cash items in process o f collection (C IP C ) and Fed
eral Reserve float. C IPC items at member and nonmember banks w ere deducted sepa
rately from demand deposits at member and nonmember banks, respectively. Since Fed
eral Reserve float was not divisible on the basis o f a member-nonmember attribution, it
was deducted in whole from the member bank demand deposit component.
(See footnote on J.3 release).
/
1/
Thursday Release
Day of the week released and release time.
Immediate Release
Bi-monthly basis
MARCH/APRIL 1994
34
1961
,
J ,
F , M ,
A
, M ,
J,
J,
A,
S,
O,
N,
D,
MIA
< --------------------------------------------------------------------------------------------------------------------------------►
M1/M1B
M1+
M1 - shift adjusted
M2
M3
M4
M5
L
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
Thursday Release
Immediate Release
Bi-monthly basis
35
1962
,
J
,
F
, M
.
A
,
M
.
J
, J
,
A
.
S
, Q
,
N
. P
,
MI A
-------------------------------------------------------------------------- 4
f
-
..... ---- -------------
M1/M1B
M1 +
M1 - shift adjusted
M2
M3
M4
M5
L
-
Septem ber 11,1962
Annual benchmark and seasonal review.
Benchmarked to call reports available for 1961.
The definition o f M I A was expanded to include demand deposits held by banks located
in U.S. territories and possessions at U.S. commercial banks plus foreign demand bal
ances at Federal Reserve banks. Foreign demand balances included demand deposits
due to foreign governments, central banks and international institutions.
(See Federal Reserve Bulletin (F R B ), August 1962).
'
.......................... .................... V
Thursday R elea se
Im m ed ia te R elea se
B i-m o n th ly basis
MARCH/APRIL 1994
36
1963
J ,
F , M ,
A , M ,
J,
J,
A,
S,
O,
N,
D,
MIA
--------------------------------------------------------------------------------------------------------------
M1/M1B
M1+
M1 - shift adjusted
M2
M3
M4
M5
L
http://fraser.stlouisfed.org/RESERVE BANK OF ST. LOUIS
FEDERAL
Federal Reserve Bank of St. Louis
Thursday Release
Immediate Release
Bi-monthly basis
37
1964
.
J ,
F . M ,
A , M .
J,
J ,
A.
S,
O,
N,
P
MI A
M1/M1B
M1 +
M l - shift adjusted
M2
M3
M4
M5
L
June 29,1964
Annual benchmark and seasonal review.
Benchmarked to call reports available for 1962 and 1963.
(See FRB, June 1964).
Thursday Release
Immediate Release
Bi-monthly basis
MARCH/APRIL 1994
38
1965
,
J
F , M ,
A
M,
J,
J
A
S
O
MIA
l---------------------------------------------------------------------
M1/M1B
M1+
M l - shift adjusted
M2
M3
M4
M5
L
J u ly 3 0 , 1965
Annual benchmark and seasonal review.
Benchmarked to the June and December 1964 call
reports. The J.3 release was replaced by the H.6
release, published weekly on Thursday.
The H.6 release showed week averages o f daily
data on a week ending Wednesday basis.
(See FRB, July 1965).
Thursday Release
Immediate Release
Bi-monthly basis
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
Thursday Release
! Immediate Release
-L
Week ending Wednesday basis
N,
D
39
1966
,
J ,
F , M ,
A . M ,
J ,
J,
A .
S,
O,
N,
D,
MIA
M1/M1B
M1+
M l - shift adjusted
M2
M3
M4
M5
L
June 23, 1966
Effective June 9, 1966, balances accumulated for payment
o f personal loans were reclassified for reserve purposes and
were excluded from time deposits reported by member banks.
Although this did not affect the reported money supply at the
time, it did affect the time deposit series reported separately
on the H.6. The estimated amount o f such deposits at all
commercial banks ($ 1,140 million) was excluded from time
deposits adjusted thereafter.
(See H.6 release).
Setem ber 29,1966
Annual benchmark and seasonal review.
Benchmarked to the June and December 1965 call reports.
(See FRB, September 1966).
Thursday Release
Immediate Release
Week ending Wednesday basis
MARCH/APRIL 1994
40
1967
J ,
F , M ,
A
, M ,
J,
J,
A,
S,
O,
N,
D,
MI A
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
Thursday Release
Immediate Release
Week ending Wednesday basis
41
1968
J,
F , M ,
A
, M ,
J,
J,
A,
S,
Q,
N,
D,
MI A
Thursday Release
Immediate Release
Week ending Wednesday basis
MARCH/APRIL 1994
42
1969
■ J.
F , M ,
a
.
m
,
j
,
j
,
a
.
s
,
o
.
n
,
p
,
MIA
M1/M1B
M1+
M l - shift adjusted
M2
M3
M4
M5
L
August 14,1969
Effective August 6, 1969, the demand deposit component
o f the money supply was increased substantially due to a
change in accounting procedures associated with bank
clearing o f Eurodollar transactions. Previously, an
increasing volume o f such transactions had increased
C IPC without increasing demand deposits. Since C IPC was
deducted from gross demand deposits in computing the
money supply, the net demand deposit concept measured
in the money supply had been understated by an increasing
amount in recent years. A tentative revision was made to
correct the downward bias from June 1967 to July 1969.
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
Septem ber 25,1969
Annual benchmark and seasonal review.
Benchmarked to the June and December 1968
and June 1969 call reports.
(See FRB, October 1969).
Thursday Release
Immediate Release
Week ending Wednesday basis
43
1970
J ,
F , M ,
A
, M ,
J,
J,
A,
S,
O,
N,
D
MIA
M1/M1B
M1+
M1 - shift adjusted
M2
M3
F ebru ary 1,1970
Mr. Arthur F. Bums replaced Mr. W illiam McChesney Martin, Jr.
as Chairman o f the Federal Reserve Board. Chairman Martin had
served since April 2, 1951.
N ovem b er 27,1970
A nn ual benchm ark and seasonal review .
Benchmarked to the December 1969 and June 1970 call reports.
The revision this year encompassed for the first time certain new data,
mainly from agencies and branches in the U.S. o f foreign banks and from
subsidiaries o f U.S. banks organized under the Edge act to engage in
international banking business. These new data served to correct a
downward bias in the money supply series caused by the generation o f
C IPC on the books o f U.S. domestic banks as a result o f clearing a large
daily volume o f international transactions.
(See FRB, December 1970).
Thursday Release
Immediate Release
Week ending Wednesday basis
MARCH/APRIL 1994
44
1971
,
J ,
F , M ,
A , M ,
J,
J ,
A,
S,
O,
N,
D,
MIA*
M1*/M1B
M1+
M l - shift adjusted
M2
M3
M4
M5
L
A p ril 22,1971
The Federal Reserve started to publish 3 monetary aggregates. M l , M 2, M3. M l and M2
were reported on a w eekly and monthly basis while M 3 was reported only on a monthly
basis due to a lack o f data sources at the time.
*M 1 was the same as the previously published money stock, listed above as M I A , only
the name had changed.
M 2 was a broader aggregate that included M 1 plus commercial banks’ savings deposits,
time deposits open account, and time certificates o f deposit other than negotiable CDs
issued in denominations o f $100,000 or more by large weekly reporting commercial
banks.
M 3 was M 2 plus deposits at mutual savings banks and savings and loan associations.
FEDERAL RESERVE BANK OF ST. LOUIS
N ovem ber 18,1971
Annual benchmark and seasonal review.
Benchmarked to the December 1970 and
June 1971 call reports.
(See FRB, Novem ber 1971).
j D ecem ber 9,1971
M oney stock measures have been revised, beginning
in September 1971 to reflect the formation o f new
banking institutions doing primarily international
business. The vague description listed above was
taken from a footnote on the H.6 release.
To what this refers is subject to some debate.
Thursday Release
Immediate Release
Week ending Wednesday basis
45
1972
,
J ,
F ,
M ,
A
M ,
J ,
J , A , S , O
N,
D,
MI A
^
M1/M1B
I
M1 +
I. . . .
M l - shift adjusted
.......................................................................
^
M
................................................................................................................................................................................................................................................................................................................................................................
M2
I
M3
-------------- 1------------------------------------------------------------------------ --------M4
M5
I
L
►
|
........................... I
........................... I
Febru ary 24,1972
Benchmark and seasonal review o f M 3 data.
Benchmarked to reflect new data fo r deposits
at mutual savings banks and savings and loan
shares.
N ovem b er 24,1972
A change in Regulation J, governing check collection procedures, was implemented on
Novem ber 9,1972. Because o f its effects on clearing accounts on bank balance sheets, it
had the effect o f raising demand deposits as calculated for inclusion in the money supply.
However, to avoid any discontinuities in the series, the resulting increase had been elim i
nated from the current series until the annual benchmark and seasonal review.
Thursday Release
Immediate Release
Week ending Wednesday basis
MARCH/APRIL 1994
46
1973
J , f , m , a , m ,
j
,
j
, a ,
s
, o , n , d ,
MIA
M1/M1B
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
Thursday Release
Immediate Release
Week ending Wednesday basis
47
1974
,
J , F . M . A , M . J , J , A . S , Q , N . D
MIA
M1/M1B
M1+
M1 - shift adjusted
M2
M3
M4
M5
L
J a n u a r y 3 1, 1974
Annual benchmark and seasonal review.
Benchmarked to the December 1972 as w ell as
the March, June and October 1973 call reports.
1973 was the first year since the early
1960s when call report data appropriate
for money supply benchmarks had been
available for the spring and fall.
(See FRB, February 1974).
M a y 23,1974
Benchmark.
Benchm arked to the Decem ber 1973 c a ll report.
(See H .6 release).
' August 22,1974
Benchmark.
Benchmarked to the April 1974 call report.
(See H.6 release).
N ovem ber 21,1974
Annual benchmark and seasonal review.
Benchmarked to the June 1974 call report.
(See FRB, December 1974).
Thursday Release
Immediate Release
Week ending Wednesday basis
MARCH/APRIL 1994
48
1975
,
J , F , M , A , M , J , J , A , S , Q , N , D ,
MIA
■
' i ................. i ....................................................... i .......................... ........................
i
i
i
1
1
1
I
I
1
-
M1/M1B
- i ................. i ....................................................... i ...................................................
i
i
i
j
M1+
M1
-
M2
M3
s h ift a d ju s te d
-
----------------- 1.............. ........................ ................ 1 ...................................................
I
1
!
1
1
M4
"
M5
W
|
I
^
1
i\
1
1
1
I
|
1
™
'
^
|
- - - - - 1i l
1
L
......................... I .................
I
I
/ February 20, 1975
-
_ - - - - - -j
- ................. i ....................................................... i ...................................................
1
i
■
/ |
i
i
/ Benchmark and seasonal review.
/
/ Benchmarked to the October 1974 call report.
/
(See H .6 release).
/
i
i
A p ril 3, 1975
On April 3, 1975, the Federal Reserve published two additional monetary aggregates,
M4 and M5.
M l and M 2 remained unchanged from their inception in 1971.
The definition o f M3 was revised to include credit union shares.
M 4 was defined as M2 plus large negotiable time certificates o f deposits issued by large
weekly reporting commercial banks.
M5 was defined as M3 plus the same large time deposits added to M4.
✓
............................................................................................................................. is
_______I_________________________
_________________________ I_____
F O M C M eeting, A p r il 14-15,1975
Septem ber 18,1975
First target growth cones announced for the
Benchmark.
monetary aggregates.
Benchmarked to the April 1975 call report.
(See Anderson and Kavajecz, 1994, Table 4)./
(See H.6 release).
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
M a y 22,1975
Benchmark.
Benchmarked to the December 1974 call report.
(See H.6 release).
Thursday Release
Immediate Release
Week ending Wednesday basis
49
1976
,
J . F . M ,
A
M,
J,
J , A , S , Q , N ,
D
MI A
/ O ctob er 21, 1976
/ Benchmark.
/
/
Benchmarked to the March 1976 call report.
(See H.6 release).
Thursday Release
Immediate Release
Week ending Wednesday basis
MARCH/APRIL 1994
50
1977
J .
f
.
m
.
a
.
m
.
j
.
j
.
a
.
s
.
o
.
n
.
p
MI A
http://fraser.stlouisfed.org/
FEDERAL RESERVE
Federal Reserve Bank of St. Louis BANK OF ST. LOUIS
June 23,1977
Benchmark.
Benchmarked to the December 1976 call report.
(See H.6 release).
Thursday Release
Immediate Release
Week ending Wednesday basis
51
1978
J,
F , M ,
A
, M
,
J,
J,
A,
S
O
D
N
MI A
T' 1
r ■ ■r
M1 +
M l - shift adjusted
T* 1
M2
M3
M4
M5
June 1,1978
February 10,1978
Money Market Time Deposits
Data from the Boston District estimatec
were authorized by Congress. i
Money stock measures for the week o f
I
I
February 1, 1978 subject to larger than
normal revisions.
I June 22,1978
Benchmark.
September 21,1978
Annual benchmark and seasonal review.
Benchmarked to the
Benchmarked to the March 1978 call report.
December 1977 call report.
Corrected a recently discovered downward cash
(See H.6 release).
items bias over the period mid-1975 through
September 1978. The bias was created by foreign j
March 8,1978
related institutions transferring funds fo r their
Mr. G. William M iller replaced
parent or subsidiaries.
Mr. Arthur F. Burns as Chairman
(See H.6 release).
o f the Federal Reserve Board.
Chairman Bums resigned on
January 31, 1978.
November 16,1978
On Novem ber 16, 1978, the Federal Reserve published yet another money stock mea
sure, M1+.
M arch 23,1978
M l, M2, M3, M 4 and M5 remained unchanged from the definitions outlined in 1975.
Annual benchmark and seasonal review.
M 1 + was defined as the narrow money stock measure, M 1, plus savings deposits at com
Benchmarked to the December 1976
mercial banks, N O W accounts at banks and thrift institutions, credit union share drafts,
as well as March, June, and
and demand deposits at mutual savings banks.
September 1977 call reports.
nr*
(See H.6 release).
Thursday Release
Immediate Release
Week ending Wednesday basis
MARCH/APRIL 1994
52
1979
J
F . M
A
M
. J . J . A
S . O
N
D,
MI A
M 1/M1B
^
1
M1 +
M l - shift adjusted
M2
\
M3
1
■|...................r -------------- 1------- 1 '
i
i
i
i
i
i
i
i
1
1
1
1
1
1
1
1
i
i
i
i
i
i
i
i
- i - ................ i-.................. i------- 1i
i
i
i
i
i
i
i
I
I
|
i
1
!
i
I
!
I
|
i
■
\
M4
^
I
I
I
!
i
^
^
^
!
f-
^
M5
L
I
i
/F ebru ary 8,1979
/
/ Annual benchmark and seasonal review. /
/ Benchmarked to the June 1978 call report. /
/ (See H.6 release).
/
i
■
i
i
i
i i
-|...................r .................. i------- 1 i
i
i i
i
i
/ August 6,1979
/ j
/ Mr. Paul A . Volcker replaced
/
/ Mr. G. W illiam M iller as Chairman /
/ o f the Federal Reserve Board.
/
1
1
f M a y 24,1979
Benchmark.
1
O ctob er 6,1979
On Saturday October 6, 1979, Chairman Volcker
Benchmarked to the September 1978 call report.
called a special meeting o f the F O M C where he
(See H.6 release).
announced the Federal Reserve would switch to
http://fraser.stlouisfed.org/
FEDERAL St. Louis
Federal Reserve Bank of RESERVE BANK OF ST. LOUIS
a nonborrowed reserve operation procedure.
The m ove placed a greater emphasis on the M l
aggregate due to its close relation to the
outstanding supply o f reserves.
N ovem ber 8,1979
The money supply figures published on Novem ber 8, 1979 for the weeks
ending October 3, 10, 17, and 24th incorporated minor corrections made
to the data due to an understatement o f the deposits provided by
Manufacturers Hanover Trust Company in the last four weeks. The
Federal Reserve had begun an inquiry, with the help o f outside counsel,
to provide assurance that recent errors in the money supply data were
inadvertent and that no individual or institution obtained improper
advantage from the preparation, revision and release o f these figures.
Thursday Release
Immediate Release
Week ending Wednesday basis
53
1980
M
A ■ M , J , J
O
N
D
MIA
M1/M1B
«*-
M1+
«*-
M1 - shift adjusted
M2
M3
M4
•<-
M5
■<-
January 10,1980
June 20, 1980
N ovem ber 7,1980
Benchmark.
Benchmark.
The money supply figures that would normally be
Benchmarked to the December 1978
Benchmarked to the June and
published on Novem ber 14, 1980 may be delayed fo r /
and March 1979 call reports.
September 1979 call reports.
a time in view o f changes in the flows o f data
(See H.6 release).
(See H.6 release).
required by the Monetary Control A ct o f 1980.
The next H.6 release went out on Novem ber 18th.
Febru ary 8,1980
On February 8, 1980, the Federal Reserve radically reorganized how the monetary aggregates were defined.
M l was renamed M I A without changing its definition.
M 1B was defined to be M I A plus N O W and automatic transfer service (A T S ) accounts at banks and thrift institutions, credit union
share draft accounts and demand deposits at mutual savings banks.
M 2 was redefined to be M 1B plus overnight (and continuing contract) repurchase agreements (R P ) that are issued by commercial
banks to the non-bank public, overnight Eurodollars issued by Caribbean branches o f member banks to U.S. non-bank customers,
money market mutual fund shares, savings deposits and small time accounts (those issued in denominations less than $100,000) at
commercial banks and thrift institutions. N ote that M 2 w ill differ from the sum o f its components by a consolidation adjustment
made to avoid double-counting the public’ s monetary assets, namely, the amount o f demand deposits held by thrift institutions at
commercial banks.
M 3 was defined to be M 2 plus large time deposits (those issued in denominations o f $100,000 or more, net o f the holdings o f
domestic banks, thrift institutions, the U.S. government, money market mutual funds, and foreign banks and official institutions),
and term RPs at commercial banks and thrift institutions, net o f term RPs held by money market mutual funds.
A new aggregate, L , was created and defined to be M 3 plus the non-bank public’s holdings o f U.S. savings bonds, short-term
Treasury securities, commercial paper and bankers acceptances (which excludes money market mutual fund holdings o f these assets).
In addition, two addenda were included on the H.6 release, overnight RPs at commercial banks plus overnight Eurodollars and
money market mutual fund shares.
Feb ru ary 15,1980
Seasonal factors for the newly defined aggregates were released on the H.6.
(See FRB, February 1980).
Friday Release
Immediate Release
Week ending Wednesday basis
MARCH/APRIL 1994
54
1981
, J ,
M IA
F , M .
A , M .
J,
J.
A,
S,
O,
N,
D.
M1/M1B
M1+
!
..................................... I.....................
M1B - shift adjusted
-►
M2
-►
M3
-►
M4
M5
L
__ L.
January 16 and 23,1981
M a y 22,1981
The H.6 emphasized caution when
Another monetary aggregate, called M lB -sh ift adjusted, was introduced. It was defined
interpreting the monetary aggregates
to be M 1B less shifts to O C D from non-demand deposit sources.
because o f the introduction o f N O W
A ll the definitions o f the other monetary aggregates remained unchanged.
accounts on a nationwide basis with
heavy promotional efforts.
January 23,1981
Benchmark.
June 26,1981
Benchmarked to the December 1979
Benchmark.
and March 1980 call reports.
Benchmarked to the September and December 1980 call reports.
This incorporated all the changes due to
The definition o f the narrowest measure o f the money stock, M 1, was revised to include
the implementation o f the Monetary
non-bank travelers checks.
Control Act.
A ll the definitions o f the other monetary aggregates remained unchanged.
(See H.6 release).
M a y 1,1981
Annual seasonal review.
Adjustment o f the monetary aggregates
to include the effects o f N O W accounts. I
(See H.6 release).___________________
M a rch 13,1981
Septem ber 18,1981
The H.6 cautioned the interprepation o f the aggregate measures
The term R P component o f M 3 was revised
due to the shifting o f demand deposits and savings deposits into
and benchmarked to a survey o f ’’retail RPs”
other checkable deposits (O C D ) accounts. Estimates o f the shifts
conducted on August 31, 1981. The current
obtained from various depository institution samples suggested
methods o f estimation did not pick up the increase
that in January and February, 75 to 80% o f the increase in
which was attributed to recent active promotion.
excess o f ’’trend” came from demand deposits and the other 20
(See H.6 release).________________________________
to 25% came from savings deposits and other sources.
(See H.6 release)._________________________________________________
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
Friday Release
Immediate Release
Week ending Wednesday basis
55
1982
J . F
M
A
M
J . J
A
S . O
N . D ,
MI A
Friday Release
Friday Release
@ 4:10 PM EDT_____________________________________________________________________________________*4:15 PM EDT
Week ending Wednesday basis (W.E.W.)
* (W.E.W.)
MARCH/APRIL 1994
56
1983
, J , F , M , A
M,
J ,
J , A , S , O
N,
D,
MI A
M1/M1B
M1+
L
M1B - shift adjusted
M2
-►
M3
-►
M4
M5
L
' January 28,1983
The Gam-St. Germain A ct o f 1982 had recently authorized money market deposit ac
counts. Beginning on January 28, 1983, M M D A s were reported separately as a
component o f the broader monetary aggregates. Due to the lack o f historical data, they
were reported on a not seasonally adjusted basis. Note that this did N O T revise the
monetary aggregates because the deposits had previously been included in the savings /
component o f M2.
I
F eb ru a ry 14, 1983
A nn ual benchm ark and seasonal re view .
Benchmarked to the December 1981 and March, June, and September 1982 call reports.
T w o definitional changes have been implemented.
M 2 was revised to include general purpose/broker dealer (GP/BD) tax-exempt money
market mutual funds and exclude all IRA/Keogh balances at depository institutions and
money market mutual funds.
O ctob er 1,1983
The D ID C m oved to amend Regulation
Q by eliminating interest rate ceilings
on time deposits with maturities greater
than 31 days and principal greater
than $2,500.
(See FRB, Novem ber 1983, Table 1.16).
M 3 was revised to include institution-only (I/O) tax-exempt money market mutual
funds.
(See H.6 release).
M a y 20th through June 10th 1983
/
W eekly data on savings deposits and small time deposits were not reported due to report
ing difficulties associated with M M D A s. In addition, historical data were revised to re
flect corrections o f reporting errors beginning in December 1982.
j
(See H.6 release dated June 10, 1983).______________________________________________j
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
Friday Release
@4:15 PM EDT
Week ending Wednesday basis
57
1984
, J , F , M , A , M , J , J , A , S , Q , N , D ,
M IA
M 1/M1B
M1+
. . . . . . . . . . . . .I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. .. .. .. .. .. .. .. .. .. .. . . . . . . . . . . . . . . . . . . . . . . . . . . . -. -. -. -. .- .- .-. - r - - i
i
i
i
_ _ _ _ _ L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ............................................ i - - - - - - - - - - - - - _
.........
M1B - shift adjusted
.............
................................... r ..................
i
1
M2
M3
^ • M4
■
W
W
1
£
...........................
..................................... h ..................
i
i
..................................................................... r ..................
i
---------------------------------------------------------- j----------------- ►
M5
L
-----------February 16,1984
Annual benchmark and seasonal review.
Benchmarked to recent call reports.
The H.6 published on February 10, 1984 was the last one that
presents deposits data on a week-ending Wednesday basis.
A ll data shown on the H.6 dated February 16, 1984, was shown on
a week-ending Monday basis to correspond with the new reporting
cycle under contemporaneous reserve requirements (C R R ).
In addition, M 3 was redefined to include term Eurodollars in Canada
and the United Kingdom that are held by U.S. residents.
The rest o f the aggregates remained unchanged definitionally.
(See H.6 release).
M arch 22, 1984
The H.6 began being released at 4:30 PM E D T on Thursdays. /
November 1,1984
Benchmark.
Benchmark due to revised data received in conjunction with annual shifts among
weekly, quarterly and annual reporting panels. Similar benchmarks were not needed
in later years because o f improvements in the procedure used to handle the panel shifts
at the Federal Reserve. In addition, institution-only money market mutual fund shares y
were revised back to Novem ber 1980 to reflect new data.
Friday Release
Thursday
Thursday Release
@ 4:15 PM EDT| 4:15 PM
j @ 4:30 PM EDT
W.E.W.
I Week ending Monday (W .E.M .)
I W .E.M.
MARCH/APRIL 1994
58
1985
,
J . F . M ,
A
M,
J,
J , A , S , O
N,
D
MI A
http://fraser.stlouisfed.org/
FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
/ N ovem ber 21,1985
/ The Bank o f N ew York experienced a computer
j
/
failure that resulted in a substantial transitory
increase in reported demand deposits.
Thursday Release
@ 4:30 PM EDT
Week ending Monday
59
1986
, J , F , M ,
A
M,
J,
J
A
S
O
N,
D,
MI A
M1/M1B i
M1 +
M1B - shift adjusted
M2
-►
M3
►
M4
M5
L
February 13,1986
Annual benchmark and seasonal review.
Benchmarked to call reports through June 1985.
(See H.6 release).
August 21,1986
January 1,1986
Estimates o f M 2 and M3 were revised upward,
Regualtion Q was further revised by
reflecting new data for RPs obtained from regular
the D ID C by abolishing interest rate
quarterly and annual surveys for the end o f June.
ceilings on both N O W accounts and
(See H.6 release).
time deposits with maturities less than
31 days.
(See FRB, March 1986, Table 1.16).
O ctob er 22,1986
Demand deposits increased sharply during the next
A
two months follow in g passage o f the Tax Reform Act. ,
A p ril 1,1986
The D ID C alleviated the interest rate
ceilings on savings deposits.
(See FRB, June 1986. Table 1.16).
.......-
.
V
Thursday Release
@ 4:30 PM EDT
Week ending Monday
MARCH/APRIL 1994
60
1987
,
J,
F , M ,
A
, M ,
J,
J,
A,
S,
O,
N,
D,
MI A
http://fraser.stlouisfed.org/
FEDERAL St. Louis
Federal Reserve Bank ofRESERVE BANK OF ST. LOUIS
(O c to b e r 19,1987
The D ow Jones Industrial Average plummeted 500
points sending other major stock exchanges into a
significant decline as well. The effect on the
monetary aggregates was to boost liquid components
due to the increased volume o f transactions.
Thursday Release
@ 4:30 PM EDT
Week ending Monday
61
1988
M
M
O
N
D
MIA
\11/M 1B
M1 +
M1B - shift adjusted
M2
►
M3
►
M4
M5
+
l
February 18, 1988
Annual benchmark and seasonal review.
Benchmarked to call reports through June 1987.
Beginning on February 18, 1988, the H.6 included weekly estimates of M2 and M3 sea
sonally adjusted and seasonally unadjusted on the same publication schedule as M 1.
M 1 was redefined to make the treatment of thrift institutions identical with that of com
mercial banks in the construction of the monetary aggregates. Under the new definitions,
all vault cash held by thrift institutions was excluded from the currency component of
M l, and all demand deposits and OCDs held by thrifts were excluded from the demand
deposit and OCD components, respectively. Previously, only a portion of the vault cash
and transactions deposits held by thrifts were excluded at the M 1 level— representing the
estimated amount held to service their OCD liabilities— while the remainder was sub
tracted at the M2 level.
In addition to the redefinitions noted above, ATS accounts at credit unions— like those at
commercial banks and all other thrift institutions— were now included in the OCD com
ponent of M l, rather than in the savings deposit component of M2.
The monetary aggregates M2 , M3 and L had no change in their definitions.
(See H.6 release).
y
i
i
/
March 10,1988
/
Weekly seasonal factors for the nontransactions component of M2 /
beginning with the week of March 28, 1988 were revised to
/
incorporate further analysis of certain holiday-related effects.
/
(See H.6 release).
/
Thursday Release
______________________________________________________________________________________@ 4:30 PM EDT
Week ending Monday
MARCH/APRIL 1994
62
1989
.
J ,
f
.
m
,
a
,
m
,
j
,
j
,
a
,
s
.
o
,
n
.
d
,
MIA
M l/M lB ir
M ----------------- 1
----------------------------------------------------------------------------------------------------------------------►
M1 +
M1B - shift adjusted
RESERVE BANK OF ST. LOUIS
FEDERAL
Thursday Release
@ 4:30 PM EDT
Week ending Monday
63
1990
MIA
M1/M1B
M1 +
M1B - shift adjusted
M2
-►
M3
-►
M4
M5
L
February IS, 1990
Annual benchmark and seasonal review.
Benchmarked to call reports through June 1989.
M2 was revised to include overnight RPs issued by thrift institutions, formerly included
with term RPs in the non-M 2 component of M3.
This redefinition had no effect on the levels of M l , M3 or L.
(See H.6 release).
............................................................................................. 1 '
^
Thursday Release
@ 4:30 PM EDT
Week ending Monday
MARCH/APRIL 1994
64
1991
I __ J . I f , m
_ ___ _______L
,
a
, m .
j
,
j
.
a
,
s
,
o
,
n
,
d
,
MIA
M1/M1B
I----------
M1+
M1B - shift adjusted
M2
l--------
M3
►
l--------
M4
M5
L
February 7,1991
Annual benchmark and seasonal review.
Benchmarked to call reports through June 1990.
(See H.6 release).
FEDERAL RESERVE BANK OF ST. LOUIS
I October 3,1991
There was a change in the format of the H.6 release. The change is necessary because, on
September 17, 1991, depository institutions began reporting to the Federal Reserve only
their combined savings deposits and MMDAs, rather than reporting them separately,
owing to changes in the deposits reports (FR2900). In order to calculate consistent
seasonally adjusted data, the new seasonal factors are equal to the inverse of the weighted
average of the inverses of the seasonal factors for savings deposits and MMDAs, where
the weights are defined as the ratio of each component to the sum of the components
during the month of August. In other words, the total of savings and MMDAs was split
into its two components, ’savings’ and ’MMDAs’ for both commercial banks and thrifts.
Then its old seasonal factors (published in February 1991) continued to be used, namely,
the seasonal factors for bank savings, bank MMDAs, thrift savings, and thrift MMDAs.
(See H.6 release).
Thursday Release
@ 4:30 PM EDT
Week ending Monday
65
1992
I
i J i
MIA
F
A i M ,
A , M ,
J ,
J ,
A,
S,
O,
N,
D,
.............................................................................................. ..................
M1/M1BI
^
I
w
M1 +
_________ I. . L _____________________________________________________________________
M1B - shift adjusted
M2
1
M3
^
1
.................. I .
.
M5
M4
.
.................... L . .
^ L
!
1
1
1
1
1
February 13,1992
/
Annual benchmark and seasonal review.
Benchmarked to call reports through September 1991.
(See H.6 release).________________________________
I
March 5, 1992
I
The release dated March 5, 1992 incorporates further
/ revisions to historical data. The change was due to the
/ reclassification of some brokered deposits from large time
/
to small time deposits in addition to those reported in the
/
annual benchmark on February 13, 1992.
/
(See H.6 release).
Thursday Release
@ 4:30 PM EDT
Week ending Monday
MARCH/APRIL 1994
66
1993
,
J
,
F
,
M
.
A
,
M
,
J
,
J
.
A
,
S
.
O
,
N
.
D
.
MIA
M1/M1B I"
M ----------------- 1
---------------------------------------------------------------------------------------------------------------------- ►
M1+
.................. I .........................................................................................................................................
M1B - shift adjusted
FEDERAL RESERVE BANK OF ST. LOUIS
Thursday Release
@ 4:30 PM EDT
Week ending Monday
67
Charles W. Calom iris
Charles \N. Calomiris is an associate professor a t the Universi
ty o f Illinois, Urbana-Champaign, a nd is a co-director for the
university’s Office for Banking Research. He is also a faculty
research fellow, N ational Bureau o f Econom ic Research, and
a visiting scholar at the Federal Reserve B ank o f St. Louis.
Com m entary
M. N THEIR PAPER, Anderson and Kavajecz pro
vide the rare public service of a careful exami
nation of the construction of m onetary data.
The paper is im portant because the data on
m onetary aggregates are central to academic
and policy research in macroeconomics. I expect
that by the m etric of the percentage of m one
tary economists who will have this paper in
their file cabinets 10 years from now, this will
be one of the most successful works in m one
tary economics. Data are forever. Like the Feder
al Reserve Board’s Banking and Monetary
Statistics and All Bank Statistics, Friedman and
Schwartz’s Monetary Statistics o f the United
States, Capie and Wood’s Monetary Statistics o f
the United Kingdom, and Eisner’s How Real is the
Federal Deficit?, Anderson and Kavajecz pose and
answ er descriptive questions of lasting interest
to macroeconomists. Judging from the paucity
of this kind of work, its im portance seems to be
underestim ated.
I found little to quibble w ith in the way the
authors organized their description. In my dis
cussion I will focus on the question of why
researchers doing empirical m onetary economics
should care about the details of how m onetary
aggregates are m easured and how those m eas
urem ents have changed over time.
Five sets of issues seem central in motivating
the potential usefulness of this exercise. First,
and most obviously any attem pt to construct
m onetary aggregates for long stretches of time
m ust do its best to ensure comparability of
measures. This m eans coming to grips not only
w ith financial innovations that affect the range
of definitions of money, but also with changes
in sampling procedures, seasonal adjustment,
and other choices made by the data con
structors.
Second, the Fed’s procedure of revising data
retrospectively to m aintain consistent definitions
and seasonal adjustm ent factors—which some
times have produced large retrospective revi
sions of the aggregates—makes it difficult to
compare empirical research of different vin
tages. For example, two studies of Ml money de
m and over the same period, perform ed at
different dates, may differ not only because of
specification, b ut because of the vintage of data
used in each. It would be worthwhile to ask
how m uch of the differences across studies
of money dem and can be attributed to retro
spective revision of data, as opposed to the
incorporation of additional periods of data, or
differences in specification.
Third, there should be an objective outside
evaluation of the Federal Reserve Board's choices
of definitions of money and methods of seasonal
and benchm ark adjustment. Prior to this study,
this was not feasible because relatively little was
known about the Fed’s procedures. Anderson
and Kavajecz suggest that the Fed’s decisions
MARCH/APRIL 1994
68
regarding w hat to include in the m onetary
aggregates are often influenced by w hether
adding a new com ponent helps to stabilize the
relationship betw een money and economic
activity. While this procedure may make sense,
in general, given the Fed's desire to use m one
tary aggregates as targets, it would be interest
ing to describe clearly how the Fed decides (and
how it should decide) that the improvement in
stability will persist (that is, it reflects a lasting
behavioral change rath er than a tem porary
statistical coincidence). How long should the Fed
wait before incorporating new (apparently
stabilizing) elements of money into its defini
tions of aggregates? Would an increased em pha
sis on Divisia indices be w arranted in light of
the difficulties posed by having to make an
all-or-nothing decision about w hether to include
financial assets in one or m ore of the aggregates?
Regarding seasonal adjustment, it would be in
teresting to consider how the Fed should deter
mine w hen a change in seasonal factors has
occurred—and how far back retrospective
changes in seasonality should be made. W hat is
the optimal choice of the period over which de
term inistic seasonals should be estimated? How
much less relevant is distant information for
estimating seasonal com pared to recent inform a
tion? Anderson and Kavajecz have provided
researchers interested in these questions with a
wealth of detail that will allow them to con
struct counterfactual rules for defining m one
tary aggregates, and to compare these with
those adopted by the Fed.
Fourth, if the Fed attem pts to keep m onetary
aggregates "on track” relative to economic activi
ty (by altering definitions and adjustm ent fac
tors), then this makes the reported aggregates
unsuitable for perform ing hypothesis tests about
the stability of money demand. Researchers in
terested in w hether money dem and is stable,
therefore, should perform sensitivity analysis to
examine w hether reasonable counterfactual defi
nitions of the aggregates lead to different con
clusions about the stability of money demand.
Finally, there is a problem I will label the "ex
pectations erro r effect.” The essence of this
problem is that (unforecastable) errors in m eas
urem ent, which affect expectations of agents in
"real time,” may weaken the apparent connec
tion betw een money and output using ex post
(corrected) m onetary data. Assume for the sake
of argum ent (unrealistically) that the current
retrospective data on the m onetary aggregates
FEDERAL RESERVE BANK OF ST. LOUIS
are "correct.” That is, assume that all definitions,
seasonal adjustm ents and revisions that have been
made so far are perfectly accurate, and that no
fu rth e r revisions will be made in the series. Fur
therm ore, assume th at we can agree upon an
econometric procedure for m easuring the close
ness of the relationship betw een money and
output (using, for example, a "structural VAR”
model of money, output and other variables).
Even under these ideal circumstances, the
m easured relationship betw een "true” money
(measured ex post) and economic activity will
be biased toward zero if money is initially
m easured w ith error. The reason is that "true”
money, as well as errors in m easuring aggregate
money, will elicit responses that affect economic
activity and money subsequently. Money and
output are linked through “fundam ental” struc
tural links and through "expectational” effects.
For example, an increase in an individual’s hold
ings of money may lead him to rebalance his
portfolio (putting pressure on interest rates to
fall and output to rise in the standard IS-LM
model). Second, estimates of m onetary aggregates
(which include initial m easurem ent error) will
also be taken into account by the public in
economic activity if aggregates are used as
economic indicators.
In the absence of m easurem ent error, the in
dividual agent can observe w ithout e rro r not
only his own m oney b u t also the aggregate. In
the presence of m easurem ent error, the ag
gregate is observed w ith error, and these errors
will elicit real responses from agents. So, both
announced and tru e money will be linked to
output. Neither will be as strongly linked to out
put as tru e money in the absence of m easure
m ent error, and empirical analysis using ex post
data (after removing errors) may underestim ate
the link betw een money and output.
Thus, tem porary inaccuracies in m onetary ag
gregate estimation (which elicit real responses)
might explain weak correlations betw een money
and output using ex post (accurate) data. How
can one come to grips w ith this problem em piri
cally to decide w hether bias arising from "expec
tations erro r effects” is im portant for conclusions
about the role of money in the economy? One
simple first step is to compare various m easures
of m onetary aggregates (and m onetary grow th
rates) for a given period reported at different
dates. If the differences among these m easures
are small, then the problem of potential bias is
of little practical importance. If the differences
69
Figure 1
M2 Against HM2
Billions of dollars
1981
82
Quarterly data
83
84
85
86
are large, then one would have to take on the
m uch harder job of m easuring the extent of the
bias by gauging the reaction of the public to
m easurem ent errors.
As Anderson and Kavajecz point out, there are
several types of potential error, and each involves
a different correction horizon. First-published
num bers (which appear one or two weeks after
the fact) are updated w ithin a m onth or so be
cause of the arrival of new data. They are
changed (roughly) annually to adjust for changes
in benchm arks and seasonals, and change with
new definitions of the aggregates as well.
As an illustrative exercise, I chose the easiest
case—M2 from January 1981 to January 1993. I
chose this period because, as Anderson and
Kavajecz show, there was no im portant change
87
88
89
90
91
92 1993
in the definition of M2 during this period, so
th at one can focus on the role of revisions from
new data, benchm ark changes, and changes in
seasonal factors as sources of error. I construct
ed m easures for this period using three differ
ent timings of m easurem ent. I used the first
date of publication of m onthly M2 in the H.6
statistical release as my definition of the initial
m easure of M2. This was released roughly two
weeks after the end of the m onth. My second
date of m easurem ent is the M2 figure reported
in the Federal Reserve Bulletin, which appears
with a two-month lag. My third m easure is the
retrospective series as of January 1993.1
Using seasonally adjusted data from these
sources for January, April, July and October, I
constructed m easures of the level of M2 and of
1Table 3 in Anderson and Kavajecz decomposes revisions in
money into three different adjustments and expresses them
in absolute terms. This is interesting for some purposes,
but not for my purpose. I am interested in whether errors
coming from all sources are potentially large relative to the
actual number.
MARCH/APRIL 1994
70
Figure 2
DM2 Against DHM2
Quarterly data
1981
82
83
84
85
86
87
88
89
90
91
92 1993
Figure 3
DM2 Against DOM2
Quarterly data
1981
82
83
FEDERAL RESERVE BANK OF ST. LOUIS
84
85
86
87
88
89
90
91
92 1993
71
that q u arter’s grow th in M2 m easured at the
time the M2 num ber was reported. For example,
M2 grow th for the first q uarter of 1982 accord
ing to the H.6 release is the log difference be
tw een the first H.6 num ber for M2 in April and
the January 1982 num ber reported in that same
release. Figures 1-3 compare these definitions of
money and money growth using these three
m easurem ent horizons. The level and growth
data from the 1993 series are labeled M2 and
DM2; the data from H.6 are labeled HM2 and
DHM2; and the data from the Bulletin are la
beled OM2 and DOM2.
conclusions would be reached for M l in the
1980s, or for these and other aggregates during
other periods, rem ains an open question. As An
derson and Kavajecz note, Depository Institution
Deregulation and M onetary Control Act (DIDMCA) improved the accuracy of m onetary statis
tics in the 1980s, and M2 tends to be a sm oother
series than M l. Thus, my results may understate
the im portance of m easurem ent erro r for other
aggregates and earlier periods.
These figures indicate that revision of M2 has
been trivial in the 1980s, and so I conclude that
for these series over this period, "expectations
e rro r effects” were not important. To the extent
revisions did matter, long-term retrospective
changes (the difference betw een M2 and 02, or
DM2 and DOM2) are m ore im portant than those
occurring w ithin two m onths of initial publi
cation.
Board of Governors of the Federal Reserve System. All-Bank
Statistics 1986-1955. Board of Governors of the Federal
Reserve System, 1959.
One conclusion to draw from these findings is
that, if there has been a breakdown in the rela
tionship betw een M2 and output during the past
decade, it cannot be attributed to tem porary
m ism easurem ent of money. W hether similar
REFERENCES
________ . Banking a nd M onetary Statistics 1914-1941. Board of
Governors of the Federal Reserve System, 1976.
________ . Banking a nd M onetary Statistics 1941-1970. Board of
Governors of the Federal Reserve System, 1976.
________ . Federal Reserve Bulletin.
________ . M oney Stock, L iq u id Assets, a n d D ebt Measures,
supplement to the Federal Reserve statistical release, H.6.
Capie, Forrest, and Alan Webber. M onetary H istory o f the
United Kingdom, 1870-1982. Allen & Unwin, 1985.
Eisner, Robert. How Real is the Federal Deficit? Free Press,
1986.
Friedman, Milton, and Anna J. Schwartz. M onetary Statistics
o f the United States. Columbia University Press, 1970.
MARCH/APRIL 1994
73
K. Alec Chrystal an d R on ald M acDonald
K. Alec Chrystal is N ational Westminster Bank professor of
econom ics at City University o f London. Ronald M acD onald is
professor o f econom ics at the University o f Strathclyde, Glasgow.
E m pirical E viden ce on
the R ecen t B eh avior an d
U sefulness o f Sim ple-Sum
a n d W eighted M easures o f
the M oney S tock
"We m ust have a good definition o f Money, For if we do not, then what have we got, But a Quantity
Theory o f no-one-knows-what...”
Boulding (1969, p. 555)
.M.HE FEDERAL RESERVE BANK of St. Louis
has been, for the last th ree decades or so, at
the center of an approach to macroeconomic
policy which became universally known as
“M onetarism.” Indeed, the very term entered
the public domain through an article in the Federal Reserve Bank of St. Louis’ Review by Karl
Brunner in 1968. The central tenet of m onetarism
was that there is a stable dem and function for
something called "money.” Policy advice came
down to recom m ending th at the m onetary
authorities should deliver a steady rate of the
grow th of m oney within some target range.
The 1970s w ere a good time for monetarists.
Velocity in the United States appeared to be on
a stable trend, and the adoption of floating exchange rates generated a need for independent
m easures of m onetary stance in most of the in
dustrial countries. M onetary targeting was
widely adopted and m onetarism became a worldwide credo. Since the end of the 1970s, however,
life has been m uch h a rd e r for m onetarists. The
stability of empirical m onetary relationships
became m uch m ore difficult to maintain, and
governm ent after governm ent has given up
even the notional attem pt to target m onetary
aggregates. The allegedly m onetarist governm ent of M argaret Thatcher abandoned m onetary
targets in the United Kingdom in 1985. The
Chairman of the Federal Reserve Board has
recently announced that the Fed has ceased to
m onitor M2 and, instead, will be using the real
interest rate as an indicator of m onetary stance.
Only the Bundesbank appears to be retaining
any faith in the significance of m onetary aggregates, though they have been widely criticized
for so doing. (Norbert W alter, the chief econo-
MARCH/APRIL 1994
74
mist of Deutsche Bank, has, for example, been
quoted as saying that "...M3, the broad money
supply indicator targeted by the central bank,
was obviously distorted and devalued as an indi
cator.” Financial Times, August 10, 1993, p. 2).
The standard explanation for w hy previously
stable m onetary relationships have broken
down is financial innovation. In particular,
liberalization and competition in banking have
generated shifts in dem and betw een compo
nents of money which have underm ined earlier
empirical regularities. Interest payments on
transaction deposits have made it m ore difficult
to distinguish money held for transaction from
money held for savings.
Robert Rasche (1993) in his paper to the
St. Louis Fed conference 12 m onths ago identi
fied the beginning of the 1980s as a time of a
critical regime change. This structural change,
he claimed, had destroyed the validity of the
traditional St. Louis reduced-form methodology
as a m eans for explaining and forecasting the
course of GNP. Policy m akers around the w orld
have clearly also been convinced that m onetary
aggregates provide little useful inform ation to
guide m acro policy.
Presumably, nobody would argue that no
guide to m onetary policy was necessary. How
ever, the advocates of a simplistic policy based
upon any traditional m easure of money as the
sole guide are disappearing rapidly.
At the theoretical level, the significance of ex
ogenous m onetary shocks as a cause of business
cycles has been under threat from the so-called
Real Business Cycle school. For them, m onetary
disturbances are not the trigger to cycles but,
rath er, are an endogenous response to shocks
em anating in the real economy. While this ap
proach does not necessarily eliminate the validity
of countercyclical m onetary policy, it certainly
reduces the significance of the traditional m one
tarist line that m onetary shocks are the prim ary
trigger to the cycle. Several recent empirical
studies have apparently produced evidence to
support the contention that money does not
have any explanatory pow er—at least for real
economic activity. (De Long and Summers, 1988;
Friedm an and Kuttner, 1992, 1993.)
The consensus view emerging from all of this
appears to be th at trying to target and control
money is no longer a very sensible thing for
policy m akers to do. M onetary policy is now
mainly about setting short-term interest rates,
FEDERAL RESERVE BANK OF ST. LOUIS
despite all the well-known difficulties that
choosing the “correct” interest rate entails
(Friedman, 1959).
This paper follows an alternative line of
reasoning, for which th ere is an overwhelming
theoretical case. T here has been a m ajor m eas
urem ent e rro r in virtually all of the previous
literature on money. Instability in empirical rela
tionships has been prim arily due to the fact that
simple-sum m easures of money are not admissi
ble aggregates on index-theoretic grounds. This
e rro r has been especially im portant in a period
w hen characteristics of com ponents w hich are
added together have been changing.
We do not claim that correction of this m eas
urem ent e rro r salvages entirely the role of
money as a m acroeconomic indicator (though
such may still be the case). Rather, ou r prim ary
focus is to see w hether acceptable indexes of
money outperform traditional money m easures
in conventional tests. As is often the case in
applied studies, the evidence tu rn s out to be
mixed but leaning in favor of the superiority of
weighted over simple-sum aggregates.
Before presenting our own empirical evidence,
we shall first review briefly the evolution of the
concept of m oney and then the case for an ap
propriately constructed index.
W h at Is M o n ey ?
The definition of money has not been static
over time. The first identifiable m easure of
money was undoubtedly the stock of the physi
cal commodity which served as currency—
typically precious metal. At some point, certain
ly by the 18th century in England, it was clear
that bank notes had become a major elem ent of
the money stock so th at a m onetarist at that
time would have had to extend the definition of
money to include notes plus specie in the hands
of the public. By the 19th century, financial in
novation had moved things a stage fu rth e r and
the relevant concept of money had expanded
yet again to include bank deposits, which could
be used on dem and and could be tran sferred by
w riting a check.
In recent times, the issue has been: Which of
the other highly liquid assets held by the public
should be included? The Radcliffe view in the
United Kingdom and the view of Gurley and
Shaw in the United States was that the bound
ary betw een money and other liquid assets was
impossible to draw because so many close sub
stitutes w ere available. This contention was
75
countered successfully for a while by the evi
dence that elasticities of substitution w ere
relatively small (Chetty 1969) and also by the
evidence that predictions of m onetarist ap
proaches w ere fairly robust to m inor definitional
changes. In other words, the general message of
the evidence was not so different if one used
M l or M2, or even M3.
Such a defense would be m uch harder to
m aintain today than it was 15 years ago. The
introduction of interest paym ents on checking
accounts in the United States led to a major
reversal of the velocity tren d —at least for M l in
about 1980. In the United Kingdom, abolition of
quantitative ceilings on bank interm ediation,
also in 1980, led to a period of rapidly rising
broad money coinciding w ith very slow narrow
money grow th. The innovations which followed
w ere clearly associated w ith big movements of
deposits from non-interest bearing to interestbearing accounts. In such circumstance, neither
narrow nor broad money proved to be reliable
indicators—at least in the short term .
It would be a mistake to believe that the
composition changes of the 1980s w ere a new
phenom enon. In Volume I of A Treatise on
Money, Keynes argued that an unchanged quan
tity of m oney could conceal im portant changes
in circulation as holders tran sferred money be
tw een cash and savings deposits, and betw een
income and business accounts. In Volume II, he
reported the statistical finding that the p ropor
tion of deposit (savings) accounts to total ac
counts had risen in Britain from 38 percent to
46 percent betw een 1920 and 1926. According
to Keynes, "... The continual transference from
cu rren t to deposit accounts ... [acted as] a con
cealed m easure of deflation...” (Keynes, 1930b,
p. 10) sufficient to explain a drop in the price
level of 20 percent over the period.
There is nothing rem arkable about the fact
that these composition changes have been
noticed before. W hat is rem arkable is that so
m any economists w ere happy to ignore them
for so long in the post-W orld W ar II period.
Partly, this was because the regulatory regime
in most countries (interest ceilings and/or quan
titative controls on intermediation) limited for
some time the significance of the interface be
tw een checking and savings accounts, as well as
the significance of nonbank competitors.
Fisher, 1989, Chapter 1, for a survey). At the
risk of oversimplifying, it is sufficient for present
purposes to note that the traditional reason for
regarding money as critically different from
other assets is that it has a direct role in tra n s
actions and, hence, has a direct role in the tra d
ing activity of a m arket economy. According to
the Quantity Theory, the money stock will de
term ine the general level of prices (at least in
the long term) and, according to m onetarists, it
will influence real activity in the short run.
For this reason, empirical m easures of the
money stock have tried to identify as compo
nents of money those instrum ents which can be
used directly in transactions. The problem of
our time is that a whole range of types of
deposits which can be spent, m ore or less,
directly also yield an interest rate and could,
thus, be chosen as a form of savings as well.
From a m icro-demand perspective, it is hard
to justify adding together assets which have
different and varying yields (Barnett, Fisher and
Serletis, 1992). It has long been know n that only
things that are perfect substitutes can be com
bined as one commodity. T here is ample evi
dence that the assets which are commonly
combined in money m easures are not in fact
perfect substitutes.
From a micro-foundations perspective this
leaves only tw o alternatives. The first is to res
trict attention to a very narrow definition of
money, w hich only needed non-interest bearing
components. The alternative is to construct an
index num ber of "m onetary services” which
could, in principle, capture the transactions
services yielded by a wide range of financial as
sets in a superlative way (Diewert 1976, 1978).
Two potential index num bers are the Divisia
index proposed by Barnett (1980) and the Cur
rency Equivalent (CE) index proposed by Botemberg (1991) at the St. Louis conference in 1989.
M o n e y M e a su re m e n t
The attraction of both of these m onetary serv
ices indicators is that they internalize the substi
tution effects betw een components of a potential
aggregate and, thus, solve the problem of com
position changes w hich was discussed above.
They do not in themselves guarantee the weak
separability of any chosen aggregate, but they
do approxim ate optimal aggregator functions for
those collections of aggregates which have been
found "admissible” on separability grounds
(Belongia and Chalfant, 1989).
A substantial am ount of literature discusses
the concept of money and its m easurem ent (see
The theoretical case for weighted m onetary
aggregates is overwhelm ing—at least to anyone
MARCH/APRIL 1994
76
w ith a training in microeconomics and/or index
num ber theory. The only objection could be on
the grounds that it does not make an im prove
m ent over flawed simple-sum aggregates in
practice. There has been a significant accum ula
tion of evidence, however, to suggest that Divisia
aggregates outperform their simple-sum equiva
lents. For example, Barnett (1980) showed that
some apparent shifts in money dem and in the
United States w ere rem oved w hen Divisia m eas
ures replaced simple sum. Barnett and Spindt
(1979) showed the informational superiority of
Divisia over simple-sum measures. Belongia and
Chalfant (1989) find Divisia MIA to have superior
informational content to other admissible ag
gregates. Barnett, O ffenbacher and Spindt (1984)
also find evidence for the superiority of Divisia.
F urther support is provided by Serletis (1988).
Lindsey and Spindt (1986) is one of the few
papers which have looked at this comparison to
come out against Divisia, though Fisher and Ser
letis (1989) is inconclusive.
Belongia (1993) has recently discovered that
using weighted, as opposed to simple-sum,
m onetary aggregates alters significantly the con
clusions th at should have been reached by
several recent influential studies. These studies
have, on the whole, adduced evidence that
money is not a "cause” of cycles in real activity.
Hence, this suggests th at the problem s w ith
tests of money in the economy in recent years
may be m ore due to bad m easurem ent theory
rath e r th an to an instability in the link betw een
the tru e m oney and the economy. Rather than a
problem associated w ith the Lucas Critique, it
could instead be a problem stemming from the
"Barnett Critique.”
The idea of weighted m onetary aggregates has
spread outside the United States. Studies include
Horne and M artin (1989) for Australia; Cockerline and M urray (1981) and Hostland, Poloz and
Storer (1987) for Canada; Ishida (1984) for
Japan; Yue and Fluri (1991) for Switzerland; and
Belongia and Chrystal (1991) and Drake and
Chrystal (forthcoming) for the United Kingdom.
A recent Bank of England study in the United
Kingdom context concludes: "A Divisia m easure
of money appears to have some leading indica
tor properties for predicting both nominal out
put and inflation...a case can clearly be made
for including Divisia in the range of indicators
analyzed by the authorities w hen form ing their
judgments on m onetary conditions.” (Fisher,
Hudson and Pradhan, 1993, p. 63).
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A variation on the traditional “closed economy”
tests is provided by Chrystal and MacDonald
(1993). They point out that exchange rate
models have been just as dependent upon
money m easures as have dem and for money
studies or reduced form tests of m onetary policy.
It is no coincidence th at exchange rate equations
started to misbehave at the same time as velocity
trends appeared to shift (in the early 1980s). By
replacing simple-sum aggregates in an exchange
rate model by Divisia aggregates, for the dollarpound rate, they show th at a simple, flexible,
price m onetary model can be salvaged as a
long-run proposition. They also find that, w hen
Divisia m easures are used, the short-run fore
casting perform ance is far superior on out-ofsample tests.
We now tu rn to some empirical results of our
own. The results we shall present fall into two
distinct sections. In the first section, we rep o rt
comparisons of simple-sum and weighted m eas
ures of the money supply in the context of St.
Louis Equations. The dependent variable is ac
cordingly nominal GNP. We are aw are of the
problems encountered in the past w ith such
m ethods (Rasche, 1993). However, it is a simple,
familiar and well-known context w ithin which
to com pare money m easures. We are not con
cerned w ith the absolute validity of the results
b u t only w ith the relative perform ance of
different m easures. Non-nested testing tech
niques w ere used to distinguish betw een vari
ous indicators of money.
In the second section, we use the m ore so
phisticated m odern time-series methodology to
test for the existence of short-run and long-run
causal links betw een money and real activity. It
is this latter question which has dom inated the
recent literature. We add to this literature both
by including alternative money m easures and by
providing international comparisons.
EMPIRICAL RESULTS WITH
ST. LOUIS EQUATIONS
In this section, we rep o rt results of com pari
sons betw een traditional simple-sum aggregates,
Divisia m easures and the Rotemberg Currency
Equivalent (CE) m easure. We use the environ
m ent of a modified St. Louis Equation as a vehi
cle for these comparisons, and we use non nested
testing m ethods to identify superior inform a
tional content. We are well aw are w ith all the
77
difficulties associated w ith the St. Louis Equa
tion methodology. If we cannot use this struc
tu re at a St. Louis Fed conference, however,
w here else can we? More seriously, this m ethod
offers simplicity and transparency. It does at
least give us a feel for the properties of the
data we are dealing with. A methodology m ore
acceptable to the econometric purist will be
reported in the following section.
None of the data we used was original to this
study. The bulk of it was made available to us
by Michael Belongia at the Federal Reserve Bank
of St. Louis, though the U.K. Divisia series
(post-1977) was constructed by the Bank of En
gland (Fisher, Hudson and Pradhan, 1993). It
should be noted that the time period of the
study differs for each country, depending upon
data availability. Data definitions also vary from
country to country, b u t space does not perm it
an extensive discussion of such differences.
Seasonally adjusted data w ere used in all cases.
The dependent variable is taken as the first
difference of the log of nominal GDP or GNP.
The first difference of the log of nominal
governm ent spending (federal in the United
States case) on goods and services is used as a
fiscal variable in all cases. A w orld trade varia
ble was tested as an external dem and variable
but was not found to add explanatory pow er in
the countries tested. Also tested was an interest
rate variable. This was found to be im portant in
this context only for the United States. Hence,
the U.S. Equation includes the first difference of
the Treasury bill rate.
The original St. Louis Equation contained lags
of order 0-3. On quarterly data, most economists
would expect to use at least 0-4, so, given the
short data series for some countries, this is the
standard lag length we adopted.
In parallel to the simple St. Louis Equation
form at, we also rep o rt tests in a version of the
equation which includes the lagged dependent
variable, lagged 1-4 periods. Additionally in this
latter context we rep o rt an F test on the exclu
sion of money from the equation entirely. This
provides useful information, not only about the
relative inform ational content of different money
m easures b u t also about w hether money m at
ters at all. In some cases Divisia money m atters
but simple-sum m oney does not. The reverse is
never true.
The basic test is to use the same equation in
one case w ith simple-sum money and in another
case Divisia or CE money. Three test statistics
are reported for comparisons betw een the two
form ulations—the Davidson and MacKinnon
J-test, the Fisher and McAleer JA-test and the
Akaike Inform ation Criterion (AIC). O ther tests
have been m onitored, including the NT test of
Pesaran and Godfrey and the Wald-type test.
These other tests differ in detail but they do
not alter the overall picture produced. Accord
ingly, they are not reported here. We refer to
the J-test and the JA-test as being inconclusive
w hen both form ulations reject each other and
indeterm inate if neither rejects the other.
The results are reported in Tables 1 to 7 for
the United States, the United Kingdom, A ustra
lia, Germany, Switzerland, Canada and Japan,
respectively. Let us consider each.
U n ited S ta te s
The U.S. results are sum m arized in Table 1.
Simple-sum aggregates M l and MIA in general
dominate their Divisia equivalents. From M2 on
w ards to broader aggregates, however, the
domination is reversed. This is clear for M2 and
M3, though the difference betw een Divisia L
and simple-sum L is probably not significant.
This general picture is not altered by the inclu
sion or exclusion of the lagged dependent
variable.
From the F-tests it is clear th at simple-sum
MIA, Divisia MIA and Divisia M l do not add
significant explanatory pow er to the equation at
norm al significance levels. However, Divisia M2
has the greatest informational content of all the
aggregates tested, though it is only marginally
m ore significant than simple-sum M2.
The CE aggregate holds its ow n against M l
and MIA, though never establishing statistically
significant domination in either direction. It
loses out to the broader simple-sum aggregates,
however, and also to the broader-based Divisia
m easures (the latter result is implied but not
shown).
Overall, the M2 level of money aggregation
seems superior, though the Divisia aggregate at
this level does not dominate its simple-sum
equivalent sufficiently to make an overwhelming
case for preferring one to the other.
U n ited K in g d o m
The U.K. results appear in Table 2. There are
far few er aggregates to choose from in the U.K.
case. The Bank of England even stopped report-
MARCH/APRIL 1994
78
Table 1
St. Louis Equations for the United States: Simple-Sum vs.
Weighted Money_________________________________________
Dependent variable: first difference of the natural log of nominal GNP.
Independent control variables: first difference of the natural log of federal spending on goods and
services; first difference of the T-bill rate; the current period value and four lags of each variable
are included as regessors.
Part 1: no lagged dependent variable in regression
M1 vs. Divisia M1
Akaike Information Criterion (AlC)
J-test
JA-test
favors M1
favors M1
favors M1
(4.42)
(-.1 ; 3.06)
(-.7 2 ; 2.26)
M1 vs. Rotemberg Currency Equivalent (CE)
AlC
J-test
JA-test
favors CE
inconclusive
indeterminate
(-2 4 )
(2.74; 2.64)
(1.56; 1.39)
M1A vs. Divisia M1A
AlC
J-test
JA-test
favors M1A
favors M1A
favors M1A
(3-78)
(-.5 9 ; 2.7)
(-.67; 2.6)
M1A vs. CE
AlC
J-test
JA-test
favors CE
inconclusive
indeterminate
(-.5 5 )
(2.7; 2.4)
(1.66; 1.16)
M2 vs. Divisia M2
AlC
J-test
JA-test
favors Divisia M2
favors Divisia M2
favors Divisia M2
(-1.1)
(2.42;1.8)
(2.04;1.4)
M2 vs. CE
AlC
J-test
JA-test
favors M2
inconclusive
favors M2
(8.75)
(2.4; 4.9)
(.92; 3.6)
M3 vs. Divisia M3
AlC
J-test
JA-test
favors Divisia M3
favors Divisia M3
favors Divisia M3
(-1.76)
(2.4; 1.5)
(1.9; 1.2)
M3 vs. CE
AlC
J-test
JA-test
favors M3
inconclusive
inconclusive
(6.45)
(3.07; 4.7)
(2.05; 2.72)
L vs. Divisia L
AlC
J-test
JA-test
favors Divisia L
inconclusive
inconclusive
(-.3 1 )
(2.35; 2.18)
(1.6; 1.34)
L vs. CE
AlC
J-test
JA-test
favors L
inconclusive
inconclusive
(7.27)
(2.9; 4.8)
(2.2; 3.98)
Note: The Akaike Information Criterion is an adjusted difference between two values of the likeli
hood function. It indicates the direction of informational advantage but has no critical bounds. The
J and JA tests are f-statistics for the rejection of one model over the other and then the reverse.
"Inconclusive" = both significant; “ Indeterminate” = neither significant. Data period is 60:1-92:4.
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Federal Reserve Bank of St. Louis
79
Table 1 (continued)
Part 2: four lags of the dependent variable included
M1 vs. Divisia M1
AIC
J-test
JA-test
favors M1
favors M1
indeterminate
(3.74)
(.27; 2.8)
(-.4 5 ; 1.78)
M1 vs. CE
AIC
J-test
JA-test
favors M1
inconclusive
indeterminate
(.46)
(2.49; 2.59)
(1.6; 1.15)
M1A vs. Divisia M1A
AIC
J-test
JA-test
favors M1A
favors M1A
favors M1A
(3.2)
(-.4 2 ; 2.44)
(-.5 5 ; 2.3)
M1A vs. CE
AIC
J-test
JA-test
favors CE
inconclusive
indeterminate
(-.8 4 )
(2.7; 2.3)
(1.4;.62)
M2 vs. Divisia M2
AIC
J-test
JA-test
favors Divisia M2
inconclusive
indeterminate
(-.7 4 )
(2.4; 2.1)
(1.87; 1.56)
M2 vs. CE
AIC
J-test
JA-test
favors M2
inconclusive
favors M2
(5.76)
(2.4; 4.3)
(.62; 3.4)
M3 vs. Divisia M3
AIC
J-test
JA-test
favors Divisia M3
favors Divisia M3
indeterminate
(-1 .5 )
(2.24; 1.5)
(1.63; 1.14)
M3 vs. CE
AIC
J-test
JA-test
favors M3
inconclusive
favors M3
(3.4)
(3.05; 3.99)
(1.32; 2.26)
L vs. Divisia L
AIC
J-test
JA-test
favors Divisia L
inconclusive
indeterminate
(-.4 2 )
(2.38; 2.21)
(1.42; 1.29)
L vs. CE
AIC
J-test
JA-test
favors L
inconclusive
favors L
(3.93)
(2.9; 4.0)
(1.85; 3.4)
MARCH/APRIL 1994
80
Table 1 (continued)
Part 3: F-tests on exclusion of money from St. Louis Equation
probability
M1
M1A
M2
M3
L
Divisia
Divisia
Divisia
Divisia
Divisia
CE
F(5,107)
M1
M1A
M2
M3
L
”
”
”
”
=
=
=
=
=
=
=
=
=
=
=
2.36
1.88
4.43
3.49
3.69
1.01
0.73
4.73
4.09
3.86
2.19
[0.045]
[0.103]
[0.001]
[0.006]
[0.004]
[0.418]
[0.600]
[0.001]
[0.002]
[0.003]
[0.060]
Note: Exclusion test conducted in equation including lagged dependent variable shown in Part 2
of the table. This is equivalent to the concept of Granger causality tests, but includes contem
poraneous observations on independent variables.
ing M l and M3 in 1989 because it considered
the data too distorted by financial innovation.
Hence, the only choice using official statistics is
betw een MO (the m onetary base) and M4. The
results show a clear domination of Divisia M4
over simple-sum M4 both w ith and w ithout the
presence of lagged GDP. The non nested tests,
however, make it impossible to choose betw een
Divisia M4 and MO. Also, while the Akaike In
form ation Criterion favors MO over simple-sum
M4, the J-test and the JA-test are inconclusive
and indeterm inate, respectively. On the other
hand, the F-test gives informational advantage to
MO, w ith Divisia M4 running second. Simplesum M4 has no significant explanatory pow er at
norm al probability levels. This suggests that
Divisia M4 should replace simple-sum M4 as an
indicator of the course of broad money in the
United Kingdom.
A u stra lia
Results for Australia appear in Table 3. They
show comparisons betw een M2, M3 and their
Divisia equivalents. The inform ation criterion is
always in favor of Divisia, and the significant
J-tests favor Divisia. More dram atic perhaps are
the F-tests which show that neither simple-sum
aggregate m atters at anything close to norm al
probability levels, while both Divisia aggregates
do have significant inform ational content. This
is probably the clearest case available w hich il
lustrates the domination of Divisia over simple
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sum aggregates—especially for broad money
measures.
G e rm a n y
Table 4 contains the results for Germany. The
inform ation criterion generally favors Divisia
measures over their simple sum counterparts,
with the exception of M3 in the absence of the
lagged dependent variable. All the J- and JA-tests
are indeterm inate w ith the exception of the J-test
which shows dominance of Divisia M2 over M2
(in the presence of the lagged dependent varia
ble). The same test for M3 is very close to ac
cepting Divisia M3 as dominating M3.
The overwhelm ing impression of the German
results, however, is th at conveyed by the F-tests,
which show the very low informational content
of all money measures. In this respect, only
Divisia M3 is significant at even the 10 percent
level and the simple-sum aggregates do not obvi
ously m atter at all. This is a surprising result
for a country which has a reputation for sound
m onetary policy and adheres to a simple-sum
M3 target. It is possible that the very success of
m onetary policy is responsible for a low varia
tion of nominal income grow th, which makes
it hard to establish statistical relationships.
However, it is also possible th at Divisia money
m easures do a better job in tracking nominal
GDP than their simple-sum equivalents.
81
Table 2
St. Louis Equations for the United Kingdom: Simple-Sum vs.
Weighted Money
Dependent variable: first difference of the natural log of nominal GDP.
Independent control variables: first difference of the natual log of government spending on
goods and services.
Part 1: no lagged dependent variable included in regression
Divisia M4 vs. M4
AIC
J-test
JA-test
favors Divisia M4
favors Divisia M4
favors Divisia M4
(3.136)
(1.05; 3.1)
(-.4 5 ; 2.2)
Divisia M4 vs. MO
AIC
J-test
JA-test
favors Divisia M4
inconclusive
indeterminate
(.168)
(2.77; 2.72)
(1.52; .96)
M4 vs. MO
AIC
J-test
JA-test
favors MO
inconclusive
indeterminate
(-3 .2 )
(3.5; 2.5)
(■49; .77)
Part 2: four lags o f dep end ent variable included
Divisia M4 vs. M4
AIC
J-test
JA-test
favors Divisia M4
favors Divisia M4
indeterminate
(2.32)
(1.3; 2.7)
(-.1 6 ; 1.82)
Divisia M4 vs. MO
AIC
J-test
JA-test
favors MO
inconclusive
indeterminate
(-.7 8 )
(3.17; 2.8)
(15; .73)
M4 vs. MO
AIC
J-test
JA-test
favors MO
inconclusive
indeterminate
(-3 .6 9 )
(3.8; 2.7)
(-.1 8 ; -.3 6 )
Part 3: F-tests on exclusion o f money from St. Louis Equation
probability
M4
Divisia M4
MO
F(5, 78)
”
= 1.45 [0.215]
= 2.33 [0.050]
= 2.83 [0.021]
Note: Test is done in equation from Part 2 including lagged dependent variable. Data period is
1968:3-1992:4.
S w itz e r la n d
In Switzerland, (Table 5) Divisia aggregates
dominate on inform ation grounds, though the
JA-test is always indeterm inate and the J-test
only gives clear dominance to Divisia on one oc
casion (Divisia M2 beats M2 in the presence of
lagged GDP). The F-tests suggest that M l and
Divisia M l are very similar in informational con
tent (with a tiny advantage to Divisia). Simple
sum M2, by contrast, is overwhelmingly domi
nated by its Divisia counterpart. This confirms
the simple (and obvious) conclusion from other
countries that Divisia clearly dominates w hen it
comes to broad m oney measures, but at the
narrow money level it does not make m uch
difference. This is clearly almost a tautology
w hen narrow aggregates have minimal interestbearing components.
MARCH/APRIL 1994
82
Table 3
St. Louis Equations for Australia: Simple-Sum vs. Weighted
Money
Dependent variable: first difference of the natural log of nominal GDP.
Independent control variable: first difference of the natural log of government spending.
Part 1: no lagged dependent variable included in regression
M2 vs. Divisia M2
AIC
J-test
JA-test
favors Divisia M2
inconclusive
indeterminate
(-3 .7 4 )
(3.63; 2.67)
(-.7 ; -.1 9 )
M3 vs. Divisia M3
AIC
J-test
JA-test
favors Divisia M3
favors Divisia M3
indeterminate
(-3 .9 )
(3.2; .9)
(1.1; -.8 2 )
Part 2: four lags of dependent variable included
M3 vs. Divisia M3
AIC
J-test
JA-test
favors
Divisia M3
indeterminate
(-5 .6 )
(3.5; 1.1)
I
(-6 .6 )
(4.4; 3.3)
(-1 .5 ; -.0 7 )
C
O
favors Divisia M2
inconclusive
indeterminate
(J)
M2 vs. Divisia M2
AIC
J-test
JA-test
Part 3: F-tests on exclusion of m oney from St. Louis Equation
probability
M2
M3
Divisia M2
Divisia M3
F(5,43)
”
=
=
=
=
0.99
0.82
3.46
2.84
[0.430]
[0.540]
[0.010]
[0.027]
Note: Data period is 1974:2-1989:4.
C an ada
Japan
The Canadian results (Table 6) confirm the
general p attern established above. M l has a
m arginal edge over Divisia M l (in the presence
of lagged GNP, but not otherwise) but for
b roader aggregates the Divisia m easure domi
nates w here any discrimination is possible.
Divisia L sweeps the board w ith its simple-sum
equivalent and both Divisia M2 and Divisia M3
exhibit obvious domination. The F-tests confirm
this general story. Simple-sum M l has the
greatest inform ational content, b ut it is closely
followed by Divisia M l. Simple-sum M2, M3 and
L do not have significant informational content
at the 5 percent level, though all of their Divisia
equivalents do so.
Japan does not fit in at all w ith the p attern of
all the other countries in the sample (Table 7).
On the basis of the Akaike Inform ation Criteri
on, all of the simple-sum aggregates marginally
dom inate their Divisia counterparts. However,
none of the J- or JA-tests are able to discriminate
and the F-tests make it clear than none of the
money m easures has any explanatory pow er at
all. In this context it makes no sense to try to
distinguish betw een sets of num bers, none of
which m atter.
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Japan’s m onetary aggregates differ from m any
others at the M2 and M3 level, because they in
clude negotiable CDs. However, this would not
83
Table 4
St. Louis Equations for Germany: Simpie-Sum vs. Weighted
Money
Dependent variable: first difference of the natural log of nominal GDP.
Independent control variable: first difference of the natural log of government spending.
Part 1: no lagged dependent variable included in regression
M2 vs. Divisia M2
AIC
J -te s t
J A -test
favors Divisia M2
indeterminate
indeterminate
(-.8 5 )
(1.84; 1.54)
(.25; .93)
M3 vs. Divisia M3
AIC
J -te s t
J A -test
favors M3
indeterminate
indeterminate
(1.3)
(.57; 1.73)
(-.0 6 ; .92)
Part 2: four lags of dependent variable included
M 2 vs. Divisia M2
AIC
J -te s t
JA -test
favors Divisia M2
favors Divisia M2
indeterminate
(-1 .8 )
(2.9; 1.89)
(-.3 6 ; -.014)
M3 vs. Divisia M3
AIC
J -te s t
JA -test
favors Divisia M3
indeterminate
indeterminate
(-1.17)
(1.88; 1.12)
(.91; .24)
Part 3: F-tests on exclusion of m oney from St. Louis Equation
probability
M2
M3
Divisia M2
Divisia M3
F(5,41)
”
”
=
=
=
=
0.71
1.66
1.77
2.08
[0.620]
[0.167]
[0.140]
[0.087]
Note: Data period is 1975:1-1990:1.
explain the poor perform ance of M l. Also, this
should give an advantage to Divisia M2 and
Divisia M3 which is not supported by the data.
Either the Japanese economy behaves very
differently from the others studied o r there are
serious data errors underlying this evidence.
We now tu rn to tests of the causal links be
tw een money and real activity using m odern
time-series methods.
TIME SERIES TESTS OF MONEY/
REAL ACTIVITY CAUSALITY
In this part of the paper, we consider Granger
causality tests for a selection of Divisia and
simple-sum money aggregates for each of the
countries referred to in our St. Louis tests. The
causality tests are based on vectors consisting of
real GDP, the GDP deflator, a Treasury bill rate
and the relevant m easure of the money supply.
Defining our causality vectors in this way facili
tates separate modelling of the effect th at differ
ent m onetary impulses may have (particularly in
the short run) on the real and price compo
nents of GDP. The Treasury bill rate is also in
cluded in the vector because of the well-known
spurious effect m oney can have on output if an
interest rate effect is excluded (Sims, 1980). Our
causality tests have a num ber of other features,
some of w hich are novel to this paper.
First, for reasons w hich are now widely ac
cepted, it is extrem ely im portant that the varia
bles entering the causality vector should be
stationary and that any indication of cointegratability should be determ ined (see, Engle and
Granger, 1987; MacDonald and Kearney, 1987).
The latter aspect of the time-series properties of
MARCH/APRIL 1994
84
Table 5
St. Louis Equations for Switzerland: Simpie-Sum vs. Weighted
Money
Dependent variable: first difference of the natural log of nominal GDP.
Independent control variable: first difference of the natural log of government spending.
Part 1: no lagged dependent variable included in regression
M1 vs. Divisia M1
AIC
J-test
JA-test
favors Divisia M1
indeterminate
indeterminate
(-.0 6 4 )
(1.37; -1.31)
(1.35; -1.3 3 )
M2 vs. Divisia M2
AIC
J-test
JA-test
favors Divisia M2
inconclusive
indeterminate
(-1 .8 4 )
(2.99; 2.76)
( -.6 ; .76)
Part 2: four lags of dependent variable included
M1 vs. Divisia M1
AIC
J-test
JA-test
favors Divisia M1
indeterminate
indeterminate
(-0 5 )
(.93; -.87 )
(.91; -.8 8 )
M2 vs. Divisia M2
AIC
J-test
JA-test
favors Divisia M2
favors Divisia M2
indeterminate
(-4 .0 2 6 )
(3.1; 1.5)
(.35; -.2 7 )
Part 3: F-tests on exclusion of m oney From St. Louis Equation
probability
M1
M2
Divisia M1
Divisia M2
F(5,39)
”
”
= 2.9 [0.026]
= 0.41 [0.840]
= 2.92 [0.025]
= 2.11 [0.085]
Note: Data period is 1975:2-1989:4.
the vector is im portant, since if there is one (or
more) cointegrating relationships among the vec
tor, then it is inappropriate to test for causality
among a vector of first-differenced variables,
because the Granger representation theorem
asserts th at such a vector will be misspecified; it
will exclude im portant "long-run” information
contained in the levels of the variables. (This
was a point recognized by Friedm an and Kuttner,
1992, in th eir causality tests on U.S. data [see
their footnote 19], b ut they did not include such
long-run elements in their testing framework.) A
second im portant aspect of any causality test is
that it should be robust to non-norm al errors.
Holmes and Hutton (1992) suggest handling this
issue using a non-param etric rank F-test (instead
of the standard F-test used in conventional
causality studies). In this paper, we argue that
since most departures from normality arise
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from heteroskedasticity, this issue may be dealt
w ith using the Hansen-White non-param etric
correction for heteroskedasticity.
The general class of causality tests employed
in this section of the paper have come in for
some criticism in the literature (see: Zellner,
1979, 1988; Basmann, 1963; and Cooley and
LeRoy, 1985). In particular, it is argued th at to
be interpreted as indicating causality from, say,
money to output, Granger-type causality tests
have to be em bedded in a structural setting and
appropriate identifying restrictions imposed (see
Holmes and Hutton, 1992, for a partial rebuttal).
However, given our purpose is not to examine
causality for a single m easure of money, but
rath e r to determ ine which m easures from a
range of simple-sum and Divisia money magni
tudes have the greatest informational content,
85
Table 6
St. Louis Equations for Canada: Simple-Sum vs. Weighted
Money
Dependent variable: first difference of the natural log of nominal GNP.
Independent control variable: first difference of the natural log of government spending.
Part 1: no lagged dependent variable included in regression
Divisia M1 vs. M1
AIC
J-test
JA-test
favors Divisia M1
indeterminate
indeterminate
(.34)
(.45; .78)
(.09; .46)
Divisia M2 vs. M2
AIC
J-test
JA-test
favors Divisia M2
favors Divisia M2
favors Divisia M2
(6.0)
(1.7; 4.8)
(-.8 4 ; 2.5)
Divisia M3 vs. M3
AIC
J-test
JA-test
favors Divisia M3
favors Divisia M3
favors Divisia M3
(3.67)
(1.29; 3.5)
(-.3 9 ; 2.4)
Divisia L vs. L
AIC
J-test
JA-test
favors Divisia L
favors Divisia L
favors Divisia L
(8.43)
(-.4 3 ; 4.3)
(-.9 9 ; 3.72)
Part 2: four lags of dependent variable included
Divisia M1 vs. M1
AIC
J-test
JA-test
favors M1
indeterminate
indeterminate
(-.1 9 )
(.81; .56)
(.44; .25)
Divisia M2 vs. M2
AIC
J-test
JA-test
favors Divisia M2
favors Divisia M2
indeterminate
(3.34)
(1.26; 3.3)
( -.8 ; 1.04)
Divisia M3 vs. M3
AIC
J-test
JA-test
favors Divisia M3
favors Divisia M3
indeterminate
(2.87)
(.55; 2.71)
(-.7 4 ; 1.53)
Divisia L vs. L
AIC
J-test
JA-test
favors Divisia L
favors Divisia L
favors Divisia L
(3.49)
(.49; 2.8)
(-.4 9 ; 2.17)
Part 3: F-tests on exclusion of m oney from St. Louis Equation
probability
M1
M2
M3
L
Divisia
Divisia
Divisia
Divisia
F(5,55)
M1
M2
M3
L
”
”
”
”
=
=
=
=
=
=
=
=
7.05
2.03
1.37
1.25
6.95
3.34
2.43
2.53
[0.000]
[0.088]
[0.250]
[0.299]
[0.000]
[0.010]
[0.047]
[0.039]
Note: Data period is 1968:3-1987:1.
MARCH/APRIL 1994
86
Table 7
St. Louis Equations for Japan: Simple-Sum vs. Weighted
Money
Dependent variable: first difference of the natural log of nominal GNP.
Independent control variable: first difference of the natural log of nominal government spending.
Part 1: no lagged dependent variable included in regression
M1 vs. Divisia M1
AlC
J-test
JA-test
favors M1
indeterminate
indeterminate
(.32)
(-1.57; 1.86)
(-1 .7 ; 1.72)
M2 vs. Divisia M2
AlC
J-test
JA-test
favors M2
indeterminate
indeterminate
(■5)
( - 7 ; 1.45)
(-1.09; 1.05)
M3 vs. Divisia M3
AlC
J-test
JA-test
favors M3
indeterminate
indeterminate
(.72)
(-.6 2 ; 1.53)
(-1.01; 1.17)
Part 2: four lags of dependent variable included
M1 vs. Divisia M1
AlC
J-test
JA-test
favors M1
inconclusive
inconclusive
(.503)
(-1 .9 6 ; 2.23)
(-2 .0 3 ; 2.16)
M2 vs. Divisia M2
AlC
J-test
JA-test
favors M2
indeterminate
indeterminate
(.44)
(-.4 5 ; 1.49)
(-1.19; .72)
M3 vs. Divisia M3
AlC
J-test
JA-test
favors M3
indeterminate
indeterminate
(.77)
(-.6 4 ; 1.56)
(-1 .0 8 ; 1.15)
Part 3: F-tests for exclusion of m oney from St. Louis Equation
probability
M1
M2
M3
Divisia M1
Divisia M2
Divisia M3
F(5,42)
”
”
”
=
=
=
=
=
=
.79 [0.559]
.24 [0.942]
.38 [0.861]
.63 [0.675]
.11 [0.990]
.14 [0.981]
Note: Data period is 1976:1-1991:2.
we do not believe that the standard criticisms
of our fram ew ork have as m uch im port as they
may have for m ore conventional studies. We
also take encouragem ent from the fact that
even in recent papers which only address the
causality properties of a single money m easure
(see, for example, Friedm an and Kuttner, 1993),
Granger-type tests have still been employed
(although, we would argue, incorrectly since
such tests only involve a vector of differenced
variables).
FEDERAL RESERVE BANK OF ST. LOUIS
U nit R o o t A n d M u ltiv a rite
C o in te g rtio n R e s u lts
We begin the empirical analyses of this sec
tion by testing for unit roots in the variables
entering ou r causality vector. Although the coin
tegration m ethod we employ below is due to
Johansen and is, therefore, a m ultivariate test
for the num ber of unit roots in a given vector,
we nevertheless thought it w orthw hile to exa
mine some simple univariate unit root rests for
87
motivational purposes, and also to guide us in
the appropriate ord er of differencing for the
variables entering the cointegrating tests.
There have been, in fact, a variety of pro
posed m ethods for implementing univariate unit
roots tests (for example, Dickey and Fuller,
1979; Phillips and Perron, 1988; Stock, 1990;
and Park and Choi, 1988) and each has been
used in the applied macroeconomics literature.
Since, however, th ere is now a growing consen
sus that the earliest, unit root test—due to Dickey
and Fuller (1979)—has superior small sample
properties com pared to its com petitors (see
Campbell and Perron, 1991, for a discussion),
we employ it. In particular, we estimate the fol
lowing regression equation for the series en ter
ing our causality vector:
(1) A*, = ^ + fir + 7r^(1 + S YA!<;-i + u,>
w here * is the variable of interest, /x and t
denote determ inistic regressors (a constant
and a time trend, respectively). Equation 1
represents a reparam eterization of an auto
regression of in levels, w here the length of
the autoregression is set to ensure that ut is
serially uncorrelated. In this context, a test for
a unit root in the series ^ am ounts to a f-test of
7r = 0 (that is, the sum of the autoregressive
param eters in the levels autoregression is unity).
The alternative hypothesis of stationarity re
quires that 7r be significantly negative. Since u n
der the null hypothesis of non-stationarity the
calculated t-ratio will not have a student’s
t-distribution, critical values calculated by Fuller
(1976) m ust be used instead.
In estimating equation 1 for so many coun
try/variable combinations, we initially used a
common lag length, q, of 4 for all variables.
However, given the sensitivity of Augmented
Dickey-Fuller (ADF) tests to the chosen lag
length we also experim ented w ith shorter lag
lengths in instances w here the estimated f-ratio
on 7 was close to its critical value, this being
r
particularly so w hen a variable appeared to be
1(2). (In particular, and following the recom m en
dation of Hall, forthcoming, and Campbell and
Perron, 1991, we sequentially deleted insignifi
cant lags of the dependent variable until we a r
rived at a parsimonious relationship which
satisfied the non-autocorrelation criterion.) In
the reported tables that follow, a shorter lag
length than 4 is denoted by the num ber in
parenthesis after the variable mnemonic. W here
the default value of 4 is reported for the ADF
statistic, it m eans that either all four lags are sig
nificant or, in instances w here some lags are in
significant, reducing the lag length from 4
would not have m ade a qualitative difference to
the interpretation.
In Tables 8 through 14, we present our
estimates of the f-ratio for the estimated coeffi
cient 7 in equation 1 for the levels and first and
r
second differences of each series in question. This
procedure facilitates a test for one and two unit
roots, respectively. The f-ratio has been calculated
w ith the time tren d included in the regression
equation, as in equation 1 (referred to as fT
),
and the tren d excluded (referred to as t ). This
follows the sequential testing strategy recom
m ended by, for example, Perron (1988): If a de
term inistic com ponent is excluded from a unit
root test b u t such a com ponent features in the
data generation process (DGP) of the series, the
resulting test will have low pow er. However, if
the deterministic com ponent is absent from the
DGP, greater pow er may be obtained by esti
mating p w ithout the trend component. In our
unit root tests, all variables, apart from the in
terest rate series, have been transform ed into
natural logarithms. In order to capture any
rem aining seasonality in the variables, three
seasonal dummies have been incorporated into
our estimated version of equation 1.
*
A num ber of findings em erge from Tables 8
to 14. First, th ere are only two variables which
appear to be stationary around a deterministic
trend, namely the Australian Treasury bill rate
and the Rotemberg C urrency Equivalent m easure
—all the other variables appear to contain
stochastic trends. As is common in many other
studies of the time series properties of macroeconomic series, the level of the price deflator
for a num ber of countries appears to be an 1(2)
process; that is, inflation in these countries is an
1(1) process. Interestingly, it is also the case that
some of ou r m onetary series appear to be 1(2)
processes. In general we found that this result
(but not the result for the deflator) was particu
larly sensitive to the lag length specified in the
estim ated equation.
For example, in the case of the United States,
all of the simple-sum money m easures appeared
to be 1(2) w hen q was set equal to 4 (DM1A and
DM1 also appeared 1(2) with four lags). However,
in these instances it appeared that this lag
length resulted in an overparam eterized regres
sion equation and the deletion of a single lag
MARCH/APRIL 1994
88
Table 8
Unit Root Tests for the United States
L
t
SSM1
DM1
SSM1A
DM1A
SSM2
DM2
SSM 3 (1)
DM3
SSL
DL
GDP
DEF
TB
RCE
BCE
A
*T
—
1.61
-1.97
0.03
0.77
1.40
0.80
1.66
1.17
1.40
0.95
-1.7 3
-1.01
-2.31
-1.31
0.67
-2 .0 8
-2 .1 6
-2 .7 0
-2 .0 5
-0 .2 3
-1.78
0.44
-1 .2 7
-0.61
-1.6 6
-2 .7 3
-1 .9 4
-2 .0 3
-3 .7 0
-2 .5 9
A2
t
tT
-3 .8 0
-3.61
-3.61
-4 .1 3
-3 .2 0
-4.1 9
-2 .9 3
-3 .9 3
-1.7 3
-3 .6 8
-4.51
-1.74
-5 .4 9
-4 .7 3
-3 .5 8
-4 .3 5
-4 .3 4
-3.61
-4.21
-3.4 7
-4 .2 2
-3 .3 6
-4 .0 6
-2.01
-3.7 4
-4.71
-1 .5 9
-5 .6 4
-4 .7 6
-3 .6 8
t
/•
*T
-9.1 8
-8 .3 8
-9 .2 9
-9 .5 2
-8.3 7
-8.21
-9.1 4
-7.79
-7.05
-7.81
-7.69
-6 .5 2
-11.84
-5.1 6
-6 .3 8
-9 .1 6
-8 .3 5
-9 .2 9
-9 .4 9
-8.3 7
-8.1 9
-9.1 4
-7.79
-7.12
-7.8 0
-7.6 6
-6.1 0
-11.78
-5.1 4
-6 .3 6
Note: Unless otherwise noted, each ADF statistic was computed with a lag of 3. SS denotes a
simple-sum monetary aggregate; D denotes a Divisia aggregate; M denotes money; L denotes
liquidity; GDP denotes real Gross Domestic Product; DEF denotes the GDP deflator; and TB
denotes a Treasury bill rate. L, A and A2 denote, respectively, the level and first and second differ
ence of a variable, t^ and tT are augmented Dickey Fuller statistics with allowance for a constant
mean and for a trend in mean, respectively. The 5 percent critical values for t and t are -2 .8 9
and -3.4 3 , respectively (Fuller, 1976).
Table 9
Unit Root Tests for the United Kingdoim
L
t
SSM4 (2)
DM 4 (1)
GDP
DEF
TB
A
»
•
tT
-0 .4 4
-0 .7 2
-1 .0 6
-2 .0 7
-2 .7 8
-1.6 0
-1 .2 2
-1.9 2
-0 .6 6
-3.12
Note: See Table 8.
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t
A2
»
<
tT
-3.07
-3.64
-3.81
-2.71
-5.26
-3 .0 6
-3 .6 4
-3 .8 5
-3 .3 5
-5 .2 5
t
*
<
-7.3 9
-10.42
-8 .2 2
-5 .0 2
-8.07
t
-7.35
-10.36
-8.1 8
-5.0 7
-8 .0 3
89
Table 1 0
Unit Root Tests for Australia
L
t
SSM2
DM2
SSM 3 (2)
DM3 (2)
GDP
DEF
TB
A
t
m
0.97
0.28
2.55
2.39
-0 .2 2
-1.15
-1.7 3
-2 .4 4
-1.7 3
-0 .2 6
-0 .4 3
-2 .4 8
-1.19
3.46
t
A2
t
-3.21
-3 .0 2
-3.1 8
-3.01
-3 .6 8
-3 .3 4
-3 .3 3
-3 .3 0
-3 .0 2
-4 .2 4
-3 .8 8
-3 .6 4
-3 .4 6
-3.31
t
t
-4 .7 6
-5 .4 5
-4 .5 6
-5.17
-5.0 7
- 4 .2 4
-5.17
-4 .7 3
-5 .4 0
-4 .4 9
-5.1 5
-4 .9 7
-4.41
-5.12
Note: See Table 8.
Table 1
1
Unit Root Tests for Germany
L
t
SSM2 (1)
DM 2 (1)
SSM 3 (2)
DM3 (1)
G DP (1)
DEF (2)
TB (2)
A
tT
-1.7 2
-1.9 7
-2 .7 2
-2 .6 2
-1.0 8
-0 .9 2
-1.9 7
-0 .7 5
-0 .4 5
-2 .0 2
-1.01
0.24
-1 .9 9
-1 .9 9
t
A2
tT
-2 .9 7
-3 .6 9
-3 .2 3
-3 .8 4
-6.21
-3.21
-3 .5 8
-3.11
-3 .7 4
-2 .9 6
-3 .7 8
-6 .2 3
-2 .7 6
-3 .6 3
t
/*
»T
-9 .3 8
-8 .2 7
-6.81
-7 .6 5
-11.18
-7 .2 4
-6 .9 8
-9 .4 3
-8 .2 0
-6 .7 5
-7.57
-11.08
-7.17
-6 .9 3
Note: See Table 8.
Table 12
Unit Root Tests for Switzerland______________________
L
t
SSM1
DM1
SSM2 (1)
DM2 (1)
GDP
DEF
TB
-1.17
-1.18
0.15
-1.19
0.95
-1.0 6
-1.7 6
A
tT
-2 .3 2
-2 .3 5
-1 .4 4
-1.91
-1.5 7
-0 .9 4
-1 .9 9
t
A2
t
»
•
-3 .4 3
-3 .4 4
-3 .3 0
-3.19
-2 .1 0
- 2 .2 2
-3 .0 3
-3 .4 0
-3 .4 0
-3.31
-3 .1 8
-2 .7 8
-2 .0 3
-2 .9 9
»
*
*T
-5.11
-5 .1 0
-7.16
-7 .2 5
-4.81
-4 .7 6
-5 .8 4
-5 .0 7
-5 .0 6
-7.07
-7 .2 2
-4 .7 5
-4 .8 7
-5.81
Note: See Table 8.
MARCH/APRIL 1994
90
Table 13
Unit Root Tests for Canada
L
t
SSM1
SSM 2
SSM 3
SSL
DM1
DM 2
DM 3
DL
GDP
DEF
TB
A
tT
-1.21
-1.15
-0 .7 0
1.48
-1.18
-0 .7 4
-1 .4 0
-0 .7 9
-1.87
-2.2 1
-1 .3 6
-2 .6 4
-1 .6 5
-2 .0 4
-1 .8 0
-2 .7 2
-2 .0 6
-2 .6 3
-2 .2 7
-1 .2 8
-1 .2 3
-1 .4 4
t
A2
tT
-3 .0 2
-2 .2 1
-1.7 2
0.32
-2 .9 3
-2 .6 8
- 2 .2 5
-2 .5 3
-2 .9 9
-1.79
-3 .2 4
-3 .7 3
-2.61
-2 .3 7
-0 .3 6
-3 .6 6
-3.21
-3 .2 0
-3 .2 6
-3.11
-1.9 4
-3 .2 6
t
tT
i*
-5 .7 7
-4 .8 5
-5.6 7
-1 .9 9
-5 .2 3
-5 .4 4
-5 .4 7
-5 .0 6
-5 .7 2
-4 .1 3
-5 .8 6
-5 .7 2
-4 .8 6
-5 .6 6
-2 .3 8
-5 .1 8
-5 .4 5
-5 .5 2
-5 .1 2
-5 .6 6
-4 .1 8
-5.81
Note: See Table 8.
Table 14
Unit Root Tests for Japan
A
L
t
tT
t
A2
tT
t
b
tT
SSM1
-1.18
-2 .7 8
-3 .0 8
-3.19
-4 .7 2
-4 .6 7
DM1
-1.19
-2 .7 4
-3.01
-3.1 3
-4 .6 4
-4 .6 0
SSM2
-1.14
-2.31
-2 .5 5
-2 .6 5
-3 .2 6
-3.19
DM2
-0 .8 5
-2.31
-2 .0 8
-1.9 6
-3 .5 2
-3 .5 3
SSM 3
-2.11
- 2 .2 2
-2 .4 4
-2.41
-2 .6 9
-2 .5 9
DM 3
-1 .3 4
-2 .5 8
-1.7 0
-1 .9 2
-3 .2 8
-3 .2 8
-9 .2 9
0.38
-1.16
-5.1 5
-5 .1 2
-9.41
DEF
-2 .0 7
-2 .4 7
-2 .4 5
-2 .3 5
-4 .8 7
-5 .1 0
TB
- 2 .2 3
-3 .3 6
-3 .9 0
-3 .6 4
- 2 .8 3
-2.7 1
GNP (1)
Note: See Table 8.
FEDERAL RESERVE BANK OF ST. LOUIS
91
made a dram atic difference to the estimated fratio on ir (without significantly affecting the
non-autocorrelatedness properties of the residu
als). Indeed, w ith three lags all of the money
m easures w ith the exception of simple-sum M3
(SSM3) and simple-sum L (SSL) appear to be 1(1);
the form er variable appears 1(1) w hen q = l,
while SSL appears 1(2) at all lag lengths (again,
the residuals in each of these cases w ere non
autocorrelated).
The country with the greatest preponderence
of m onetary aggregates being 1(2) is Canada, in
which six out of the eight chosen m onetary ag
gregates appear to have tw o unit roots. The
finding that the level of a country’s price series
is an 1(2) process finds confirmation in a num
ber of other empirical studies (see, for example,
Johansen and Juselius, 1990). Furtherm ore, the
finding that m onetary aggregates are 1(2) has
also been reported by other researchers
(Rasche, 1993), although this finding does not
appear to be as robust as that for price defla
tors.
We now tu rn to an analysis of the cointegra
tion properties of a vector of variables for each
of our chosen countries. In particular, for each
country w e use the m ethods of Johansen (1988,
1991) to estimate the num ber of cointegrating
vectors in y ' = [^m, gdp, def, tb], w here m
denotes the money supply, ^ is either ss (for
simple-sum) or d (for Divisia), gdp is real output,
d e f is the deflator corresponding to output, and
tb denotes the relevant interest rate (usually a
Treasury bill rate). The fact that the variables
entering y ' may for any one country be a mix
of 1(1) and 1(2) processes has to be taken into
account in our implem entation of the Johansen
procedure, since the latter is only appropriate
for 1(1) variables and driftless 1(0) variables. We
therefore use the inform ation from our unit
root tests to reduce the order of integration of
any 1(2) variables to 1(1), by entering the first
difference of the level of such a variable. Thus,
if a country's price level is 1(1), we enter the
change in the price level (equivalent to the infla
tion rate, since the price level is transform ed
logarithmically) and/or if the m oney m easure is
also 1(2), it is also entered in differences.
In the context of estimating a conventional
money dem and function (which has the same
set of variables as are contained in our y vec
tor), Johansen (1991) has suggested dealing with
the two unit roots in m and p by respecifying
the y vector to consist of (m-p), y, i and Ap.
However, given the nature of the c u rren t exer
cise, and also since, in m any instances it is only
p that appears to be 1(2), we do not believe that
such a specification is as attractive as the one
adopted here. To determ ine the num ber of unit
roots in y ' we use the following method, due to
Johansen (1988, 1991). This m ethod may be
thought of as the m ultivariate equivalent of (1).
It is assumed that y t has the following autore
gressive representation w ith Gaussian e rro rs £,:
(2) y t = n ^ , . , +
n2 + . . . + n k y ,.k + £,
y,_2
t = 1,2, ...,T.
Equation 2 may be reparam eterized as
(20 Ay, = n + Uyt_k + J j T Ay,.,. + u,,
k
w here q = k - 1, II = S B. - /, Bj is an (n x n)
m atrix from the lag polynomial in the (levels)
k
VAR and T. = -T , B for i=l,...q. The key
1
j-i+1 ^
difference betw een 1 and 2 is th at in 2 there is
no allowance for a deterministic trend (or that
the series are driftless). The long-run static
equilibrium corresponding to 2 is1
(3) n * = 0.
The m atrix II is the m ultivariate analogue of 7r
in equation 1. Assuming that the variables en
tering the y vector do not have an order of in
tegration greater than 1, then the right-hand
side of equation 2 can only be stationary if the
components of Ily, k are stationary. This, in
turn, may be determ ined by the rank, r, of the
m atrix II, and, in particular, w hether 0 < r <
n, w here n denotes the num ber of variables in
y. If r=n (that is, II has full rank) then Ily, t
can only be stationary if all n linearly indepen
dent combinations of y t_k form ed using II are
stationary: A standard VAR analysis in levels is
appropriate here. If, at the other extreme, r= 0
(and 11 = 0) then there are no linear combina
tions in y, which are stationary, and (2) th ere
fore becomes a VAR in first differences (this is
the kind of VAR specification used in the
1Dynamic steady-state equilibrium simply involves the addi
tion of a term in the constant vector of steady-state growth
rates to equation 2, which we omit here for expositional
purposes; this does not affect the subsequent discussion.
MARCH/APRIL 1994
92
majority of traditional G ranger causality tests).
If, how ever 0 < r < n , II will be of reduced rank
and there m ust exist (n x r) m atrices a and /J
such that II = ap', and for IIyt_t to be station
ary p'y,_k m ust be stationary. The ft matrix
therefore contains the cointegrating vectors and
a represents the m atrix of adjustm ent vectors.
For example, if P\ is the ith row of /?' then:
(4) P \yt ~ /(0).
Johansen (1988, 1991) has proposed a maxi
mum likelihood m ethod of estimating all of the
cointegrating vectors contained in II and sig
nificance tests to determ ine how many of the
vectors are statistically significant. Since the Jo
hansen technique is now well-known, we do not
present it here. Instead, we simply note the two
test statistics used to determ ine the num ber of
significant cointegrating vectors.
In our application the likelihood ratio, or
trace, test statistic (LR1), for the hypothesis that
there are at most r distinct cointegrating vec
tors, is
(5) Lfll = T t
ln( 1 -A),
l-P +1
w here A
r+1,...,An are the n - r smallest squared ca
nonical correlations betw een the y t k and Ay,
corrected for the effect of the lagged differ
ences of the y( process (for details of how to ex
tract the A/s, see Johansen 1988). Additionally,
the likelihood ratio statistic for testing at most r
cointegrating vectors against the alternative of
r + 1 cointegrating vectors is given by equation 4
(6) LR2 = T/n(l-A r+1).
Johansen (1988) shows that equations 5 and 6
have a non-standard distribution under the null
hypothesis. He does, however, provide approxi
m ate critical values for the statistic, generated
by Monte Carlo methods. (The critical values
recorded in Johansen’s 1988 paper are for a
VAR w ithout an intercept term or seasonal
dummies. Since these w ere included in our em
pirical analysis, we used the critical values for 5
and 6 reported in Johansen and Juselius, 1990.)
In Table 15, our estim ated values of LR1 and
LR2 are presented, and the critical values and
relevant null hypothesis are reported at the bot
tom of the table. Consider first the results for
the United States. Interestingly, th ere is no evi
dence of cointegration for any of the narrow
m onetary m easures (i.e. M l and MIA). However,
w ith the exception of SSM3, th ere is clear evi
dence of one unique cointegrating vector for all
FEDERAL RESERVE BANK OF ST. LOUIS
m onetary m easures which are broader than M l.
It follows from this that it is the introduction of
these broader m onetary m easures that produces
a cointegrating set (and not the income, interest
rate or inflation rate). Since the Rotemberg cu r
rency equivalent m easure appears to be station
ary around a determ inistic trend, it would
appear not to be an ideal candidate for the
Johansen methodology. However, for complete
ness, and also since it is often difficult to dis
crim inate betw een a variable w hich is stationary
around a tren d and one which has a stochastic
unit root, we also test for the num bers of coin
tegrating vectors in a y vector defined for RCE.
Interestingly, this also gives strong evidence of
one cointegrating vector, as does the BCE m ea
sure. (BCE is a variety of currency equivalence
which uses Divisia weights.) The evidence for
other (non-U.S.) countries in Table 15 is also
suggestive of there being long-run relationships
contained in different specifications of the y ’
vectors: The vast majority of m onetary m ea
sures produce at least one cointegrating vector
and m any produce two. Again, th ere does not
appear to be any split betw een Divisia and
simple-sum m onetary m easures in term s of the
production of cointegrating relationships.
The broad picture to em erge from Table 15 is
that there is strong evidence of at least one
cointegrating vector for most country/m oney
combinations. It also seems that, at least in this
long-run modelling context, th ere is no sharp
distinction betw een Divisia and simple-sum
money. It may be, however, th at one or other
m onetary m easures produce m ore "sensible”
estimates of the cointegrating vector and we
re tu rn to this point in a later section (where we
also examine sample specific issues which may
be im portant for the United States). However,
for the im plem entation of our causality tests,
the main implication to be draw n from Table 15
is that a causality relationship specified simply
in differences will be misspecified for the vast
majority of country/m oney combinations. We
therefore propose estimating the vector e rro r
correction models implied by our cointegration
results and subjecting them to exclusion tests on
the lags of each of the differenced (either first
or second differenced, depending on the out
come of the results reported in Tables 8 to 14)
and also on the lagged cointegrating term s. Since
we correct the coefficient variance-covariance
matrix for heteroskedasticity (using the m ethods
of Hansen, 1980; and White, 1978), the exclusion
tests are perform ed using linear Wald statistics,
93
Table 15
Estimated Trace and AMax Statistics
U nited States
Trace (LR1)
SSM1
DM1
SSM1A
DM1A
SSM2
DM2
SSM3
DM3
SSL
DL
0.02
5.19
18.55
40.17
0.10
0.07
18.05
38.13
0.07
7.66
17.83
33.73
0.14
7.73
18.69
40.25
3.80
10.38
23.34
57.92
5.13
12.80
23.34
58.85
3.45
8.14
20.54
47.67
5.08
11.59
21.91
52.35
2.31
8.05
20.65
54.99
4.77
10.99
21.53
53.27
United States
AMAX (LR2)
SSM1
DM1
SSM1A
DM1A
SSM2
DM2
SSM3
DM3
SSL
DL
0.02
5.18
13.35
21.61
0.01
5.06
12.88
20.08
0.07
7.59
10.16
15.90
0.14
7.58
10.97
21.56
3.80
6.58
12.94
34.58
5.13
7.66
10.63
35.41
3.45
4.66
12.39
27.13
5.08
6.51
10.32
30.44
2.31
5.73
12.60
34.34
4.77
6.22
10.53
31.74
United Kingdom
T race (LR1)
AMax (LR2)
SSM4
DM4
SSM4
OM4
1.89
10.20
38.34
88.45
3.85
12.17
37.53
64.20
1.89
8.31
28.13
50.12
3.85
8.32
25.36
26.67
MARCH/APRIL 1994
94
Table 15 (continued)
Estimated Trace and AMax Statistics
Australia
T race (LR1)
AMax (LR2)
SSM2
DM2
SSM3
DM3
SSM2
DM2
SSM3
DM3
0.01
10.51
21.89
53.96
0.75
5.74
26.93
55.67
0.61
10.77
31.97
67.61
0.12
6.23
23.12
56.41
0.01
10.50
11.38
32.07
0.74
4.99
21.18
28.74
0.06
10.71
21.19
35.64
0.12
6.12
16.88
33.79
G erm any
T race (LR1)
AMax (LR2)
SSM2
DM2
SSM3
DM3
SSM2
DM2
SSM3
DM3
0.02
11.11
29.62
63.38
0.28
12.62
39.21
77.27
0.81
17.08
40.02
70.38
0.68
18.44
43.56
81.55
0.01
11.10
18.51
33.75
0.03
12.34
26.58
38.06
0.81
16.26
22.94
30.37
0.68
17.76
25.11
37.98
Sw itzerland
Trace (LR1)
AMax (LR2)
SSM1
DM1
SSM2
DM2
SSM1
DM1
SSM2
DM2
0.59
15.54
35.55
56.74
0.60
15.50
35.57
57.08
0.49
12.41
33.91
64.82
1.53
13.29
33.71
60.78
0.59
14.93
20.01
21.18
0.60
14.89
20.07
21.51
0.49
11.91
21.49
35.91
1.53
11.76
20.41
27.08
FEDERAL
http://fraser.stlouisfed.org/RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
95
Table 15 (continued)
Estimated Trace and AMax Statistics
Canada
Trace (LR1)
AMax (LR2)
SSM1
DM1
SSM2
DM2
SSM1
DM1
SSM2
DM2
2.35
15.06
41.85
79.71
2.67
15.00
43.42
81.55
0.77
8.28
21.36
53.38
0.16
6.66
17.74
55.68
2.35
12.71
26.79
37.86
2.67
12.33
28.41
38.13
0.77
7.51
13.07
32.03
0.16
6.50
11.08
37.95
Japan
Trace (LR1)
AMax (LR2)
SSM1
DM1
SSM2
DM2
SSM3
DM3
SSM1
DM1
SSM2
DM2
SSM3
DM3
3.09
12.74
32.26
65.14
30.08
12.97
32.19
67.00
2.42
16.28
38.76
71.17
0.62
15.03
34.97
69.63
3.46
16.91
39.39
67.29
3.03
15.41
35.25
64.82
3.04
9.64
19.51
32.88
3.08
9.89
19.21
34.81
2.42
13.85
22.47
32.41
2.62
12.41
19.95
34.65
3.46
13.45
22.48
27.90
3.03
12.37
19.83
29.56
Null hypotheses and 5 percent critical values for T race and AMax statistics.
Trace
AMax
Null
Hypothesis
5 % Critical
Value
r< 3
r< 2
r< 1
r= 0
8.18
17.95
31.53
48.28
Null
Hypothesis
r= 3
r=2
r= 1
r= 0
| r= 4
| r= 3
jr=2
| r= 1
5 % Critical
Value
8.18
14.90
21.07
27.14
Note: Variables are defined in Table 8. The Trace and AMax statistics are defined in the text.
which have a central chi-squared distribution.
C a u sa lity T e sts
The exclusion tests for each country are
reported in Tables 16 through 22. Consider first
the results for the United States, reported in Ta
ble 16. Since there is some ambiguity regarding
the stochastic properties of the Rotemberg cu r
rency equivalent m easure (see discussion above),
we present two systems for this variable: one in
w hich the variable enters as a level and a deter
ministic time tren d is included in each equation
of the system (the system with RCE1), and one
in which it enters as a first difference and the
ECM term from the Johansen estimates re p o rt
ed in Table 15 is also included in each equation
of the system (the system w ith RCE2).
In term s of the U.S.’ real output relationship,
there is a very clear, significant, short-run in
fluence of the Treasury bill rate. This influence
is repeated in all of the other equations as well,
(apart from the deflator equation w hen SSM1
and DM1 are used). This confirms the findings
of m uch other research on the im portance of
including an interest rate in the causality
specification (see: Sims, 1980; and Friedm an and
Kuttner, 1993). In equations in which an ECM
term appears, the majority of significant impacts
tend to occur in equations w hich feature the
deflator or money (Divisia or simple sum) as the
dependent variable. W hat then of the potential
short-run differential impact of simple-sum and
Divisia money? Interestingly, and in contrast to
our initial discussion of the long-run impact,
MARCH/APRIL 1994
96
Table 16
Causality Tests for the United States
SSM1
SSM1
GDP
DEF
TB
87.21
1.22
2.85
4.00
(0.00)
(0.87)
(0.58)
(0.00)
DM1
DM1
GDP
DEF
TB
37.88
0.17
1.39
17.32
(0.00)
(0.99)
(0.84)
(0.00)
SSM1A
SSM1A
GDP
DEF
TB
68.74
2.73
4.90
21.86
(0.00)
(0.60)
(0.29)
(0.00)
DM1A
DM1A
GDP
DEF
TB
57.30
3.45
3.77
16.81
(0.00)
(0.48)
(0.44)
(0.00)
SSM2
SSM2
GDP
DEF
TB
ECM
48.63
13.67
20.93
27.36
17.23
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
DM2
DM2
GDP
DEF
TB
ECM
23.71
10.09
6.72
95.24
18.39
(0.00)
(0.04)
(0.15)
(0.00)
(0.00)
SSM3
SSM3
GDP
DEF
TB
ECM
89.12
11.88
12.32
10.52
8.50
FEDERAL RESERVE BANK OF ST. LOUIS
(0.00)
(0.02)
(0.02)
(0.03)
(0.00)
GDP
4.19
28.67
5.55
27.45
(0.38)
(0.00)
(0.23)
(0.00)
GDP
5.38
28.08
5.86
28.33
(0.25)
(0.00)
(0.21)
(0.00)
GDP
1.07
22.40
5.16
21.22
(0.89)
(0.00)
(0.27)
(0.00)
GDP
1.12
26.46
5.59
21.17
(0.89)
(0.00)
(0.23)
(0.00)
GDP
7.34
9.73
8.51
13.97
2.25
(0.12)
(0.04)
(0.07)
(0.00)
(0.13)
GDP
9.97
7.78
6.95
18.35
4.52
(0.04)
(0.09)
(0.14)
(0.00)
(0.03)
GDP
5.04
15.23
6.84
22.28
0.68
(0.28)
(0.00)
(0.14)
(0.00)
(0.41)
DEF
4.22
4.63
56.56
6.28
(0.38)
(0.33)
(0.00)
(0.18)
DEF
5.04
4.53
52.46
6.81
(0.28)
(0.34)
(0.00)
(0.15)
DEF
12.78
2.37
64.57
9.45
(0.01)
(0.00)
(0.00)
(0.05)
DEF
12.54
3.30
61.65
9.29
(0.01)
(0.51)
(0.00)
(0.05)
DEF
4.82
1.50
23.76
14.23
8.29
(0.31)
(0.83)
(0.00)
(0.00)
(0.00)
DEF
10.74
2.45
26.71
18.51
12.19
(0.03)
(0.65)
(0.00)
(0.00)
(0.00)
DEF
8.74
2.61
25.13
13.14
13.25
(0.07)
(0.63)
(0.00)
(0.01)
(0.00)
TB
17.43
10.61
13.44
19.59
(0.00)
(0.03)
(0.00)
(0.00)
TB
5.66
10.85
11.85
10.01
(0.23)
(0.03)
(0.02)
(0.04)
TB
40.14
11.39
10.51
24.78
(0.00)
(0.02)
(0.03)
(0.00)
TB
17.12
13.79
12.39
23.56
(0.00)
(0.00)
(0.01)
(0.00)
TB
6.75
7.53
14.57
12.42
0.60
(0.15)
(0.11)
(0.00)
(0.01)
(0.44)
TB
9.23
18.64
6.73
14.47
4.74
(0.05)
(0.00)
(0.15)
(0.00)
(0.03)
TB
1.04
9.80
10.49
9.91
2.67
(0.90)
(0.04)
(0.03)
(0.04)
(0.10)
97
Table 16 (continued)
Causality Tests for the United States
DM3
DM3
GDP
DEF
TB
ECM
38.22
9.20
6.45
78.27
14.58
(0.00)
(0.05)
(0.17)
(0.00)
(0.00)
SSL
SSL
GDP
DEF
TB
ECM
92.18
24.22
13.82
20.53
17.05
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
DL
DL
GDP
DEF
TB
ECM
33.11
12.87
6.47
68.23
14.45
(0.00)
(0.01)
(0.16)
(0.00)
(0.00)
RCE1
RCE1
GDP
DEF
TB
37.52
17.22
3.55
17.83
(0.00)
(0.00)
(0.47)
(0.00)
RCE2
RCE2
GDP
DEF
TB
ECM
26.14
16.07
2.86
16.66
7.64
(0.00)
(0.00)
(0.58)
(0.00)
(0.00)
BCE
BCE
GDP
DEF
TB
ECM
12.78
7.41
4.09
62.27
0.27
(0.01)
(0.12)
(0.39)
(0.00)
(0.60)
GDP
8.64
9.37
6.58
18.73
3.02
(0.07)
(0.05)
(0.16)
(0.00)
(0.08)
GDP
7.16
15.34
6.94
27.57
0.75
(0.13)
(0.00)
(0.14)
(0.00)
(0.38)
GDP
12.01
10.37
7.07
23.47
2.76
(0.02)
(0.03)
(0.13)
(0.00)
(0.09)
GDP
11.78
9.47
7.18
15.47
(0.02)
(0.05)
(0.13)
(0.00)
GDP
8.57
13.65
7.11
16.36
1.72
(0.07)
(0.00)
(0.13)
(0.00)
(0.18)
GDP
5.66
9.83
6.05
17.52
4.46
(0.23)
(0.04)
(0.19)
(0.00)
(0.03)
DEF
10.82
3.21
29.61
18.79
13.77
(0.03)
(0.52)
(0.00)
(0.00)
(0.00)
DEF
7.96
3.17
16.05
13.11
13.69
(0.09)
(0.53)
(0.00)
(0.01)
(0.00)
DEF
7.79
2.91
26.05
16.64
11.96
(0.09)
(0.57)
(0.00)
(0.00)
(0.00)
DEF
5.27
0.87
53.72
4.92
(0.26)
(0.93)
(0.00)
(0.79)
DEF
10.33
1.69
42.38
8.02
4.34
(0.04)
(0.79)
(0.00)
(0.09)
(0.04)
DEF
5.61
1.46
30.72
12.19
5.79
(0.23)
(0.83)
(0.00)
(0.02)
(0.02)
TB
7.16
18.27
6.61
15.62
5.66
(0.13)
(0.00)
(0.16)
(0.00)
(0.02)
TB
2.54
10.07
10.64
11.04
1.17
(0.64)
(0.04)
(0.03)
(0.03)
(0.27)
TB
7.39
14.26
7.05
15.57
3.94
(0.12)
(0.00)
(0.13)
(0.00)
(0.04)
TB
32.10
11.08
6.94
10.16
(0.00)
(0,02)
(0.14)
(0.04)
TB
28.56
13.13
7.11
10.04
4.74
(0.00)
(0.01)
(0.13)
(0.04)
(0.03)
TB
7.02
20.56
8.51
12.95
6.44
(0.11)
(0.00)
(0.07)
(0.01)
(0.01)
Note: The variables are as defined in Table 8. The variable at the column head is the dependent
variable. The numbers not in parentheses are linear Wald statistics, while the numbers in paren
theses are marginal significance levels.
MARCH/APRIL 1994
98
Table 17
Causality Tests for the United Kingdom
SSM4
SSM4
GNP
DEF
TB
ECM
39.89
11.20
28.74
4.44
4.26
(0.00)
(0.02)
(0.00)
(0.35)
(0.12)
GNP
0.26
2.39
2.79
3.97
8.46
15.58
1.43
16.30
6.58
4.54
(0.00)
(0.84)
(0.00)
(0.16)
(0.10)
(0.99)
(0.66)
(0.59)
(0.41)
(0.01)
GNP
DM4
DM4
G NP
DEF
TB
ECM
DEF
4.88
1.91
2.17
3.58
0.92
1.90
9.08
5.28
11.99
24.38
(0.75)
(0.06)
(0.26)
(0.02)
(0.00)
DEF
(0.30)
(0.75)
(0.70)
(0.46)
(0.63)
14.59
6.18
12.23
5.74
27.67
(0.00)
(0.19)
(0.02)
(0.22)
(0.00)
TB
17.59
10.22
3.97
8.66
10.71
(0.00)
(0.04)
(0.41)
(0.07)
(0.00)
TB
13.52
7.60
8.15
2.11
2.03
(0.00)
(0.11)
(0.08)
(0.72)
(0.36)
Note: See Table 16.
th ere is a clear differential impact. For example,
in term s of the output equation, the Divisia
m onetary m easure is significant at the 5 percent
level in th ree cases (namely, DM2, DL and
RCE1) and at the 7 percent level in two in
stances (that of DM3 and RCE1), but none of
the simple-sum money term s enters significantly
even at the 10 percent level. It is also interesting
to note th at among the tw o currency equivalent
m easures, it is only the RCE m easure which fea
tures significantly in the real output equation
(confirming the significant influence for this
m onetary m easure noted by Belongia, 1993).
The significance of these Divisia m easures is
repeated in the deflator equations (apart from
RCE1, although, additionally, DM1A is also sig
nificant), although in these equations one of the
simple-sum m easures is also significant (for
SSM1A). W ith respect to m onetary causality in
the United States, TB equations, both simple
sum and Divisia seem to do equally well in that
each m easure has significant strikes.
The U.K. evidence, reported in Table 17, con
trasts sharply w ith that for Switzerland. Neither
M4 nor Divisia M4 affects real GNP. However,
Divisia M4 does influence the inflation rate.
Both m oney m easures influence interest rates.
Thus, the superiority of Divisia M4 over M4 is
confirm ed (at least so far as inflation is con
cerned), but the lack of causality from money to
real activity is notew orthy.
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FEDERAL RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
The Australian results, recorded in Table 18,
differ from the U.S. results in that the TB rate
does not have a significant short-run influence
in any of the real output equations or in the
price equations. However, in common w ith the
U.S. results, Divisia money is significant—both
M2 and M3—in the real output equation, w hereas
the simple-sum m easures are not. In contrast,
however, it is the simple-sum m easures which
have a significant short-run impact in the TB
equations rath e r than the Divisia measures.
There are also significant long-run influences in
all of the equations, although these do not seem
to be confined to any particular m easure of
money.
For Germany, none of the m onetary impulses
—neither Divisia nor simple-sum—appears with
a significant influence in the real output equa
tions, although there would appear to be an in
terest rate effect in this equation for the two
sum m easures of money. Real GDP has a signifi
cant influence in all of the money equations,
apart from SSM2. The joint effect of the TB rate
is significant in all of the money equations and
inflation, in turn, has a significant impact on in
terest rates.
Both simple-sum and Divisia m onetary meas
ures have also a significant influence on infla
tion and the TB rate in the Swiss case (Table
20), although in contrast to the German case
99
Table 18
Causality Tests for Australia
SSM2
SSM2
GDP
DEF
TB
ECM
18.76
3.21
5.40
21.29
0.68
(0.00)
(0.52)
(0.25)
(0.00)
(0.41)
DM2
DM2
GDP
DEF
TB
ECM
1 9 .24 (0 .0 0)
4.07 (0.39)
6.08 (0.19)
4.49 (0.34)
4.07 (0.04)
SSM3
SSM3
GDP
DEF
TB
ECM
17.40
15.78
10.38
12.91
18.76
(0.00)
(0.00)
(0.03)
(0.01)
(0.00)
DM3
DM3
GDP
DEF
TB
ECM
27.15
4.24
7.99
5.05
0.13
(0.00)
(0.37)
(0.09)
(0.28)
(0.72)
GDP
9.05
16.06
17.95
2.51
2.32
(0.06)
(0.00)
(0.00)
(0.64)
(0.12)
GDP
9.15
15.68
16.68
4.24
8.07
(0.00)
(0.00)
(0.00)
(0.37)
(0.00)
GDP
7.27
11.46
12.67
2.67
10.14
(0.12)
(0.02)
(0.01)
(0.61)
(0.00)
GDP
14.94
24.13
24.23
4.99
5.41
(0.00)
(0.00)
(0.00)
(0.28)
(0.02)
DEF
7.06
30.92
19.35
6.18
0.07
(0.13)
(0.00)
(0.00)
(0.18)
(0.79)
DEF
4.24
22.32
19.61
4.75
3.59
(0.37)
(0.00)
(0.00)
(0.31)
(0.06)
DEF
2.91
38.99
18.73
6.21
7.54
(0.57)
(0.00)
(0.20)
(0.18)
(0.02)
DEF
2.53
30.65
15.79
4.88
0.02
(0.64)
(0.00)
(0.00)
(0.29)
(0.88)
TB
18.18
3.45
5.33
13.15
8.68
(0.00)
(0.48)
(0.25)
(0.01)
(0.00)
TB
3.87
4.91
4.01
11.81
0.70
(0.42)
(0.79)
(0.40)
(0.02)
(0.40)
TB
9.72
4.66
5.74
19.21
6.52
(0.04)
(0.32)
(0.22)
(0.00)
(0.04)
TB
1 .4 7 (0 .8 3 )
5.45 (0.24)
6.71 (0.15)
11.33 (0.02)
6.78 (0.00)
Note: See Table 16.
MARCH/APRIL 1994
10 0
Table 19
Causality Tests for Germany
SSM2
SSM2
GDP
DEF
TB
ECM
6.92
1.49
3.99
10.56
3.91
(0.14)
(0.83)
(0.41)
(0.03)
(0.05)
DM2
DM2
GDP
DEF
TB
ECM
8.92
18.82
5.15
24.47
50.64
(0.06)
(0.00)
(0.27)
(0.00)
(0.00)
SSM3
SSM3
GDP
DEF
TB
ECM
4.71
17.41
37.78
21.18
38.10
(0.32)
(0.00)
(0.00)
(0.00)
(0.00)
DM3
DM3
GDP
DEF
TB
ECM
16.73
30.32
50.59
41.28
55.30
Note: See Table 16.
FEDERAL
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Federal Reserve Bank of St. Louis
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
GDP
3.17
31.97
1.62
16.55
6.41
(0.53)
(0.00)
(0.81)
(0.00)
(0.01)
GDP
1.54
9.08
3.28
5.05
5.54
(0.82)
(0.05)
(0.51)
(0.78)
(0.06)
GDP
3.79
24.94
1.52
10.68
6.46
(0.43)
(0.00)
(0.82)
(0.03)
(0.04)
GDP
2.37
19.03
1.08
1.68
1.22
(0.66)
(0.00)
(0.89)
(0.79)
(0.54)
DEF
9.08
9.39
24.15
7.68
11.79
(0.00)
(0.06)
(0.00)
(0.10)
(0.00)
DEF
9.88
6.52
33.66
12.75
21.10
(0.04)
(0.16)
(0.00)
(0.01)
(0.00)
DEF
0.04
1.58
9.92
12.55
3.79
(0.99)
(0.81)
(0.04)
(0.01)
(0.19)
DEF
14.54
4.63
7.29
7.14
30.37
(0.00)
(0.33)
(0.12)
(0.13)
(0.00)
TB
0.81
3.90
9.33
14.35
0.85
(0.74)
(0.42)
(0.05)
(0.00)
(0.36)
TB
6.93
6.87
10.16
5.02
1.82
(0.14)
(0.14)
(0.04)
(0.78)
(0.40)
TB
6.32
3.22
3.37
9.99
25.81
(0.18)
(0.52)
(0.49)
(0.04)
(0.00)
TB
7.16
4.64
11.17
9.15
0.53
(0.13)
(0.33)
(0.02)
(0.06)
(0.76)
101
Table 20
Causality Tests for Switzerland
SSM1
SSM1
G NP
DEF
TB
ECM
7.47
22.21
14.71
10.35
25.22
(0.11)
(0.00)
(0.00)
(0.03)
(0.00)
DM1
DM1
GNP
DEF
TB
ECM
7.26
20.11
15.04
9.75
24.11
(0.12)
(0.00)
(0.00)
(0.04)
(0.00)
SSM2
SSM2
GNP
DEF
TB
ECM
7.69
5.70
11.74
30.06
14.15
(0.10)
(0.22)
(0.02)
(0.00)
(0.00)
DM2
DM2
GNP
DEF
TB
ECM
10.17
4.54
5.07
5.86
3.66
(0.04)
(0.33)
(0.28)
(0.21)
(0.16)
GNP
18.96
50.69
13.43
26.68
10.65
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
GNP
18.83
50.48
12.91
26.38
10.66
(0.00)
(0.00)
(0.02)
(0.00)
(0.00)
GNP
5.59
46.40
17.95
49.45
32.73
(0.23)
(0.00)
(0.00)
(0.00)
(0.00)
GNP
10.64
76.37
8.85
25.41
19.53
(0.03)
(0.00)
(0.06)
(0.00)
(0.00)
DEF
24.09
18.80
21.44
7.15
13.21
(0.00)
(0.00)
(0.00)
(0.13)
(0.00)
DEF
24.75
19.68
21.76
7.59
13.95
(0.00)
(0.00)
(0.00)
(0.11)
(0.00)
DEF
13.10
12.01
35.34
15.47
10.53
(0.01)
(0.02)
(0.00)
(0.00)
(0.00)
DEF
30.98
23.46
44.67
12.71
50.06
(0.00)
(0.00)
(0.00)
(0.01)
(0.00)
TB
6.56
25.46
10.05
12.74
2.54
(0.16)
(0.00)
(0.04)
(0.01)
(0.28)
TB
6.59
24.96
10.18
12.75
2.67
(0.16)
(0.00)
(0.04)
(0.01)
(0.26)
TB
29.64
13.26
14.81
23.78
11.94
(0.00)
(0.01)
(0.01)
(0.00)
(0.00)
TB
18.57
26.24
19.76
15.15
19.04
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
Note: See Table 16.
MARCH/APRIL 1994
102
Table 21
Causality Tests for Canada
SSM1
SSM1
GNP
DEF
TB
ECM
3.48
6.32
2.09
8.94
15.08
(0.48)
(0.18)
(0.72)
(0.06)
(0.00)
GNP
10.22
7.11
15.89
1.91
11.46
DM1
DM1
GNP
DEF
TB
ECM
5.39
11.20
2.34
7.88
16.96
(0.25)
(0.02)
(0.67)
(0.09)
(0.00)
TB
ECM
22.25
5.24
10.13
49.24
0.04
(0.00)
(0.76)
(0.04)
(0.00)
(0.83)
(0.03)
(0.13)
(0.00)
(0.75)
(0.00)
GNP
8.89
7.09
34.00
9.18
46.18
6.65
2.75
7.57
5.11
9.85
4.79
3.27
10.53
3.98
1.80
(0.31)
(0.51)
(0.03)
(0.41)
(0.40)
DEF
(0.06)
(0.13)
(0.00)
(0.05)
(0.00)
GNP
SSM2
SSM2
GNP
DEF
DEF
5.16
5.95
16.58
1.39
0.68
(0.27)
(0.20)
(0.00)
(0.84)
(0.71)
DEF
(0.16)
(0.60)
(0.11)
(0.28)
(0.00)
12.36
4.74
29.68
6.06
0.68
(0.01)
(0.31)
(0.00)
(0.19)
(0.41)
DM2
GNP
DEF
DM2
GNP
DEF
30.89 (0.00)
8.97 (0.06)
8.61 (0.07)
1.24 (0.84)
2.02 (0.73)
11.33 (0.02)
5.46 (0.24)
2.89 (0.68)
19.24 (0.00)
TB
2 5 .8 5 (0 .00)
2.41 (0.66)
3 .5 4 (0 .47)
2.81 (0.09)
7.53 (0.00)
0 .6 0 (0 .44)
ECM
both Divisia m easures appear significant in the
output equation, as does SSM1. In common with
a num ber of other countries, the TB rate has a
statistical influence in all of the output equa
tions and in three of the m oney equations. It is
notew orthy that the joint effect of inflation is
statistically significant in three out of four of
the output equations.
The Canadian results (Table 21) portray little
significant impact of money on any variable (the
exceptions being SSM3 and DM3 in the TB equa
tion). Interest rates also do not have the same
significant role to play as they did in the U.S.
case for real output, although they do feature
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TB
2.77
11.55
5.54
16.95
9.02
(0.54)
(0.02)
(0.23)
(0.00)
(0.01)
TB
3.82
9.65
7.17
16.68
5.01
(0.43)
(0.04)
(0.12)
(0.00)
(0.08)
TB
4.62
15.11
19.07
11.16
0.78
(0.33)
(0.00)
(0.00)
(0.02)
(0.38)
TB
6.97
12.25
19.59
9.88
0.11
(0.14)
(0.01)
(0.00)
(0.04)
(0.74)
in the majority of m oney equations. The effects
of price (or, m ore correctly, inflation) feature
prom inently in almost all of the TB equations.
The Japanese causality p attern (reported in
Table 22) is in many ways similar to th at for
Germany. Thus, neither simple-sum nor Divisia
money enters significantly into the output equa
tion, although there is a significant impact of
both types of money in the inflation and TB
equations. The TB rate also features significantly
in all of the Japanese real output equations but,
in contrast to the German case, only enters sig
nificantly into one other equation (apart from
its ow n lags)—that for DM3.
103
Table 21 (continued)
Causality Tests for Canada
GNP
SSM3
SSM3
GNP
DEF
TB
ECM
64.96
8.25
7.34
16.58
0.00
(0.00)
(0.08)
(0.12)
(0.00)
(0.95)
6.30
4.25
8.13
7.00
13.33
22.32
12.82
26.96
13.52
2.96
(0.00)
(0.01)
(0.00)
(0.00)
(0.23)
1.27
4.67
6.08
1.88
12.18
SSL
SSL
GNP
DEF
TB
ECM
15.36
3.51
3.98
7.50
1.15
(0.00)
(0.48)
(0.41)
(0.11)
(0.78)
1.63
1.67
11.92
1.78
11.48
59.15
14.29
15.84
9.34
1.97
(0.00)
(0.00)
(0.00)
(0.05)
(0.16)
(0.86)
(0.32)
(0.19)
(0.76)
(0.00)
(0.12)
(0.12)
(0.00)
(0.06)
(0.56)
5.27
4.01
18.74
3.00
1.20
(0.26)
(0.40)
(0.00)
(0.56)
(0.55)
DEF
(0.80)
(0.79)
(0.02)
(0.86)
(0.00)
GNP
1.38
2.25
9.52
2.04
8.55
7.25
7.24
20.25
9.04
0.34
DEF
GNP
DL
DL
GNP
DEF
TB
ECM
(0.17)
(0.37)
(0.08)
(0.14)
(0.00)
GNP
DM3
DM3
GNP
DEF
TB
ECM
DEF
0.97
4.97
20.64
3.87
0.51
(0.91)
(0.29)
(0.00)
(0.42)
(0.48)
DEF
(0.84)
(0.68)
(0.04)
(0.73)
(0.00)
1.38
3.98
21.27
3.78
0.58
(0.84)
(0.41)
(0.00)
(0.44)
(0.44)
TB
13.12
15.93
27.09
10.08
1.02
(0.01)
(0.00)
(0.00)
(0.04)
(0.31)
TB
10.69
13.26
21.38
7.74
0.52
(0.03)
(0.01)
(0.00)
(0.10)
(0.77)
TB
6.39
11.61
20.11
14.04
0.57
(0.17)
(0.02)
(0.00)
(0.00)
(0.45)
TB
4.19 (0.38
9.38 (0.05)
16.82 (0.00)
10.11 (0.04)
0.09 (0.76)
Note: See Table 16.
We may summ arize the results reported in
this section in the following way. First, there
appear to be countries in which Divisia money
has greater informational content than simplesum money and this is most clear in the U.S.
and Australian cases. This is possibly because
the pace of financial innovation has varied
across countries. Such differential impacts across
countries also holds tru e for other variables. In
particular, the widely cited effect that the in
terest rate has in U.S. causality tests does not
seem to carry over to other countries. Also,
although Divisia m oney does not have a signifi
cant impact in all countries, the evidence for
the United Kingdom suggests th at this, at least
in part, may be attributable to the sophistication
w ith which the Divisia m easure is constructed.
Thus, although none of the U.K. Divisia m easures
has a significant effect on real output, the Bank
of England Divisia m easure (BOED) does have
significant inform ational content for inflation.
This m easure is widely regarded as being superi
or to the other m easures, perhaps because the
Bank economists had access to detailed data on
asset compositions w hich are not publicly
available.
MARCH/APRIL 1994
104
Table 22
Causality Tests for Japan
SSM1
SSM1
GNP
DEF
TB
ECM
6.82
4.81
2.56
3.84
10.66
(0.15)
(0.31)
(0.63)
(0.43)
(0.00)
DM1
DM1
GNP
DEF
TB
ECM
11.93
5.25
2.21
4.57
11.36
(0.02)
(0.26)
(0.69)
(0.33)
(0.00)
SSM2
SSM2
GNP
DEF
TB
ECM
39.02
6.02
7.75
7.13
9.15
(0.00)
(0.19)
(0.10)
(0.13)
(0.01)
DM2
DM2
GNP
DEF
TB
ECM
57.64
4.36
9.19
8.84
6.83
(0.00)
(0.36)
(0.05)
(0.06)
(0.03)
SSM3
SSM3
GNP
DEF
TB
ECM
47.24
4.06
6.97
7.03
7.74
(0.00)
(0.39)
(0.14)
(0.13)
(0.02)
DM3
DM3
GNP
DEF
TB
ECM
66.52
3.19
9.70
9.41
6.07
Note: See Table 16.
FEDERAL RESERVE BANK OF ST. LOUIS
(0.00)
(0.53)
(0.04)
(0.05)
(0.05)
GNP
1.69
25.08
7.61
9.83
12.33
(0.79)
(0.00)
(0.11)
(0.04)
(0.00)
GNP
1.46
24.64
8.04
9.17
12.17
(0.83)
(0.00)
(0.08)
(0.06)
(0.00)
GNP
1.10
21.36
6.37
12.22
14.14
(0.89)
(0.00)
(0.17)
(0.02)
(0.00)
GNP
1.04
22.02
8.15
14.81
13.31
(0.90)
(0.00)
(0.08)
(0.00)
(0.01)
GNP
0.74
19.25
6.39
10.49
12.69
(0.94)
(0.00)
(0.17)
(0.03)
(0.00)
GNP
0.73
20.91
8.13
13.93
13.05
(0.94)
(0.00)
(0.08)
(0.00)
(0.00)
DEF
4.30
3.82
32.52
7.39
6.55
(0.37)
(0.43)
(0.00)
(0.12)
(0.04)
DEF
3.97
3.75
34.01
7.17
6.54
(0.41)
(0.44)
(0.00)
(0.13)
(0.04)
DEF
10.41
4.33
35.58
7.10
3.61
(0.03)
(0.36)
(0.00)
(0.13)
(0.16)
DEF
11.72
3.92
34.41
6.40
3.78
(0.02)
(0.42)
(0.00)
(0.17)
(0.15)
DEF
8.53
3.44
34.03
6.97
3.57
(0.07)
(0.48)
(0.00)
(0.14)
(0.16)
DEF
12.16
3.23
33.71
6.40
3.87
(0.02)
(0.52)
(0.00)
(0.17)
(0.14)
TB
8.37
3.47
7.85
10.65
10.94
(0.07)
(0.48)
(0.09)
(0.00)
(0.00)
TB
8.89
3.39
7.92
19.25
11.16
(0.06)
(0.49)
(0.09)
(0.00)
(0.00)
TB
14.06
6.16
5.18
17.47
10.97
(0.00)
(0.18)
(0.27)
(0.00)
(0.00)
TB
11.08
4.48
8.04
21.34
15.57
(0.03)
(0.34)
(0.09)
(0.00)
(0.00)
TB
13.92
7.37
6.49
17.58
10.03
(0.01)
(0.11)
(0.16)
(0.00)
(0.00)
TB
10.93
4.59
8.20
21.08
14.56
(0.02)
(0.33)
(0.08)
(0.00)
(0.00)
105
Table 23
Estimated Trace and AMax Statistics : United States
Sub-Samples
TRACE (LR1)
SSM1
DM1
1.02
11.23
29.31
53.90
0.86
12.42
30.18
53.92
SSM1A DM1A
0.02
12.96
30.33
52.67
0.57
13.50
29.34
51.00
SSM2
DM2
SSM3
DM3
SSL
DL
RCE
BCE
3.25
18.55
36.89
62.29
0.02
10.29
27.23
49.45
0.83
12.11
27.47
54.19
0.01
11.13
27.33
50.09
1.44
14.31
34.77
63.07
0.06
1.44
28.69
50.37
6.07
20.99
41.70
67.90
0.16
9.01
30.04
56.69
AMAX (LR2)
SSM1
DM1
1.02
10.22
18.07
24.60
0.86
11.56
17.76
23.74
SSM1A DM1A
SSM2
DM2
SSM3
DM3
SSL
DL
RCE
BCE
0.57
13.44
15.84
21.66
3.25
15.30
17.34
26.40
0.02
10.28
16.94
22.21
0.83
11.29
15.35
26.72
0.01
11.12
16.19
22.76
1.44
12.86
20.46
28.91
0.06
9.38
20.46
28.91
6.08
9.38
20.46
26.28
0.16
8.84
21.03
26.66
0.02
12.93
17.37
22.34
S u b -S a m p le R e s u lts f o r th e
U n ited S ta tes: th e P o st-1 9 7 9
R e g im e C h ange
The causality results reported in the previous
section are for the longest span of data for
w hich consistent simple-sum and Divisia data
are available for each country. W ithin each
country-specific data sample, there may be one
or two changes in the way m onetary policy has
been implemented. Thus, some countries have
switched from targeting one particular aggregate
to another or have switched from m onetary ta r
geting to interest rate targeting, or vice versa.
Therefore, it is of interest to inquire if the
results reported in the previous section carry
through for sub-samples corresponding to
specific m onetary regimes. One of the possible
examples of a regime change arises in the Unit
ed States around 1980, w hen a combination of
reform s (including a change in Fed operating
procedure and a liberalization of deposit m ar
kets) produced an apparent shift in previously
stable m onetary relationships (Rasche 1993).
Given this, and also since the U.S. data sample
is one of the longest, we concentrate our sub
sample tests on our U.S. data set. In particular,
we have re-estimated our U.S. causality tests for
the first q u arter of 1960 to the third qu arter of
1979 (lags being generated within this sample).
In Table 23, the estim ated Trace and Amax
statistics are reported for our chosen U.S. sub
sample. In contrast to the full sample results, it
is notew orthy that all of the m onetary m easures
produce at least one cointegrating vector (for
the full sample, none of the M l m onetary meas
ures produced any cointegrating vectors). We
therefore use the inform ation concerning the
num ber of cointegrating vectors to set up ap
propriate VECMs for each m onetary m easure.
The sub-sample exclusion tests based upon
these VECMs are reported in Table 24. The
broad conclusion to em erge from this table is,
perhaps not surprisingly, that the sub-sample
produces a very different picture w ith respect
to the relative m erits of simple-sum and Divisia
money. More specifically, w e note th at the sig
nificant impact of money in the real output
equations occurs for the narrow M l m easures
of money and not for the broader m easures
(and, in term s of the M l m easures, simple sum
seems to outperform Divisia since tw o of the
sum m easures are significant at the 5 percent
level against one Divisia m easure at this sig
nificance level). Of the two currency equivalent
measures, RCE is insignificant in the GDP equa
tion, while BCE is significant (albeit at the 6 p er
cent level of significance) the reverse of our
findings for the full sample. O ther notable fea
tures of the sub-sample results, which are dis
MARCH/APRIL 1994
106
Table 24
Sub-Sample Causality Tests for the United States
SSM1
SSM1
GDP
DEF
TB
ECM
57.23
5.87
8.87
15.20
5.55
(0.00)
(0.21)
(0.06)
(0.00)
(0.02)
GDP
11.28
2.44
5.34
5.94
9.99
27.14
0.62
3.80
22.95
1.20
(0.00)
(0.96)
(0.43)
(0.00)
(0.27)
10.69
4.29
7.31
5.28
10.22
SSM1A
SSM1A
GDP
DEF
TB
ECM
40.06
7.13
4.79
15.13
1.81
(0.00)
(0.13)
(0.31)
(0.00)
(0.18)
10.76
3.64
6.82
5.14
10.80
26.63
0.85
3.74
25.91
0.00
(0.00)
(0.93)
(0.44)
(0.00)
(0.97)
tinct from the full sample results, include the
finding of a strongly significant effect of money
on the deflator for all m easures of money (ex
cept RCE) and a m uch less im portant role for
the interest rate in the output equation. (The TB
rate is only significant in two instances, w hereas
it was significant in all cases for the full sample.)
CONCLUSION
The evidence from the St. Louis equations
is fairly straightforw ard: Divisia weighted ag
gregates appear to offer advantages over broad
simple-sum m onetary aggregates. The credibility
of narrow simple-sum aggregates has universally
been underm ined by the spread of financial
innovation. Although results of our real income
FEDERAL RESERVE BANK OF ST. LOUIS
(0.03)
(0.37)
(0.12)
(0.26)
(0.00)
(0.01)
(0.74)
(0.00)
(0.16)
(0.52)
15.16
3.53
11.99
8.33
3.29
(0.00)
(0.47)
(0.02)
(0.08)
(0.07)
DEF
(0.03)
(0.46)
(0.14)
(0.27)
(0.00)
16.73
4.18
20.98
8.94
2.96
(0.00)
(0.38)
(0.00)
(0.06)
(0.08)
DEF
GDP
8.14
4.69
8.36
5.31
9.33
13.04
1.98
39.38
6.52
0.42
DEF
GDP
DM1A
DM1A
GDP
DEF
TB
ECM
(0.02)
(0.65)
(0.25)
(0.20)
(0.00)
GDP
DM1
DM1
GDP
DEF
TB
ECM
DEF
(0.08)
(0.32)
(0.08)
(0.26)
(0.00)
19.14
7.34
4.94
11.08
7.17
(0.00)
(0.12)
(0.29)
(0.03)
(0.00)
TB
32.78
6.99
1.11
41.57
0.49
(0.00)
(0.14)
(0.89)
(0.00)
(0.48)
TB
18.57
8.27
1.04
22.31
0.03
(0.00)
(0.08)
(0.90)
(0.00)
(0.87)
TB
30.93
5.72
0.41
42.39
0.04
(0.00)
(0.22)
(0.98)
(0.00)
(0.83)
TB
17.75
7.02
0.22
23.14
0.12
(0.00)
(0.13)
(0.99)
(0.00)
(0.73)
causality tests are less persuasive. However,
they still give a clear edge to Divisia aggregates
over simple sum. The results are not so strong
that we can conclude that Divisia money m at
ters while simple sum does not. Nonetheless, it
is clear from the U.S. evidence that the advan
tages of Divisia are particularly strong after
1980, the period in which financial innovation is
greatest. Pre-1980 data do not show any sup
port for Divisia. It may well be that if we could
base our tests on post-1980 data alone, we
would find m uch stronger support for Divisia.
Also, the existence of reverse causality (from
real income to money) is not particularly sur
prising given the fact that most authorities are
pegging short-term interest rates or exchange
rates. Superficially, this would support the “real
business cycle” view or even the "money doesn’t
107
Table 24 (continued)
Sub-Sample Causality Tests for the United States
GDP
SSM2
SSM2
GDP
DEF
TB
ECM
45.44
3.53
5.73
46.46
8.08
(0.00)
(0.47)
(0.22)
(0.00)
(0.01)
6.54
7.48
9.99
2.02
15.69
DM2
DM2
GDP
DEF
TB
ECM
45.70
5.31
4.53
76.87
3.63
(0.00)
(0.26)
(0.34)
(0.00)
(0.05)
74.22
5.00
4.35
15.43
4.23
(0.00)
(0.29)
(0.36)
(0.00)
(0.04)
6.06
9.10
5.14
2.69
0.16
1.01
5.27
9.62
10.61
10.22
98.38
8.00
9.88
38.56
6.14
(0.00)
(0.09)
(0.04)
(0.00)
(0.01)
m atter” view. However, it may instead be the
old problem of observational equivalence.
The policy significance of these results may
be limited. M onetary authorities can no m ore
control Divisia aggregates than they can broad
money. However, Divisia aggregates undoubtedly
offer potential inform ation to m onetary authori
ties about the relative ease or tightness of
m onetary stance—m uch m ore so than do broad
simple-sum aggregates. However, the body of
research supporting Divisia is not yet sufficiently
large or robust that we would wish to recom
m end direct targeting at this stage. W hat is im
portant, however, is that official credible Divisia
index num bers should be produced so that
researchers can test exhaustively the p erfo r
m ance of these indicators. Only w hen a clear
(0.19)
(0.06)
(0.27)
(0.61)
(0.69)
(0.02)
(0.57)
(0.88)
(0.17)
(0.00)
17.51
4.16
20.15
8.02
3.26
(0.00)
(0.39)
(0.00)
(0.09)
(0.07)
DEF
(0.91)
(0.26)
(0.05)
(0.03)
(0.00)
GDP
2.89
5.71
8.99
3.23
10.94
11.22
2.93
1.14
6.48
9.66
DEF
GDP
DM3
DM3
GDP
DEF
TB
ECM
(0.16)
(0.11)
(0.04)
(0.73)
(0.00)
GDP
SSM3
SSM3
GDP
DEF
TB
ECM
DEF
20.52
7.44
2.72
11.13
14.81
(0.00)
(0.11)
(0.61)
(0.03)
(0.00)
DEF
(0.57)
(0.22)
(0.06)
(0.52)
(0.00)
18.94
9.10
2.68
18.72
9.25
(0.00)
(0.06)
(0.61)
(0.00)
(0.00)
TB
17.30
7.22
4.03
35.07
1.38
(0.00)
(0.12)
(0.40)
(0.00)
(0.50)
TB
8.73
10.08
5.75
26.04
2.13
(0.07)
(0.04)
(0.22)
(0.00)
(0.14)
TB
4.88
7.26
1.99
25.20
0.79
(0.29)
(0.12)
(0.74)
(0.00)
(0.37)
TB
9.85
4.34
0.94
25.78
0.18
(0.04)
(0.36)
(0.92)
(0.00)
(0.67)
consensus emerges should policy be directly
linked to such indicators. Just because an indi
cator does well in the 1980s does not m ean it
will do well in the 1990s. Divisia aggregates did
particularly well at handling the introduction of
interest on checking accounts. They may be less
useful in a period of, say, the w idespread adop
tion of "sm art” cards.
In short, while our results are encouraging
enough to suggest th at m onetary authorities
should commission fu rth e r w ork on Divisia, the
picture w hich em erges is not sufficiently clearcut to lead to immediate policy recom m enda
tions. However, the message for the economics
profession is m uch clearer. All those who do
applied research using money should take on
board the fact that simple-sum m easures are
MARCH/APRIL 1994
108
substantially distorted and a better m easure is
likely to be provided by a m onetary services
index constructed along something like Divisia
lines. Rejections of the role of money based
upon flawed money m easures are themselves
easy to reject.
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MARCH/APRIL 1994
110
Charles R. Nelson
Charles R. Nelson is professor o f econom ics a t the University
o f Washington.
Com m entary
W
ARE INDEBTED TO K. Alec Chrystal
and Ronald MacDonald (1994) for assembling a
valuable body of evidence on the relative ex
planatory pow er of simple-sum and Divisia ver
sions of the money supply aggregates across a
range of countries. This contribution comes at a
time w hen the usefulness of money supply
m easures is called into question by economists
across the policy spectrum . I am dismayed at
the wide agreem ent among macroeconomists
ranging from Alan Blinder to Robert Rasche
th at the money to income relationship is broken
and that our conventional understanding of
money dem and is at a loss to e x p la i n the decline
in velocity that has occurred during the past
decade. Has the quickening pace of financial
innovation rendered old relationships obsolete,
as m any are suggesting? Somehow this all
sounds too familiar. Those of you who w ere
around in the 1970s may recall “The Case of
the Missing Money.” Then it was a puzzling rise
in velocity, and one explanation put forw ard
was the quickening pace of financial innovation
(see: Enzler, and others, 1976; Goldfeld, 1976;
and Ham burger, 1977). Economists, neverthe
less, continued to think that m onetary aggregates
w ere im portant, enough so th at they w ere dis
appointed again a decade later w hen their
models seemed to go off track.
Even the “m onetarists” are in disarray among
themselves on the issue of w hich aggregate to
watch. At a Federal Reserve Bank of San Fran
cisco conference last spring, the Bank’s presi
dent, Robert Parry, quipped that Milton Friedm an
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had told him that M2 was growing m uch too
slowly while Allan M eltzer had told him that M l
was growing m uch too fast, so he figured that
m onetary policy m ust be just about right. In the
face of that kind of disagreem ent, it becomes
difficult at best to explain to skeptical colleagues
or the public w hy they should take any m one
tary aggregate seriously as an indicator of
m onetary policy. But as one of the few teachers
of introductory macroeconomics (perhaps the
only one) who bases their course on the Quanti
ty Theory of Money rath e r th an the Keynesian
Expenditure Model, I can’t afford to take such a
pessimistic view.
The first and perhaps prim ary set of results
presented in this paper uses regressions of the
grow th rate of nominal income on the grow th
rate of a money aggregate, the grow th rate of
federal spending on goods and services, and, in
the case of the United States, the change in the
yield on Treasury bills. Lags of zero to four
quarters are included. A second set of results
adds four lags of the dependent variable to the
regression. Test statistics com pare each simplesum (SS) aggregate w ith its Divisia (D) counter
part. The Akaike Inform ation Criterion (AIC)
statistic com pares the likelihoods of the two
regressions, and tw o other tests each produce a
pair of /-statistics, one that can reject SS in favor
of D and another that can reject D in favor of SS.
Finally, F-statistics for the exclusion of all the
money term s in each regression address the
question, “Does money m atter at all?”
In thinking about these regressions, I found it
111
useful to keep in mind the distinction betw een
a money dem and equation and a reduced form
equation by Leonall C. A ndersen and Jerry L.
Jordan (1968) and Leonall C. Andersen and Keith
M. Carlson (1970) in their landm ark papers. A
simple money dem and equation might be of the
form:
(1) M = K(i) Y
e£
,
w here Y is nominal income and K{i ) a function
of the nominal interest rate i. Taking logs,
denoted by lower case letters, and rearranging
we have:
(2) y = m - k(i) - t.
This is a structural equation and to get to the
reduced form w e need a model for the interest
rate, something like:
(3) i = pe + rigov, real shocks),
w here pe is expected inflation and r(gov, real
shocks) is the real rate as a function of govern
m ent fiscal variables denoted gov, say the deficit
as a fraction of GDP, and real shocks which
may not be directly observed. In form ing pc,
economic agents will presum ably use inform a
tion in the past history of m and gov. Substitut
ing for pe and then i, we have the reduced form
equation:
(4) y = y[m with lags, gov with lags)
+ E(£, real shocks),
which is akin to the equation estim ated by
Andersen and Carlson. The U.S. regressions run
by Chrystal and MacDonald, w hich include an
interest rate, are structural and therefore have
no obvious role for governm ent spending, while
regressions w ithout the interest rate for other
countries are in reduced form. In the latter
case, I would expect the deficit ra th e r than
spending on goods and services to be the m ore
appropriate governm ent fiscal variable.
I w ant to m ention in passing that there is
nothing here that says that velocity m ust be
constant, or deterministically trended, or sta
tionary, or even cointegrated w ith the interest
rate for there to be a useful and predictable
relationship betw een money and income. The
e rro r processes £ and E may be integrated
processes like random walks and indeed coeffi
cients may also be stochastic processes w ithout
destroying our ability to estimate models and
make predictions, although the kinds of processes
involved will affect the accuracy of predictions
and the deterioration of accuracy with forecast
horizon. Certainly the fact that velocity did not
continue to move along its upw ard tren d of the
1970s does not in itself imply that money-income
models are invalid, as some people seem to be
saying. Tw enty years ago, John P. Gould and I
(1974) noted th at velocity has experienced trend
reversals in the past, behaving m uch like a ra n
dom walk. Neither the characterization of velocity
as a random walk, no r its link to nominal inter
est rates should have lead us to expect the veloc
ity trend of the 1970s to continue indefinitely.
Turning to the results of the U.S. regressions,
I am struck by how weak the evidence is for
using Divisia in comparisons with the simplesum aggregates. I expected that the superiority
of the D versions would increase w ith aggrega
tion since the idea is to extract the transactions
part of the aggregate. Indeed, according to the
Akaike Inform ation Criterion which looks at the
difference in log likelihoods, SSM1 is favored
over DM1; DM2 has a slight edge over SSM2;
and DM3 is strongly favored over SSM3, although
the progression fails with L. One reason that I
am surprised how small the AIC statistics are
for D aggregates is th at in a sense they are al
ready fitted to the data. It would be interesting
to see a comparison betw een SSM1 and DM2 to
see w hether most of the benefits of purging
SSM2 are captured by SSM1, which is more
readily available to most of us in real time.
Similarly, it would be interesting to see direct
comparisons betw een the relatively simple Cur
rency Equivalent (CE) aggregate proposed at this
conference last year by Rotemberg (1993) and
the D aggregates. It would be helpful to the
reader to have goodness-of-fit m easures and log
likelihoods reported for all the regressions so
that other comparisons could be made easily.
The (-tests give very puzzling results, frequently
giving inconclusive results in which each ver
sion is rejected, in tu rn , in favor of the other.
The character of the results does not change
w hen lags of the dependent variable are included.
Does money m atter? Does it m atter if money
matters? Perhaps less than I might have thought
in the context of structural regressions which
include an interest rate. Certainly, variation in
velocity, proxied by the interest rate, may ac
count for a considerable variation in nominal
income, so money is not the only m onetary vari
M ARCH/APRIL 1994
112
able in the model. Indeed, it is not surprising
then that in the results for the U.S. reported in
Table 1 SSM2 m atters, in the sense of the F-test
for inclusion of that variable, m uch more than
SSM1, since the velocity of SSM1 varies m uch
m ore than the velocity of SSM2. W hat puzzles
me is that DM1 m atters so m uch less than
SSM1, in fact not at all, and results are even
w orse for DM1A.
Has the money-to-income relationship broken
down since the early 1980s? It might be in ter
esting to see if the regressions using the D
aggregates are m ore stable th an those for
SS aggregates.
For the rem aining countries, the regression
does not include the interest rate, so for the
non-U.S. countries, we are looking at a reduced
form. As explained above, however, I might
have expected the fiscal variable to be the budget
deficit ra th e r than spending on goods and serv
ices. The message I get from these countries
overall is th at DM2 w orks better than SSM2,
b ut it is not im portant to use the D version of
M l. Japan, of course, is a special case. I say “of
course” because Japan seems to be different in
m any economic studies, a fact often pointed out
w ith pride in my experience by Japanese
economists. In the case of money aggregates,
not only does Divisia not m atter, but nothing
about the aggregates m atters. It would be inter
esting to see how the time series for Japan
differs from the other countries to see w hat ac
counts for this result. I suspect it reflects lack
of variation ra th e r than lack of a relationship.
The unit root tests are of particular interest to
me because we have a chance here to compare
across countries. It w arm ed my heart to see
only one variable th at is apparently stationary
in levels less than expected by chance out of the
54 variables if these series w ere all unrelated.
And that one variable is a T-bill rate (for Aus
tralia), w hich is already first differenced because
it is a grow th rate. W hat is perhaps m ore su r
prising is how few other variables are station
ary in grow th rates. For Australia, stationary
inflation and grow th rates for GDP and SSM3
go along w ith stationarity in the level of the Tbill rate. But only 13 of the 54 series are sta
tionary in first differences at the .05 level. In
deed, countries as seemingly regular as
Switzerland have non-stationary grow th rates,
and for Japan it is only the T-bill rate that is
stationary in first differences. Evidently, we live
in an 1(2) world.
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Chrystal and MacDonald draw on the technol
ogy of cointegration to try to detect long-run
relationships among the variables. Since the
variables are generally 1(2) while the VAR model
used for detecting cointegrating vectors is to be
estimated in first differences of 1(1) variables,
it is grow th rates which become the relevant
“levels” for this analysis. The authors report
finding one or two cointegrating vectors for all
the countries, implying that there is a long-run
relationship among grow th rates of the varia
bles. The M l aggregates for the United States
are an im portant exception. In general, though,
we would be missing some long-run inform ation
if we looked only at relationships among the
stationary second differences of these variables.
It would be interesting to see w hat those coin
tegrating relationships look like, w hether they
resemble a money-demand function or are
something quite unexpected.
The VAR is then combined w ith the e rro r cor
rection term implied by cointegration (where
applicable) so that each variable (in turn, the
change in the grow th rates of money, real GDP,
the deflator and the T-bill rate) is predicted by
four lagged values of itself and each of the
other variables, as well as by the e rro r correc
tion mechanism (ECM). As in so many VAR
studies, it tu rn s out th at the strongest predictor
is simply the lagged value of the variable being
predicted. For the United States, lags of other
variables are generally not useful in predicting
GDP or the inflation rate, except that the T-bill
rate helps to predict—and, in turn, is predicted
by—GDP inflation and M. The ECM also helps to
predict inflation in the case of the broader ag
gregates. As we look across countries, the most
striking regularity is the pow er of awkward,
unclear lags in predicting each variable. O ther
wise there is little regularity in the pattern of
results w hich range from Switzerland, w here
almost every variable helps to predict every
other variable, to the United Kingdom, w here
only the ECM seems to m atter for GNP. Why
the great differences?
If there is one variable that m oney should be
able to predict, it is inflation. If the Divisia ag
gregates are superior m easures of money, then
one might expect them to be superior predic
tors of inflation. There is, however, very little
difference in the significance of lags of Divisia
aggregates verses simple sum, and no clear m ar
gin in favor of the form er. However, the ECM
also presum ably includes the m oney aggregate,
so differences in the contribution of the ECM
113
m ust be attributed to the distinction betw een
the aggregates. In the case of Australia, for ex
ample, lags of SSM2 are m ore significant in ex
plaining inflation than are lags of DM2, but the
e rro r correction term that appears in the DM2
equation is m ore significant. Since the two equa
tions differ only in the choice of the money ag
gregate, one m ust credit DM2 w ith the greater
predictive pow er of the ECM in that equation.
In fact, lags of the aggregate may not m atter
at all given the ECM, and yet the aggregate may
be playing an essential role in the ECM. There
are m any examples in the tables w here the
money aggregate itself is not significant b u t the
ECM is. We cannot conclude in these cases that
money does not m atter, and for that reason I
would not call these causality tests.
A nother reason to be cautious in concluding
that money does not m atter if the lags of it are
not significant is that the VAR is a restrictive
fram ew ork in which to detect dynamic relation
ships. A few lags of a noisy variable will contain
little information if the variable operates with a
long lag. The interest rate is a pow erful leading
indicator probably because it smoothes m uch of
the inform ation contained in the very noisy
money-growth series. I think that this limitation
of VARs is one of the main reasons why we
have learned so little from the large volume of
w ork based on them . Perhaps it is time to take
seriously again distributed-lag modelling, which
allows for differing lag structures on different
variables.
I would like to conclude with a plea for visual
presentation of data. Economists are traditionally
afraid to look at their data—it is considered
cheating. I find, on the contrary, that plotting
the data is an invaluable tool for understanding
models, why they w ork or do not work, and
how specification might be improved. I am u n
comfortable w ith a statistical result that I can
not see in the data. Often, plotting the data
reveals w hy a relationship we expected to find
does not show up in formal tests and w here it
has gone off track. In this spirit, I have p re
pared a few charts that may be very familiar to
many, but which I found helpful in putting in
perspective the notion of a long-run relationship
betw een money and income.
In Figure 1, I have plotted the velocities of M l
and M2 along with the T-bill rate. I did not
have ready access to the Divisia counterparts.
It makes clear the huge difference betw een the
stability of the M2 velocity and the great varia
tion in M l velocity. Clearly, in a model of the
money-income relationship, it will be very im
portant to be able to explain the latter but rela
tively unim portant to explain the form er. It also
makes clear the fact that M l velocity reflects
long-term variation in the short-term interest
rate but not short-term variation, as Rotemberg
(1993) and others have noted. It is by no means
obvious to me that the decline in M l velocity
since the early 1980s is in any way inconsistent
w ith the decline in interest rates. M l velocity
and the interest rate are plausibly cointegrated;
that is, they appear to track over a long time
period, although they move apart over shorter
periods.
These dynamics are evident in Figure 2, which
is a scatter plot with the log of the velocity of
M l on the vertical axis and the log of the T-bill
rate on the horizontal. There is a clear differ
ence betw een the small, short-run response of
velocity to a change in the T-bill rate and the
large, long-run response. The last several points
represent the period since the recession w hen
the sharp decline in short-term interest rates
has been accompanied by only a modest decline
in M l velocity. But it is not clear that this slug
gish short-term response is out of line with
experience.
Since the velocity of M l evidently responds to
the T-bill rate with a lag, I have smoothed the
T-bill rate by replacing it in Figure 3 w ith the
T-bond yield. While the long-term bond m arket
may not provide the optimal sm oother for this
purpose, it is free and was not contrived. Now
the scatter follows a smooth curve and recent
experience is indistinguishable from past ex
perience, a fact noted by Poole (1988) and others.
I fail to see why we should abandon the idea
that there is a stable, long-run relationship in
levels betw een money, interest rates and nomi
nal income. I w onder w hether the substantial
changes in param eters associated in this paper
with the 1979 change of m onetary regime would
hold if the bond rate replaced the bill rate.
I do w ant to call your attention to the scatter
plot for M2 velocity and the T-bond yield in
Figure 4, because this presents m ore of a puzzle
in its recent behavior. Keep in mind that we are
looking at relatively little variation in the velocity,
b u t certainly the bond yield accounts for little
of it. Indeed, the recent rise in the velocity of
M2 runs counter to the decline in both shortand long-term interest rates. W hat gives? Perhaps
it is the beginning of the end for M2 as Higgins
MARCH/APRIL 1994
114
Figure 1
Percent
Velocity
Figure 2
Log of velocity of M1
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Log of Treasury bill yield
115
MARCH/APRIL 1994
116
(1992) and others have suggested. My own view
is that this is a tem porary phenom enon related
to the discovery of equity mutual funds by
traditional holders of CDs. Even relatively
sophisticated individuals have been explaining to
me recently how m utual funds pay 15 percent
com pared to only 3 percent at the bank. There
is an expected opportunity cost to holding M2
that we do not m easure. My expectation is that
M2 velocity will again fall into line after the
public is awakened, perhaps rudely, to the fact
that m utual fund shares are not CDs.
Chrystal, K. Alec, and Ronald MacDonald. “Empirical Evi
dence on the Recent Behavior and Usefulness of SimpleSum and Weighted Measures of the Money Stock,” this
Review (March/April 1994).
Enzler, Jared, Lewis Johnson, and John Paulus. “Some
Problems of Money Demand,” Brookings Papers on
Econom ic Activity, 1976:1, pp. 261-80.
Goldfeld, Stephen M. "The Case of the Missing Money,”
Brookings Papers on Econom ic Activity, 1976:3, pp. 683-730.
Gould, John P., and Charles R. Nelson. “The Stochastic
Structure of the Velocity of Money,” The Am erican Econom
ic Review (June 1974), pp. 405-18.
Hamburger, Michael. “Behavior of the Money Stock: Is There
a Puzzle?” Journal o f M onetary Econom ics (July 1977), pp.
265-88.
Higgins, Byron. “Policy Implications of Recent M2 Behavior,”
Federal Reserve Bank of Kansas City Econom ic Review
(third quarter 1992), pp. 21-36.
REFERENCES
Andersen, Leonall C., and Keith M. Carlson. “A Monetarist
Model for Economic Stabilization,” this Review (April 1970),
pp. 7-25.
________ , and Jerry L. Jordan. “Monetary and Fiscal Actions:
A Test of Their Relative Importance in Economic Stabiliza
tion,” this Review (November 1968), pp. 11-24.
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Federal Reserve Bank of St. Louis
Poole, William. “ Monetary Policy Lessons of Recent Inflation
and Disinflation,” Econom ic Perspectives (summer 1988),
pp. 73-100.
Rasche, Robert H. “Monetary Aggregates, Monetary Policy
and Economic Activity,” this Review (March/April 1993), pp.
1-35.
Rotemberg, Julio J. “Commentary,” this Review (March/April
1993), pp. 36-41.
117
Douglas Fisher and Adrian Fleissig
Douglas Fisher is professor o f econom ics a t North Carolina
State University. Adrian Fleissig is assistant professor of
econom ics at the University o f Texas-Arlington. The authors
wish to acknowledge the assistance o f Ron Gallant, Douglas
Pearce, Walter Thurman a nd M ichael Belongia, who m ade im
portant suggestions for the revision o f this paper.
M oney D em an d in a Flexible
D yn am ic Fourier E xpenditure
S ystem
I n WELL-KNOWN SURVEYS of the growing
literature on expenditure systems, Deaton and
M uellbauer (1980) and Poliak and Wales (1992)
describe many of the shortcomings of the exist
ing work in this genre. Among the problems
they list that inhibit the acceptance of these
methods, the ones that seem most critical to us
are (1) the failure to link theory to application,
(2) im proper aggregation techniques, (3) im pre
cise estimation of partial derivatives, (4) the
failure of locally integrable models at some
data points and (5) the misspecification of the
dynamics. We can address several of these
problem s by extending the Fourier Flexible Form
of Gallant (1981). Most notably, his technique
provides global flexibility and arbitrarily ac
curate estimates of partial derivatives. In fact,
the technique is capable of approximating the
unknow n function (an aggregator function, for
example) to any desired degree of accuracy. The
version of the Fourier model in current use,
however, is static in nature, which inhibits its
application to time-series data; in particular,
studies by Gallant (1981), Ewis and Fisher (1985),
and Fisher (1989, 1992), all employ the static
model and all produce residuals that are not
white noise for each share; see also Barnett,
Fisher, and Serletis (1992). This may be due to
inadequately modeled dynamics; in fact, there
are no examples of a dynamic Fourier in the
literature. The task of this paper is to produce
and evaluate two dynamic alternatives in the
context of the Fourier model.
In the traditional literature on consum er
choice, the indirect utility function is approxi
m ated by a specific functional form in order to
obtain expenditure shares and estimates of the
im portant own- and cross-elasticities. One might
attem pt to estimate a param etric model, of
course, but the results of such exercises have
not been satisfactory. The chief problem has
been model failure, partly related to the choice
of specific (nonflexible) functional forms. To
finesse this problem, a flexible functional form
can be employed in order to estimate the un
known indirect utility function. Diewert (1974)
defines a flexible functional form as a secondorder approximation to an arbitrary twice con
tinuously differentiable fu n ctio n /fc/ at any
given point x*; the popular translog is an exam
ple. The difficulty, however, is th at this defini
tion, and the resulting approximation, fails to
impose precision on the partial derivatives of
the function. Indeed, it is well-known that away
from the point of approximation, the translog
can perform quite poorly in its task of tracking
the unknow n function. The result is imprecise
estimation of the expenditure shares.
MARCH/APRIL 1994
118
THE TIME SERIES APPROACH
Gallant (1981) developed the Fourier flexible
form in order to approximate the unknow n
indirect utility function and its first derivatives
arbitrarily accurately within a Sobolov norm.
The first derivatives are im portant since the
expenditure shares are derived by differentia
tion. The Fourier model, w ith its global p roper
ties, can then provide integrability over a finite
region for the estimated model, assuming con
vergence. In particular, since integrability n o r
mally implies a convex closure over a finite
region, one can presum e desirable separability
properties for data examined under the Sobolov
norm. This contrasts, as noted, with the possible
lack of closure on procedures th at provide an
approximation only at a single point in the data
space; in particular, it contrasts w ith locally integrable models (such as the Tl'anslog).
Following Gallant (1981), the static Fourier flex
ible form approximation of an indirect utility
function h(v) may be w ritten as
A
J
(1) hk(v,d) = a0+b'v+ i v 'C v+ YJ £ ajae ijk'av
,
a = l j= - J
w here
C —
m
a=J
ao’ aoa and b are real-valued, and v is a vector of
the expenditure-norm alized user costs of the
particular assets involved in the exercise (Gal
lant, 1981). In this expression the overbar denotes
complex conjugation and / is the imaginary
number. A multi-index ka, is an n-vector with
integer com ponents and is used to denote p a r
tial differentiation of the utility function (see the
example in section four). The elem ents of a multi
index can be considered to be the weights (when
multiplied by v) of the norm alized price indexes.
In this paper, we produce two versions of the
dynamic Fourier expenditure system; these are
then com pared w ith the static model in various
ways. In section two we briefly discuss the
static model before going into considerable
detail over w hat we will be calling the "timeseries approach” to making the Fourier model
dynamic. This basically follows the lead of
Anderson and Blundell (1982, 1983), whose
results are both well-known and have been
applied in the literature on flexible functional
forms (see Serletis, 1991). In section three, we
continue w ith a second version of the dynamics,
this time involving the construction of the
dynamic Fourier utility function. We term this
the "dynamic utility function approach." In sec
tion four, we present examples of the two
dynamic models in order to clarify the ideas
and explain the notation. It is here possible to
establish clear distinctions betw een the models
in the context of the Fourier. In section five, we
go over the procedures used to prepare the
data, and in section six, finally, we discuss
estimates of the two dynamic models th at utilize
the U.S. data previously described. We also
discuss how the two models perform in com
parison w ith their static equivalents. O ur con
clusions follow.
In an empirical investigation, it is actually
m ore convenient to work with a sine/cosine for
mulation rath e r than the exponential just w rit
ten and so the following form is generally
employed:
(2) h.iVfO) = u + b'v + — v'Cv
A
Uoa + 2 E [U,»CO ( K V ~ W
Sj
]
jaSin VKvH
+z
a =l
j =1
in which
C = -Y u
^
a =l
(3) y j (v,0) =
RESERVE BANK OF ST. LOUIS
FEDERAL
-
E
a
oa
k a k'.
a
After differentiating equation 2 and applying
Roy’s identity, Gallant arrives at the following set
of equations:
A
vP i
aoak a a ana aja — a ja,
k pnrl a - a
J
( u oov ' K
+ 2
E
j ^ jasm (jkv) + wJacos (jk'v)])ki vi
= 1 _____________________ ___________________________________________________________________
A
J
b'v - £ (uo v'ka + 2 'E jlujasm(jk v) + wjacos (jk v)])k'v
a=1
j =1
119
for i = 1, ..., n expenditure shares. This system
is w hat is estimated w ith a vector of erro r
term s appended. Equation (3) can be more
compactly expressed as:
A(L) = I + A,L + A 2L2 + ... + ALT
B (L) = I + B,L + B2L2 + ... + B L q.
Consider the following ARMA(1,1):
(4) y„ = / M ' Note that we have attached a time subscript in
order to emphasize the static nature of the
equations. This completes the discussion of the
static Fourier Flexible model.
Consumption, m onetary and production th e
ories use past variables—in the utility function,
in the constraints, or by time-series m ethods—
to model habit persistence, adjustm ent costs
and/or expectations. In a demand systems ap
proach, incorporating dynamics in any of these
ways complicates the calculation of the restric
tions, which still m ust hold. In the following ex
ercises we present results for the time-series
function and, in section three, for the utility
function. We present the models first, including
w ith each a discussion of the restrictions, before
presenting examples of both.
For the time series model, applying an ARMA
(p,q) directly to equation (4) is one approach
toward modeling the dynamic behavior of the
consumer. This approach is taken by Anderson
(1980) for the special case w hen f(vt 8) is linear
in the expenditure-norm alized prices v, and the
param eters 9. He shows that adding up, as the
direct result of adopting the ARMA approach,
implies four additional restrictions. Anderson
and Blundell (1982, 1983) extend the results for
the case in which f(v t,6) may be nonlinear in the
parameters but linear in the normalized prices v;
i.e., f(v t,d) = n(0)v(. W hen applying an Al\MA(p,q)
to equation (4), they can extract a term , y n(6)vtq, the gap betw een the shares lagged p
periods and normalized prices lagged q periods,
representing the long-run structure for a system
of simultaneous equations. This approach is not
applicable w hen the m atrix tt(0) cannot be ex
tracted, as is the case w ith the Fourier flexible
functional form; as a consequence, we use an al
ternative approach for analyzing the long-run
structure. First, an ARMA(p,q) is applied to equa
tion (4). The result is:
(5) A(L)y, = B(L)f(vt,8).
Here, w here L is the lag operator, the term s
A(L) and B(L) represent the following distributed
lags
(6) y, = A*yt] +f(vl, 9) + B*f(vtl,9)+et.
As in Anderson and Blundell (1982, 1983), the
addingup restrictions require a transform ation
A* of A, w here the columns of A* m ust sum to
zero, and aJ* = a. - aln for i=l,...,n and
V
’ '
t
j= l,...,n-l. Similar restrictions for the matrix B,
apply. In sum, then, the dynamics appear as
lagged shares yM and lagged normalized prices
THE DYNAMIC UTILITY
FUNCTION APPROACH
Individuals are unlikely, generally, to be able
to adjust their consum ption plans instantaneous
ly. Rather than apply an arbitrary lag to the
shares derived from a static optimization exer
cise, an attractive alternative is to allow past
behavior to affect cu rren t decisions directly
through the utility function. We can define the
set of past decisions on a commodity to be an
np.1 vector of shares (s) that are functions of all
past values of v:
(7) s = f ( v j fo r r=l,...,n-l.
Here, each share depends on its own lagged
normalized price and the lagged normalized
prices of the rem aining n-1 shares. In this case,
the representative consum er’s dynamic indirect
utility function can be expressed as
(8) U = U(v,s),
w here v = P/M and s represents the dynamics.
M is total "expenditures" on this class of assets.
This is, in effect, a structural approach for
obtaining dynamic shares since the dynamics
are em bedded in the decision process rath er
than appearing as dynamic extensions of the
static shares (as in the time-series model). It
produces a new version of the Fourier model,
accordingly, lb begin with, we will let s = jct l,
so that each share depends on its own lagged
value as well as on lags from the rem aining n-1
shares.
MARCH/APRIL 1994
120
The dynamic Fourier Flexible Form is defined as
A
(9) g^(z,0J = uo + b'z + |z 'C z +
J
y ajaeiJk'oz
a = l j= -J
and
A
z =
C= - Z uo a W a
a =l
V
",
v'.
Parallel to equation 2, we may express the
model as
(10) g^(z,0J = uo + b'z + iz 'C z
A (
,
+a ? i '
J
.
" + 2j= j [uj«cos(j k '«z) ~ wi°sin ( k 'az)Il ’
?
j
in which
A
C= - Z uo a W
a =l
In this formulation, a multi-index is now a 1 by
(r+1) (n) vector w ith integer components; in
the static case, it was 1 by (n). Here, r is the
num ber of lags. The dynamic shares for this
problem are obtained by applying Roy’s identity
to equation 10:
normalized prices. In the dynamic utility func
tion model, the dynamics enter only as lagged
normalized prices in each of the share equa
tions. The dynamic models can be m ore clearly
com pared w ith an example, w hich is w hat we
now present. Note that we use w hat are term ed
"multi-indices” in the process of estimating the
Fourier model. This is a notational convenience,
as we have explained, for expressing the partial
differentiation of the indirect utility function
and can be considered as weights (linear combi
nations k a 'v ) of normalized prices.
In this example we will be looking at four
share equations, w ith A =4 and J=1 in the Fouri
er model. The multi-indices used for the timeseries approach, assuming an ARMA(1,0), are:
ka
k-za
Ka where k t
k-4a1
i
0
1
i
0 K — l
k, =
1
,
0
0
(l
0
0
1 t k2 — 1
0)
V
(v»
V»
with V - V„
v j
A
J
v,A - £ (uo z 'k a + 2 £ j[ujasm(jk z) + vvocos (jk z)])ki z i
(ID
y, =
* = 1__________ h i ______________________________
n
A
J
Z b.v i ~ Z (uo z 'K + 2 £ i [u»sir# C z) + w^cos (jk z)))k'z
a
1= 1
a =\
j= 1
w here i =
expressed as
(
This can be more compactly
12 ) y, = f l w j O ) .
In this model, adding up is guaranteed, and no
additional restrictions need to be applied at the
estimation stage.
EXAMPLES OF THE TWO MODELS
In the two models just presented, the dynam
ics are captured in quite different ways. For the
time-series approach, the dynamics enter in the
form of lagged shares and lagged expenditure
FEDERAL RESERVE BANK OF ST. LOUIS
Note th at V defines the four expenditurenormalized prices. The multi-indices are set up
in the same way as in Gallant (1981) and one
m ust be careful, w hen taking partial derivatives,
to ensure that the corresponding k.a is used. In
this example, the first element of each of the
multi-indices, zero or one, corresponds to the
first element in V this is the normalized price,
;
Vu. Since the dynamics are modeled by adding
lagged expenditure shares, the dimension of the
multi-indices, which only appears in f(v t,6) in
equation 5, stays the same w hen one moves
from the static to the dynamic time series
model.
121
On the other hand, in the dynamic utility ap
proach, the inclusion of lagged normalized
prices increases the length of each multi-index
[see f(v t, vl t,d) in equation 12]; we use the fol
lowing eight indices, accordingly:
0
II
1
0
1
0
0
0
0
0
1
1
0
0
0 ’
0
01
^3
1
0
1
1
0
0 ’ K
0
0
=
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0 ' K = 1 , k 7 = 0 ’ ks = 1
0
1
1
1
1
0
2
3!
In this case the vector of normalized prices is
is based directly on economic theory. The
Divisia index, indeed, is designed to internalize
the substitution effects (at constant utility) that
arise from relative price changes. In fact, the
simple-sum index cannot produce this result u n
less the com ponents of the proposed aggrega
tion are perfect substitutes. We have reason to
believe this is not the case for the m onetary
aggregates in common use.
Having a satisfactory procedure such as the
Divisia does not, however, tell us exactly w hat
set of assets to consider or how to group the
subsets of the data for efficient estimation. A
procedure that is available is the linear NONPAR
program of Varian (1982, 1983), which is based
directly on the Generalized Axiom of Revealed
Preference (GARP). Satisfaction of GARP on a set
of data implies that there exists a non-satiated,
concave, monotonic utility function across that
particular set. Such a set of data, if it exists, can
be examined for logical groupings, again using
the program NONPAR. If such groupings can be
established—that is, if weak separability holds—
then, according to the Leontief-Sono definition
of separability, the marginal rates of substitution
betw een any two commodities in the m onetary
index are independent of changes in relative
prices outside the m onetary group. This group
is then available for (Divisia) aggregation.
Z' = lVu'V*>V#V4l’VU-*V2,f-*V3J-l’V4,,JThe first four elem ents of each ka correspond to
the static p art of the vector z and the last four
elements of each ka to the dynamic elements of
z. This separation of multi-indices enables one
to test the static against the dynamic utility
function because each multi-index has an as
sociated parameter.
THE CONSTRUCTION OF DIVISIA
MONETARY AGGREGATES
Most of the studies of money demand in the
literature employ m onetary aggregates th at are
simple sums of their components (for example,
M l = Currency plus deposits) and are constructed
essentially w ithout benefit of index-num ber th e
ory. While simple-sum aggregation might serve
policy makers well w hen interest rate fluctuations
are relatively mild, it is at a disadvantage w hen
the relative interest rates on the m onetary com
ponents fluctuate significantly. A Divisia index is
an alternative approach for aggregating data that
On the quarterly U.S. data from 1970:1 to
1985:2, Swofford and W hitney (1987) have con
structed a set of real per capita m easures of
m onetary quantities and a set of related nominal
user costs to represent the prices of these quan
tities. With M l denoting narrow money (ex
cluding the deposits of businesses); OCD, other
checkable deposits; SD, savings deposits in finan
cial institutions; and STD, small time deposits in
financial institutions, they find that the follow
ing arrangem ent passes the necessary and suffi
cient conditions for the General Axiom of
Revealed Preference:
U[V(DUR, NONDUR, SERV, LEIS), M l, OCD, SD,
STD],
Here, the first three items in the equation refer
to components of total consumption, while LEIS
refers to leisure (evaluated at the wage rate).
Note that SD and STD describe vectors of the
liabilities of the various financial institutions
(for example, SD = small time deposits in com
MARCH/APRIL 1994
122
mercial banks, S&Ls, and so on).1 Also, notice
th at in the arrangem ent just listed, the con
sumption and leisure activities are separable
from the financial assets but not the converse.
This implies the existence of an aggregate utility
function defined across these m onetary entities
(for this time and place).
Because of the failure to establish a sub
grouping of the m onetary assets, it proves
necessary to work w ith the following four
aggregate commodities:
M l, OCD
SDCB, SDSL, SDSB, SDCU
STDCB, STDTH, STDCU
DUR, NONDUR, SERV, LEIS.
A1
A2
A3
A4
Here, SDCB and so on are savings deposits at
commercial banks, S&Ls, m utual savings banks
and credit unions, while STDCB and so on are
small time deposits at commercial banks, thrifts
and credit unions. Tb attem pt to preserve the
economic characteristics of this set of data up to
a third-order rem ainder term , Divisia index
num bers are constructed from the individual
quantities and their associated user costs; these
are designated as Al, ..., A4. Note th at M l and
OCD are summ ed for convenience; this can be
justified by fu rth e r noting that the correlation
coefficient betw een the user costs of these two
items is .994.
Putting all the pieces together, then, we have
m onetary data (and user costs) that satisfy an
empirical test for revealed preference, we have
aggregated the data in a way that is designed to
preserve their economic characteristics in the
face of changes in relative prices and, finally, we
propose to estimate the elasticities using a
model w hich can come arbitrarily close to the
elasticities implied by the true (but unknown)
aggregate indirect utility function known to be
defined (by the GARP test) over these entities.
Note, especially, that satisfaction of GARP im
plies th at there is a firm link betw een the in
1The original variables were supplied by the Federal
Reserve and appear in several publications by Farr and
Johnson (1985a, 1985b). In this study, the monetary data
are employed in per capita real form (where the latter is
achieved by deflation with the CPI). SD represents savings
deposits in commercial banks, S&Ls, mutual savings banks
and credit unions, while STD represents the small time
deposits of the same institutions. OCD is other checkable
deposits and includes NOW accounts. See Swofford and
Whitney’s two papers for more details on the construction
of the data.
As discussed in Swofford and Whitney (1987, 1988), the
L RESERVE BANK O F ST. LOUIS
FE D ER A
direct utility that is actually estimated and the
underlying utility function that actually gener
ates these data.
EMPIRICAL RESULTS
In our empirical work, we compare the results
of the estimation of the three systems: the stat
ic, the time series dynamic and the utility fun
ction dynamic. Because the static theory is
nested in each of the two dynamic theories, we
present the results in that form. The com pari
sons are in term s of the significance of the
coefficients, the characteristics of the residuals
and the relevance of the dynamic form ulations
using the results of the Gallant-Jorgenson (1979)
chi-square test. Unfortunately, the two dynamic
approaches are not nested, so that we cannot
compute a Gallant-Jorgenson test statistic. We
do, however, offer a comparison utilizing the
other statistics just m entioned. As it tu rn s out,
neither model has a clear advantage, although
we do prefer the dynamic utility model in view
of its economic properties and adequate perfor
mance. We also offer some comparisons with
earlier work that utilized the static Fourier
model over the same data space (Fisher, 1992).
Here, there are dramatic differences in the esti
m ated elasticities of substitution; we believe the
dynamic results (utilizing the estimates from the
dynamic utility approach) are considerably more
reasonable than the earlier static results.
The share equations, w ith the across-equations
restrictions, were estimated in the SAS system
using PROC MODEL w ith nonlinear seemingly
unrelated regression. The results for the dynam
ic time-series model appear in T&ble 1.
In this table, the Bs correspond to the quadratic
term s in the Fourier Flexible Form, the Us and
Vs to the Fourier series expansion, and the As
to the lagged shares yM
.
These results describe reasonable fits, with 10
of the 12 adjustment param eters (AJ having tdata were prepared as follows. Each monetary asset is
deflated by the consumer price index for urban areas.
OCD includes super NOW accounts. The user cost is the
concept defined by Barnett (1978). For leisure, the quantity
is 98 hours less average weekly hours worked during the
quarter (times 52). The wage rate measures the opportuni
ty cost of time. The consumption figures are taken from
Department of Commerce data that also provides the im
plicit deflator for each category. A 10 percent depreciation
rate is used in calculating the one-period holding cost of a
durable good.
123
Table 1
Time Series Model: Dynamic Fourier Flexible Functional Form
Nonlinear SUR sum m ary of residual errors
Eqn.
DF
model
DF
error
SSE
MSE
Root
MSE
square
Adjust
R-square
SM1
SM2
SM3
9
9
9
53
53
53
0.00438
0.01650
0.02445
0.0000827
0.0003113
0.0004613
0.00909
0.01764
0.02148
0.915
0.848
0.923
0.902
0.825
0.912
R-
Nonlinear SUR param eter estim ates
Parameter
B1
B2
B3
U01
U11
W11
A11
A12
A13
A14
U02
U12
W12
A21
A22
A23
A24
U03
U13
W13
A31
A32
A33
A34
U04
U14
W14
Estimate
Approxim ate standard
error
“ T ” Ratio
Approxim ate
prob>|T|
0.175462
0.007578
-0.448512
-0.007955
-0.009762
0.023864
0.419255
0.259118
0.197632
0.190888
-0.014187
0.011554
-0.019444
-1.000371
0.958742
-0.0 3 4 4 8 0
0.766254
0.020581
-0.0 0 2 2 3 5
0.002259
0.572904
-0.381781
0.276142
-0.119175
-0.009973
-0.000714
0.000171
0.08184
0.25542
0.15285
0.02828
0.00710
0.02545
0.07229
0.03873
0.02071
0.04239
0.01355
0.01015
0.00809
0.13602
0.06774
0.03080
0.08967
0.00692
0.00216
0.00146
0.11232
0.07622
0.04249
0.08974
0.00554
0.00236
0.00287
2.14
0.03
2.93
0.28
1.37
0.94
5.80
6.69
9.54
4.50
1.05
1.14
2.40
7.35
14.15
1.12
8.55
2.97
1.03
1.55
5.10
5.01
6.50
1.33
1.80
0.30
0.06
0.0367
0.9764
0.0049
0.7796
0.1752
0.3526
0.0001
0.0001
0.0001
0.0001
0.3000
0.2599
0.0197
0.0001
0.0001
0.2680
0.0001
0.0044
0.3062
0.1272
0.0001
0.0001
0.0001
0.1899
0.0778
0.7638
0.9527
N = 62
Objective = 2.0164
Objective'N = 125.0495
The Aij represent the dynamics.
values in excess of 2. Note th at it is the surfaces
of (dld)0g*()d and {d2ld^cd^c') g*(z) that one
aims to estimate accurately; it is not required
that all param eters be significant. The coeffi
cients capturing the dynamics tend to be the
most significant param eters. We also calculated
the autocorrelation and partial autocorrelations
for each of the three share equations; the
residuals here w ere white noise. In order to
compare the dynamic and static results, we
apply the Gallant-Jorgenson chi-square test to
provide a comparison w ith the static equivalent
of the time series model. The test statistic uses
the value "objective*N” in the table. For the stat
ic model (the estimates are not shown here), the
value of this statistic is 527.9597; for the dynam
ic it is 125.0495 as shown in the table. The
value of the Gallant-Jorgenson statistic is then
527.9597-125.0495 = 402.9102 with degrees of
freedom equal to the difference in the num ber
of param eters, of 27-15 = 12. This calculation
decisively rejects the static model.
MARCH/APRIL 1994
124
Table 2
Utility Function Model: Dynamic Fourier Flexible Functional Form
Nonlinear SUR sum m ary of residual errors
Eqn.
DF
Model
DF
Error
SSE
MSE
Root
MSE
RSquare
Adjust
R-square
SM1
SM 2
SM 3
9
9
9
53
53
53
0.01057
0.01885
0.03803
0.0001995
0.0003556
0.0007175
0.01412
0.01886
0.02679
0.796
0.826
0.880
0.765
0.800
0.862
Nonlinear SUR param eter estim ates
Parameter
Estimate
Approxim ate standard
error
B1
B2
B3
U01
U11
W11
U05
U15
W15
U02
U12
W12
U06
U16
W16
U03
U13
W13
U07
U17
W17
U04
U14
W14
U08
U18
W18
-0.163039
-1.187580
-1.028066
0.016757
-0.002319
0.027816
0.002500
0.009921
-0.064331
-0.111290
0.061322
0.022699
-0.0 0 8 5 5 9
0.006524
0.001616
-0.006461
0.006416
-0.113939
-0.013340
0.000898
-0.016214
-0.070695
-0.010984
-0.070924
0.123303
0.024230
0.020177
0.38557
0.32865
0.35163
0.03275
0.01498
0.02235
0.02955
0.01450
0.03009
0.03773
0.01864
0.01756
0.01160
0.00869
0.00993
0.01692
0.01338
0.00800
0.01127
0.00873
0.01118
0.01156
0.01223
0.00896
0.00850
0.01013
0.01199
“ T ” ratio
0.42
3.61
2.92
0.51
0.15
1.24
0.08
0.68
2.14
2.95
3.29
1.29
0.74
0.75
0.16
0.38
0.48
1.42
1.18
0.10
1.45
6.12
0.90
7.91
1.45
2.39
1.68
Approxim ate
prob>|T|
0.6741
0.0007
0.0051
0.6110
0.8776
0.2187
0.9329
0.4968
0.0372
0.0047
0.0018
0.2023
0.4637
0.4561
0.8713
0.7041
0.6335
0.1604
0.2419
0.9185
0.1530
0.0001
0.3730
0.0001
0.1530
0.0204
0.0982
N = 62
Objective = 2.3732
Objective'N = 147.1362
The dynamic utility model features interaction
among the asset choices over time. This charac
teristic distinguishes the dynamic utility system
from the time series approach. For this model
the results are not quite as satisfactory as those
just given. They follow in Table 2. Here, the Rsquares are slightly lower, the objective*N statis
tic is higher, and there are fewer significant
param eters. The static Fourier is nested within
the dynamic utility function in term s of the
multi-indexes (see section four). Consequently,
we analyze the reduction in the residuals due to
the dynamic specification (see Gallant, 1981).
FEDERAL RESERVE BANK OF ST. LOUIS
The residual sum of squares from the dynamic
model is less than half the size of those ob
tained from the static model.
Quite often, the m ethods discussed to this
point would be applied to systems of dem and
equations, as they are here. While the estimated
structural equations themselves might be of in
terest, and for the dynamic versions presented
here they could be used to generate forecasts, a
typical concern is the elasticity of substitution
among the assets. W hat the Fourier provides in
this connection is precise estimates of a set of
125
own- and cross-elasticities of substitution (and
income) at each data point. This can reveal the
nature of the substitutability or com plem entari
ty among the assets and the time-series behavior
of this concept.
While we do not wish to explore the fine
points of the data set just examined, a fu rth er
illustration, because it reveals an im portant
characteristic of the dynamic models, is in ord
er. For the m ore interactive dynamic utility
function model, Table 3 presents the estimates
of the Allen partial elasticities of substitution
among the four commodity bundles studied
here. In the table, Eij is the elasticity of substitu
tion betw een Ai and Aj. The Fourier Flexible
Form provides a global approximation and hence
we can calculate the asymptotic standard errors
for each elasticity (Eij) at each point in time and
then evaluate the significance of the estimate.
The Tij in the table are the corresponding tstatistics for Eij.
Here, we show a complete set of substitution
elasticities along with their associated f-values.
Note that a positive value for the elasticity indi
cates substitution, while a negative indicates a
complementary relation.
Several things stand out in Tkble 3. Most im
portantly, the elasticity of substitution between
cash and savings assets (E12 in the table) and
betw een cash and time deposits (E13) are very
precisely estimated at all data points. This was
not the case for static estimates published else
w here (Fisher, 1992). While we cannot say a pri
ori w hat value of the elasticity of substitution is
high, an elasticity over unity, as most are in the
first column of the table, could be term ed “elas
tic.” Note that the result here is that cash and
savings accounts are substitutes, as many would
expect on the basis of intuition.
More provocatively, however, cash and time
deposits appear to be "elastic” complements.
This spells trouble for a simple-sum M3 defini
tion of money, if these results are correct, since
the simple-sum approach to aggregation treats
all components as (perfect) substitutes. Clearly,
we are not in a position to doubt our results.
We have adopted a rigorous aggregation-theoretic
approach and tied the empirical work to that as
closely as our data would perm it. In fact, the
very theory we are using can be invoked in our
defense: Economic theory does not say w hether
commodities will be substitutes or complements
in practice. That is, in practice, economic agents
decide w hat assets are substitutes and w hat are
complements. Our results indicate that they use
cash and time deposits as if they are comple
ments, at least over this data sample. We also
should point out that this is not an unusual
finding in this literature (see the survey in Bar
nett, Fisher and Serletis, 1992).
Another interesting finding, and one that
dem onstrates the power of the dynamic ap
proach, is that the elasticities shown in Table 3
are m uch m ore stable than those obtained from
the static model. For this comparison, we refer
to the elasticities produced in the static Fourier
from the same data set, as published in Fisher
(1992). In Figure 1 we show the results for the
substitution relation betw een cash and savings
deposits. Note especially that the two series are
scaled differently, an adjustm ent necessary be
cause the static estimates fluctuate so wildly.
While both series are generally positive (indicat
ing that they are substitutes), the static esti
mates are occasionally negative (although they
were not significantly less than zero). This sort
of result is not ruled out by economic theory,
but is still hard to explain in term s of the
known characteristics of these assets.
In Figure 2 we present a comparison betw een
the results for the static Fourier and the dynam
ic utility model w here the form er results are,
again, draw n from the earlier study. In this case
we compare cash (A 1) and small time deposits
(A3), a relation that is consistently that of com
plem entarity in T&ble 3.
Once again the dynamic elasticities are rela
tively constant. In addition, the static elasticities
are sometimes positive and sometimes negative
(and statistically so, in both cases, at some
dates). Clearly, then, the complementary rela
tionship betw een cash and small time deposits is
clearly established in the dynamic utility func
tion results. We note that such results are quite
common in this literature (see Barnett, Fisher
and Serletis, 1992).
CONCLUSIONS
In the introduction to this paper, we listed five
areas in which existing studies of expenditure
systems frequently fall short, in Diewert’s opin
ion. Obviously, the innovation of this paper is to
convert a static system into a dynamic one; this
deals w ith one of his concerns. Diewert is also
concerned th at existing studies do not link the
theory to the application firmly enough. This we
have attem pted to address both by setting out
MARCH/APRIL 1994
126
Table 3
Substitution Elasticities: Dynamic Utility Model
E12
70:2
70:3
70:4
71:1
71:2
71:3
71:4
72:1
72:2
72:3
72:4
73:1
73:2
73:3
73:4
74:1
74:2
74:3
74:4
75:1
75:2
75:3
75:4
76:1
76:2
76:3
76:4
77:1
77:2
77:3
77:4
78:1
78:2
78:3
78:4
79:1
79:2
79:3
79:4
80:1
80:2
80:3
80:4
81:1
81:2
81:3
81:4
82:1
82:2
82:3
82:4
83:1
83:2
83:3
83:4
84:1
84:2
84:3
84:4
85:1
85:2
T12
E13
T13
E14
T14
E23
T23
E24
T24
E34
T34
1.291
1.276
1.255
1.167
1.163
1.166
1.115
1.101
1.077
1.052
1.010
1.033
0.995
1.041
1.008
0.920
1.152
1.284
1.184
1.231
1.216
1.199
1.190
1.169
1.137
1.107
1.055
1.041
1.030
0.997
0.977
1.003
1.031
0.982
0.994
0.992
1.000
1.067
1.139
1.194
1.299
1.267
1.265
1.296
1.323
1.382
1.329
1.319
1.338
1.395
1.349
1.460
1.479
1.485
1.483
1.483
1.493
1.465
1.470
1.471
1.463
2.983
3.163
3.389
3.669
3.744
3.896
4.050
3.896
4.083
4.269
4.451
4.524
4.672
4.739
4.726
4.791
4.725
4.358
4.615
4.094
3.977
4.134
4.117
4.137
4.249
4.347
4.499
4.487
4.515
4.611
4.651
4.625
4.612
4.718
4.692
4.653
4.632
4.658
4.448
4.103
4.479
4.593
3.983
3.675
3.688
3.333
3.513
3.653
3.774
4.130
4.221
3.505
3.353
3.344
3.396
3.421
3.241
3.392
3.640
3.447
3.319
-0 .2 5 0
-0 .2 5 9
-0 .2 7 0
-0 .2 7 2
-0 .2 7 0
-0 .2 7 8
-0 .2 7 9
-0 .2 6 5
-0 .2 6 6
-0 .2 7 3
-0 .2 8 2
-0 .2 9 7
-0 .3 3 5
-0 .4 4 6
-0 .4 6 5
-0.507
-0 .4 2 6
-0 .3 6 4
-0 .3 9 2
-0 .3 0 6
-0.281
-0 .2 9 4
-0 .2 8 7
-0 .2 8 2
-0 .2 8 6
-0.291
-0 .3 0 3
-0.291
-0 .2 9 5
-0.318
-0 .3 3 0
-0 .3 2 3
-0 .3 2 8
-0 .4 2 0
-0.5 2 7
-0 .5 6 9
-0.5 7 6
-0 .5 4 5
-0.618
-0 .6 3 4
-0 .5 0 3
-0.4 7 2
-0 .5 9 0
-0 .5 8 6
-0 .5 5 2
-0.581
-0 .5 7 3
-0 .5 6 2
-0 .5 3 2
-0 .4 3 5
-0 .3 8 0
-0 .3 2 3
-0 .3 2 8
-0.341
-0 .3 4 2
-0.3 4 7
-0 .3 2 6
-0 .3 8 8
-0.376
-0 .3 2 9
-0 .3 0 6
2.367
2.532
2.751
3.026
3.071
3.216
3.368
3.202
3.382
3.596
3.873
4.058
4.543
5.808
5.944
5.954
5.233
4.063
4.663
3.543
3.352
3.577
3.539
3.551
3.713
3.880
4.207
4.157
4.235
4.586
4.813
4.654
4.605
5.550
6.350
6.378
6.336
6.507
6.911
6.714
5.621
5.429
6.200
5.700
5.332
4.869
5.281
5.401
5.211
4.379
4.034
2.887
2.730
2.768
2.826
2.874
2.581
3.119
3.254
2.814
2.615
0.509
0.445
0.371
0.290
0.273
0.233
0.195
0.236
0.188
0.134
0.065
0.046
-0 .0 4 7
-0.150
-0.194
-0 .3 0 2
-0.074
0.090
-0.010
0.169
0.204
0.162
0.168
0.165
0.136
0.107
0.049
0.056
0.041
-0 .0 2 0
-0 .0 5 4
-0 .0 2 2
-0 .0 0 8
-0.159
-0 .2 7 4
-0 .3 2 9
-0 .3 3 5
-0 .2 6 0
-0.319
-0 .2 8 9
-0.074
-0.0 6 7
-0.164
-0.110
-0 .0 4 0
-0 .0 2 4
-0 .0 5 2
-0 .0 5 4
-0.011
0.102
0.117
0.358
0.410
0.401
0.385
0.373
0.438
0.318
0.287
0.379
0.429
1.394
1.329
1.218
1.107
1.057
0.932
0.832
0.987
0.825
0.623
0.328
0.230
0.261
0.875
1.167
2.083
0.386
0.375
0.049
0.669
0.790
0.659
0.685
0.683
0.588
0.482
0.240
0.273
0.206
0.109
0.299
0.118
0.044
0.944
1.722
2.097
2.119
1.529
1.806
1.456
0.332
0.313
0.707
0.409
0.140
0.071
0.172
0.191
0.038
0.362
0.443
0.951
0.996
0.953
0.940
0.917
0.978
0.775
0.782
0.971
1.067
-0.614
-0.601
-0 .5 9 2
-0.610
-0.610
-0 .5 9 5
-0 .6 0 2
-0 .6 2 5
-0.619
-0 .6 0 5
-0 .5 8 2
-0 .5 6 8
-0.5 2 7
-0.421
-0.412
-0.381
-0.419
-0 .4 4 4
-0 .4 6 0
-0 .5 4 8
-0.5 7 9
-0.5 6 7
-0 .5 7 6
-0.5 8 7
-0 .5 8 8
-0 .5 8 6
-0 .5 7 6
-0 .5 8 6
-0.581
-0 .5 5 5
-0 .5 3 9
-0 .5 4 9
-0 .5 4 6
-0 .4 6 3
-0 .3 5 7
-0.319
-0.313
-0 .3 3 5
-0 .2 3 7
-0.2 1 2
-0.301
-0 .3 5 3
-0 .2 2 4
-0 .2 0 8
-0 .2 2 3
-0.1 3 5
-0.1 9 3
-0.2 1 5
-0 .2 3 8
-0 .3 3 0
-0.416
-0 .4 4 4
-0.414
-0 .3 8 3
-0 .3 8 8
-0 .3 8 2
-0.381
-0.317
-0.3 6 7
-0.413
-0 .4 4 4
1.106
1.164
1.241
1.462
1.490
1.491
1.609
1.643
1.712
1.763
1.820
1.755
1.738
1.359
1.383
1.464
1.228
1.091
1.292
1.353
1.416
1.442
1.471
1.526
1.596
1.654
1.738
1.785
1.797
1.805
1.801
1.772
1.715
1.578
1.232
1.119
1.090
1.083
0.718
0.569
0.751
0.927
0.524
0.427
0.440
0.223
0.364
0.427
0.478
0.688
0.940
0.772
0.671
0.610
0.629
0.622
0.580
0.507
0.643
0.696
0.733
0.146
0.102
0.049
-0 .0 4 7
-0 .0 6 8
-0 .0 8 4
-0.1 2 9
-0.1 2 4
-0.1 6 5
-0.1 9 8
-0 .2 3 6
-0 .2 2 6
-0 .2 3 8
-0.1 2 5
-0.141
-0.176
-0.0 6 7
0.010
-0.079
-0.074
-0 .0 9 4
-0.111
-0.121
-0.1 3 9
-0.1 6 6
-0.1 8 9
-0 .2 2 4
-0 .2 3 9
-0 .2 4 5
-0 .2 5 7
-0 .2 6 2
-0 .2 4 8
-0 .2 2 7
-0 .2 0 2
-0.1 0 4
-0.079
-0.071
-0.051
-0 .0 6 2
0.113
0.128
0.052
0.202
0.268
0.289
0.422
0.328
0.292
0.283
0.207
0.081
0.237
0.324
0.359
0.340
0.339
0.382
0.388
0.296
0.294
0.291
1.153
0.857
0.438
0.491
0.718
0.890
1.480
1.436
1.979
2.450
3.052
2.766
3.071
1.304
1.538
2.098
0.666
0.083
0.811
0.702
0.898
1.085
1.195
1.413
1.761
2.083
2.632
2.827
2.935
3.201
3.253
2.987
2.663
2.430
1.061
0.788
0.716
0.492
0.464
0.782
0.907
0.427
1.035
1.128
1.212
1.295
1.244
1.221
1.286
1.252
0.599
1.454
1.823
1.881
1.832
1.814
1.855
1.744
1.676
1.714
1.733
-1 .2 8 6
-1.291
-1.301
-1 .2 6 9
-1 .2 8 0
-1.3 0 7
-1 .2 9 2
-1 .2 5 6
-1.271
-1 .2 8 2
-1 .2 8 2
-1.314
-1.3 2 0
-1.3 8 3
-1.375
-1 .3 2 3
-1 .4 3 4
-1 .4 6 0
-1.4 3 8
-1.397
-1.374
-1.381
-1.373
-1.361
-1 .3 5 2
-1 .3 4 6
-1 .3 3 3
-1.321
-1.319
-1.316
-1.313
-1.322
-1.3 3 8
-1.3 4 9
-1.3 8 8
14.957
14.973
14.906
14.076
14.219
14.273
13.771
13.693
13.523
13.165
12.547
12.436
11.475
9.225
8.904
8.123
10.784
13.096
12.212
14.327
14.565
14.093
14.101
13.984
13.559
13.145
12.371
12.366
12.199
11.491
10.997
11.359
11.573
9.671
7.894
7.546
7.581
8.127
7.332
7.133
9.679
10.522
7.546
7.396
7.778
7.238
7.567
7.760
8.378
11.357
13.092
15.850
15.791
15.192
15.251
15.054
15.085
12.801
14.393
15.821
16.458
FEDERAL RESERVE BANK OF ST. LOUIS
-1 .4 0 1
-1.407
-1.437
-1 .5 2 8
-1.5 9 6
-1.5 4 5
-1.510
-1.6 2 6
-1.679
-1.677
-1.7 8 3
-1.707
-1.6 8 0
-1.6 5 9
-1 .5 7 7
-1.5 0 5
-1 .5 5 8
-1 .5 9 3
-1 .6 3 2
-1 .6 2 2
-1.6 2 8
-1 .6 5 4
-1.695
-1 .6 2 3
-1.579
-1.547
127
Figure 1
Substitution Elasticities Between Cash (A1) and
Savings Deposits (A2), 1970-1985
Figure 2
Substitution Elasticities Between Cash (A1) and
Time Deposits (A3), 1970-1985
MARCH/APRIL 1994
128
the theory and by dealing w ith two of his fu r
th er concerns: aggregating in a consistent
fashion and employing a system that provides
arbitrarily accurate estimates of the partial
derivatives of the system. W hat we did not do,
w hich is in his list of concerns, is examine the
model at every data point.
In our results, the dynamic models derived
and estimated appear clearly superior to the
(nested) static models. We are not able to com
pare the two dynamic form ulations directly,
because they are not nested, but we find the
statistical perform ance of the time series ap
proach to be superior, while the dynamic-utility
approach seems better able to capture the eco
nomic interactions among the assets studied.
Furtherm ore, most of the estimated share equa
tions produced white noise residuals, and this is
a characteristic that is not shared by the static
estimates, w hether of the nested form in this
paper or in the earlier (static) Fourier results
that we have been using as a benchm ark.
For the dynamic utility model, we have
produced a set of elasticities of substitution and
charted those betw een cash (Ml + OCD) and
savings deposits and betw een cash and small
time deposits. The form er are shown to be sub
stitutes in the dynamic system, and, m ore im
portant, to be m uch more stable than static
estimates produced in an earlier study. The lat
ter are actually complements, although the nega
tive elasticity of substitution is generally less
than m inus one, a finding th at is not w ithout
foundation theoretically. We anticipate that
fu rth e r study of the model and/or the U.S.
data will provide fu rth e r observations on
this phenomenon.
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on Consumption, Leisure, and Money,” Journal o f Business
a nd Econom ics Statistics (April 1988), pp. 241-46.
Varian, Hal R. “ The Nonparametric Approach to Demand
Analysis,” Econom etrica (July 1982), pp. 945-73.
________ “ Nonparametric Tests of Consumer Behaviour,”
Review o f Econom ic Studies (January 1983), pp. 99-110.
129
Jam es L. S w o fford
James L. Swofford is a professor a nd chair o f the Departm ent
o f Economics, University o f South Alabam a.
Com m entary
D
OUG FISHER AND ADRIAN FLEISSIG
develop and estimate a Dynamic Fourier Expen
diture System in an attem pt to meet some criti
cisms that have been raised against the literature
on expenditure systems. First, I will discuss Fish
er and Fleissig's model in term s of their own
criteria set forth in their introduction. Then I
will discuss their specification in term s of some
criteria for an ideal model that Carl F. Christ
proposed in his paper at last year’s Federal
Reserve Bank of St. Louis Economic Policy
Conference. Finally, I will make some general
comments about research on money stock
m easurem ent.
FISHER AND FLEISSIG’S
CRITERIA
In their introduction, Fisher and Fleissig m en
tion five of w hat they feel are the most telling
shortcomings of the expenditure system litera
ture. The first they m ention is a failure to link
theory and application. On one level they have
m et this criticism admirably. They chose to use
the Fourier form as a flexible form specification
that is able to approximate any unknow n in
direct utility function. They have also modeled
the dynamics in a way that makes economic
sense with their dynamic utility function specifi
cation. On another level they have not linked
theory and application. Their discussion of the
elasticities of substitution that they have estimat
ed is fairly terse. While they show th at the
elasticity of substitution betw een two assets is
more stable w ith one dynamic specification,
they do not discuss the sign, m agnitude o r eco
nomic interpretation of their estimated elastici
ties more than in passing. They say that their
elasticities are typical for this literature, but is
that good or bad? They do not cite specific
previous studies nor do they m ention the size
or sign of elasticities from other studies. Are we
surprised that old consum er M l and other
checkable deposits (OCD) and savings accounts
are substitutes but old consum er Ml and OCD
and small time deposits are complements? These
results make sense to me b u t their implications
should be explained in the paper. W hat about
the size of these elasticities? W hat is their
meaning? My view is that other economists may
miss the im portance of the expenditure system
literature, if those of us doing research using
such systems continue to omit a thorough dis
cussion of the elasticities that these systems
produce and a comparison of these elasticities
w ith those produced by previous research.
The second shortcoming of the expendi
tu re system literature that Fisher and Fleissig
address is im proper aggregation over goods. In
my view they have handled this problem in a
very nice way. Expenditure systems like the Fou
rier system are very parameter-intensive, and
aggregation over goods is required to make
them tractable. Fisher and Fleissig have used
both revealed preference results and good
judgment about which goods to aggregate. I feel
that in estimating systems such as these both
are needed. However, I feel I m ust point out
th at Fisher and Fleissig have used a revealed
preference test for a direct utility function to
MARCH/APRIL 1994
)
130
back up the specification of an indirect utility
function. Direct utility function results may be
suggestive of the structure of the indirect utility
function, but they are not necessarily m ore than
suggestive.
Fisher and Fleissig's third and fourth problems
with the expenditure system literature are
imprecise estimations of partial derivatives and
use of locally integrable models, for which the
first- and second-order conditions do not obtain
at some data points. The Fourier System was de
veloped to handle these criticisms of other
specifications, such as the translog, so Fisher
and Fleissig have admirably handled these criti
cisms as they set out to do.
The last problem Fisher and Fleissig set before
themselves to solve is misspecification, often
nonspecification, of dynamics in expenditure
systems. They model the dynamics w ith two
very general specifications. One, the time series
model, is statistical in nature. Another, the dy
namic utility function model, is consistent with
economic theory. My view is th at they are cor
rect to model the dynamics in very general
ways. Gerald W hitney and I (1994) have found
that data in similar categories to those that Fish
er and Fleissig have used can only be rational
ized by a well-behaved direct utility function
w ith some incomplete category adjustm ent wi
thin some quarters. But since Fisher and Fleissig
are unable to choose betw een their two dynam
ic specifications, we cannot yet say that they
have correctly specified the dynamics. They
have, however, certainly done a better job
modeling the dynamics than other researchers
in this area. In a sense they have begun the de
bate on how to correctly model the dynamics
w ithin flexible consum er expenditure systems.
In summary, with a couple of reservations,
Fisher and Fleissig have done a good job in
meeting the criteria they set forth for their
model. Next, I tu rn to the question of how their
models compare w ith someone else’s criteria for
an ideal econometric specification.
CARL CHRISTS CRITERIA FOR
AN ECONOMETRIC MODEL
At last year’s St. Louis Fed conference, Carl F.
Christ suggested seven characteristics of an ideal
econometric model. I will next examine Fisher
and Fleissig's paper in light of this ideal.
FEDERAL RESERVE BANK OF ST. LOUIS
Christ’s first criterion is th at the estimated
model should provide a good description of
some interesting set of past data. Certainly, Fish
er and Fleissig’s model has been used to inves
tigate an interesting issue—money holdings.
There are also a reasonable num ber of coeffi
cients that are statistically different from zero,
and they test and find the residuals of their
model are w hite noise.
The second criterion that Christ sets out (and
one that he stressed) is that the model should
be testable against data that w ere not used to
estimate it and were not available w hen it was
specified. Fisher and Fleissig have not done this.
Since their sample ends in 1985, and Fisher and
Fleissig have presum ably form ulated their model
in recent years, this would be a tough challenge.
A model estimated on data th at ends eight years
ago could not be expected to predict today’s
data very accurately. The new data set collected
by the research staff of the St. Louis Fed could
be used to estimate a dynamic flexible model,
which then could be put to this test over the
next few years.
Christ’s third criterion, related to his second,
is that the estimated model should describe
events for at least a few quarters after it was
form ulated and estimated. As w ith Christ's se
cond criterion, Fisher and Fleissig’s specification
cannot be reasonably put to this test. But a
specification estimated w ith the St. Louis Fed’s
updated data could be.
The fourth criterion is that the model should
make sense in the light of our knowledge of
economics. Of course, the dynamic Fourier
specification is flexible w ith respect to arbitrary
elasticities, and it also does not generate negative
shares. But Fisher and Fleissig’s specification
does generate asset pairs th at switch from sub
stitutes to complements over their sample. This
is a puzzling result that they do not explain.
Christ’s fifth criteria is that a simple model is
superior to a complex model. Fisher and Fleis
sig’s model is not simple, leaving open the possi
bility that an otherwise equal b ut simpler model
will be found. Of course, this could be said of
any specification. This does suggest that some
one might w ant to test Barnett’s Asymptotically
Ideal Model w ith this type of data since it has
similar characteristics to the Fourier model and
may be simpler, depending on the form ulation
used.
131
The sixth criteria for judging a model is that,
other things being equal, a model that explains
a wide variety of data is better. Fisher and Fleissig’s model does explain a wide variety of data,
but some of it has been aggregated. An argu
m ent could be made to estimate this model be
fore aggregating the data. But Fisher and Fleissig
have used the soundest aggregation techniques
in the literature, the model they necessarily
used is very parameter-intensive, and the disag
gregate data series is of a relatively short du
ration.
Christ’s seventh and final criterion is that
models that nest special cases are preferable.
Fisher and Fleissig’s dynamic Fourier models
nest the static Fourier and, in that respect, meet
Christ’s ideal. Unfortunately, these models do
not nest other Flexible Functional forms nor do
the dynamic specifications nest each other.
Of course, Fisher and Fleissig’s dynamic
Fourier flexible functional form does not meet
all of Christ’s ideals. Fisher and Fleissig did not,
nor would they, claim that it does, and I do not
mean to give the impression that they would
make such a bold claim for their model. Their
model seems to m eet the first and the fourth
through the seventh criteria fairly well. Criteria
two and three concern the ability of flexible ex
penditure systems to predict future behavior,
which seems a worthwhile area of investigation
to pursue w ith such specifications.
For the most part, Fisher and Fleissig’s specifi
cations meet their own criteria that they set out
to meet, and Christ’s criteria for an ideal specifi
cation that they were probably only generally
trying to meet. Their paper is an im portant con
tribution to a growing literature on economic
m onetary aggregates. I want to close w ith a few
comm ents on this literature.
THE ECONOMIC MONETARY
AGGREGATES LITERATURE
I feel that Fisher and Fleissig's paper is an im
portant contribution to the question of w hat is
money. Much of my w ork in this area has in
volved nonstochastic revealed preference tests.
Not much is known about the power of such
tests, and there are doubts about the validity of
these tests, so w ork such as Fisher and Fleissig’s
showing that per capita behavior is consistent
w ith stochastic models is very important.
The literature on economic m onetary ag
gregates suggests that the aggregates on which
the central bank focuses may not be the ones
that people use. If people are using one ag
gregate and the central bank is controlling
another, then stable "policy” may lead to an u n
stable price level. Policy in such a situation
might be destabilizing, because the public and
the central bank are engaged in a two-sided
game, w ith each side having a different
objective—the m onetary aggregate each uses.
This implies that it is im portant for central
banks to attem pt to identify w hat the public in
their country is using as money.
Also, there may not be an economic m onetary
aggregate in an area. W hen looking for an eco
nomic m onetary aggregate, the question we are
really asking is, "Is there a common currency
for a particular area?” This area may or may
not be a nation state. If there is no economic
m onetary aggregate in an area, then, again,
"m onetary” policy would not likely lead to
predictable results.
Finally, there may be multiple economic m one
tary aggregates in use. Consumers may be using
one aggregate and business another. Controlling
both aggregates may be mutually exclusive. In
such a case, optimal m onetary policy may re
quire minimizing some loss function over the
aggregates, w ith each one weighted by how
closely related each aggregate is to the price
level.
REFERENCES
Christ, Carl F. “Assessing Applied Econometric Results,” this
Review (March/April 1993), pp. 71-94.
Swofford, James L. “ Microeconomic Foundations of a Com
mon Currency Area,” working paper, University of South
Alabama, 1991.
________ , and Gerald A. Whitney. “A Revealed Preference
Test for Weakly Separable Utility Maximization with Incom
plete Adjustment,” Journal o f Econom etrics (January/ Febru
ary 1994), pp. 235-49.
MARCH/APRIL 1994
133
William A. B arnett and Ge Zhou
William A. Barnett is a professor o f econom ics a t Washington
University, St. Louis. Ge Zhou recently received a doctorate in
econom ics from Washington University, St. Louis. Research on
this project was p a rtia lly supported by NSF grant SES 9223557.
We wish to thank William Brainard for his comments, which
substantially influenced the final revision o f this paper.
Financial Firm s’ P ro d u ctio n
a n d Supply-Side M on etary
A ggregation U nder D ynam ic
U ncertainty
. HIS PAPER IS FOCUSED ON the production
theory of the financial firm and supply-side
m onetary aggregation in the fram ew ork of dy
namics and risk. On the dem and side, there has
been m uch progress in applying consum er de
m and theory to the generation of exact m one
tary aggregates and integrating them into
consum er demand system modeling.1 However,
on the supply-side, m onetary services are
produced by financial firms through financial
intermediation, and, hence, exact supply-side
m onetary aggregation m ust be based upon
financial firm output aggregation. Most of the
literature on exact aggregation theory is based
upon perfect certainty, w hich often is a reasona
ble assum ption regarding contem poraneous con
sum er goods allocation decisions. Risk, however,
is an im portant consideration in modeling the
decisions of financial intermediaries. F urther
more, that risk not only applies to future prices
’ See Barnett, Fisher and Serletis (1992).
2“ Demand-side” and “supply-side” imply respectively the
demand for monetary services by consumers and manu
facturing firms, and the production of monetary services by
financial intermediaries. Barnett (1987) has shown that con
sumer’s demand for money and manufacturing firm’s de
mand for money result in the identical aggregation
problem, at least in the perfect certainty case. However,
supply-side aggregation of produced monetary services
and interest rates, b u t also to contem poraneous
interest rates and thereby to the contem porane
ous user costs of produced m onetary services.
In this paper we derive a model of financial
firm behavior under dynamic risk, and we find
the exact m onetary services output aggregate.
We estimate the Euler equations that comprise
the first-order conditions for optimal behavior
by financial firms.
Barnett (1978,1980) introduced economic
aggregation and index num ber theory to demandside m onetary aggregation by applying Diewert’s
(1976) results on superlative index num bers. The
proposed Divisia index in B arnett’s w ork is an
elem ent of Diewert’s superlative index num ber
class. Analogous to demand-side m onetary aggre
gation, Hancock (1985,1987), Barnett (1987), and
Barnett, Hinich and W eber (1986) have provided
results on supply-side m onetary aggregation.2
They use neoclassical economic theory to model
creates uniquely different aggregation problems resulting
from the existence of required reserves, which alter the
user cost of produced monetary services. For further
results regarding demand for monetary services by
manufacturing firms, see Robles (1993) and Barnett and
Yue (1991).
MARCH/APRIL 1994
134
financial firm s’ production, so the existing eco
nomic aggregation and index num ber theory are
directly applicable. In fact, throughout the litera
tu re on applying economic aggregation and in
dex num ber theory to m onetary aggregation,
researchers usually assume perfect certainty.
Exceptions are Barnett and Yue (1991) and Poterba and Botemberg (1987), who generalize to
demand-side exact m onetary aggregation under
risk. Supply-side m onetary aggregation under
risk has not previously been the subject of
research.
Introduction of dynamics and uncertainty into
supply-side m onetary aggregation requires
extensions of earlier research in this area. A
financial firm ’s portfolio is generally diversified
across different investment instrum ents, and the
portfolio’s rate of re tu rn is unknow n at the time
th at the investment decision is made. Hence, the
assum ption of perfect-certainty and single-period
modeling is not appropriate. Furtherm ore, super
lative index num bers, such as the discrete time
Divisia index, have known tracking ability only
un d er the assum ption of perfect certainty. In this
paper, we develop a dynamic approach to supplyside m onetary aggregation under uncertainty.
Historically, the literature on financial inter
mediation has produced many diverse models,
often linked only weakly w ith neoclassical eco
nomic theory and having various objectives. The
early view of the creation of money by financial
firms, prim arily viewed to be banks, was the
deposit multiplier approach. By this theory in its
original form, the process of creating money is
simply determ ined by the reserve requirem ent
ratio. A nother approach is based upon the
Miller-Modigliani theorem , which asserts the
irrelevance of financial firm s to the real econo
my in a setting of a perfect capital m arket. In
recent years, many economists have questioned
the appropriateness of either of those two very
different propositions and attem pts have been
made to extend those theories by weakening the
underlying assumptions.
Another approach is based upon the capitalasset pricing model (CAPM). U nder the assum p
tions of th at model, either the financial firm’s
portfolio rate of re tu rn is normally distributed
or investors have a quadratic utility function de
fined over end-of-period wealth. Under either of
3The papers of Tobin (1961) and Brainard and Tobin (1963,
1968) were the first to argue forcefully for the use of micro
economics and equilibrium theory in modeling the financial
firm.
FE D ER A L RESERVE BANK O F ST. LOUIS
those assumptions, the financial firm ’s optimal
portfolio behavior can be represented by max
imizing utility over the portfolio’s expected rate
of retu rn and variance. This approach has been
useful in modeling the optimal portfolio allocation
decision conditionally upon the real resource in
puts, w hich are not explained endogenously.
A nother im portant approach is represented by
Diamond and Dybvig (1983). They apply tradi
tional consum ption-production theory and use
an intertem poral model subject to privately ob
served preference shocks to examine the equi
librium betw een banks and depositors. The
studies in this tradition have been successful in
explaining bank runs. However, banks, serving
solely as a production technology to depositors,
play only a passive role in that approach.
Another approach is represented by Hancock
(1985,1987), Barnett (1987), and Barnett, Hinich
and Weber (1986). They treat the financial inter
m ediary in the same m anner as a conventional
production unit and use neoclassical firm theory
to model a financial interm ediary’s production
of output services and employment of inputs
subject to the firm’s technological feasibility con
straint.3 This approach fully models the role
played by financial firms as producers of m one
tary services. Moreover, it provides the needed
tools to apply existing economic aggregation th e
ory to aggregation over financial firm s’ output
m onetary services, which comprise the econo
my’s inside money. However, those studies have
not developed a dynamic model of financial
firm s’ production u n d er uncertainty. This paper
provides that difficult extension of financial firm
modeling and output aggregation u n d er neoclas
sical assum ptions w ith dynamic risk.
With the theoretical model of a financial
firm's m onetary services production and the
derived exact theoretical output aggregate, we
estimate the model’s param eters and test for
weak separability of output services from factor
inputs. We then substitute the param eter esti
mates into the weakly separable output aggrega
tor function to generate the estim ated exact
supply-side m onetary aggregate.4 Tb this end,
we develop a procedure for testing weak
separability and for estimating the param eters
of a flexible functional form specification of
bank technology. The estimation is accomplished
“Diewert and Wales (1987) and Blackorby, Schworm and
Fisher (1986) have illustrated the difficulty of maintaining
flexibility, regularity and weak separability simultaneously.
135
through Hansen and Singleton's (1982) general
ized m ethod of m om ents approach to estimating
Euler equations.
O ur empirical results are based upon com
mercial banking data. Our evidence indicates
th at banks’ outputs are weakly separable from
factor inputs in the transform ation function.
Moreover, even under uncertainty, the Divisia in
dex provides a better approximation to the
estimated theoretical aggregate than does the
simple-sum or CE index.5 These findings support
the existence of a supply-side m onetary ag
gregate and the potential usefulness of the
Divisia index to aggregate over the weakly
separable m onetary assets on the supply side of
money markets. The result is a m easure of in
side money, in the sense of m onetary services
produced by private financial firms.
The paper proceeds as follows. In the next
section, we construct our theoretical model of
m onetary service production by financial firms
u n d er dynamic uncertainty. The model reduces
to a dynamic stochastic choice problem, for
w hich we derive the Euler equations. In the
third section, we present our approach to flexi
ble param etric specification, weak separability
testing and param eter estimation using Hansen
and Singleton’s (1982) generalized m ethod of mo
m ents estimation. The fourth section formulates
the empirical application using banking industry
data. The fifth section contains the empirical
results, including param eter estimates, weak
separability test results, the estimated theoretical
aggregate, and the comparison among index
num ber approximations to the estimated exact
aggregate, w here the index num bers considered
include the Divisia, simple-sum and CE indexes.
Section G brings together the dem and side with
the supply side to investigate the implications of
our model in general equilibrium. Section 7 pro
vides a graphical illustration of the errors-in-thevariables problem produced by the use of the
simple-sum index as a m easure of the m onetary
service flow. The final section presents a few
concluding rem arks.
5The formula for computing the Divisia index is in Barnett
(1980). Further details regarding the data sources used
with the index are in Thornton and Yue (1992), who also
provide instructions on downloading the data from the Fed
eral Reserve Bank of St. Louis’ public electronic bulletin
board, called FRED. The formula for computing the CE
(“currency equivalent” ) index is in Rotemberg, Driscoll and
Poterba (1991).
6See Barnett (1987).
7As used in this paper, portfolio is the sum of all
investments.
THEORETICAL MODEL
In this section, we derive our theoretical model
of m onetary services production by financial
firms under dynamic uncertainty. Consider a
financial firm which issues its own liabilities and
reinvests the borrow ed funds in prim ary finan
cial markets. In this process, real resources such
as labor, m aterials and capital are used as fac
tors of production in creating the services of
the produced liabilities. Those produced liabili
ties are deposit accounts providing m onetary
service combinations that would not have exist
ed in the economy w ithout the financial firm.
The liabilities of the financial firms include, for
example, dem and deposits and passbook ac
counts, and are assets to the depositors. The
value added through the creation of those assets
by a financial interm ediary is that firm ’s contri
bution to the economy’s inside money services.
W ithout the existence of financial firms and the
accounts that they create, investors in money
m arkets would be limited to the use of prim ary
money-market securities as the short m aturity
assets in their portfolios. While the produced
liabilities of financial firms may not appear to
be "outputs” to an accountant looking at the
firm’s balance sheet, the produced liabilities of
financial firm s are the outputs of the firm s’
production technologies.6
The financial firm ’s profits are made from the
interest rate spread betw een the financial firm ’s
financial assets (loans) and the firm’s produced
liabilities. That spread m ust exceed the real
resource costs, in order for the firm to profit
from its operation. Let Yt be the real balances of
the financial firm ’s asset (loan) portfolio during
period t.7 Let Rt be the portfolio rate of return,
which is unknow n at the beginning of each
period. Financial firms also hold excess reserves
in the form of cash, which has a nominal
retu rn of zero. The real balance of cash holding
is Cr Let y Hbe real balances in the firm ’s z'th
produced account type and hit be holding cost
per dollar for that liability, w here i= l, ...,/.8 The
am ount of the jth real resource used is zjt, and
8The holding cost h:, is defined as hit = rjt + R tk jt. In this for
mula, rit is the account’s net interest rate, which is defined
such that all the benefits (for example, service charges)
and costs (for example, deposit insurance) generated by
the borrowed funds have been factored into the interest
rate, and R fa is the implicit tax rate on the financial firm
from the existence of a reserve requirement on that ac
count type. Required reserves are assumed to yield no
interest and hence, produce an opportunity cost to the
financial firm, since the firm otherwise could have invested
the required reserves at a positive rate of return.
MARCH/APRIL 1994
136
its price is w y where
Let Pt be the
general price index, which is used to deflate
nominal to real units. All financial transactions
are contracted at the beginning of each period,
b u t interest is paid or received at the end of the
period. The cost of employing resource zjt is
paid at the start of the period.
The firm ’s variable profit at the beginning of
period t in accordance w ith Hancock’s (1991,
equation 3.1) formula, is
(1) tt, = (1+fl.j yt_p|_ - y I
1 1 pI+cf. 1 1- c (
pt.
pt
+
iP r J
i-i
" S
j-i
W jtZr
The first two term s in equation 1 represent the
net cash flow generated from rolling over the
loan portfolio during period t. The third and
fourth term s represent the change in the nom i
nal value of excess reserves. The fifth term is
the net cash flow from issuing produced finan
cial liabilities. The last term is total payments for
real resource inputs.
Portfolio Yt investment, however, is constrained
by total available funds, under the assumption
that all earnings are paid out as dividends. The
relationship is
(2) Y,P, = £
( l -k„) y f . - C f i - t ,
i-l
(4) Max £ ,[ f ] (— )'"M 7 rs)|
- f 1+M
s.t. Q(yl s y Is, Cs, z ls,..„ z js) = 0
V s > t,
w here Et denotes expectation conditional on the
information known at time t, /t is the subjective
rate of time preference and is assum ed to be
constant, U is the utility function, irs is the vari
able profit at period s given by equation 3, and
Q is the firm’s transform ation function, defining
the firm ’s efficient production technology from
(5) Q(yl s
y ls, Cs,
z j =0 V s> t.
In accordance with the usual properties of a
neoclassical transform ation function, Q is con
vex in its argum ents. In addition, the inputs are
distinguished from the outputs by the inequality
constraints:9
(6) A Q <o, AQ. < o v ; = 1 ,..., J
dC,
dzj,
and
(7)
7-1
w here kit is the reserve requirem ent ratio for
the i'th produced account type, with 0 < kjt < 1.
Rearranging, equation 2 can be seen to state
I
that total deposits
y itPit are allocated to
1= 1
required reserves, excess reserves, investment in
loans, and payments for all real resource inputs.
Substituting 2 into 1 to eliminate Yt, we obtain
the firm’s profit function subject to its balance
sheet constraint:
(3) 7 , = 2
T
subject to the firm’s technology. We fu rth e r as
sume the financial firm ’s intertem poral utility
function is additively separable. Then, the firm’s
maximization problem can be expressed by the
following dynamic choice problem:
{[<!+*,_.)
> o V (= 1 ,..., /.
dy„
We also assum e that Q is continuous and
second-order differentiable.
Substituting equation 3 into 4, we have
(8) Max £, [ | ] (—
r 'u i j ^ H d + R ^ t t - k .'j
=
i 1
s =t
+ky A }
- ^ - iC .- i^ - i- S
j-1
+
s.t. Q(yls ,..., y Is, Cs, z u
W j, r - l Z>, - l ' )
z j = 0 V s > f.
1-1
- < V i )]> V ipt- i+ W
1+
-
n . - A - A - l - T ,
(l+ « ,-l)
,I}
w j, t - 1 z j,
(-1 •
y-1
We assume the financial firm chooses the level
of borrow ed funds, excess reserves, and real
resource inputs to maximize its expected dis
counted intertem poral utility of variable profits,
9See Barnett (1987), Hall (1973) and Diewert (1973).
FE D ER A L RESERVE BANK O F ST. LOUIS
We now proceed to derive the Euler equations,
comprising the first-order conditions, for this
stochastic optimal control problem. We use
Bellman’s method. To do so, we m ust put the de
cision into Bellman’s form, w hich requires iden
tifying the state and control variables and
determ ining that the decision, stated in term s of
those variables, is in the form providing known
Euler equation structure.
137
We assume that the financial firm behaves
competitively, so that the prices his_t and w _1
are taken as given by the firm. In addition, hjs l
and wjs_j are nonstochastic, since they are lagged
one period. From the same perfect competition
assumption, it follows that Rs, k.s, and P are
random processes that are not controllable by
the firm. We select as state variables during
period s: y. , V i, z , V /. C ,, R „ R , k , h ,
V i. w. - 1 V j. P —1 and P . We choose yIS V i and
,
„
7
zjs V j to be the control variables during period s.
1
J
l,S - l
J ,S
7
J '
J ,S - 1
J '
s
s —1
s —1
s
s'
is '
1,S —1
J
Define w to be the vector of all of the state
variables, and define us to be the vector of all
control variables. Let A be the subset of state
variables defined by A = (R . k . h
, V i, w ,
V j,Ps). We assume that As follows a first-order
Markov process, w ith transitions governed by
the conditional distribution function F(As+1|As).
Hence, the transition equation for state variables
(R „ R , k , h , V i, w. , V P , P ) is implicitly defined by F(As+1|As). The transition
equations for y.s l V / and zjs_1 V j are the trivial
identities
s
s
J
S —1
s'
is '
1 ,8 - 1
S
7
J ,s - 1
sr
j '
is
S - l7
1 ,8 - 1
7
J ,S - 1
is implicitly determ ined by the transform ation
function 5.
The objective function in equation 8 is an in
finite summ ation of discounted utilities of varia
ble profits, starting at period t. Recalling the
time shifts appearing in our definition of the
state and control variables during period s, we
see th at the discounted utility of variable profit
at period s depends only on that period's state
variables and control variables. By examining the
transition equations, it is evident that each state
variable is a function of only previous controls
and not of previous values of the states. In p a r
ticular, if we let g represent the vector of all
transition functions, we can rew rite the dynamic
decision problem as
Ma*- E, [ £
S-t-
UJ1 i
1+ M
+ = g<UJ ' S ^ L
1
S
0) y> = y,v v s
This dynamic problem m eets all of the condi
tions to be a recursive problem in the Bellman
form. Using Bellman’s principle, we can derive
the first-order conditions for solving the dynam
ic problem 8. The Bellman recursive equation
and
(10) zjs = zy
V
s.
The role played by these two equations in our
application of Bellman’s m ethod follows from the
fact that each of the variables in equations 9
and 10 are included both among the control
and state variables, although w ith a time shift
distinguishing them in each of their roles.10
Hence, with the appropriate time shift in the
subscript, equations 9 and 10 can be viewed
as connecting together some of the control and
state variables. This connection accounts for the
function of those equations as transition equa
tions. In particular, the left-hand sides can be
identified as next-period state variables, while
the right-hand sides can be identified as currentperiod control variables. Hence, each of those
equations can be interpreted as defining the
evolution of a state variable conditionally on a
control variable. The transition equation for Cs l
v ( » r ()
=
m a x
E t [ U l i r t( w t, u , ) ]
+
v(w l+l) | wt, s.t. w l+ = g(u,)),
1
1+ M
w here v(»r() is the optimized value of the objec
tive function.
The first-order conditions for the Bellman
equation are
11
11
L r
37 (
’ Iatt
+ -f - 1 H
l +H out
owt
K J
I
‘
= o.
The functional form of v is unknown. However,
since
=Q we can use the Benveniste and
3 iv.
10The use of such trivial identities as transition equations
(laws of motion) in optimal control and dynamic program
ming is not unusual. For example, it is common in optimal
growth models to define current capital stock to be a state
variable, while next period’s capital stock is defined to be a
control, with those state and control variables tied together
by a trivial identity. The nontrivial dynamics is found in the
objective function of such models. See, for example, Sar
gent (1987, p. 24).
MARCH/APRIL 1994
138
Scheinkman equations to eliminate ^2L.(wl+
1)}1
dw t
The general form of the Benveniste and
[irt:
Scheinkman equations is
dv , .
dU , > 3 tt
a—, {w'] = Io-7 , (7r< ^ — {w'' u ‘]
aw
T ) 9
a§'
(«V M
,)
1+ M
K j]-
Since d g ' = 0, the above equation implies
3 »v.
, , o1
3v
,
4
3(7 ,
,
fies the relevent theoretical regularity conditions
w hen the domain of U(7r() is constrained to
37T,
— irt+d > 0 j with h constrained to satisfy
h > 0. W hen p > 1, absolute risk aversion (ArrowPratt) is decreasing, and w hen p > l , absolute
risk aversion is increasing. The power utility
function special case is very widely used. Since
that functional form exhibits constant relative
risk aversion (CRRA), the pow er utility function
often is called the CRRA or isoelastic case.13
Differentiating (14) w ith 7r(, we get
(12) — (»v,) = — (7 — JL (w,, Ut).
r,)
OH'
07T
OIV
(15) — = h
dir;
l-p
Substituting 12 into 11, we get
Using equations 13 and 15 along w ith the de
fined state variables, control variables and tra n
sition equations, we obtain
3 i ,) 9
<
>
(13) E, —U (7T\ —w>(»V„ U,)
07Tf
01^
! 3g'
3(7
T— T — (“ ,) T - < 0
1 + fu 3u,
37T(
0 7,
T
in',f+l' U, J I " 'J = °-
(16) E,{Ptkit { h
l-p
w here p, h and d are three param eters to be
estimated. The following useful utility functions
are fully nested special cases of the HARA
class:1
2
'
\
+d)P~'
+ p ~ ~ w +fi,) (i-fc,)-(i+ /i„)
l+M
+
A very general specification of utility to
represent risk is the hyperbolic absolute risk
aversion (HARA) class, defined by
____ T -d)P
(14) U(ir) = 1 - P v h 7 , H ,
P 'l - p
tt +d)P
= 0
V y.,
and
r
3 Q /3 z
h
o-i
(17) EU’Ji.
" ( - 2 - 7 +d f
T
'I ' '3Q /3C , l - p
,+1
- (l + fl,)vv,
= 0
^ 7 I+ +d)P_1
T1
l-p
V z , j =1
J.
a. risk neutrality: p = 1, U(7r,) = /j7rt,
b. quadratic: p = 2, U
(,Trt) = -(1/2) (-fi7r, + d)2
,
c. negative exponential: p = -oo and d= 1,
U(irt)= - e - hr',
d. power: d=0 and p < 1, (7<7r() = (7rf/p),
e. logarithmic: d = p =0, U(tt) = log irr
The general HARA specification for LKtt) satis
" S e e Sargent (1987) for an excellent presentation of dynamic programming.
12See Ingersoll (1987, pp. 37-40). In case (d) below, imposing
the restriction d = 0 alone on equation 14 will not produce
the exact form provided for the power function. However,
the form acquired subject to that sole restriction is a posi
tive affine transformation of the power function. Hence both
forms represent the same risk behavior.
FEDERAL RESERVE BANK OF ST. LOUIS
Equations 16 and 17 are a system of I+J
nonlinear equations. Theoretically, from 16 and
17 plus the transform ation function 5, we
could solve for {Yu, ■■ y„f C„
■)
z Jt).
However, in practice the solution could be
produced only numerically, since a closed
form algebraic solution rarely exists for such
Euler equations.
13See, for example, Barnett and Yue (1991).
139
In the following discussion, w e extend the
dynamic decision 8 into the m ore general case
incorporating learning by doing technological
change. In the econom etric literature on es
timating returns to scale in manufacturing,
increasing returns to scale usually are found,
despite the fact that increasing returns to scale
violates the second-order conditions fo r profit
maximization. W e believe that a likely source o f
this paradox is the potential to confound techno
logical change w ith returns to scale, w hen
learning by doing technological change exists
but is not incorporated within one’s model.
Let y t be the vector o f y it fo r all i and z ( be
the vector o f zJt fo r all j. We then w rite the
maximization problem as
(18) May.
e \Y\
VjLj.
1+ u
s .t. Q (y ^ Cy z ^ j V j )
= 0
V s > t.
The appearance o f y s_1 in the transformation
function represents learning by doing. Firm
technology improves through experience.
At the present stage o f this research, w e are
not using the learning by doing extension o f our
model in our empirical work, so w e only pro
vide the Euler equations below, without supply
ing the details o f the derivation. Those Euler
equations under learning by doing are
3 7(
T
(7r() ^
(w , u )
(19) E t{
ay,
1
+
rd U ,
Tqi ‘ a i ; 3
4 9lr,
,
3 T 7
1
d C l/d y^
TTm
d O / a c~
",
dU
,+i'
dir,
dir.
K + * ut J
1 2 dC.
+
3Q /dyt ,
,3 [/ ,
,
---—
----- L (Wt, U,) ---- w ,)
T
'
dCl/dC.
' dir.
11
+
dir,
a c,
-
K
+ i'
“
m
W
=
0
*y,
14While the risk-neutral case is acquired directly by making
those substitutions in the original decision problem, the
resulting Euler equations are not acquired simply by mak
ing those substitutions in the risk-averse Euler equations,
16 and 17. The reason is that a cancellation within the
Euler equations that is produced when the rate of discount
is the constant, n, does not apply when the rate of dis
count becomes the variable, Rt. In particular, after replac
ing p with 1.0, and ^ with Rt, it also is necessary to
multiply the two terms within equation 17 by 1/(1 +Rt) to get
the risk neutral case Euler equations. No such adjust
and
(20) E,
O
TTt
(ir,) ^
(w t, u )
OZ{
1
fd U ,
, dir
+ - — h - (7
r-+.’ ^ — (yv'^> u< )
+i
1 + / oirt
^
" z ,_i
3 Cl/d C.
dir,
dir,
~
3 C,
u ,J l) = O
Vz,
Equations 19 and 20 are generalizations o f
(16) and (17). If learning by doing is excluded by
imposing dCl/dyt^ = 0, then (19) and (20) reduce
to (16) and (17), respectively. In the rest o f the
current paper, w e return to the special case o f
no technological change.
A further nested special case is also interest
ing. W e acquire risk neutrality by setting p = 1.
As is conventional under risk neutrality, dis
counting is acquired objectively by replacing the
subjective rate o f time discount, /*, by Rt}4 One
reason fo r interest in that special case is that, in
general equilibrium theory, the assumption o f
complete contingent claims markets combined
with perfect competition can be shown, under
certain additional assumptions, to produce the
conclusion that firm s w ill be risk neutral, even
if their owners are risk-averse. The risk aversion
o f the owners then is captured within the
contingent claims prices, which are taken as
given by the firm s’ managers under perfect
competition.1
5
W hile this theoretical issue is interesting, w e
do not consider it alone to be a convincing rea
son to impose risk neutrality on the manage
ment o f an industry that behaves in a manner
exhibiting clear risk aversion. However, w e are
interested in that fact that the Divisia index,
along with virtually all o f the literature on index
number theory, is produced under the assump
tion o f perfect certainty. This fact would suggest
that the tracking ability o f such index numbers
may degrade as the level o f risk aversion inment is needed within equation 16, since no relevant fac
tors cancelled out in the derivation of equation 16. This
observation also is relevant to the risk-neutral Euler equa
tions 80 and 81 below.
15See, for example, Debreu (1959, ch. 7) and Duffie (1991,
section 6.3). Regarding the complications produced by in
complete markets, see Magill and Shafer (1991, section 4).
MARCH/APRIL 1994
140
creases. Hence, w e produce results both with
and without risk neutrality imposed, as a means
o f exploring the extent to which the tracking
ability o f index numbers is degraded in the risk
averse case relative to the risk-neutral case.
Under risk neturality, our Euler equations
reduce to1
6
R f X - k } - r.(
(19') e [ p , ~ v ~
----- -a + P , ------------------ 1
r ) E\P, ~
l + R.
' l + R, dCl/dC)
V yit,
and
(20') Et[p,
R,
dCl/d z,,
l+R ao/ac.
- wj = 0
V zjt, j = l J .
The assumption o f perfect competition is itself
sufficient fo r the existence o f a representative
firm . See Debreau 1959, p. 45, result 1. Hence,
the theory acquired from our model can be
applied w ith data aggregated over banks.1
7
SUPPLY-SIDE MONETARY
AGGREGATION AND A WEAK
SEPARABILITY TEST
Having form ulated our dynamic model o f
financial firm production under uncertainty and
having derived the Euler equations, w e can pro
ceed to investigate the exact supply-side m one
tary aggregates that are generated, if the firm ’s
output m onetary services are weakly separable
from inputs.
Supply-Side Aggregation
Most m oney in m odern economies is inside
money, which is simultaneously an asset and a
liability o f the private sector. Inside m oney pro
vides net positive services to the economy, as a
result o f the value added that is created by the
'^Observe that only one time subscript exists in the riskneutral Euler equations, so that the solution becomes stat
ic. Once the nonlinear utility function has been removed
from the objective function, the terms with common time
subscripts can be grouped together. However, under risk
aversion, even under our assumption of intertemporal
strong separability, more than one time subscript exists wi
thin the utility function for each time period, since both
current and lagged t appear as subscripts in equation 3
for each value of profit, r t . Hence, the dynamics found wi
thin the objective function of equation 4 cannot be re
moved by regrouping terms.
17ln fact, Debreu’s theorem can be used to aggregate over
all firms of all types in the economy to produce the ag
gregated technology of the country. The representative firm
maximizes profits subject to that aggregated technology.
However, we use the theorem only to aggregate over the
RESERVE BANK OF ST. LOUIS
FEDERAL
financial intermediation that produces the inside
money. In our model, the borrow ed funds that
are outputs produced by financial intermediaries
are inside money. Inside money may take vari
ous form s such as demand deposits, interestbearing checking accounts, small time deposits,
and checkable money market deposit accounts.
The sum o f the dollar value in such accounts
does not measure the services o f inside money,
any m ore than the sum o f subway trains and
roller skates measures transportation services,
since the components o f the aggregate are not
perfect substitutes. The aggregation-theoretic
exact quantity aggregate does, however, measure
the service flow.1
8
Th e procedures involved in identifying and
generating the exact quantity aggregates o f
microeconomic theory are described in detail
by Barnett (1980). The approach necessarily
involves tw o steps: identification o f the com po
nents over w hich exact aggregation is admissible
and determination o f the aggregator function de
fined over those components. The first step de
termines w hether or not an exact aggregate
exists, and the second step creates the exact ag
gregate that is consistent w ith m icroeconom ic
theory. The second step cannot be applied
unless the first step succeeds in identifying a
component cluster that satisfies the existence
condition. That existence condition, which is the
basis fo r the first stage clustering o f com po
nents, is blockwise weak separability. In accor
dance w ith the definition o f weak separability, a
blocking o f components is admissible if and only
if the goods in the block can be factored out
o f the structure o f an econom y through a sub
function. In other words, it must be possible to
formulate the economic structure in the form
o f a composite function, w ith the goods in the
cluster being the sole variables entering into the
inner function o f the structure. I f that condition
firms in one industry. It should be observed that the ease
of aggregation over firms under perfect competition is in
marked contrast with the complexity of the theorems on
aggregating over consumers.
18See, for example, Blackorby, Schworm and Fisher (1986)
regarding the importance of using appropriately aggregated
output data from firms.
141
is satisfied, an exact quantity aggregate exists
over the goods in the cluster and the aggregator
function that produces the exact aggregate over
those goods is the inner function within the
composite function.
Let y = {y ll,...,y iy and * = (C(, z lt,...,z Jt)' w here y
is the vector o f the firm ’s outputs and x is the
vector o f the firm ’s inputs. The transformation
function becomes
Q (y,*)= 0 .
An exact supply-side aggregator exists over all o f
the elements o f y if and only if y is weakly
separable from x within the structure o f Q.
Mathematically, that statement is equivalent to
the existence o f tw o functions H and y 0 such
that
Q(y,x)=H(y0
(y),x),
w here y 0
(y) is a convex function o f y.ia In aggre
gation th eory y 0(y) is called the output aggrega
tor function. Furthermore, suppose that y0(y ) is
linearly homogeneous in y. Under this assump
tion, if each y. grows at the same common rate,
the theoretical aggregate y n
(y) w ill grow at that
rate. Clearly, without that condition, y 0(y) could
not serve as a reasonable aggregate.2
0
As shown by Leontief (1947a, 1947b), the
weak separability condition is equivalent to
(2 1 )
= 0 f o r a ll k.
d?ck dQ(y,x)/dy.'
If a subset o f the components o f y w ere weakly
separable from all o f the other variables in Q,
then an exact output aggregate would exist only
over the services o f that subset o f components
and not over the services o f all outputs. I f w e
can test fo r the separability structure o f the
transformation function and acquire the func
tional form o f y 0
(y), when y is weakly separable
from x, then w e could estimate the parameters
o f y 0(y) to acquire an econom etric estimate o f
the exact output aggregate.
,9See Barnett (1987).
“ Without linear homogeneity of y0, the exact aggregate
would become the distance function, rather than y0, and
would reduce to y0, only under linear homogeneity of y0.
We do not pursue that generalization in this study, but see
Barnett (1980) for details.
21The Divisia monetary aggregate index was introduced by
Barnett (1978, 1980). The simple-sum index is the tradition
al monetary index acquired by simply adding up the com
Although aggregation theory can provide us
with the tools to estimate the exact aggregator
function, the resulting aggregate is specification
and estimator dependent. Alternatively, the
literature on statistical index number theory
provides nonparametric approximations to aggre
gator functions w hen the existence o f the aggre
gator can be demonstrated through a weak
separability test. Statistical index numbers pro
vide only approximations to the theoretical ag
gregate, however, and w hen uncertainty exists,
little is known about the tracking ability o f
statistical index numbers as approximations to
the exact aggregates o f microeconomic theory.
In this paper w e consider the Divisia, simplesum and CE indexes to explore their abil
ities to track the econom etrically estimated exact
output aggregate.2 We produce our econometric
1
estimate o f the exact theoretical aggregate, fo r
comparison w ith the index numbers, by using
generalized method o f moments (GMM) estima
tion o f the parameters o f the Euler equations
under rational expectations. We do the GMM
estimation both under risk aversion and under
the imposition o f risk neutrality, to investigate
sensitivity o f our conclusions to risk aversion.
Flexibility, Regularity and Weak
Separability
In empirical applications, there are tw o w idely
used approaches to testing fo r the weak separa
bility condition that is necessary fo r economic
aggregation: the nonparametric, nonstochastic
approach based upon revealed preference and
the statistical, parametric approach.2 Since w e
2
are working from within a parametric specifica
tion, the conventional parametric approach to
testing the hypothesis is to be preferred. In fact,
w e shall see that weak separability w ill be a
strictly nested null hypothesis within our para
metric specification, and, hence, conventional
statistical testing is available immediately. In ad
dition, the nonparametric approach, at its cur
rent state o f development, is nonstochastic and,
hence, has unknown power.
ponent quantities without weights. The CE index is the cur
rency equivalence aggregate, originated by Rotemberg
(1991) and Rotemberg, Driscoll and Poterba (1991). For an
alternative interpretation of the CE index as an economic
monetary stock index connected with the Divisia service
flow, see Barnett (1991).
22See Swofford and Whitney (1987).
MARCH/APRIL 1994
142
Restrictive parametric specifications can bias
inferences. As a result, flexible functional form s
have been developed and are w idely used in
current studies. A flexible functional form,
by definition, has enough free parameters to
approximate locally to the second-order any
arbitrary function.2 However, using flexible
3
functional form s creates a new problem. These
models, unlike earlier, m ore restrictive models,
may not globally satisfy the regularity conditions
o f economic theory, including the monotonicity
and curvature conditions. It would be desirable
to be able to impose global theoretical regularity
on these models, but most o f the models in the
class o f flexible functional forms lose their flexi
bility property, w hen regularity is imposed.2 We
4
use a model that permits imposition o f regulari
ty, without compromise o f flexibility.
W hile flexibility and regularity are desirable in
any neoclassical empirical study, weak separabil
ity in some blocking o f the goods is also needed
to perm it aggregation over the goods in that block.
W e again are presented with the risk o f losing
flexibility by imposing a restriction, and in fact
imposing weak separability on many flexible
functional form s greatly damages the specifica
tions’ flexibility. For example, imposing weak
separability on the translog function does great
damage to its flexibility.2 Because o f the difficul
5
ties in imposing regularity and separability simul
taneously without damage to flexibility, parametric
tests o f w eak separability have been slow to ap
pear and have been applied only to the static,
perfect certainty case in which duality theory is
available. In our case o f dynamic uncertainty,
very little duality theory is currently available.
In this section, w e develop an approach that
permits testing and imposing blockwise weak
separability within a globally regular and locally
flexible transformation function that is arising
from a dynamic, stochastic choice problem. Our
approach uses D iew ert and Wales’ (1991) sym
23The flexibility here is sometimes called Diewert-flexible or
second-order flexible. See Diewert (1971). The flexibility ap
plies only locally. However, Gallant (1981, 1982) introduced
the Fourier semi-nonparametric functional form, which can
provide global flexibility asymptotically. Barnett, Geweke
and Wolfe (1991) have developed the alternative seminonparametric asymptotically ideal model (AIM), which is
globally flexible asymptotically and has advantages in
terms of regularity.
24See Gallant and Golub (1984), Lau (1978) and Diewert and
Wales (1987). However, if we can choose a model whose
regularity region contains the data, then the regularity will
be satisfied without imposing additional restrictions.
25See Blackorby, Primont and Russell (1977). Denny and
Fuss (1977) propose a partial solution to avoid destroying
FEDERAL RESERVE BANK OF ST. LOUIS
metric generalized McFadden functional form to
specify the technology o f the firm .2 In the dis
6
cussion to follow, w e first specify the m odel’s
form under the null hypothesis o f w eak separa
bility in outputs. W e then provide the m ore
general form o f the m odel that remains valid
without the imposition o f weak separability.
Using the notations defined previously, if y is
weakly separable from x, then
Q (y ,x)= H (y 0(y),x).
W e further assume that the transformation
function is linearly homogenous. Instead o f
specifying the form o f the full transformation
function Q directly and thereafter imposing
weak separability in y, w e impose weak separa
bility directly by specifying H(y0
,x) and y 0(y)
separately. W e acquire our weakly separable
form fo r Q by substituting y 0 (y) into H(y0
,x).
Since our specifications o f ytt(y) and H(y0,x) are
both flexible, it follows that our specification o f
Q is flexible, subject to the separability
restriction.
W e specify H to be the symmetric generalized
McFadden functional form
(22) Hty^x) = a(y ()+ a'x + - I y^ x ' ] A [^'] / a'x,
w ith a '*# 0 , w here a0, a '= (a i; ...,an and A
),
consist o f parameters to be estimated. The
matrix A is (n + l)x (n + l ) and symmetric. The
vector a'=(aj,...,an) is a fixed vector o f nonnegatvie constants.27 Th e division by a 'x in 22
makes H linearly homogeneous in y0 and XTb conform w ith the partitioning o f the vector
(y0
,*'), w e partition the matrix A as
w here A n is a scalar, A 1 is a l x n row vector,
2
flexibility. Their approach is to impose weak separability
conditions at a point. However, local weak separability is
not sufficient for the existence of a global aggregator
function.
26Diewert and Wales (1987) alternatively also developed the
generalized Barnett model. Although we have not used
that model in this study, the generalized Barnett model has
been applied to the analogous perfect-certainty case by
Barnett and Hahm (1994). Regarding the merits of the
generalized Barnett model in testing for weak separability,
also see Blackorby, Schworm and Fisher (1986).
27We use the term “ fixed constants” to designate constants
that the researchers can select a priori and treat as cons
tants during estimation.
143
A 2 is an n x l column vector, and A an nxn
1
symmetric matrix. Since A is symmetric, it fol
lows that A 12
=A'2V
Let (y*,;«*)#0 be the point about which the
functional form is locally flexible. That point is
selected by the researcher in advance, in a man
ner analogous to the selection o f the point
about which a Taylor series is expanded. Since
the transformation function is assumed to be
linearly homogeneous, the specification in the
above form is not parsimonious, and hence, w e
further can restrict the model without losing the
local flexibility property.2 We therefore impose
8
(23) a 'x * = 1,
(24) A ny * + A l2 * = 0,
x
and
(29) y0(y) = b y + ± y 'B y lp 'y ,
w ith the parameters satisfying
(30) p 'y * = 1,
(31) y * = b ’y*,
and
(32) B y * = Ow
w here b ’ = ( b t , ... ,bm and the m x m symmetric
),
matrix B consists o f parameters to be estimated,
p '= (p v -,p m is a fixed vector o f nonnegative
)
constants, and ^ * # 0 is the point at which local
flexibility o f equation 29 is maintained.
Substituting 29 into 28, w e get
(25) A ^ y * + A x * = On,
w here On is an n-dimensional vector o f zeros.
Under 23, 24 and 25, it can be verified that
the number o f free parameters in equation 22
equals the minimum number o f free parameters
needed to maintain flexibility.
Solving 24 and 25 fo r A n and A 12, w e have
(26) A ;2 = - Ax*/y0
*
(33) Q (y,*) = H{y0(y),x)
= a0 ( b 'y + - (p'y) y 'B y ) + a 'x
2
+ — (a ’x) x 'A x
2
~ (y *a 'x ) 1 * 'A x (b 'y + - (P 'y f 'y 'B y )
x
2
and
(y * 2 'x ) 1 * 'A x * (b 'y )
a
x
(27) A n = x * ’ x*/y*2.
A
Substituting 26 and 27 into 22 yields
(28)
(P 'y f 'y 'B y f ,
= afy n+ a 'x + ^ (a 'x) 'x 'A x
- (a 'x)~'x*'A x(yJy*)
+ - (a',*:) 1
x*'Ax*(yJy*f.
2
D iew ert and Wales (1987) have proved that
H(y0
,x), defined by equation 28, is flexible at
Oft**)In a similar w ay w e define y 0(y) to be
which is a flexible functional form fo r Q ^ ,* )
and satisfies weak separability in outputs.
Neoclassical curvature conditions require
Q(y,^) and y 0(y) to be convex functions, and neo
classical monotonicity requires d O J d y > 0 and
dCl/dx^O . D iew ert and Wales (1987), theorem
(10) have shown that H(y0
,x), defined by 28, and
v jy ), defined by 29, are globally convex if and
only if A and B are positive semidefinite.
28A flexible functional form is parsimonious if it has the mini
mum number of parameters needed to maintain flexibility.
Diewert and Wales (1988) have acquired the minimum
number of parameters needed to provide a second-order
approximation to an arbitrary function. If a specification for
an arbitrary function with n variables is flexible, it must
have at least 1+n+n(n+1)/2 independent parameters. In our
case, the linear homogeneity imposes 1+n extra con
straints on the first and second derivatives of H, so the
minimum number of parameters needed to acquire flexibili
ty is reduced by 1+n.
MARCH/APRIL 1994
144
For 0(y„*:) to be convex, w e further need
If w e evaluate these derivatives at (y * * * ), w e
have
a 0
,34)
dYu
(39)
If 34 holds, then Q(y,;t) is globally convex in
w hen H(yn,x) is convex in (y0
,*) and y 0(y ) is
convex in y .2
9
If the unconstrained estimates o f A and B are
not positive semidefinite symmetric matrices,
positive semidefiniteness can be imposed w ith
out destroying flexibility by the substitution
(35) A = q q '
and
30
W
.
“’b
and
(40)
dn
dx
= a.
Applying the method o f squaring technique,
w e impose on 39 and 40 the monotonicity
conditions3
1
(41)
90, *
j y (y * , X * ) = a „ b > 0
(36) B = u u '
w h ere q is a low er triangular n xn matrix and u
is a low er triangular m x m matrix.3 In estima
0
tion, w e replace A and B by low er triangular
matrixes q q ' and uu', so that the function 33 is
globally convex if 34 is true.
Monotonicity restrictions are difficult to im
pose globally. However, w e can impose local
monotonicity w ith simple restrictions. D ifferen
tiating 33 with respect to (y,*), w e get
(37) ^
= a0 [b + i (2(fi'y) 'B y - ( f t ’y ) 2 y 'B y )]
P
dy
2
- (v *a 'x )~ 'X* A x lb + - (2(/3'y)~'Bv
2
and ^ Q { y * ,x * )
=
a<0.
Equation 41 assures that the monotonicity condi
tions are satisfied locally at {y*,x *)•
We have shown that the functional form de
fined by equation 33 and restricted to satisfy
equations 23, 30-32, 34-36 and 41 is flexible,
locally monotone, and globally convex, provided
that the assumed weakly separable structure is
true. Although w e do not impose global m onoto
nicity, w e do check and confirm that m onotonic
ity is satisfied at each observation within our
data. In the following discussion, w e w ill define
a m ore general flexible functional form that
does not require weak separability.
- ( P ’y ) zp y 'B y )] + (y*za 'x f 'x * A x *
[b + i (2(P’y )~ 'B y -(P 'y )~ 2[)y 'B y )]
The number o f independent parameters in
equation 33 is
(b 'jr + I ( p 'y f 'y 'B y )
(42)
and
(38)
an
dx
a + - [2 (a'x) A x -(a'x ) otX'Ax1
£
.
n(n + l)
m (m -l)
l + n + -------- + m - l + --------- .
2
2
We know that the minimum number o f param
eters required to maintain flexibility fo r a linear
ly homogeneous function w ith n + m variables is
j
- [(y0 a 'x)
*
A x * - (y* a 'x ) \v*ax * 'Ax]
(43)
l + n+ m +
(n + m ) (n + m + 1)
(1 + n + m).
(b 'y + — (p 'y V 'y 'B y )
2
~ ~ (yTi2® '* ) V o * a,X * A x * ( b ' y
+ ^ (p 'y )~ 1 'B y ):
y
29See Diewert and Wales (1991) for the proof.
30See Lau (1978) and Diewert and Wales (1987).
3 See Lau (1978).
1
FEDERAL RESERVE BANK OF ST. LOUIS
Subtracting 42 from 43, w e get n (m - l), which is
the num ber o f additional parameters that must
be introduced into equation 33 to acquire
145
a flexible functional form fo r a general transfor
mation function. Let
(44)
Q (y,x) = H(ya(y),x) + c 'y + y 'C x / (y 'y +A'*),
w here y and A are vectors o f nonnegative fixed
constants, the vector c ’ = (c t,...,cm and the m xn
)
matrix C are new parameters to be estimated,
and the division by y 'y + A '* makes Q linearly
homogeneous. Because o f the linear hom ogenei
ty p rop erty w e have m ore free parameters than
needed fo r flexibility and, hence, w e can im
pose the following additional restrictions
without losing local flexibility:
c 'y * = 0,
(47) y * ’C = 0 'n
,
C x *= O m
,
(54) v (q 'x * ) = Om
,
and
(55) u 'y * = O m.
(56) 3 Q
3 7 = a«b + c
w here (y *,x*) is the point at which local flexibil
ity is maintained. Under equations 45-48, the
number o f new free parameters added into 44
is exactly equal to n (m -l). Diew ert and Wales
(1991) have proved that the function 44 is a
flexible functional form at (y *,**) fo r a general
nonseparable transformation function.
Global convexity is difficult to impose in this
case. However, w e can derive the restrictions fo r
local convexity at (y *,¥*). D eriving the Hes
sian matrix o f 44 and evaluating at (y * x * ), w e
have
and
(57) a o
dx
~ a'
As above, w e use the m ethod o f squaring to
impose nonnegativity on 56 and nonpositivity on
57. The estimated results then satisfy local
monotonicity.
Comparing 33 w ith 44, w e see that weak
separability o f outputs in 44 is equivalent to:
(58) H0 ' c = Om and v m x n = Om x n
(49) V 2 (y * * * ) =
Q
a0 + b b 'x * 'A x * /y*z C -b x * 'A / y *
B
C ' - A x * b'/y*
(53) y * 'v = 0 'n,
W e now turn to imposing local monotonicity.
Differentiating 44 with respect to (y,x) and
evaluating at (y*,jK*), w e have
and
(48)
Using 50-52, w e rew rite 47, 48 and 32 as
The function defined by 44 and satisfying
23, 30-31, 45-46 and 50-55 is a flexible function
al form fo r a general transformation function at
(y *jtr*). In addition, local convexity is satisfied.
(45) y'y* + A '** = l,
(46)
w h ere q and u are low er triangular matrices in
troduced fo r reasons described above, and v is
an unrestricted m xn matrix. Then V 2 (y *„**) is
Q
a positive semidefinite symmetric m atrix.3
2
A
J*
If V 2
Q(y*„*r*) is positive semidefinite, then
Q ^ * ^ .* ) js convex
(y * x *). Let
(50) A = q q ',
(51) C = vq',
and
(52) B = a - ‘ [v ir' + u u '],
Note that under the null hypothesis, H0, equa
tion 44 reduces to 33. Hence, y is weakly
separable from x if and only if H0 is true.
We have derived tw o flexible functional forms
with appropriate regularity properties. One
structure holds in the general case and the
other under the null hypothesis o f weak sep
arability. W e now are prepared to test weak
separability and to estimate the parameters o f
the transformation function. The basic tool is
Hansen and Singleton’s generalized m ethod o f
moments (GMM) estimator.
32See Lau (1978) and Diewert and Wales (1991).
MARCH/APRIL 1994
146
Substituting the functional form given by
either 33 or 44 into the Euler equations 16 and
17, w e obtain our structural model, which con
sists o f a system o f integral equations. A closed
form solution to such Euler equations rarely ex
ists. However, GMM permits estimating non
linear rational expectations models defined in
terms o f Euler equations. Hansen (1982) has
proved that under very weak conditions, the
GMM estimates are consistent and asymptotically
normally distributed.3
3
In the GMM fram ework, there are tw o methods
o f testing hypotheses.3 The first approach ap
4
plies Hansen’s asymptotic x2 statistic to test for
no overidentifying restrictions. We impose the
w eak separability restrictions 58 on the flexible
functional form 44, estimate the restricted sys
tem, and then run Hansen’s test fo r no overiden
tifying restrictions. Since 44 reduces to 33 after
imposing the weak separability restrictions, w e
can substitute equation 33 itself directly into the
Euler equations to impose the null fo r testing. If
the test o f no overidentifying restrictions is re
jected, then the restrictions imposed under the
null hypothesis are rejected, w here in our case
the null is the weakly separable structure im
posed on the transformation function.
The second approach to hypothesis testing
w ith GMM is based on the asymptotically n or
mal distribution o f the GMM parameter estima
tors. Let 6 be the vector o f parameters to be
estimated in equation 44. Then the GMM esti
m ator 6 has an asymptotically normal distribu
tion with mean 9 and covariance matrix 2.
Let r be an [n ( m - l ) ] x l vector w hich contains
all n ( m - 1) independent parameters in the vector
c and the matrix v. The hypothesis o f weak
separability can be rew ritten now as t = 0 or
equivalently as a set o f linear restrictions o f the
form
(59) S6 = t= 0 ,
w h ere S is an [n (m -l)]x [(n + m + l)/2] matrix
whose elements are all zeros and ones.
33Hansen (1982), Hansen and Singleton (1982), and Newey
and West (1987) provide a detailed discussion of GMM
estimation.
34See Mackinlay and Richardson (1991).
35Demand deposits consist of checking accounts, official
checks, money orders, treasury tax accounts and loan ac
counts. Time deposits consist of regular savings, money
market deposit accounts, other time accounts, retirement
accounts, and certificates of deposit under $100,000. Non
FEDERAL RESERVE BANK OF ST. LOUIS
From the known asymptotic distribution o f 6,
w e have
(60) \/f (Sd -SO ) 3 M O,SSS'),
w h ere T is the num ber o f observations. Under
the null hypothesis, H0: SQ = 0, w e have
V
f j 2 M O ,S Z S '.),
w here t
statistic
=
(61)
( V f t ) '[ S Z S '] 1 ( V r t )
<t> =
Sd. W e obtain the follow ing x 2
Although 2 is unknown, w e can replace it by a
consistent estimate without changing the asymp
totic results. The test is one sided, with the null
o f separability rejected if < is large.
t>
EMPIRICAL APPLICATION
Barnett and Hahm (1994), and Hancock (1985,
1987, 1991) have analyzed m onetary service
production by the banking industry in detail,
under the assumptions o f perfect certainty and
neoclassical joint production. The balance sheet
o f a bank consists o f fund-providing functions
and fund-using functions. The fund-providing
functions include demand deposits, time
deposits and nondeposit funds.3 The fund-using
5
functions include investment, real estate m ort
gage loans, installment loans, credit card loans
and industrial loans. In our theoretical model,
the sources o f funds are the firm ’s borrow ed
funds, and the uses o f funds are the firm ’s port
folio. The total available funds on the balance
sheet are total assets minus premises and other
assets.
On the average, demand deposits and time
deposits account fo r over 85 percent o f total
available funds. The equity capital included in
the non-deposit funds can be treated as a fixed
factor that does not enter the variable profit
deposit funds consist of equity capital, federal funds pur
chased, borrowed money, capital notes and debentures,
time deposits of $100,000 and over, other money market
instruments, and other liabilities.
147
function.3 For these reasons, w e only choose
6
demand deposits and time deposits as borrow ed
funds in our model. Tlirning to inputs, excess
reserves are total cash balances minus required
reserves. Other real resource inputs are labor,
materials and capital.3 Capital is treated as
7
fixed, and w e include only variable factors in
the transformation function. An obvious direc
tion fo r possible future extension o f this
research would be the incorporation o f some or
all capital as variable factors to produce in fer
ences applicable to a longer run perspective
than that implicit in our definition o f variable
and fixed factors.
Using equations 16 and 17, the Euler equa
tions are
(62) E, iP ,k J T = p » , + d )p-1
w here D t is demand deposits, T t is time deposits,
L t is labor input, M ( is materials input, and wlt
and w2 are the prices o f labor and materials
t
respectively.
Using the notations in section three, w e can
w rite
y '= ( D ;,T,) and x '= (C t,L t,M t).
If the weakly separable structure o f the trans
form ation function is true, then equation 33 is
the transformation function. As discussed in sec
tion three, the weak separability hypothesis can
be tested by applying Hansen’s %2 statistic.
The derivatives o f O w ith respect to its argu
ments are given by equations 37 and 38. The
fixed constants and the center o f the local ap
proximation need to be selected before estima
tion. We choose
/0 =1, y * '= ( 1,1), and **'=(1,1,1)
+ P ,U ^ [{1 + R, ) {1~ ku ] ~ (1 + /,1.)
0 30/3D,, , h
+ R,
'
,p-k n
—=------ ----------7T . + d) 1= 0,
3 0 / 3 C
,
-p
1
,+ 1
(63) E, [P ,k J 1Z p * t+ d )P~l
+P
.
„
(64)
30/3T, . h
,,P-u „
f (— 7
r(+1+ d )p }= o ,
' SO/3C, l - p
' ' 3 0/3 C,
- ( 1 + R ,)w «] ^
* l+i +d )P ~'}= 0,
/X
-
V i = l, 2, 3 and
E, j [ pR 3 0 / 3 M,
' ' 3 0/3 C,
36See Barnett (1987). Equity capital includes preferred and
common stocks, surplus, undivided profits and reserves,
and valuation reserves.
2,
w here t* represents the midpoint observation.3
8
We correspondingly rescale each price by mul
tiplication by the midpoint observation. That
rescaling o f prices keeps dollar expenditures on
each good unaffected by the rescaling o f its
quantity.
We select the fixed nonnegative constants a.
and / . such that
?
(67) a = |^|/£] |^|
y-i
and
and
(65)
(66)
y,=y\/y- v /=i,
1
[p R 3 0/3 L t
"
as the center o f approximation. To locate that
center within the interior o f the observations,
w e rescale the data about the midpoint obser
vation
V i = l , 2, 3
(68) pi = l ^ l / J |^|
V 1 1, 2,
=
j-1
w here £ and y are the sample means o f £ and y
respectively. Note that a. and
satisfy equations
23 and 30, as is required. W ith our data sam-
38The data point at which all quantities are set to unity can
be arbitrary,
37Labor includes managerial labor and nonmanagerial labor.
Materials include stationery, printing and supplies, tele
phone, telegraph, postage, freight and delivery.
MARCH/APRIL 1994
148
pie, w e find a^=0.33, a, = 0.35, a^ = 0.32, ^ = 0 .5 8 ,
and p., = 0.42.
Before estimating the independent parameters,
w e need only impose the inequality restrictions.
Equation 31 implies b2= l - 6 , , and the monoto
nicity condition (41) requires b > 0. Hence, it
also follows that b <2. Combining these condi
tions, w e can replace b1 and b2 by
(69) bj = sin'(^) and b., = cos'C^)
and estimate
ize a0= l.
Since
= 0, w e also normal
The monotonicity condition 41 requires
ai < 0, which w e impose by replacing a, by
- a f V i= l,2 ,3 , w here
V i= l,2 ,3 , are the new
parameters to be estimated. The convexity con
ditions are imposed by replacing A and B by
the low er triangular matrices q q ' and u u '
respectively, w here q and u are
EMPIRICAL RESULTS
0
^21 ^22 0
.^ 1 ^32 *? 3
3
3
<„ 0
7
and
n =
U„ 0
Equation 32 implies
(70)
u„ 0
0
11,
Solving 70, w e get u2 = - u n and u = 0. Sub
]
.lz
stituting them into equation 36, w e have
(71) B = u~
The prim ary data source is the Federal Reserve’s
Functional Cost Analysis (FCA).3 W e got our
9
data from the Federal Reserve Bank o f St. Louis.
The data used are the National Average FCA
Report, which contains annual data from 1966
to 1990. Hence, there are a total o f 25 observa
tions in our annual data. Monthly data is not
available from the FCA. From the FCA, w e ac
quired banks’ portfolio rate o f return, the net
interest rates on demand deposits and time
deposits, and the nominal quantity o f demand
deposits, time deposits and cash balances.4 The
0
prices and quantities o f labor and materials are
aggregate producer prices and quantity indexes
from the data in the FCA Report and the Survey
o f Current Business.4 The required reserve ratio
1
is from the Federal Reserve Bulletin. The implicit
price deflator is the implicit GNP deflator from
the Citibank data base. W e deflate the nominal
dollar balances o f all financial goods to convert
them into real balances.
1 -1
-1
U
The above discussion identifies all the in
dependent parameters to be estimated in the
specification o f the transformation function.
They are
un, the low er triangular matrix q,
and the vector a '= (a 1 ,a3
,a2 ).
39The Functional Cost Analysis program is a cooperative
venture between the Federal Reserve Banks and the par
ticipating banks. This program is designed to assist a par
ticipating bank in increasing overall bank earnings as well
as to improve the operational efficiency of each bank
function.
40The net interest rate equals the interest paid minus service
charges earned plus FDIC insurance premiums paid.
41See Barnett and Hahm (1994) for a detailed discussion
about the aggregation of labor and material.
FEDERAL RESERVE BANK OF ST. LOUIS
We use the GMM estimator in the TSP main
fram e version (version 4.2) to estimate our
model. In the disturbances w e allow fo r condi
tional heteroskedasticity and second-order
moving average serial correlation. Using the
spectral density kernels in TSP, our estimated
results are robust to heteroskedasticity, auto
correlation and positive semidefinite weighting
matrix. To use the GMM method, instrumental
variables must be selected. We choose as instru
ments the constant, the federal funds rate, the
discount w indow rate, the composite bond rate
(maturities over 10 years), the holding cost o f
demand deposits and time deposits, the lagged
banks’ portfolio rate o f return, excess cash
reserves, and capital. In estimation, w e replace h
by h2 to impose nonnegativity o f the resulting
h2. That nonnegativity is needed fo r regularity
in the definition o f the H ARA class.
The GMM parameter estimates, subject to
imposition o f weak separability o f outputs from
inputs, are reported in Table 1. A ll three para
meters in the utility function are statistically
149
Table 1
GMM Estimates Using the HARA Utility Function with Weak
Separability in Outputs Imposed_________________________
Param eter
h2
p- 1
d
M+ 1
k
U11
9n
921
931
922
932
933
!1
a2
®3
Estimate
Standard error
0.003
2.330
0.001
1.090
58.382
0.232
0.186
0.418
0.105
0.477
0.120
0.116
0.323
0.436
0.280
0.122
25.625
0.0 44
0.1 6 5
0.201
0.4 18
0.0 78
0.1 0 6
0.0 48
0.101
0 .1 6 2
0 .5 0 5
0 .0 3 5
0.0 58
0.0 38
insignificant at the 5 percent level. As a result
o f the very low precision o f those three para
m eter estimates, it is clear that w e have in
troduced risk aversion in a manner incorporating
too many parameters fo r the available sample
size. Hence, w e need to restrict HARA to one o f
its less deeply param eterized special cases. As
observed in the second section, the HARA class
reduces to the popular pow er (CRRA isoelastic)
utility function. We now test w hether that popu
lar special case is accepted.
Equation (61) in the third section provides a
statistic to test that a set o f parameters is jointly
equal to zeros. W hen the set o f parameters in
cludes only one element, the x2 test statistic 0,
given by equation (61), equals the number o f ob
servations multiplied by the square o f the
t-statistic o f that parameter. We calculated that
0=0.0033, w hile the critical value is 6.635 at
the one percent significance level. Hence, w e
cannot reject d=0, and the pow er utility func
tion is accepted. W e reestimate the model using
that specification.
42Actually only the upper bound imposed on p is required by
theory. Hence, if we had found that the lower bound im
plied by our substitution was binding, we would have
switched to the more sophisticated substitution of 2 -co sh
(p) in place of p. But in practice our estimate of p was
strictly positive, so we did not have to resort to the in
troduction of hyperbolic functions. Furthermore, our imposi
tion of nonnegativity on ^ was equally as harmless, since
no corner solutions were acquired on that inequality res
triction either. In fact, in the HARA case, we did not im
pose nonnegativity on n at all, since we got nonnegativity
t-Statistic
0.024
0.091
0.012
6.602
290.459
0.555
2.372
3.931
2.178
4.725
0.743
0.230
9.117
7.523
7.448
To impose the inequality restriction 0 < p < 1,
which is sufficient fo r regularity o f the power
utility function special case, w e replace p by
sin2
(pi and estimate p. In addition, to prevent the
implausible possibility o f a negative subjective
rate o f time discount, w e replace n by Ji2 and
estimate jj..*2 The estimated results, subject to
imposition o f weak separability o f outputs from
inputs, are reported in 'Fable 2.4 All parameters
3
are significantly different from zero at the 5
percent level except fo r J un, and q3 . M onoto
i,
3
nicity is necessarily satisfied at
since
local monotonicity was imposed at that point.
W e use the estimated parameters to determine
w hether monotonicity is satisfied elsewhere in
the sample. Substituting the estimated param
eters into equations 37 and 38, w e find that
d Q / d y > 0 and 3 Q / 3 * < 0 everyw h ere in the
sample. Hence, no violations o f monotonicity oc
curred within the sample. Regarding curvature,
w e have imposed global convexity on H(y0 and
,x)
y 0(y). To verify global convexity o f Q (y,*), w e
must check equation 34 at each data point.
from our estimates without the need to impose it, and in
retrospect it is evident that we could have done the same
in the power utility case.
43The instrumental variables are the constant, the federal
funds rate, the discount window rate, the composite bond
rate (over 10 years), the three-month T-bill rate, the yields
on demand deposits and time deposits, the lagged bank’s
portfolio rate of return, and capital.
MARCH/APRIL 1994
150
Table 2
GMM Estimates Using the Power Utility Function with Weak
Separability in Outputs Imposed
Parameter
Estimate
Standard error
t-S tatistic
P
-524.629
0.351
60.692
0.171
0.240
0.461
0.103
0.418
0.093
-0.025
0.330
0.482
0.217
9.410
0.187
0.019
0.283
0.050
0.077
0.018
0.047
0.029
0.412
0.031
0.045
-55.754
1.877
3122.720
0.605
4.821
5.980
5.908
8.958
3.147
-0.062
10.762
10.607
10.836
\
U1
1
P11
Q21
Q31
Q22
Q32
P33
3
1
a2
S3
Differentiating H(y0,x) w ith respect to y0 w e get
,
(72) dH^
0.020
mated parameters and fixed constants into equa
tion 29 to get
X) = a 0-(a 'x V 'x *' Ax/y*
(74) y (D ,T ) = 0 .7 6 D + 0 .2 4 T + — [ 1 7
+ (a 'x f'x *'A x *y i/y *2
,
w h ere y0 is given by equation 29. Substituting
the estimated parameters into equation 72, w e
find that d H{y0
,x)l dy0> 0 at every data point.
Convexity o f Q is satisfied throughout the
sample.
The weak separability hypothesis is tested by
using Hansen’s yj test fo r no overidentifying
restrictions. His test statistic is
(73) < = T Q rx e_f ,
D
w here T is the number o f observations, Q is the
value o f the objective function, e is the number
o f orthogonal conditions, and / is the number o f
parameters estimated.4 The calculated statistic
4
is 27.6, w hile the critical value is 41.64 at the 1
percent significance level. We cannot reject the
w eak separability hypothesis. Hence, the exis
tence o f a theoretical monetary aggregate over
the outputs produced by banks is accepted.
Substituting the parameter estimate o f £ from
,
Thble 2 into equation 69, w e obtain b 1 = 0.76
and b2 = 0.24. The estimated theoretical ag
gregate then is acquired by substituting the esti
44The value of the objective function is defined as
0 = gN(9)'WNgH(d), where gN(d) is the sample mean of the
moment conditions and l/VN is the_ weighting matrix that
defines the metric in making gN (8) close to zero in the
GMM estimation procedure.
RESERVE BANK OF ST. LOUIS
FEDERAL
0 ' '
'
'2
----- 1
L.58D( + 0.42T(J
It is important to recognize that this aggregator
function should not be used fo r forecasting or
simulation outside the region o f the data, and
hence its usefulness is limited to research within
the sample. W hile w e have confirm ed m onoto
nicity within the region o f the data, this aggre
gator function is not globally regular fo r all
possible nonnegative values o f the variables out
side that region.
Having our econom etrically estimated theoreti
cal supply-side m onetary aggregate, w e now pro
ceed to investigate w hether any o f the w ell
known nonparametric statistical index numbers
can track the estimated exact aggregate ade
quately. By converting from p back to p and
then computing the degree o f relative risk aver
sion, 1 - p , w e find that the degree o f relative
risk aversion is l - . 0 7 = .93. Since risk neutrality
occurs only fo r zero values o f relative risk aver
sion, w e do not have risk neutrality. But there is
no currently available theory regarding the
tracking ability o f nonparametric statistical in
dex numbers w hen risk aversion exists. Hence,
our only m ethod o f investigating the tracking
151
ability o f the m ore easily computed nonparametric statistical indexes is to estimate the exact in
dex econometrically, as w e just have done, and
compare its behavior w ith that o f the statistical
index numbers.
In this paper, w e compare the estimated theo
retical aggregate w ith the Divisia, simple-sum
and CE indexes. Rotemberg, Driscoll and Poterba
(1991) have found that the growth rate o f the
CE index is very volatile w ith monthly data.
Hence, they have proposed (see their footnote
11) a m ethod o f smoothing that index’s growth
rates by replacing the index’s weights by 13month, centered moving averages. Since w e are
using annual data, there already is a form o f
smoothing implicit in the data construction.
Nevertheless, in addition to computing the annu
al contemporaneous CE index, w e compute the
smoothed index in accordance w ith the method
selected by Rotemberg, Driscoll and Poterba.
To parallel the 13-month centered movingaverage smoothing as closely as possible with
annual data, w e use a three-year centered m ov
ing average. In a sense, our results w ith uns
moothed annual data slightly undersmooths
relative to Rotemberg, Driscoll and Poterba’s
method, w hile the three-year centered moving
average oversmooths relative to Rotemberg, Dris
coll and Poterba’s method. Nevertheless, as w e
shall see, the CE index’s grow th rate remains too
volatile. A centered moving average is not de
fined at the start and end o f a sample. Hence, a
special m ethod is needed to phase in the cen
tered moving average at the start o f the sample
and phase it out at the end o f the period. For
that purpose, w e use the procedure advocated
by Rotemberg, Driscoll and Poterba. Figure 1
contains plots o f the levels o f all those ag
gregates. Figure 2 contains plots o f their growth
rates. W e also separately plot the grow th rate o f
each o f the fou r statistical index numbers (sim
ple sum, Divisia, unsmoothed CE and smoothed
CE), w ith the grow th rate o f the estimated theo
retical path superimposed. These plots are given
in Figures 3, 4, 5 and 6.
W hile no econom etric estimation is needed to
compute the Divisia index, it is important on the
supply side to incorporate the required reserves
implicit tax into the user cost formula, w hen
computing the Divisia output index. The usercost form ula is needed to compute the prices o f
m onetary services, since the Divisia quantity in
dex is a function o f prices as well as quantities.
On that subject, also see Barnett and Hahm
(1994), Barnett, Hinich and W eber (1986), Han
cock (1985, 1987, 1991) and Barnett (1987), w ho
derive and supply the user cost o f supplied
m onetary services, w hen required reserves yield
no interest. The resulting real user-cost price
fo r account type i is
(l-/c,) R ,-r „
(75)
=
1 + fi.
M l
1 + R.
(76)
w here r., is the ow n rate o f return defined in
it
footnote 8, and w here
(77)
=
R , - r it
1+ R.
Th e nominal user cost is P t ^ tjr The second
term on the right-hand side o f equation 76 is
the discounted implicit tax on banks resulting
from the nonpayment o f interest on required
reserves. Equation 77 is the same form as the
user-cost price paid on the demand side by
depositors, w h ere Rt is the benchmark yield on
a pure investment asset producing no services
other than its ow n yield, so that equation 77 is
the discounted foregone interest given up by the
depositor in return fo r the services provided by
asset type i.
Clearly the Divisia index tracks the theoretical
aggregate m ore accurately than any o f the other
tw o indexes. The smoothed and unsmoothed CE
index’s level paths are almost identical to each
other, as shown in Figure 1, despite the im
provem ent in the perform ance o f the CE index’s
growth rate plot after smoothing. Before 1972,
the Divisia and estimated theoretical index are
almost identical. A fter 1972, a small gap opens
betw een them.
The CE index almost always underestimates
the theoretical aggregate throughtout the sample
period, w ith the gap grow ing to be larger after
1980. The simple-sum index always overesti
mates the theoretical aggregate, w ith the gap
grow ing to be large and remaining large after
only a few years. In terms o f levels, the tracking
error o f the CE index is smaller than that o f the
simple-sum index, especially early in the same
period. However, the CE index is much more
volatile than the theoretical aggregate, especially
from 1979 to 1983. Comparing Figures 5 and 6,
w e see that the CE index w ith smoothed
weights is less volatile than the unsmoothed in-
MARCH/APRIL 1994
152
Figure 1
Levels of Five Monetary Aggregates (parameters of theoretical
monetary aggregate estimated with risk aversion permitted)
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1966
68
70
72
74
76
78
80
82
84
86
88
1990
Figure 2
Growth Rates of Five Monetary Aggregates (parameters
of theoretical monetary aggregate estimated with risk
aversion permitted)
0 .1 5 -i------------------------------------------------------------------------------------------------------------------- Estimated theoretical aggregate
----- Divisia index
Simple-sum index
CE index
Smoothed CE index, in which the weights
are three-year, centered moving averages
0.1
0.05
0
-0.05
-
0.1
-0.15
-
0.2
-0.25
T— I I— I— I— i— i— i— r
—
1966
68
70
FEDERAL RESERVE BANK OF ST. LOUIS
72
74
76
78
80
82
84
86
88
1990
153
Figure 3
Growth Rates of Theoretical Monetary Aggregate and Divisia
Index (with risk aversion permitted)
Figure 4
Growth Rates of Theoretical Monetary Aggregate and
Simple-Sum Index (with risk aversion permitted)
MARCH/APRIL 1994
154
Figure 5
Growth Rates of Theoretical Monetary Aggregate and CE Index
(with risk aversion permitted)
Figure 6
Growth Rates of Theoretical Monetary Aggregate and Smoothed
CE Index (with risk aversion permitted)
RESERVE BANK OF ST. LOUIS
FEDERAL
155
Table 3
GMM Estimates with Weak Separability in Outputs and Risk
Neutrality Imposed
Parameter
5
un
Q11
P21
Q31
cl22
^32
933
®
1
a2
33
Estimate
Standard error
t-Statistic
61.82
0.27
0.18
0.38
0.07
0.44
0.11
0.16
0.33
0.50
0.23
0.005
0.019
0.005
0.022
0.007
0.023
0.063
0.132
0.002
0.003
0.006
11968.80
14.31
32.78
17.01
10.14
19.09
1.68
1.25
162.74
164.39
36.50
,
dex, but the volatility still remains larger than
that o f the estimated theoretical index. W e could
experim ent w ith even m ore smoothing o f the
CE index than is advocated by Rotemberg, Dris
coll, and Poterba, but w e feel that fu rth er ex
perimentation in that direction w ould produce
an index having dynamics determined m ore by
the ad hoc method o f smoothing than by the
theory that produces the index. Furthermore,
w e suspect that smoothing adequate to fix the
index between 1979 and 1983 would oversmooth
elsewhere. Hence, it seems that there is no way
that the CE index can track the growth rates
adequately throughout the sample.
In short, as a measure o f the level o f the
money stock, the simple-sum index perform s
most poorly, w hile in terms o f grow th rates, the
CE index perform s most poorly. In both cases,
the Divisia index perform s best. These results
are in the accordance with index number the
ory, although most o f that theory is available in
rigorous form only under the assumption o f
perfect certainty. Our weak separability test sup
ports the existence o f an inside-money output
aggregate in banking, and our plots support the
use o f the Divisia index as the best currently
available statistical index fo r tracking that out
put aggregate.
For comparison purposes, w e repeat the above
estimation and testing in the special case o f risk
neutrality. The Euler equations, 62-65, under
risk neutrality becom e4
5
45ln producing equations 80 and 81 as special cases of
the corresponding risk-averse Euler equations, recall foot
note 14.
v
. B(l-fcJ-r
R
dCl/dD,
--------------1
(78) E.[P.— ----- ----- ~ + P,---- 5
l + fi(
,
,
, R il- k )- r
1 + Rt 3Q /3C ,
R,
3 Q /3 T ,
(79) £,(P,—------ - ---- - + P , ------------------
1 + /J,
,
,
.
R,
= o,
1 + Rt 3 Q /3 Ct
= 0,
dCl/dL,
80 E [ P ---- 1
----- -------- w j = 0,
' l + R. dCl/dC.
and
(81) E\P;
R.
dO/dM ,
----------- —w
l + R. dd/dc,
2
1
= o.
The parameter estimates acquired from GMM
estimation under risk neutrality, w ith weak
separability in outputs imposed, are in table
3.4 Substituting the parameter estimate o f t, in
6
the risk-neutrality case into equations 69, w e
obtain b ] =0.777 and bz = 0.223. The estimated
theoretical aggregate then is acquired by sub
stituting the estimated parameters and fixed
constants into equation 29 to get
(82) y jD 'jT j = 0.777D, + 0.223T(
1 r.2752
(D[-T ,)2
2 >-.58D( + 0.427;
The value o f the weak separability test statistic,
equation 73, is 9.25, w hile the critical value is
21.666 at the 1 percent significance level. We
cannot reject the weak separability hypothesis
and, hence, the existence o f a theoretical mone46The instrumental variables are the constant, the discount
rate, the lagged banks’ portfolio rate of return, excess cash
reserves and capital.
MARCH/APRIL 1994
156
tary aggregate over the outputs produced by
banks again is accepted. Furthermore, m onoto
nicity and convexity again are accepted through
out the region o f the data.
requirements exist. M oney market equilibrium
at a fixed contingent state, w hen one or both o f
the monetary assets is subject to reserve re
quirements, is illustrated in Figure 14.
Figures 7-12 provide the risk-neutral plots
analogous to those in Figures 1-6 under risk
aversion. Imposing risk neutrality produced
negligible gain in tracking ability fo r any o f the
indexes. Hence, at least w ith this data, risk aver
sion does not seriously compromise index num
ber theory.
In Figure 13, equilibrium is produced by the
familiar separating hyperplane. The separating
hyperplane simultaneously supports an indiffer
ence curve from below and a production possi
bility curve from above. Th e axes represent
quantities o f each o f the tw o m onetary assets
demanded and supplied. Equilibrium in the two
markets exists at the mutual tangency o f the
separating hyperplane, the indifference curve,
and the production possibility curve at a given
optimal level o f factor use. In equilibrium, the
quantities demanded o f each asset are equal to
the quantities supplied at the equilibrium point
y e= (ye J- In addition, the gradient vector
^ye
to the separating hyperplane produces the
equilibrium user-cost prices. Th e vector o f usercost prices paid by the consumer, 0, are equal,
in equilibrium, to the vector o f user-cost prices
received by the financial intermediary, <r The
t
>
user cost price o f asset type i is defined by
equation 77 above.
THE REGULATORY WEDGE
Although the imposition o f risk neutrality did
not improve the tracking ability o f any o f our
indexes, the risk-neutral special case does permit
especially simple graphical illustration o f
equilibrium phenomena through the use o f
separating hyperplanes. In particular, w ith risk
neutrality and complete contingent claims m ar
kets, each consumer maximizes utility and each
firm maximizes profits conditionally upon any
fixed, realized contingency (i.e., state). Hence,
perfect certainty methods o f graphical illustra
tion are available in the risk neutral case, with
the understanding that the illustration is condi
tional upon the realization o f all contingencies.
If no regulatory w edge exists betw een the de
mand and supply side, a hyperplane separates
tastes from technology. But in the case o f com
mercial banks, a regulatory w edge does indeed
exist. This conclusion follows from the observa
tion in footnote 8 that an implicit tax is imposed
upon banks through the existence o f non
interest bearing required reserves. Hence,
the user cost price received by banks fo r the
production o f m onetary services differs from
the user cost price paid by depositors fo r the
consumption o f those services. The difference is
the implicit tax.
The formulas fo r the user cost prices on each
side o f the market fo r produced m onetary serv
ices was derived by Barnett (1978, 1980, 1987)
and computed by Barnett, Hinich and W eber
(1986). The result is most easily illustrated in the
case o f an econom y w ith one consumer, w ho
consumes all o f the econom y’s m onetary serv
ices, one financial intermediary, which produces
all o f the econom y’s m onetary services, and two
m onetary assets. Equilibrium in the monetary
sector o f the economy at a fixed contingent
state is illustrated in Figure 13, w hen no reserve
RESERVE BANK OF ST. LOUIS
FEDERAL
W ith factor employment assumed to be set in
advance at its optimum, p , the optimum level
o f aggregate m onetary service production, y * is
defined to be the solution fo r y * to the equation
H(y*,x) = 0, w h ere y * = y (y ) and w h ere Q (y ,*) =
H(y*,x) = H(y0(y),x), as explained in the sub
section above. Hence, Figure 13 is drawn condi
tionally upon that fixed setting o f y*, so that the
production possibility surface is the set [(y1 2
(y ):
y0 y ^ = y * l
(
However, the situation is very different, w hen
required reserves exist. In that case, tw o d iffe r
ent supporting hyperplanes exist in equilibrium.
One supporting hyperplane exists fo r the finan
cial intermediary, and another exists fo r the
consumer. In Figure 14, the line w ith gradient
equal to the consumer’s monetary-asset user-cost
prices, ♦ , is the consumer’s supporting hyper
plane and it is his budget constraint in equilibri
um. That line is tangent to the displayed
indifference curve in equilibrium. The financial
interm ediary’s supporting hyperplane has gra
dient equal to the financial interm ediary’s usercost prices, <f. That hyperplane is the financial
t
>
interm ediary’s iso-revenue line, which is tangent
to the firm ’s production possibility curve at the
equilibrium point. W hile the user-cost price paid
by the consumer fo r the services o f asset type z
157
Figure 7
Levels of Five Monetary Aggregates (parameters of theoretical
monetary aggregate estimated with imposed risk neutrality)
1966
68
70
72
74
76
78
80
82
84
86
88
1990
Figure 8
Growth Rates of Five Monetary Aggregates (parameters
of theoretical monetary aggregate estimated subject
to imposed risk neutrality)
0.15
—
_
__ _
——
0.1
0.05
Estimated theoretical aggregate
Divisia index
Simple-sum index
CE index
Smoothed CE index, in which the weights
are three-year, centered moving averages
0
-0.05
-
0.1
-0.15
-
0.2
-0.25
t—
1966
i— i— i— r
68
70
72
74
76
78
80
82
84
86
88
1990
MARCH/APRIL 1994
158
Figure 9
Growth Rates of Theoretical Monetary Aggregate and Divisia
Index (with imposed risk neutrality)
Figure 10
Growth Rates of Theoretical Monetary Aggregate and
Simple-Sum Index (with imposed risk neutrality)
FEDERAL RESERVE BANK OF ST. LOUIS
159
Figure 11
Growth Rates of Theoretical Monetary Aggregate and CE Index
(with imposed risk neutrality)
Figure 12
Growth Rates of Theoretical Monetary Aggregate and Smoothed
CE Index (with imposed risk neutrality)
MARCH/APRIL 1994
160
Figure 13
Equilibrium with No Required Reserves
Figure 14
Equilibrium with Required Reserves
FEDERAL RESERVE BANK OF ST. LOUIS
161
is still defined by equation 77, the user-cost
price received by the bank fo r producing those
services now is defined by equation 75, which
does not equal equation 77 unless no required
reserves exist.
The equilibrium point is the point y at which
the tw o supporting hyperplanes intersect, and
the angle between them is the regulatory w edge
produced by the implicit reserve requirement tax
paid by the financial interm ediary in the form
o f foregone interest on required reserves. A t the
equilibrium point both markets are cleared, and
the consumer is maximizing utility subject to
the displayed budget constraint, w hile the finan
cial interm ediary is maximizing revenue subject
to the displayed production possibility curve.
THE ERRORS-IN-THE-VARIABLES
PROBLEM
This same figure also can be used to illustrate
the magnitude o f the errors-in-the-variables
problem produced by the use o f the simplesum index as a measure o f the flow o f m one
tary services. Figure 15 illustrates the range o f
the error on the demand side, w hile Figure 16
does the same on the supply side. The same il
lustration could be produced on the supply side
by replacing the tw o indifference curves that
are convex to the origin with tw o production
possibility curves, that are concave to the origin.
The conclusion would be the same.
In both figures, the hyperplane represents the
set
a
= {(y„y2 y ,+ y 2 = a#J,
):
w h ere M s is the measured level o f the simples
sum index, w hile A is the set o f possible values
o f the m onetary asset component quantities
Ovy2
)
are consistent with the measured
level o f the simple-sum index.
For any such measurement on the simple-sum
index, the value o f the demand-side m onetary
service flow received by asset holders could be
anywhere within the set
(83) (u(y„y2 (yt,y2 A }.
):
)€
The range o f that set is the gap betw een the
utility levels at which the tw o indifference
curves are drawn in Figure 15. C learly the
upper indifference curve is the one w hich inter
sects the hyperplane A at the highest possible
utility level, w hile the low er indifference curve
is the one which intersects the hyperplane A at
the lowest possible utility level. We see that
magnitude o f the errors-in-the-variables problem
in that illustration, w hen measured by the range
o f the set (83), is M m M m . The same conclu
aiijn
sion is produced on the supply side from Figure
16, but with set 83 replaced by4
7
[y,0vy>>: (y,/y2>
e^)The simple-sum m onetary aggregates produce
a disturbingly large and entirely unnecessary
errors-in-the-variables problem. Figures 15 and
16 illustrate the reason. Figures 1-12 illustrate
the effect, under circumstances that are most
favorable to the simple-sum aggregates: a low
level o f aggregation over assets having similar
yields. W ith broader aggregation over assets
having very different ow n rates o f return, in
cluding currency w ith a zero rate o f return, the
continued use o f simple-sum m onetary ag
gregates by central banks becomes even more
difficult to comprehend. The days w hen all
m onetary components had zero-own rates o f
return are long gone.
CONCLUSIONS
In this paper, w e develop a theoretical model
o f m onetary service production by financial
firms. Earlier models either have perm itted risk,
but w ith minimal connection with neoclassical
economic th eory or have made full use o f neo
classical production theory, but under the as
sumption o f perfect certainty. The latter case
has been developed extensively by Barnett
(1987), Barnett and Hahm (1994), and Hancock
(1985, 1987, 1991). We extend that latter fully
neoclassical production approach to the case o f
risk aversion, subject to D iew ert and Wales’s
symmetric generalized McFadden technology
Our approach permits risk aversion without
compromising second-order flexibility or neo-
47The magnitude of the gap, Mm — Mm may differ, when a
ax
[n,
regulatory wedge is produced by required reserves, but the
difference between the conclusions on the demand and
supply side is not likely to be large. If the errors-in-thevariables problem is large on one side of the market it is
likely to be approximately as large on the other side of the
market. See Barnett, Hinich and Weber (1986) for relevant
empirical evidence.
MARCH/APRIL 1994
162
Figure 15
Demand Side Errors-in-Variables
Figure 16
Supply Side Errors-in-Variables
FEDERAL RESERVE BANK OF ST. LOUIS
163
classical regularity o f the specification. This
is true with or without the imposition o f
global blockwise weak separability, which
w e therefore are able to test and to impose,
w hen accepted. Using the resulting Euler equa
tions, w e explore exact output aggregation in
this paper.
Although applicable to all financial interm edi
aries, w e apply our approach only to the bank
ing industry. W hile it is possible to impose
regularity in curvature conditions upon the
generalized McFadden specification, monotonicity
can be imposed only locally without damaging
the models flexibility. Diew ert and Wales’s alter
native specification, called the generalized Bar
nett model, is globally regular both in terms o f
curvature and monotonicity, and hence, that
model was used by Barnett and Hahm (1994) in
the perfect certainty case. However, in the cur
rent paper, using the generalized McFadden
model, the estimated parameters satisfy the neo
classical monotonicity and convexity conditions
fo r all observations, even though only convexity
was imposed globally. Hence, w e doubt that our
conclusions would have been much different if
w e had used the generalized Barnett model in
producing our estimated Euler equations. The
hypothesis that bank’s outputs are weakly
separable from inputs is accepted. Hence, the
existence o f an exact supply-side theoretical
m onetary aggregate is accepted fo r banks. The
resulting output aggregate is the banking indus
try ’s contribution to the economy's inside money
services.
W hile our theory provides a means o f econometrically estimating the exact supply-side
m onetary aggregate, no theory currently is avail
able to support the use o f a nonparametric
statistical index number as an approximation to
the parametrically estimated exact aggregate.
Considering the complexities o f the GMM esti
mation involved in producing the estimated
exact aggregate, a nonparametric statistical
index would, in practice, be much easier to
compute and use. W e compute the currently
most popular o f those indexes and find that at
least fo r our sample, the Divisia index tracks the
estimated theoretical index m ore accurately than
the others. This conclusion holds regardless o f
w hether or not w e impose risk neutral
ity during estimation o f the exact theoretical
aggregate. Risk aversion does not appear to
produce appreciable degradation o f the tracking
ability o f the Divisia index w ith our data.
W e believe that the approach developed in this
paper could be used to investigate technological
change in banking, economies o f scale and
scope in banking, value added in banking and
its connection w ith inside m oney creation, and
the transmission mechanism o f m onetary policy.
We have in fact taken a first step in the direc
tion o f producing one o f those extensions: We
have derived and supplied the Euler equations
with learning by doing technological change in
cluded in technology. A longer-run fram ew ork
fo r the theory also could be productive. In par
ticular, some o f the factors excluded from the
variable cost function as fixed factors could be
incorporated among the variable factors. Bank
capital is one such example. Incorporating capi
tal among the variable factors could perm it in
tegration o f the m odel w ith economic growth
theory, in which capital evolves endogenously in
accordance w ith a law o f motion. In short, this
is just a start in a direction that w e expect w ill
be very productive fo r researchers interested in
the role o f financial institutions in the economy.
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MARCH/APRIL 1994
166
William C. Brainard
William C. Brainard is Arthur M. Okun professor of economics
at Yale University.
Commentary
I t IS A PLEASURE TO TAKE PART in a scholarly conference focusing on empirical and theo
retical issues relevant to the conduct o f m onetary
policy and the behavior o f financial markets.
Most o f the discussion at this conference, and
indeed most o f the w ork on m onetary aggre
gates, including a great deal by Bill Barnett, has
been about the demand side. Demand elasticities
and the degree o f substitutability o f various
m onetary assets and liabilities are not just o f
academic interest. They have direct and obvious
relevance to the conduct o f m onetary policy.
W hile there has been a great deal o f w ork on
demand, there has been relatively little w ork on
the supply side o f the market. The scarcity o f
supply studies is perhaps inherited from simpler
days when commercial banks, limited in their
ability to compete fo r deposits and constrained
in their portfolio choices, dominated the supply
o f m onetary assets. In a w orld w here currency
and demand deposits are the prim ary monetary
assets, with no close substitutes, m onetary con
trol was relatively simple; control o f bank
reserves provided a tight control on the supply
o f demand deposits and shifts betw een currency
and demand deposits w ere relatively easily
m onitored and offset. In today’s economy, w ith a
rich menu o f monies and near monies, the task
is not so simple. The instruments o f control—
the supply o f reserves, reserve requirements
and the discount rate—have remained essentially
the same w hile the menu o f m onetary assets has
proliferated. Financial firm s and markets can
alter significantly the suppliers o f their assets
and liabilities without policy accommodation. In
this environm ent not only is there a question o f
Digitized for FEDERAL RESERVE BANK OF ST. LOUIS
FRASER
what to control, but control itself is less direct
and the timing and magnitude o f the response
to policy less certain. In these circumstances,
the Barnett-Zhou examination o f the competitive
supply o f m oney and near monies by financial
firm s is a w elcom e and important enterprise.
The authors focus on the supply behavior o f
the most important o f the financial interm edi
aries, commercial banks. They m odel the bank
ing industry as a competitive profit maximizing
firm, stressing the dynamic nature o f bank’s op
timization problem and the presence o f risk.
The banking firm maximizes the present dis
counted value o f expected utility, w h ere the util
ity in each period is a function o f that period’s
" c a s h flo w ” and displays risk aversion. The bank
decides on its supply o f liabilities, taken to be
demand and time deposits in the empirical anal
ysis, and its demand fo r excess reserves and
"loans.” Both assets and liabilities mature in one
period, w ith the returns on loans being uncer
tain. A production function determines the real
resource costs associated w ith these portfolio
decisions; in the estimation this function is as
sumed to be weakly separable, so that the rela
tive costs o f demand and time deposits do not
depend on excess reserves nor on inputs o f
labor and materials.
The authors develop general methods fo r es
timating dynamic and stochastic models o f bank
behavior and demonstrate the feasibility o f us
ing these techniques in the context o f a specific
bank model. W hile the techniques could be ap
plied in a w ide range o f settings, the model
focused on in the paper incorporates tw o
assumptions that severely limit the role fo r
167
dynamics. In particular, both bank assets and
liabilities are assumed to mature in "one” period
and the net proceeds o f the borrow ing and
lending decisions made by a bank in one period
are entirely paid out w hen the assets and liabili
ties mature one period later. This is implied by
equation 2: Liabilities issued in a period exactly
cover required reserves, excess reserves, port
folio investment and the payments fo r real
resources. Hence, equity is zero (as the author’s
indicate there would be no essential difference
if it was non zero but constant); there is no
room fo r retaining earnings. As a consequence,
the only effect o f a decision in period (t) on net
cash flow occurs at the beginning o f period
(t+1). The net portfolio returns (the net cash
flo w consequence o f decisions made in the
previous period) are all paid out when they ar
rive. Hence, if dividends—the net cash generated
and distributed to the owners o f the firm —
w ere entered in the utility function, the firm ’s
optimization problem would be time separable
and decisions could be made separately, period
by period.
What, then, makes the firm ’s decision dynamic
in Barnett-Zhou? The reason is that the "cash
flo w ” entered in the utility function is not the
cash actually generated and distributed, but a
measure o f profits developed by Diana Hancock
(equation 1). This measure differs from actual
cash flow by an amount reflecting changes in
required reserves. In Hancock’s profit function
required reserves are not recorded as an asset
requiring the use o f funds. Yet, from the budget
constraint in equation 2, liabilities exceed the
sum o f excess reserves, loans and resource cost
by exactly the amount o f required reserves.
Hence, the Hancock profit function records as a
positive cash flow an amount equal to required
reserves in the period liabilities are incurred,
and records a negative cash flow in the period
they are repaid. These components o f Hancock’s
profit function simply reflect the need to place
a portion o f the deposits in reserve. I have
difficulty understanding how to motivate their
inclusion in the utility function; they do not cor
respond to payments to the owners o f the firm,
nor do they constitute an increase in the net
w orth o f the bank. Although counting these
flows as profits has essentially no effect on the
present value o f the bank, it does serve to cre
ate a link betw een time periods, making the
problem dynamic.
Several features could be added to the
author’s model o f banks which would greatly
increase the role fo r dynamics. Illiquidity and
maturity mismatch may be less important today
than earlier in the postwar period, but they re
main significant reasons fo r treating the bank as
a multiperiod firm . One extension w ould be to
incorporate the fact that some o f banks' invest
ments are in assets w ith maturities substantially
greater than the maturity o f their liabilities. If
held to maturity, investments made today have
to be financed by future borrow ing. Second,
since some bank assets are relatively illiquid, it
would be interesting to build into the specifica
tion some costs o f rapid asset disposal. Similarly,
as w ith physical investment, there are costs o f
adjustment on the rate o f acquisition o f assets.
Another important extension would be to treat
explicitly the dynamics o f equity growth. As
with any firm , grow th in equity, either by new
issue or by retention o f earnings, plays an im
portant role in the grow th o f the industry. Ex
plicit treatment o f capital accumulation seems
particularly desirable given the capital require
ments placed on bank portfolios, requirements
which many thought w ere an important con
straint on bank lending in recent years. Includ
ing these elements w ould not only substantially
increase the importance o f dynamics in the
model, it would also add to the menu o f risks
by, fo r example, allowing fo r the risks reflecting
the interaction o f illiquidity and deposit uncer
tainty. Not only can the author’s m odel be ex
tended to analyze m ore complicated models o f
banks, but it w ill undoubtably be useful in the
study o f other financial intermediaries, institu
tions that share many o f the features o f banks
and, like banks, should be analyzed within a
dynamic and stochastic fram ework.
A num ber o f the author’s results are quite in
teresting. A fter restricting the utility function to
the CRRA class, they find the degree o f risk
aversion significant and on the order o f one.
They test and find they cannot reject weak
separability, hence their estimates are consistent
w ith the existence o f a theoretical m onetary ag
gregate. The estimated aggregator function it
self, evaluated at a point w here demand and
time deposits are o f equal magnitudes, gives a
marginal rate o f transformation implying that
one dollar o f demand deposits is equivalent to
approximately three dollars o f time deposits.
This sounds like a plausible magnitude in the
current regulatory environment; it would be
interesting to know how different estimates
would be fo r an early subset o f the data w hen
MARCH/APRIL 1994
168
reserve requirements, portfolio restrictions and
capital requirements w ere so different.
In the author’s specification, excess reserves
are an important input, w hile required reserves
are seen as a sterile asset entering the firms
technology neither as an input nor as an output.
Th ere was a time w hen reserve requirements
w ere quite high relative to estimates o f bank’s
ow n transactions needs and this assumption
would seem quite plausible. As reserve require
RESERVE BANK OF ST. LOUIS
FEDERAL
ments have fallen, however, the distinction b e
tween required and excess reserves has becom e
less sharp. Another interesting extension o f the
model, therefore, would be to include required
reserves as an input and to test w hether their
importance has fallen over time.
As these comments suggest, I have found this
an innovative and stimulating paper which
opens up several new avenues fo r future
research, and I look forw ard to watching the
progress in this important enterprise.
169
William A. Barnett and Ge Z h o u 1
Response to Brainard’
s
Commentary
W 'E HAVE GREATLY BENEFITED from
,
Brainard’s stimulating comments on our paper.
W e agree w ith his suggestions fo r extensions
to this research, and in fact expect to have ex
tended versions available in the near future. For
example, Barnett, Kirova and Pasupathy (1994)
are including an extended model in their paper
being prepared fo r the Federal Reserve Bank o f
Cleveland conference in September 1994. That
model contains dynamic capital grow th through
Tobin’s q, both fo r financial intermediaries
producing m onetary services as outputs and fo r
manufacturing firms demanding m onetary serv
ices as inputs. In addition, that model contains
an endogenous dividend payout decision,
produced by entering loans into technology as
an output, along w ith the deposits which cur
rently are the sole outputs. Introducing loans
into the technology as an output eliminates the
need fo r Barnett and Zhou’s (1994) equation 2,
which determines loans as a function o f
deposits under the assumption that all earnings
are paid out as dividends.
Some readers may find Brainard’s comments
difficult to interpret, however, since they reflect
unpublished background material developed
during correspondence. The following few the
orems are relevant to understanding the nature
o f the m odel’s dynamics and the merits o f ex
tending the model further to exhibit deeper dy
namics.
Equation 2 in our paper is imposed to require
the firm to pay out all earnings as dividends,
since introduction o f an endogenous dividend
payout decision is beyond the scope o f our
paper. Equation 1 is in the general form o f the
profit function used by Hancock (1985, equation
3.1) in her book and in her papers on financial
intermediation under certainty. Equation 1
holds, regardless o f how the dividend payout de
cision is made. Our equation 3 is acquired by
imposing equation 2 on equation 1 through
direct substitution. Hence, equation 3 is Han
cock's variable profit function under the restric
tion that all earnings are paid out as dividends.
Under exactly that same payout restriction,
Barnett (1987, equation 3.7) derived a different
variable profit function fo r the same financial
intermediary, and Barnett and Hahm (1994) recendy have used Barnett's form ulation o f the
variable profit function in estimating the tech
nology o f commercial banks. In correspondence,
w e found that Brainard had a very strong
preference fo r use o f Barnett’s, rather than
Hancock’s, variable profit function under the
payout restriction. The discussion about dynam
ics in Brainard’s comment, including his discus
sion o f the accounting fo r required reserves,
'B arnett’s research on this paper was partially supported by
NSF grant number SES 9223557. We have benefited from
many discussions with Richard Anderson on this subject,
and a lengthy and highly informative exchange of faxes
with William Brainard.
MARCH/APRIL 1994
170
explains his reasons fo r preferring Barnett's
function to Hancock's.
Further changing to the notation in Barnett and
Obviously Barnett would not dispute the
merits o f Barnett’s variable profit function, and
he is not at all displeased that Brainard so
strongly prefers his variable profit function to
Hancock’s. Nevertheless, it may seem paradoxical
that tw o different variable profit function fo r
mulas exist fo r the same firm under the same
assumptions, and that w e chose to use Han
cock's rather than Barnett's formula in our
paper in this volume. As w e shall observe below,
the distinction betw een the tw o variable profit
functions is actually much more subtle than
may appear to be the case, and the choice b e
tween them in our paper is little more than an
econom etric trick—barring empirical evidence to
the contrary.
are the nonfinancial variable factors, and w,,
jt’
7 = 1,...,./, are their prices. We then can rew rite
the variable profit function as:
Zhou (1994), let B, = £ w .z ., w h ere z „ J=1,...,J,
jm 1
W e begin by verifying that equation 1 in our
paper is indeed exactly Hancock’s variable profit
function, w ith only the notation changed.
* H = - J j wj,zj, ,
+
£
J
P r o o f: Hancock's (1991, equation 3.1) variable
profit function, using her notation, is
= ~B, -
it"
p, . -
w here Bt = expenditure on variable factors; Pt
= the general price level; yit = a financial asset
quantity if i=\,...,N y or a financial liability quan
tity if i= N 1+ l,...N 1+ N 2 hit = the holding period
;
yield on yit if yu is an asset, or the holding cost
on y.t if y.t is a liability; and w e define the indi
cator function bi such that b = 1 if y.( is a liabil
ity and b = -1 if y. is an asset.
A m ore convenient notation would be to use
the symbol A to denote assets instead o f the no
tation N 1 and L to denote liabilities instead o f
the notation N 2. Making that change in notation
and using the indicator function b as defined
above, w e acquire:
= ~ B, -
s
- yM
p , M + K -M t-A -i - y fX
t= L + 1
As in Hancock (1991), the assets consist o f loan
investments and excess reserves, which in our
notation are Yt and Ct respectively. Furthermore,
let Rt be the single period holding yield on Yt
and let the yield on C( be zero, as in Hancock
(1991). The variable profit function now
becomes:
i= L + 1
+ C .- A -i ~ C,P, + < +
1
- yitpX
2Also, see equation (3) in Hancock (1985) for another state
ment of Hancock’s formula.
FEDERAL RESERVE BANK OF ST. LOUIS
- y.,p,]
-
YtP,,
which is exactly equation 1 in Barnett and Zhou
(1994).
Q.E.D.
In the next theorem, w e prove that the d iffer
ence betw een the discounted present value o f
the profit flo w produced from Hancock’s form u
la (that is, Barnett and Zhou’s 1994 equation 1)
and the discounted present value o f the profit
flow produced by Barnett’s (1987, equation 3.7)
formula is a function only o f initial conditions.
The proof is produced under imposition o f Bar
nett and Zhou’s equation 2, which requires all
earnings to be paid out as dividends.
Let yit be deposits in account type i and let r ,
be the single period holding yield on that ac
count. Let K it be the required reserve ratio on
that account. Before proving the equivalency
theorem, w e define the tw o formulations o f the
variable profit function as follows.
D e fin itio n 1: Barnett’s (1987, equation 3.7)
variable profit function is
L
A +L
+ s
J
ui + K - M t - ip.-i -
1 w],z], - s
T h e o re m 1: The variable profit function de
fined by equation 1 in Barnett and Zhou (1994)
is identical to Hancock’s (1991, equation 3.1) vari
able profit function.2
J
J
171
w here the user cost o f account yit is
n„ = P,
w hile the capitalized value o f Barnett’s profit
stream 7 is
r„
l + R,
and the user cost o f excess reserves ct is
% =
p,
Substituting the formulas fo r the profit streams
into the tw o capitalized values and manipulating
algebraically, w e find
l + R,
D e fin itio n 2: Barnett and Zhou’s (1994, equa
tion 3) variable profit function is
7TflZ, =
S
( [( ! + /!,_,)
+
C b
=
5
^ ( i + R ,J w j l _izjt_l,
T h e o re m 2: The discounted present value o f
the firm , CB produced from Barnett’s profit
,
function flow, 7rB, differs from the discounted
present value o f the firm, Cir produced from
Barnett and Zhou’s (in other words, Hancock’s
w ith no retained earnings) profit function flow,
wB by a function, K(I), containing only initial
ZI,
conditions, /. In other words, there exists K(I),
depending only upon initial conditions, such
that C„ = CB+ K(/).
P r o o f: Define the discount factor 8s such that
f 1 when s = t
=
n
v
(1+fl.) w hen s > f + l,
a=t
a
w here Ra a = t,...,s -l, are current and expected
,
future values o f the rate o f return, Rt, defined
above to be the single period holding yield on
Yt. The discounted capitalized value o f the profit
stream 7rBZ( at time f is
5
*BZs >
% B s
[ E rj v. 5
l-l
‘^ ‘S
E w z. - ri c ]
7 -1
JS JS
C S
S
and
1
w here hIS = rIS + kISRs .
Note that by Theorem 1, Definition 2 also de
fines Hancock’s (1991, equation 3.1) variable
profit function under the restriction that all
earnings are paid out as dividends (Barnett and
Zhou’s (1994), equation 2). A fter multiplying Bar
nett's variable profit function (defined by Defini
tion 1 above) through by 1 + Rt, it is easily seen
that the profit function preferred by Brainard in
his comments (as further clarified by our pri
vate correspondence) is Barnett’s profit function.
The equivalency theorem, producing a connec
tion between Definitions 1 and 2, follows.
s
= S
s .,
+Ky,,pJ - K A - A - i -
8 ~
5
= K + CB f
w here
K = S [[(l+ B ,.,) i l - k uJ - n + h itl_1
))yiil_,PtJ
Observe that K depends only upon initial condi
tions, since the intertemporal decision is made
at time t over periods t, t + 1, t + 2,....
Q.E.D.
Theorem 2 proves that under the restriction
that all earnings are paid out as dividends and
except fo r a function o f initial conditions, Bar
nett’s variable profit function and Hancock's
variable profit function are simply different
ways o f spreading the capitalized value o f the
firm over time. Any flo w o f funds or transaction
that appears in one formula necessarily also ap
pears in the other, but potentially w ith a time
shift between them. Those time shifts are all
properly discounted, however, as demonstrated
by the fact that the tw o profit streams produce
the same capitalized value up to K(I). In his com
ment, Brainard observes correctly that the
choice between the tw o profit flow formulas
“ has essentially no effect on the present value o f
the bank.” Theorem 2 above makes that point
clear.
The discussion that follows w ill extract from
Theorem 2 its precise implications fo r the model
estimated by Barnett and Zhou in this volume.
Our discussion w ill compare the solutions o f the
tw o decisions defined below.
D e c isio n 1: For some utility function, U , the
firm determines its factor demands and output
MARCH/APRIL 1994
172
supplies by maximizing, EU(CB which is the ex
),
pected utility o f the capitalized value CB
.
D e c is io n 2: For some utility function, V, the
firm determines its factor demands and output
supplies by maximizing, EV(CH w hich is the ex
),
pected utility o f the capitalized value CH
.
Observe that all terms in each capitalized
value are inside the respective utility function,
which is not assumed to be intertemporally
separable in either case. The marginal utility o f
anything varied within either capitalized value
depends upon everything else in that capitalized
value. In short, neither utility function is inter
tem porally separable and the solution o f either
decision is deeply dynamic. In fact, each solu
tion is intertem porally simultaneous w ith all
time subscripts appearing in all Euler equations.
To determine w hether there are any substan
tial differences betw een Decisions 1 and 2, w e
now define the follow ing concept.
D e fin itio n 3: TWo decision problems are observationally equivalent if the solution functions
(factor demand and output supply) functions
produced by solving one problem are identical
to the solution functions produced by solving
the other at any fixed setting o f the initial con
ditions.
Th e following theorem and corollary are now
easily proved.
T h e o re m 3: For any given fixed value o f the
initial conditions function, K(I), and any given
utility function, U, there exists a utility function,
V, such that V(CH = U(CB fo r all possible settings
)
)
o f the firm's decision variables (the controls).
P r o o f: For given K (I) and U, define V such that
V(x+K(/)) = t/W fo r all nonnegative values o f the
scalar ,x. N ow let ,x= CB and let CH=}c + K(I). By
,
substitution, the result is immediate.
Q.E.D.
C o r o lla r y 1 to T h e o re m 3: Decisions 1 and 2
are observationally equivalent.
P r o o f: The corollary follows immediately from
Definition 3 and Theorem 3.
Q.E.D.
The implications o f the above results at this
point are the following. To justify the introduc
tion o f risk aversion into the decision o f the
3lf contingent claims markets are complete, then the owner
will instruct the manager to maximize profits conditionally
upon the prices in contingent claims markets. Those prices
contain the information about the risk aversion of the own
er and, hence, the managers will be instructed to behave
in a risk-neutral manner relative to those prices. See Duffie
(1991) and Magill and Shafer (1991).
FEDERAL RESERVE BANK OF ST. LOUIS
firm , w e implicitly assume the existence o f in
complete markets.3 How to model the decisions
o f firm s w ith incomplete contingent claims m ar
kets is controversial. One approach that has
been proposed is to apply principle agent theory
in a form that produces incentive compatibility,
w hen the decision is delegated by the owners to
a professional manager. Th e source o f the risk
averse, concave utility function is the utility
function o f the principle agent.
Having introduced expected utility maximiza
tion into the firm ’s decision in that controversial
manner, w e then see from the above corollary
that it makes no difference w hether w e use
Hancock’s variable profit function or Barnett’s in
producing the Euler equations to be estimated.
The Euler equations are identical and the deci
sion is deeply dynamic, w ith all time subscripts
appearing in each Euler equation. The choice
betw een the tw o profit formulas is a choice b e
tw een tw o different methods o f spreading the
same capitalized value over time. But since it is
the capitalized value itself that enters as the sole
argument o f the utility function, the m ethod o f
spreading over time is irrelevant. Corollary 1 is
the result.
The problem at this point is that estimating a
system o f simultaneous Euler equations is b e
yond the state o f art. We need a means o f
decreasing the depth o f the m odel’s dynamics.
An obvious m ethod would be to impose a
separability restriction on the utility o f capital
ized value. W e could use complete separability,
blockwise separability, weak separability, or
strong separability. Separability restrictions are
testable structural restrictions, and behavior is
not invariant to such structural restrictions.4 In
addition, nothing in principle agent theory helps
us to choose betw een such restrictions, which
in fact all may be wrong. The utility function
may indeed be nonseparable, and the decision
may be unavoidably deeply dynamic. Further
more, w e are aware o f no empirical results that
would help us to choose betw een the many sim
plifying separability restrictions, and the few
results in that area in Barnett (1981) indicate
that separability restrictions are strong restric
tions that often are rejected in empirical tests.
4This issue does not exist in the perfect-certainty or riskneutral case, since in those cases there is no utility func
tion to be structurally separable. The invariance theorem,
then, is the end of the story.
173
Under such circumstances, applied researchers
regularly choose simplifying assumptions on the
basis o f their usefulness in estimation. One pos
sibility is intertemporal strong separability in
Hancock’s profit stream. Another possibility is
intertemporal strong separability in Barnett's
profit stream. M ore formally, those tw o possibili
ties are Assumptions 1 and 2 below, respectively.
A s s u m p t io n 1: The utility function, V, is intertemporally strongly separable in {C H(:f = l,...,°°}.
A s s u m p tio n 2: The utility function, U, is intertemporally strongly separable in {C B(:f= l,...,°°}.
Th ere are many other such possibilities pro
duced by grouping together terms in the capi
talized value in different manners. Behavior is
not invariant to choices between those possible
separability restrictions. In terms o f the degree
o f simplification o f the Euler equations, com
plete intertemporal separability in Barnett’s
profit stream (Assumption 2), as assumed by
Barnett and Hahm (1994), produces the most ex
trem e simplification. The decision becomes com
pletely static. Complete intertemporal separability
in Hancock’s profit stream (Assumption 1)
produces a more modest decrease in the depth
o f the dynamics: The solution becomes recur
sive, w ith tw o time subscripts appearing in the
Euler equations.
Barnett and Zhou (1994) selected and imposed
the latter restriction, since the resulting recur
sive form o f the solution assists in GMM estima
tion. Brainard (1994), in his commentary, argues
forcefully fo r intertemporal strong separability
in Barnett's profit stream. We have no reason to
dispute his strong prior on this subject. His
views are reasonable, and obviously Barnett
(1987) and Barnett and Hahm (1994) must have
had somewhat similar priors in mind w hen they
published their work. Nevertheless, it is also
possible that the opposite extreme may be true.
The utility function may be completely nonseparable, so that both Assumptions 1 and 2,
along with all other possible separability restric
tions, may be w rong.5 The Euler equations
would thereby be intertemporally simultaneous,
so that w e cannot readily estimate the model
w ith current methods because o f the depth o f
the dynamics. Even worse, it may be the case
that the use o f a risk averse principle agent as a
means o f introducing risk aversion into the deci
sion o f the firm may be a defective approach.
That question at present is unresolved in eco
nomic theory.6
Under these circumstances, w e feel justified in
choosing our separability restriction based upon
the resulting estimation convenience. Producing
interesting dynamics w ith long-run economic
grow th was not an objective o f Barnett and
Zhou (1994), which was an exploration in aggre
gation theory fo r firm s under uncertainty. We
agree w ith Brainard that far m ore interesting
dynamics would be produced by introducing a
law o f motion fo r capital, which indeed w ill be
included in Barnett, Kirova and Pasupathy
(1994).
We wish to acknowledge that the above
clarifying proofs resulted from our correspon
dence w ith Brainard, and w e are indebted to
him fo r motivating this exploration o f the con
nection betw een Hancock’s and Barnett’s form u
lations. Many o f his other suggestions will be
used in future extensions o f our research such
as the estimation o f the model w ith learning-bydoing technological change. Although w e have
not yet estimated that model, the Euler equa
tions fo r that extended model are provided in
Barnett and Zhou (1994) and the dynamics in
that model are indeed dynamic in an interesting
manner.
REFERENCES
Barnett, William A., Milia Kirova and Munich Pasupathy. “ Es
timating Policy Invariant Technology Parameters in the
Financial Sector, When Risk and Growth Matter,” Paper to
be presented at the Federal Reserve Bank of Cleveland,
September 1994 macroeconomics conference on Liquidity,
Monetary Policy, and Financial Intermediation.
_______ , and Ge Zhou. “ Financial Firm’s Production and
Supply-Side Monetary Aggregation Under Dynamic
Uncertainty,” this Review (March/April 1994).
_______ , and Jeong Ho Hahm. “ Financial-Firm Production of
Monetary Services: A Generalized Symmetric Barnett
Variable-Profit-Function Approach,” Journal of Business and
Economic Statistics (January 1994).
_______ . “ The Microeconomic Theory of Monetary Aggrega
tion,” in William A. Barnett and Kenneth J. Singleton, eds.,
New Approaches to Monetary Economics. Cambridge
University Press, 1987, pp. 115-68.
________Consumer Demand and Labor Supply. NorthHolland, 1981.
5ln fact, the assumption of intertemporal separability of
preferences has become controversial in the real business
cycle literature. See, for example, Kydland and Prescott
(1982).
6See for example Magill and Shafer (1991).
MARCH/APRIL 1994
174
Brainard, William C. “ Commentary,” this Review (March/April
1994).
Duffie, Darrell. “ The Theory of Value in Security Markets,”
in Werner Hildenbrand and Hugo Sonnenschein, eds.,
Handbook of Mathematical Economics, volume IV. NorthHolland, 1991.
Hancock, Diana. A Theory of Production for the Financial
Firm. Kluwer Academic Publishers, 1991.
Digitized forFEDERAL RESERVE BANK OF ST. LOUIS
FRASER
________“ The Financial Firm: Production with Monetary
and Non Monetary Goods,” Journal of Political Economy
(October 1985) pp. 859-80.
Kydland, Finn E., and Edward C. Prescott. “ Time to Build
and Aggregate Fluctuations,” Econometrica (November
1982), pp. 1345-70.
Magill, Michael, and Wayne Shafer. “ Incomplete Markets,” in
Werner Hildenbrand and Hugo Sonnenschein, eds., Hand
book of Mathematical Economics, volume IV. North-Holland,
1991.
175
Jerome L. Stein
Jerome L. Stein is professor of economics and Eastman
professor of political economy at Brown University.
Can the Central Bank Achieve
Price Stability?
i i l L FOMC’S STATED POLICY objectives are
to "foster price stability and promote sustainable
grow th in output.” Can these objectives be
achieved with the tools available? We know that
there is a long-run relationship between the
ratio M/y=Money/real GDP and the P =G D P
deflator o f the form
(a) P = V(M2/y),
w h ere V is the velocity function, shown in
Figure 1. The Federal Reserve would like to
select ranges fo r monetary growth over the
coming year consistent w ith price stability.1 This
is the policy o f monetary targeting. The ration
ale fo r the policy o f m onetary targeting is the
existence o f a stable and reliable relationship b e
tween the rate o f grow th o f monetary aggregate
Mi [denoted
and the rate o f inflation
(denoted tt) either during year t or possibly t + 1
o f the form
(b) ir(t) = c + c'Hift) or
(c) ir(t) = c + c 'n f t -1 ).
1By price stability, we mean a desired rate of change of
prices, which need not be zero.
2See Belongia and Batten (1992), Thornton (1992), Garfinkel
and Thornton (1989), and Ritter (1993).
Equation (a) is a long-run relation between the
price level and the stock o f money per unit o f
real GDP, and equations (b) and (c) are shorterrun relations betw een the rate o f grow th o f
prices and the rate o f growth o f money. They
are quite different.
It has been amply demonstrated by monetarists
that neither the grow th o f M l nor o f M2
produces a stable and reliable relationship o f
the form (b) or (c).2 The targeting o f M l was
abandoned w hen the velocity function changed
drastically after 1980, and M2 targeting was
then used. There was subsequent disappoint
ment with targeting M2. Figure 2a-d shows
w hy m onetary targeting equations (b) and (c),
either fo r M l or M2, are not reliable. The
source o f the problem is the instability and un
reliability o f the velocity function (V I fo r M l,
and V2 fo r M2 in Figure 3a). This led Alan
Greenspan (1993) to question the usefulness o f
M2 targeting [equation (b) or (c)]:3
"...the relationship betw een money [M2] and the
econom y may be undergoing a significant trans
formation....This is not to argue that money
grow th can be ignored in form ulating m onetary
policy....Selecting ranges fo r monetary growth
over the coming year consistent with desired
3The article by Ritter (1993), “ The FOMC in 1992: A Mone
tary Conundrum,” conveys the serious problems that arose
when the FOMC tried to implement the policy of monetary
targeting.
MARCH/APRIL 1994
176
Figure 1
GDP Deflator and the Ratio of M2/Real GDP
GDP deflator
M2/Real GDP
Figure 2a
Inflation and the Growth of M2
Inflation (change in GDP deflator)
FEDERAL
RESERVE BANK OF ST. LOUIS
Growth of M2
177
Figure 2b
Figure 2c
Inflation and the Growth of M1
Inflation and the Lagged Growth of M2
Inflation
Inflation
Lagged growth of M2
Growth of M1
Figure 2d
Figure 2e
Inflation and the Lagged Growth of M1
Inflation and the Growth of Divisia M2
Inflation
Inflation
Lagged growth of M1
Growth of Divisia M2
MARCH/APRIL 1994
178
Figure 3a
Velocity of M1 and M2
Figure 3b
Velocity of Divisia M2
Digitized for FEDERAL RESERVE BANK OF ST. LOUIS
FRASER
179
economic perform ance, however, is especially
difficult when the relationship [velocity] b e
tw een money and income has becom e uncer
tain. Recent experience suggests that...measuring
money against such ranges may lead to errone
ous conclusions regarding the stance o f m one
tary policy.”
Greenspan’s disappointment w ith the use o f
m onetary targeting (M2) has led him to revive
the concept o f interest rate targeting.
The ultimate question is how the central bank
should try to produce price stability and sus
tainable growth. Our paper addresses several
important questions:
1. Is there an economically significant, structur
ally stable, policy-rule-invariant relationship
between the rate o f growth o f a monetary ag
gregate and the rate o f grow th o f the price
level? If so, that m onetary aggregate is
referred to as an indicator. W hat monetary
aggregates, if any, qualify as indicators?
2. W hich monetary aggregate is an intermediate
target? An intermediate target is defined as a
variable Z which is an indicator and is also
controllable over a range o f policy regimes.
3. Under what conditions can Federal Reserve
policy be used to speed the recovery and
what w ill be the consequences fo r the rate o f
inflation?
4. Does the controllable Treasury bill rate quali
fy as an indicator or intermediate target?
Our major conclusions are:
A. The relation between the growth o f the
m onetary aggregate and inflation is indirect.
The change in the rate o f inflation depends
upon the unemployment rate and the grow th
o f real balances which changes real ag
gregate demand. Neither the grow th o f M2
nor the growth o f adjusted reserves per se
conveys very much useful information about
the course o f inflation in the near future, b e
cause the inflation and unemployment rates
4An intermediate target is an indicator, but not necessarily
the reverse.
6For economy of notation throughout the paper, the operator
D represents either the discrete first difference operator
D x = x(t)-x(t-1 ) or the continuous time derivative Dx=dx/dt
as appropriate in the context.
interact in a dynamic manner. W ithin the
context o f the dynamic model, the grow th o f
M2 is a good indicator o f the rates o f infla
tion and unemployment.
B. The grow th o f M2 has both an endogenous
component and a directly controllable part.
The link between the grow th o f M2 and
reserve grow th was tight from 1958-1975 and
then became very weak from 1975-1992.
Hence, the grow th o f M2 is prim arily an indi
cator. The grow th o f adjusted bank reserves
is an intermediate target fo r the rate o f infla
tion, but less so fo r the unemployment rate,
within the context o f the dynamical system.
C. Weighted m onetary aggregates are inferior to
M2 as an indicator.
D. The nominal or “ real” Treasury bill rate fails
completely as an indicator, so it cannot be an
intermediate target.4
The flo w chart below describes the relation
betw een the research design and the conclu
sions stated above. The Federal Reserve has
been seeking a direct relation between the
grow th o f m onetary aggregate Mi, w here
Dflog M i) is denoted /i., in a given year and the
rate o f inflation Dflog P) = tt in the subsequent
year.5 We have seen that there is no direct rela
tion between n J t - l ) and inflation ir(t). The rea
son is that the relation between inflation and
money grow th is indirect and works through a
dynamic model. We first derive the structural
equations o f a dynamical system involving the
state variables X, which are the inflation (7r), the
anticipated inflation (7r*) and unemployment
rates (u).e The input is the rate o f grow th o f a
m onetary aggregate fi = DM/M. The resulting
reduced form system (the SM dynamical system)
is o f the form D X = A X + Bfj. + e', described in
Table 1 or the flo w chart below.7
SM dynamical m odel
money growth
X *- D X=AX+Bn+e'
indicator
* - / « - [i = CX + bz + e" * - z
x
control
6The unemployment rate u(t)=U (t)-U e is the deviation be
tween the measured unemployment rate U(t) and the
equilibrium level Ue.
7SM denotes the Stein Monetarist dynamical model as
developed in Stein (1982).
MARCH/APRIL 1994
180
Table 1
The Reduced-Form Equations for the Dynamics of Inflation
and Unemployment, from the SM Model_________________
(7) Du = a„u + a 727r + a13tt* + e'; a 7 < 0, a 12 < 0, a13 > 0, a 12 + a 13 = 0
7
(8) Dtt = a21u + a 22 * + &23 ^ *
a 22
^23
^24
=
^ 24m ^
&21 ^
®22
^ Q
*^23
^
^24
^ Q
^
(9) Dir* = -C7r* + c n; 1 > c > 0
(9.1) Tr-ffj = (1-cy> r'(t-n ) + c(1-c) r f t- 1 ) + c £ ^
tff-s ; = C(L)fi
2
Note: u = U-Ue = unemployment rate U less the equilibrium rate Ue. n = inflation rate. p. =
rate of monetary growth.
We estimate a surrogate o f the SM dynamical
model, in which the dependent variables X are
the observable unemployment and inflation
rates. The equations o f the surrogate model are:
w ( t ) - i r ( t - l ) = b ’0 - b’J J b - l ) + b ’2 [f if t - D
- fift-D I + et;
U(t) -
U ( t - l ) = a’0 - a\ U (t -1 )
- a’J i i ( t - l) - ir ( t - l) I + e2;
E(et) = 0.
The effect o f the growth o f the m onetary in
put / upon the rate o f inflation is indirect: It
x
operates through the dynamical system, which
also involves the unemployment rate. The
change in the rate o f inflation depends upon the
unemployment rate and the rate o f change o f
real balances (/ —7r). The change in the unem
x
ployment rate depends upon its level and the
change in real balances. W e have already seen
that there is no direct relation betw een the rate
o f m onetary expansion n (t -1 ) and the subse
quent rate o f inflation ir(t). However, w hen we
consider how the rate o f M2 monetary expan
sion n ( t - l ) operates upon the dynamical system,
implied by the structural equations, the growth
o f M2 is a very good indicator o f the subse
quent rates o f inflation and unemployment. The
matrices A and B are structurally stable and
policy-rule invariant; and the surrogate system is
a good predictor. This is conclusion A above,
that the grow th o f M2 is a good indicator. We
show that the grow th o f M2 is better than alter
native m onetary aggregates (conclusion C).
Digitized for FEDERAL RESERVE BANK OF ST. LOUIS
FRASER
We then consider the intermediate target issue:
To what extent is the grow th o f M2 controllable?
This is the next link in the flow chart: / = CX +
z
bz + e". The rate o f monetary expansion / has
x
tw o components. One component is the grow th
o f reserves z which is controllable. The other
component is CX, the induced part o f the
grow th o f M2, which responds to the state o f the
economy. W e estimate this relationship. From
1958-75, the grow th o f M2 was determined by
the controllable grow th in reserves. A fter 1975,
and especially after 1984, the grow th o f reserves
did not have that effect and the grow th o f M2
was endogenous. The reason is that the growth
o f the non-M l component o f M2 was not con
trollable by the grow th o f reserves (conclusion
B). The grow th o f M2 was an intermediate tar
get prior to 1975, and much less so afterwards.
Combining the tw o links, w e ask w hether the
controllable growth o f reserves z operates through
the dynamical system, o f the following form:
X < ---- DX = (A + BC)X + (Bb)z + (Be" + &) < ----- z
intermediate target
control variable
The answer is that this system is acceptable for
the inflation rate and less so fo r the unem ploy
ment rate in recent years. This is in conclusion
B. Finally, w e ask w hether the controllable It'easury bill rate operating through the dynamical sys
tem can be considered to be an intermediate
target. Conclusion D is that there is no inform a
tional content to the controllable Treasury bill
rate. It is neither an indicator nor an interm edi
ate target.
181
THE SM DYNAMIC MODEL8
The Structural Equations
There are five structural equations and one
identity to the SM dynamic model. First: The
rate o f inflation 7r = Dp/p depends upon the ex
cess demand fo r goods, J(t) = aggregate real
demand less current real GDP, and the rate o f
grow th o f unit labor costs DW/W, w here IV is
unit labor costs. This is equation 1, w here
D = dJdt, y is a parameter:
(1) ir = DW/W + yj.
produces portfolio balance.9 In terms o f the
usual Keynesian 45-degree diagram, J is the ve r
tical distance between aggregate demand and
current real GDP (the ordinate on the 45-degree
line). The basic parameter o f the aggregate de
mand curve is real balances per unit o f capacity
output. Hence, the excess demand fo r goods de
pends upon the unemployment rate (which is
negatively related to the ratio o f actual to capac
ity output), real balances m (t) = M/PY* per unit
o f capacity output Y* and disturbances r\(t).
(4) yJ(t) = J(U, m; r\) = J t U + J, In (m )
+
Second: The growth o f unit labor costs de
pends upon the state o f the labor market,
reflected by the deviation between the unem
ployment rate U(t) and its equilibrium rate Ue,
and by the anticipated rate o f inflation ir*. This
is equation 2. That is, the anticipated rise in the
real unit labor costs depends negatively upon
the excess supply in the labor market, w here
the excess supply is reflected in the unemploy
ment rate.
(2) DW/W =
tt*
-
h [U (t)-U e l
Equation 3 simply states that the observed un
employment rate is positively related to the un
observed excess supply o f labor. The demand
fo r labor depends negatively upon real unit
labor costs, and the supply o f labor has an al
gebraically greater relationship w ith the real
unit labor costs than does the demand. Hence,
the observable unemployment rate, which is
positively related to the unobservable excess
supply o f labor, depends positively upon real
unit labor costs W
/P.
(3) U(t) = b0 + b, In (W/P)
The real excess demand fo r goods J(t) = real
aggregate demand less real GDP is equation 4,
when w e have solved fo r the equation, which
8This is explicitly developed in Stein (1982), and Infante and
Stein (1980). Here, we attempt to simplify and focus exclu
sively upon the basic characteristics. The SM refers to my
version of a monetarist system. The techniques of analysis
are different from conventional monetarists since the veloc
ity function is not used and the SM model involves an in
teraction of unemployment and inflation. The conclusions,
however, are quite close to those of Friedman, hence the
term monetarist. In a sense, the SM dynamic model lies
between the thinking of Friedman and Tobin.
9This is discussed in equation 19 in connection with the in
termediate target.
Y ],
J >
0.
Substitute equations 2 and 4 into equation 1
to obtain 1.1. It is clear that the inflation equa
tion is not the usual expectations augmented
Phillips curve, since it contains the real balances
as variables as well as the unemployment rate
and rate o f anticipated inflation.
(1.1) ir =
tt"
- h[U-Uel + y J j U + J2 ln (m ) + rj
The anticipated rate o f inflation slowly con
verges to the trend rate o f m onetary growth per
unit o f output, equation 5. Variable fi(t) is the
rate o f m onetary grow th and n is the trend rate
o f grow th o f output. Th ere are two established
facts:
(a) There is a long-run, positive relation between
the price level and some m onetary aggregate
(Figure 1), and
(b) On a year-to-year basis, there is no reliable
relationship 7t = c + c ' /jl between money
grow th and the subsequent rate o f inflation
(Figure 2). That is, there is very little inform a
tional content in the current rate o f monetary
expansion concerning the rate o f inflation in the
near future.1
0
In our Bayesian fram ework, there is a prior
anticipated rate o f inflation 7r*tt).1 Then, there is
1
10We have no need to use the subjective concept of antici
pated or unanticipated money growth.
1 We use the concept of Asymptotically Rational Expecta
1
tions as developed in Stein (1992a,b). Our results are not
sensitive to the specific form of the anticipated inflation
equation. Any anticipations function that satisfies the
following conditions will suffice. First, in the steady state, a
change in the rate of monetary expansion changes actual
and anticipated inflation by the same amounts. Second, a
change in the rate of monetary expansion at time t does
not change the current rate of anticipated inflation by as
much.
MARCH/APRIL 1994
182
Table 2
The Surrogate System: Estimated Inflation and Unemployment Equations
Growth M2 =
n
ir
Unemp U
Growth reserve = z
Inflation ir
Unemp U
1.96 [0.00]
0.76 [0.00]
0.29 [0.00]
-0 .2 3 [0.00]
-----0.76
0.72
1.6 [0.06]
-0.34 [0.016]
0.92 [0.00]
-----0.16 [0.02]
0.78
0.18
Variable
Inflation
constant
U(t—
1)
7r(t—
1)
„ ( t-1 )
z(t-1)
ADJ.R-SQ
LM prob (F)
1.4 [0.1]
-0.39 [0.01]
0.86 [0.00]
0.21 [0.03]
-----0.77
0.07
1.6 [0.01]
0.69 [0.00]
0.23 [0.00]
------0.13 [0.01]
0.71
0.72
Notes: Sample period 1958-92, annual, N=35. Columns one and two refer to equations 10 and 11 for growth of M2; columns
three and four refer to equations 12 and 13 for growth of reserves. The two-tail significance level is shown in brackets.
current information, which is the current rate
o f m onetary expansion [p(t) - nj. Combining the
two, the posterior anticipated inflation Tr*(t+1)
= ( I - c ) t t *(t) + clfiftj-n l, is a linear combination
o f the prior and the current information. The
coefficient c is the w eight given to the current
sample o f information. Subtract the prior from
both sides and derive:
(5) D ir* = ir*(t + l;t ) - ir*(t)
= d n (t) -
n -
ir*(t)].
The "credibility" argument is contained in the
value o f coefficient c. If the public believes that
the central bank is committed to an inflation
target [the p rior ir*(t)], then variations in the
current rate o f m onetary expansion l / i f t ) - n ]
w ill be given a low weight and coefficient c will
be small. Coefficient c reflects the predictability
that the current rate o f m onetary grow th w ill
continue fo r a long time and the tightness o f
the relation between money grow th and infla
tion over the relevant horizon.
The rate o f grow th o f real balances relative to
the trend rate o f grow th o f output n is equation
(6), which closes the system.
(6) Dm/m = p -
ir — n.
These dynamic interactions betw een the infla
tion rate, unemployment rate and m onetary poli
cy must be explicitly considered if w e are to
answer the questions posed at the beginning o f
this paper: Specifically, what is an indicator and
what is an intermediate target? Equations 1-6
are solved in the dynamic form described by
FEDERAL RESERVE BANK OF ST. LOUIS
Table 1. These differential equations im ply the
steady-state relations as well as the medium-run
dynamics. The steady-state solution is that: The
unemployment rate converges to the equilibrium
rate. The latter is independent o f m onetary fac
tors. The actual and anticipated rates o f inflation
converge to the grow th o f the money supply (or
grow th o f the m oney supply less the long-term
grow th rate o f the economy). Equation 5 or 9
may be solved to yield equation 9.1 in Table 1.
The anticipated rate o f inflation at any date t is
a w eighted sum o f past rates o f monetary ex
pansion, w ith declining weights.
AN EMPIRICAL SURROGATE
SYSTEM USING M2 AS INPUT
The system described in Ihble 1 involves the
measured unemployment and inflation rates and
the nonobservable anticipated rate o f inflation.
For empirical analysis, w e convert the SM dy
namic model in 'Iable 1 into a surrogate system,
involving measurable quantities only. These, in
the form o f equations 10 and 11 below, are used
fo r empirical estimation in Table 2. The sur
rogate system mimics the dynamical system.
First w e explicitly derive, from equations 1-6 o f
the SM model, the reduced form equations in
'Table 1. Then w e show how the surrogate sys
tem is derived from the SM model.
Differentiate equation 3 w ith respect to time
and use 2 to obtain 7:
(7) Du = b(ir * - hu -
it)
+ e'
= anu + a1 7 + a1 tr* + e!
2 r
3
183
Differentiate 1 w ith respect to time, using
4 -7 to obtain equation 8. The constraints on
the coefficients follow from definitions o f atj
and b..:
(8) Dir = - hb(Jj - h)U - I(J, - h)b + J jir
+ [(Jt - h ) b - c l
it *
+ (J, + c) (/ i-n ) + e"
= a2IU + a,,7r + a2 ir* + b2 ( - n ) + e"
3
4
Equation 9 is equation 5 above:
(9) D n* = -C7T* + c/x
The continuous time dynamical system 7-9 in
T^ble 1 may be w ritten as DX = AX + B/x + e,
w here X = (u,ir,ir*). W e use e as a generic
representation o f a random variable w ith a zero
expectation.
In this paper, w e use annual rather than
quarterly data because w e obtained clear-cut,
significant results w ith annual data (Tible 2),
whereas nothing o f economic significance
em erged w hen w e used the noisy quarterly
data, as shown in the appendix. W hen the data
are annual and one just uses the observable U,
7r and n the surrogate empirical system is equa
tions 10 and 11.
(10) ir(t) = b0 + b j U ( t - l ) + b2i r ( t - l )
+ b3 (t - 1 ) + e';
n
Hg: b, + b3 = 1; fa, < 0
(11) U(t) = a0 + atU ( t - l ) + a2n ( t - l )
a3 (t - 1 ) + e";
n
H0 a, + a3 = 0; a3 < 0
:
Th ere are tw o important theoretical con
straints concerning m onetary neutrality. Equal
rises in m oney grow th and inflation do not
12This can be seen as follows. The estimates (from Table 2)
of the surrogate system 10 and 11 are 10.1 and 11.1. The
SM model (Table 1) can be written as (A.1)-(A.3) when the
following values are used. The half-life of the deviation of:
(i) the inflation rate from its equilibrium value is two years,
(ii) the unemployment rate from its equilbrium value is 3.5
years and (iii) anticipated inflation from its equilibrium is
five years. This gives us the coefficients in the principal di
agonal of matrix A. (ii) The effects of inflation and anticipat
ed inflation upon the change in unemployment and the
change in inflation are equal and opposite (see equations
7, 8). (iii) All variables are measured as deviations from
their steady-state values. Then the SM dynamic system is:
(A.1)
(A.2)
(A.3)
Dir = -.197 7r
Du = -.7tt
Dir* =
- .1 U
- ,347u
+ .197t '
+ ,7tt*
- ,138-k *
change real balances and, hence, have no effect
upon the unemployment rate. Similarly, in the
steady state, the actual and anticipated rates o f
inflation w ill change by as much as the rate o f
m onetary expansion. One is not free to con
struct any m onetary aggregate as either an indi
cator or an intermediate target simply on the
grounds that it seems w ork over the period
considered. Instead, the m onetary aggregate
must be closely linked to the theory, such that
the variable satisfies certain neutrality con
straints. The neutrality constraints in the indica
tor system are as follows. In a comparative
steady state, money and prices change by the
same proportion, there is no effect upon the un
employment rate. The constraint in inflation
equation 10 is that in the steady state a change
in the rate o f m onetary expansion w ill change
the actual and anticipated rates o f inflation by
the same amount: b2 + b3 = 1. The constraint
in unemployment equation (11) is that, w hen
money and prices change by the same amount,
there is no effect upon real unit labor costs
and no change in the unemployment rate:
W ith these constraints, the surrogate system
10 and 11 mimics the SM dynamic system,
Table l.1
2
Regarding equations 7-9 or 10 and 11, a rise in
the rate o f m onetary expansion relative to the
initial rate o f inflation has several effects. First,
it raises real balances w hich raises aggregate de
mand. The rise in aggregate demand raises the
rate o f inflation. Second, the rise in the rate o f
monetary expansion raises the anticipated rate
o f inflation (by coefficient c in equation 5 or 9
above). The rate o f growth o f the nominal wage
w ill rise, by the anticipations effect in equation
2 above. This effect w ill not be great because a
Surrogate system (estimates from Table 2, rounded)
(10.1)
D*- = - . 2 T - .4 u
T
(11.1)
Du = ,25ir - .3 u
Let the initial conditions, corresponding to points B and C
in phase-diagram Figure 8 be as follows for the two
systems.
SM
B
t
(0 )
u (0 )
* '( o )
-2
2
-2
C
0
-2
Surrogate system
B
C
-2
2
0
-2
0
The trajectories of the inflation and unemployment varia
bles are very similar.
MARCH/APRIL 1994
184
rise in the current rate o f m onetary expansion
w ill convey little information about the rate o f
inflation, as is seen in Figure 2. The net effect
w ill be that the rate o f inflation w ill rise, as a
result o f both the rise in aggregate demand due
to the rise in real balances, and the rise in the
grow th o f nominal unit labor costs. However, real
unit labor costs w ill decline and unemployment
w ill decline. These are the short-run effects. As
time proceeds, the decline in unemployment and
a rise in the rate o f anticipated inflation w ill
raise real unit labor costs and the unemploy
ment rate w ill converge to its equilibrium rate.
Later, w e shall consider the intermediate tar
get system, equations 12 and 13, w here the
input is the growth o f reserves z.
(12) tr(t) = b’0 + b \ U ( t - l ) + b 'M t - 1 )
+ b'3 z ( t - l ) + e';
H 0 b ’z + b'3 = 1; b\ < 0
:
(13) U(t) = a’0 + a \ U (t - l) + a'2 i r ( t - l )
+ a'3 z ( t - l ) + e";
H0 a', + a’3 = 0; a'3 < 0
:
We ask in the next section whether, within the
context o f the dynamical system, there are eco
nomically significant (the neutrality constraints
are satisfied), structurally stable, policy-invariant
relations equations 10 and 11. W hen the input
n ( t - l ) is the grow th o f M2, the answer to all o f
these questions is yes, and there is no change in
the values o f the coefficients even w hen policy
changed drastically.
E m pirical Estimates o f the
Surrogate System: The Input is the
G row th o f M 2 13
Table 2 summarizes the empirical results fo r
both equations 10 and 11, w here the input is fj.
the grow th o f M2. Column one refers to inflation
equation 10, column tw o refers to unemployment
equation l l . 1 In each cell is the value o f the
4
regression coefficient and, in brackets, the two-tail
significance level. Summary and diagnostic statis
tics are at the end o f the table and in the text.
13AII of our data are from the data bank of the Federal
Reserve Bank of St Louis, and our software package is
MicroTSP® 7.0.
14The last two columns refer to the intermediate target sys
tem ^discussed later) where the input is the growth of
FEDERAL RESERVE BANK OF ST. LOUIS
The Inflation Equation
Table 2, column one, describing SM inflation
equation 10 indicates that the grow th o f M2 is a
good indicator, within the context o f the secondorder dynamical system. The coefficients have
the hypothesized and statistically significant
signs, satisfy the theoretical constraints, have
remarkable structural stability despite changes
in policy rules, and this equation has considera
ble predictive accuracy.
First, each coefficient in column one has the
hypothesized sign and is significantly different
from zero. The coefficient o f the lagged unem
ployment rate b 1 = -0 .39 , w ith a two-tail sig
nificance level o f 0.01; the coefficient o f the
lagged M2 grow th b3 = 0.21 w ith a significance
level o f 0.03. The coefficient o f the lagged infla
tion b2 - 0.86 with a significance level o f 0.00.
Second, the neutrality requirement is satisfied.
The Wald test concerns the neutrality hypothe
sis that b2 + b3 = 1: In the steady state a rise in
the rate o f m onetary expansion raises the rate
o f inflation by the same amount. The sum o f
these coefficients is not significantly different
from unity: the probability lb2 + b3 = 1] =
probl.86 + .21 = 1] = 0.52.
Third, there are some mixed results concerning
equation evaluation tests. Th ere is no strong evi
dence o f serial correlation o f the residuals. The
LM/Breusch-Godfrey statistic tests w hether the
lagged residuals add to the explanatory pow er o f
the equation. The hypothesis that the co effi
cients o f all o f the lagged residuals are zero has
a probability o f 0.07. Th e Ramsey RESET test in
dicated that there seems to be no specification
error in the formulation o f the inflation equa
tion. The ADF statistic fo r the stationarity o f the
residuals was -2.4, which is a bit low to main
tain the stationarity hypothesis. The ARCH test
statistic allows us to reject the hypothesis o f
heteroskedasticity.
Fourth, is the issue o f structural stability and
predictability, during a period w hen there w ere
changes in the policy rule. There is no single,
commonly accepted break point fo r the policy
rule change. Structural stability is examined in
tw o ways, displayed in Figures 4 and 5. W e exa
mine w hether the coefficient b3 o f lagged
money grow th in inflation equation 10 (Table 2,
reserves z. Column three refers to inflation equation 12,
and column four refers to unemployment equation 13.
185
Figure 4
Recursive Estimate of the Coefficient of Lagged M2 Growth in
Equation 10
Figure 5
Dynamic Ex Ante Forecast of Inflation, Using Lagged M2 Growth
as the Input
MARCH/APRIL 1994
186
column one) is stationary or w hether it evolves
over time and responds to changes in the policy
rule. Figure 4 is a recursive estimate o f co effi
cient b 3(t) using data through time t. If b 3(t) dis
plays significant variation as more data are
added (as time increases), it is strong evidence
o f instability. I f policy rule changes significantly
affect the structure, the coefficient estimates
w ill undergo dramatic changes. Figure 4 shows
remarkable stability fo r coefficient b 3(t), whereas
the velocity series (Figure 3) show significant
variation. The other coefficients in equation 10
(T&ble 2, column one) also are quite stable.
If the inflation equation using M2 is structur
ally stable, it should be useful fo r prediction:
Otherwise, M2 is not an indicator. Figure 5 dis
plays an AT-period-ahead dynamic forecast. There!
is never any correction fo r previous forecast e r
rors. The graph INFM2 uses previously predict
ed values o f the rate o f inflation as the lagged
dependent variable in the next prediction, but
uses actual values o f the lagged unemployment
rate and rate o f monetary expansion.1 It is
5
necessary to know the state o f the economy
measured by U (r - l) as w ell as the rate o f m one
tary expansion ^ (t - 1 ) to predict the subsequent
rate o f inflation ir(t). A comparison o f the actual
rate o f inflation w ith the dynamic ex ante fo re
cast using the grow th o f M2 as the input indi
cates that the actual rate converges to the
predicted rate. Hence, equation 10 is structurally
stable, policy-invariant and useful fo r prediction.
Compare Figure 5 w ith Figure 2 to see the im
portance o f knowing the state o f the economy
to predict inflation.
A unit root test on the grow th o f real
balances (/ - ir) indicated that it is stationary
x
at a level o f 2.8 percent per annum. That
is £(/x - tt) = 2.8 per annum. Since the steady
state rate o f inflation ir = i i - n , w h ere n is
the long term grow th rate, the estimates are
sensible. From Table 2 column one, and the
above, the half-life o f the convergence o f
inflation to its steady state value ft - 2.8 is
3.47 years.1
6
15This is the FORCST command in MicroTSP®.
16Let the growth of real balances f i- ir be denoted by x. The
UROOT equation was Dx=2.1-0.75 x +0.4 Dx(-1). The
coefficient 0.75 is significant, UROOT(C,1) = -4 .3 (MacKin
non 1 percent = -3.6). Hence, x is stationary and will con
verge to the steady-state value 2.1/0.75=2.8, used above.
From Table 2, if the unemployment rate is at its equilibrium
value, let p be the deviation between the inflation rate and
its steady state value: D p = -.2 p (rounding). This implies
that the half life is T=log 0.5 / log 0.2 = 3.47 years.
FEDERAL
http://fraser.stlouisfed.org/ RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
For all o f these reasons, w e therefore con
clude that, within the context o f difference
equation 10: (1) The growth o f M2 is a good in
dicator o f inflation, and (2) there is no evidence
that policy rule changes had any effects upon
the relation betw een money (M2) grow th and in
flation in equation 10.
The U n em p loym en t Rate Equation
and the E ffect o f M 2 G row th
We have seen that, within the context o f the
SM model, the grow th o f M2 is a good indicator
o f inflation. In that equation, the change in the
inflation rate depends positively upon the lagged
grow th o f real balances which raises the excess
demand fo r goods (aggregate demand less cur
rent GDP) and negatively upon the state o f the
labor market measured by the lagged unemploy
ment rate, which reflects the cost-push effects.
Even if one knew the path o f the growth o f M2,
it would be insufficient to predict the course o f
inflation, unless one could also predict the path
o f the unemployment rate. The omission o f the
unemployment rate is the main reason fo r the
poor relation betw een the rate o f inflation and
the grow th o f M2 in Figure 2. To understand
how the FOMC can achieve price stability and
"sustainable grow th in output,” and how M2
grow th affects both inflation and unemploy
ment, w e must examine the interactions be
tween M2 growth, inflation and unemployment.
Table 2, column two, examines the unemploy
ment rate equation 11 during the same sample
period used fo r the inflation rate. It shows how
the rate o f grow th o f M2 affects the unem ploy
ment rate and is perfectly consistent with the
theory described above. The coefficients are
subject to several constraints. The coefficient a5
o f the lagged unemployment rate must be less
than unity fo r convergence to the equilibrium
rate U e=a0/ ( l - a 1 7 The coefficient o f the lagged
).1
growth o f real balances should be negative,
since it produces the rise in aggregate demand
fo r goods. This means that the coefficient a, o f
lagged inflation should be positive (raise unem17The mean unemployment rate 1957-92 is 6 percent. The
estimate of a0 = 1.9 with a standard error of 0.55. The esti
mate of 37=0.76 with a standard error of 0.09. If a, = 0.7
and a0=1.8, then Ue is 6 percent.
187
ployment) and coefficient a3 o f lagged m onetary
expansion should be negative (lower unemploy
ment) and equal to - a 2. The neutrality con
straint is fa, + a3 = 0): A rise in the steady state
rate o f m onetary expansion w ill produce an
equal rise in the rate o f inflation, and no change
in the equilibrium unemployment rate.
Each coefficient has the correct sign and is
significant at the 1 percent level. The neutrality
hypothesis is satisfied. The prob[H 0 a2 + a3 = 0]
:
= probl.29 - .23 = 0] = 0.46 means that m one
tary factors cannot affect the steady-state unem
ployment rate. However, changes in the lagged
rate o f m onetary expansion produce short-run
changes in the unemployment rate.1
8
The equation (column two) passes the diagnos
tic tests.1 This equation is structurally stable over
9
various policy regimes, and the equation has
considerable predictive accuracy. Figures 6 and
7 indicate the predictive value and stability o f
the coefficients o f the unemployment equation,
despite the many changes in the policy regime.
Figure 6 compares the actual unemployment rate
with the rate forecasted from a dynamic ex ante
simulation, w here previously predicted values o f
the unemployment rate are used as the lagged
dependent variable, but actual values are used
fo r lagged inflation and grow th o f M2. The fo re
cast refers to the equation in column tw o in
which the input is the grow th o f M2. The actual
rate o f unemployment converges to the predic
tion. Figure 7 is a recursive estimate o f the
coefficient a3 o f the effect o f the lagged rate o f
M2 growth. Despite the many changes in the
policy rule used by the m onetary authorities,
this coefficient is remarkably stable. All o f this
evidence suggests that, if the policy variable is
the rate o f grow th o f M2, the policy ineffective
ness hypothesis is not in evidence. The struc
ture o f the model and values o f parameters have
been very stable despite changes in the policy
rule used by the Federal Reserve, the deregula
tion o f financial markets and the high mobility
o f international capital.
18These results are inconsistent with the New Classical Eco
nomics, but are consistent with basic monetarist (Fried
man) views. Notice that we only work with measurable
variables and do not use arbitrary and subjective estimates
of anticipated or nonanticipated money growth. Belongia
points out that the measure of unanticipated money growth
is very sensitive to the monetary aggregate considered (as
well as to what are the regressors in the equation for antic
ipated money growth).
W H Y THERE IS NO DIRECT
RELATION BETWEEN MONEY
GROWTH AND THE RATE OF
INFLATION
On the basis o f the theoretical and empirical
analysis, w e may explain w hy Figure 2 shows no
relation betw een the current rate o f inflation
and the current or lagged rate o f money growth.
From equations 10 and 11, w e derive a phase
diagram, Figure 8. From these equations and the
coefficient estimates in Table 2 (rounded)
columns one and two, derive equations 10.1 and
11.1. The curve die = d(inflation) = 0, which
corresponds to equation (10.1), is the set o f un
employment rates u(t) = U(t) - Ue and inflation
rates ir(t), such that inflation is not changing.
The curve d u=d (unem p)=0 is the set o f unem
ployment and inflation rates, such that the un
employment rate is not changing; and it
corresponds to equation 11.1.
(10.1) d(inflation) = i r ( t ) - i r ( t - l ) = - 0 . 2 [i r ( t - l )
-H (t -l)l -
0 .4 u (t -l) = 0
(11.1) d(unemp) = u ( t ) - u ( t - l ) = 0 .2 5 [w (t-l)
- n ( t - l ) ] - 0 .3 u (t -l) = 0
Let the rate o f money grow th (relative to ca
pacity output) be m. Point (m,0) in Figure 8 is
the steady state: w here the unemployment rate
u = U - U e is zero, and w here inflation is equal
to m oney grow th (relative to capacity growth).
The curve d(inflation) = 0 is downward sloping
fo r the following reason. W hen inflation is be
low m, there is a rise in real balances, which
raises excess aggregate demand and hence the
rate o f inflation, l b keep inflation from chang
ing, there must be a rise in u which reduces the
cost-push element. The d(inflation) = 0 is nega
tively sloped, and the directions o f horizontal
motion are towards the curve d(inflation) = 0.
The curve d(unemp) = 0 is positively sloped
fo r the following reason. Suppose that the
prob=0.16 indicates that there is no problem with heter
oskedasticity and using the Ramsey RESET test, we do
not find any evidence of misspecification.
19There is no evidence of serial correlation. The probability
of the F-statistic that all of the coefficients are zero is 0.00,
the adjusted R-square=0.76; DW=2.0; ARCH (2 lags)
MARCH/APRIL 1994
188
Figure 6
Dynamic Ex Ante Forecast of the Unemployment Rate, Using
Lagged M2 Growth as the Input (Equation 11)
Figure 7
Recursive Estimate of the Coefficient of Lagged M2 Growth
in Equation 11
FEDERAL RESERVE BANK OF ST. LOUIS
189
Figure 8
Phase Diagram
u=U-Ue
Note: Steady state is point (m,0), where m is growth of M2 less
long-term growth of the economy.
economy w ere at point m and then the unem
ployment rate rose (u > 0). The rise in unem
ployment reduces the growth o f nominal labor
costs and real unit labor costs tend to decline.
This w ill cause unemployment to decline. Tb keep
u from changing, aggregate demand must decline.
A rise in inflation above m w ill reduce real bal
ances which reduces aggregate demand. Th ere
fore, the d(unemployment) = 0 curve is positively
sloped. The vertical movement w ill be towards
this curve, because above (below) it wages are
grow ing at a smaller (greater) rate than prices.
W ith the phase diagram, w e may answer two
questions:
(1) W hy do w e find, as in Figure 2, no relation
between current or lagged m oney grow th and
current inflation?
(2) W ill a rise in the rate o f m onetary expan
sion, designed to stimulate the economy, lead to
higher inflation in the near future?
The answer to these questions depends upon
w here the economy is situated in Figure 8.
There are tw o variables:
(1) W hat is the deviation between the rate o f
inflation and the rate o f m onetary expansion?
W h ere is the economy along the abscissa?
(2) W hat is the deviation between the unem
ployment rate and its equilibrium value? W here
is the economy along the ordinate?
From any point, the system w ill converge to
point m, w here the unemployment rate is at its
equilibrium value, and the rate o f inflation is
equal to the rate o f money growth (relative to
the trend rate o f grow th o f the economy). The
trajectories vary w ith the initial conditions.
Given the estimates o f the coefficients in 10.1
and 11.1, the system w ill be damped cyclical.2
0
Consider tw o cases w h ere money grow th is m,
but the initial conditions vary. We can explain
w hy there is no relation betw een money growth
and inflation in Figure 2. Suppose that, when
the unemployment rate is above the equilibrium,
an expansionary monetary policy is undertaken
to accelerate the return to "full employment.”
The rate o f m onetary grow th is raised above the
inflation rate. The economy starts at point B.
20The characteristic equation implied by 10.1 and 11.1 is
A + .5A + .16 = 0 The roots are complex, but the
2
.
system is stable.
MARCH/APRIL 1994
190
Th e trajectory w ill be BAm. Initially along BA,
both the inflation rate and unemployment rate
decline. The weakness in the labor market more
than offsets the effect o f a rise in real balances
upon aggregate demand, and the inflation rate
declines. Wages decline relative to prices, and
unemployment declines. Along BA, a rise in the
rate o f monetary expansion does not lead to more
inflation. W hen the economy reaches point A,
the low er unemployment rate implies that the
weakness in the labor market is insufficient to
offset the effect o f a rise in real balances upon
aggregate demand, and the inflation rate rises.
Prices continue to rise relative to wages, and un
employment continues to decline. Along Am, the
inflation rate rises though the unemployment
rate is above its equilibrium level.2 Along trajec
1
tory BAm, the inflation rate declines and then
rises fo r the same rate o f money growth.
Similarly, suppose that the economy started at
point C, w here inflation is equal to money
growth, but unemployment is below the equi
librium rate. Nominal wages w ill rise which w ill
raise the rate o f inflation. Wages w ill rise faster
than prices, and the rise in real unit labor costs
w ill increase unemployment. The economy moves
along CD. At point D, the rate o f decline o f real
balances lowers aggregate demand and offsets
the wage-push effect. The rate o f inflation
declines, wages continue to grow faster than
prices and the unemployment rate continues to
rise. Along trajectory CDm, the inflation rate
rises and then declines fo r the same rate o f
money growth.
W e have explained w hy the rate o f money
growth is a good indicator o f the rate o f infla
tion only within the context o f the dynamic
system, equations 10 and 11, w here inflation
and unemployment interact. No useful inform a
tion about the rate o f inflation is conveyed just
by looking at the rate o f m onetary expansion
per se as in Figure 2. I f the rate o f m onetary
expansion is raised to speed a recovery, this
need not im ply m ore inflation in the near
21This differs from the Keynesian NIRU view. See Modigliani
and Papademos (1975, 1976). For a critique, see Carlson
(1978) and Stein (1982, ch. 4). The analysis differs funda
mentally from the New Classical propositions. Neither view
is consistent with the results in Table 2.
22The importance of Divisia indices has been developed by
Barnett. I am drawing upon Belongia (1993a,b) in the dis
cussion of weighted monetary aggregates (WMA), who sup
plied me with the data to use as WMA in the SM dynamic
model.
23A WMA is constructed as follows (See Belongia). Let
U j(t)=[R (t)-rj(t)] / [1 + R(t)], where R(t) is the return on a
FEDERAL RESERVE BANK OF ST. LOUIS
future. The exact trajectories fo r inflation and
unemployment implied by equations 10 and 11,
in T&ble 2, columns one and two, are easily
calculated.
THE USE OF WEIGHTED
MONETARY AGGREGATES2
2
Several economists have argued that w e
know that the standard measures o f m onetary
aggregates violate the basic principles o f the
economic theory o f index numbers, because
simple-sum measures incorrectly assume that
the components are perfect substitutes and,
hence, cannot internalize pure substitution
effects. Belongia stated that "T h e potential fo r
this sort o f [substitution] shift in measured
money, o f course, is exactly the type o f thing
that may be behind the break in velocity and
instability o f m oney demand functions." The
contention o f Belongia, Chrystal and MacDonald
(this Review) is that ostensible changes in the
relationships betw een money grow th and
inflation observed in the 1980s, w hich have
been subjectively attributed to “ financial innova
tions” are simply due to im proper measure
ments o f the m onetary aggregate. Instead o f
using ad-hoc, arbitrary measures o f the “ true”
monetary aggregate, W M A have been con
structed to internalize shifts among m onetary
aggregates based upon substitution effects.
These are basically Divisia indices, by which
the components o f the W M A are w eighed by
their share o f total expenditure on monetary
services.2
3
Their contention is not obvious. Figure 2e,
graphs (along w ith the regression line) the rate
o f inflation against the grow th o f Divisia M2.
There is no apparent relation betw een the two
variables. Figure 3b plots the velocity o f Divisia
M2 (nominal GDP divided by Divisia M2). The
relation does not demonstrate any m ore stability
than the velocities o f M l or M2 (Figure 3a).
long term grade B corporate bond, rtft) is the asset’s own
rate of return. Denote the vector of the u's by u = (u1
,...,un),
and the vector of the value of balances in the i-th asset
category by q = (q p ■■
■,qrJ. The weight S ;(t) of the i-th asset
is (b) si (t) = ui(t)qj(t)/u(t).q(t), where the denominator is an
inner product. The weighted monetary aggregate WMA is
(c) WMA(t)=s(t).q(t). The period denotes the inner product
operation.
191
We examine the hypothesis that the W M A are
the correct empirical counterparts o f what is
meant by money in the theory in the second
section24:
(1) The money should have the neutrality
properties, noted alongside equations (10) and
(11) above. A rise in the rate o f m onetary expan
sion should produce the same rise in the steady
state rate o f inflation. Equal changes in money
grow th and inflation should have no effect upon
the unemployment rate.
(2) Th e W M A should satisfy the requirements
fo r an indicator fo r both inflation and unem
ployment. It should be able to explain variations
in the rate o f inflation and how monetary policy
exerts short-run changes upon the unemploy
ment rate. Specifically: Given information in
year (t-1 ), to what extent can the W M A be used
to predict inflation and unemployment in year t?
The W M A have the desirable property that they
are not arbitrary measures o f “ m oney
ness.” They have the limitation that their weights,
which are interest rate differentials, are en
dogenous variables. W hen a monetary com po
nent is changed, the interest rate differentials
change. Since the weights in the index change
with the endogenous interest rates, the W M A is
not a control variable and cannot be considered
as an intermediate target.
W e already analyzed M2 as an indicator in
Table 2 fo r the sample period 1958-92. Table 3
compares three w eighted m onetary aggregates
w ith M2 during the same sample period 1961-92,
in terms o f equations 10 and 11. The three
W M A are used: DM2 = Divisia M2; CE =
Rotemberg's currency equivalent; DCE = Divisia
currency equivalent. In each case fj.lt) is the rate
o f growth (percent per annum) o f the aggregate.
Our object is to see how each responds to
points 1 and 2 above. Our conclusions, to be
discussed, are:
(1) The M2 aggregate is the best o f the poten
tial indicators.
(2) The Divisia currency equivalent DCE is ac
ceptable.
(3) The Divisia M2 (DM2) and the Currency
Equivalent (CE) are unsatisfactory.
The upper part o f Table 3 is inflation equation
10, and the low er part is unemployment rate
equation 11. The entries are the regression
coefficients and the two-tail significance levels in
brackets. We also note the adjusted R-square
and the probability implied by the LM statistic
that there is no serial correlation.
Consider the successes. First is M2 in column
one. In the inflation equation, the sum o f the
coefficients o f lagged inflation and lagged M2
growth (0.87 + 0.18) is not significiantly d iffe r
ent from unity. Each coefficient is significant. In
the unemployment equation, each coefficient is
significant. The sum o f the coefficients o f lagged
inflation and lagged M2 grow th (0.28 - 0.22) is
not significantly different from zero. Second is
the Divisia Currency Equivalent (DCE), which
also passes these tests. However, the coefficients
in the M2 equation are closer to their theoreti
cal values than those in the DCE. Th e co effi
cients o f lagged inflation and m oney grow th
should be equal and opposite in sign.
Next are the failures. The Divisia M2 (DM2)
fails in the inflation equation. The coefficient o f
its growth jx is not significant. The currency
equivalent (CE) fails in the unemployment rate
equation. The coefficient o f its grow th / is not
z
significant. M y conclusion is that M2 is the best
o f the indicators w hen it is used in the dynamic
SM model, in which both unemployment and
inflation interact.
A cogent analysis o f the deficiency o f Divisia
indices o f money has been given by Otmar Issing o f the Deutsche Bundesbank (1992, p. 296).
He wrote:
"In phases with an interest rate pattern in which
the yield on time deposits is almost that on the
yield on public bonds outstanding, time deposits to
all intents and purposes disappear from the defini
tion of the money stock (CE aggregates) or hardly
contribute at all to money stock growth (Divisia
Aggregates). Should time deposit rates exceed the
yield on bonds outstanding, then this leads to
either negative growth of these aggregates or the
changed maximum interest rate is taken into con
sideration so that monetary capital components
possibly contribute to growth in the money stock.
The reason here is that — based on a utility max
imization approach — liquidity is measured in
24lt is essential that one have a macroeconomic theory to
evaluate whether an empirical measure of money cor
responds to a theoretical concept. Barnett, Belongia and
others correctly object to the ad hoc measures of “ money
ness” that have been offered to replace M2. Many of these
measures even fail to satisfy the neutrality requirement.
MARCH/APRIL 1994
192
Table 3
Inflation and Unemployment Equations Using Alternative Measures of Money
Inflation equation 13
Constant
U(t—
1)
7r(t-1)
Mi(t~1)
ADJ-RSQ
LM-prob
i=lM2
1.88
-0.44
0.87
0.18
0.79
0.14
Unemployment equation 14
Constant
1.60
0.81
U(t—
1)
7r(t-1)
0.28
-0.22
w fl-1 )
ADJ-RSQ
0.82
LM-prob
0.80
G rowth rate o f the m onetary aggregate i
i = DM2
i = DCE
[0.03]
[0.00]
[0.00]
[0.045]
2.15
-0.39
0.90
0.13
0.76
0.07
[0.02]
[0.01]
[0.00]
[0.12]
2.44
-0.46
0.97
0.10
0.78
0.17
[0.00]
[0.00]
[0.00]
[0.07]
[0.00]
[0.00]
[0.00]
[0.00]
1.19
0.75
0.26
-0.15
0.81
0.76
[0.04]
[0.00]
[0.00]
[0.007]
0.92
0.80
0.18
-0.10
0.78
0.75
[0.10]
[0.00]
[0.00]
[0.008]
L
U
O
n
Variable
1.78
-0.19
0.85
0.027
0.78
0.12
[0.05]
[0.21]
[0.00]
[0.06]
0.84
0.68
0.24
0.001
0.71
0.65
[0.23]
[0.00]
[0.00]
[0.92]
Notes: The sample covers 1961-92. N = 32. The two-tail significance level is shown in brackets. The data are from the
Federal Reserve Bank of St. Louis. DM2 = Divisia M2; DCE = Divisia currency equivalent; CE = currency equivalent.
terms of forfeited yields, while the dimension of
risk — contrary to the portfolio optimization ap
proach — is not taken into account. The interest
rate for a particular form of investment not only
contains a premium for foregoing liquidity but
also a risk premium owing to yield volatility. As
empirical studies show, in particular the CE-M3 ag
gregate has in the past been subject to extreme
fluctuations and the correlation with growth rates
of GNP was in fact negative. Furthermore, the ve
locity of circulation of this aggregate was substan
tially more instable (sic) than that of M3.”
sues: lb what extent is money grow th endo
genous? lb what extent is money grow th
controllable? In equation 14, part CX is
endogenous, X is a vector o f the state o f the
economy and z is the grow th o f reserves.2
5
Unless variations in fi are controllable, they
are not responsible fo r variations in inflation
and unemployment; and the central bank does
not have the w herew ithal to control inflation
in the medium run.2
6
(14)
The Divisia M2 is too much dependent upon en
dogenous weights, which are interest rate
differentials, to be useful as an indicator o f a
theoretical concept o f money. It misses the
unique aspect o f m oney that it is the safe asset
used as the medium o f exchange.
The Controllability o f M o n e y
G row th
ij 2
l
-
CX + bz + e
We can relate total reserves R to M2. There is a
close relationship between reserves R and M l,
through a system o f reserve requirements. Call
the reserve requirement ratio R/Ml=a. W e can
then write:
R/M2 = (R/Ml) (M1/M2) = a (M1/M2)
and therefore,
We have shown that grow th o f M2, denoted
^ 2, is a good indicator. Th ere are tw o distinct is
25For notational simplicity, let e generically represent the ran
dom variable with a zero expectation.
26ln the long run, as Figure 1 indicates, the price level is still
closely tied to M2/real GDP.
FEDERAL RESERVE BANK OF ST. LOUIS
log M2 = log (M2/M1) + log R - log a.
193
Figure 9
Ratios of M2 to the Adjusted Monetary Base and Adjusted
Reserves
- 45
- 40
- 30
■ i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i “ 15
195658 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 1992
The rate o f change o f M i (1 = 1, 2) is denoted fi:
and the grow th o f reserves is denoted z. Thus,
w e have equation 15, which w e relate to equa
tion 14:
(15) n2 = f/x, - fx j + z + e
(14)
= CX + bz + e
The growth o f M2 in equation 15 has three
components: the growth in adjusted reserves z,
which is controllable; the grow th in the non-M l
component o f M2, which is (n2 - n j ] and the e
term, which reflects nonsystematic factors.2
7
Thornton noted several points. First, the Fed has
a tight control on M l = fl/a via reserves. Se
cond, the ratio o f M l to M2 declined from 0.5
in 1959 to 0.25 in 1977, and has then fluctuated
around this level. Third, the policy variable,
which is the grow th o f reserves, does not have a
significant effect upon (/z, - /xj. The Fed can
control only the M l component o f M2 but can
not control the other component (fi, - fxj
directly. For example, suppose that a rise in fis
cal policy or private demand tends to raise the
grow th o f nominal GDP, which induces a growth
in the demand fo r money. The given grow th o f
reserves controls the grow th o f M l. Th ere w ill
be a grow th in M2 relative to M l to accommo
date the induced rise in the demand fo r money.
This means that CX = fyt, - n j is endogenous;
and it may well be the major source o f variation
o f the rate o f m oney grow th in equation 15.
Figure 9 suggests that there has been a
structural break in the controllability o f the
grow th o f M2. The graph is the ratio o f M2 to
adjusted reserves. It has a relatively constant
positive trend until 1975. The trend rises drasti
cally to about 1984. Then it falls to zero or be
comes negative. A similar situation exists with
the ratio o f M2 to the adjusted monetary base.
We shall now be m ore precise.
We consider tw o components o f money growth
in equation 16 which correspond to 14 and 15.
(16) nz = c' D N G D P (-l) + bz + e
The control part is the controllable growth
o f reserves. The induced part is related to
the lagged grow th o f nominal GDP, denoted
27The controllability of M2 is the subject of the important
paper by Thornton (1992), upon which we draw.
MARCH/APRIL 1994
194
Table 4
The Rate of Growth of M2 as a Function of the Lagged Growth of Nominal
GDP and the Growth of Adjusted Reserves (Equation 16)________________
Variable
Constant
DNGDP(-1)
z
DW
ADJ R-SQ
1958-92
1958-75
1975-92
3.60 [0.02]
0.31 [0.05]
0.27 [0.06]
1.10
0.12
3.40 [0.01]
-0.04 [0.71]
0.90 [0.00]
1.69
0.64
2.10 [0.45]
0.56 [0.04]
0.17 [0.39]
1.10
0.14
Note: The two-tail significance level is shown in brackets.
DNGDP ( —l).2 The induced part corresponds to
8
CX in equation 14. That means that if the omit
ted fiscal variables and shocks to private de
mand induce a rise in the demand fo r money,
the grow th o f M2 w ill respond, although the
grow th o f M l is tied to the grow th o f reserves.
Th ere are several implications from Table 4,
which are consistent with Thornton’s findings.2
9
First, consider column two, which concerns the
early period 1958-75. The growth o f reserves is
the significant determinant o f the growth o f M2,
w ith a coefficient 0.9, which is not significantly
different from unity. The grow th o f lagged nomi
nal GDP is not significant.3 A regression o f
0
on z and a constant gives almost the identical
results, during the first period. Hence one could
confidently claim that /z, = c + z + e, w here c
is a trend which corresponds to the grow th o f
M2/M1. The m oney supply was both controllable
and the controllable part was the dominant
component. Hence from 1958 to 1975, the
grow th o f M2 was an intermediate target for
both the inflation and unemployment rates. This
is "Monetarism Triumphant.”
Second, consider column one containing the
entire period 1958-92. It would seem that both
28The lag is used to avoid a simultaneous equation problem.
We also used for the induced part the Treasury bill and
Treasury bond rates, which could reflect changes in the
structure of interest rates, which would ultimately induce
substitutions between M1 and M2. However, they were not
significant additions to the growth of reserves.
29Similar results were obtained when the regressors were the
lagged unemployment and inflation rates.
30The equation for this period passes all of the equation
evaluation tests: There is no serial correlation (LM test),
heteroskedasticity (ARCH test).
RESERVE BANK OF ST. LOUIS
FEDERAL
the growth o f reserves and the grow th o f nom i
nal GDP are significant. However, the equation
evaluation tests tell a different story. The recur
sive residuals (not shown) keep m oving outside
the plus-or-minus-2 standard error bands, which
implies that the structure is progressively chang
ing. Figure 10 is a recursive estimate o f the
coefficient o f the growth o f reserves. This co
efficient has a clear downward trend from unity
towards zero, indicating that the control part is
becoming less significant since the mid-1970s.
The reason is shown in column three containing
the period 1975-92. This column is a direct con
trast to column two, the 1958-75 period. The
growth o f reserves is not significant. Th e lagged
growth o f nominal GDP is significant. However,
the regressors only explain 14 percent o f the
variation in the growth o f M2. During the peri
od 1975-92, it is not apparent that the grow th o f
M2 was an intermediate target.
THE INTERMEDIATE TARGET
SYSTEM
It is quite possible that w e have omitted sig
nificant variables from the induced part CX o f
money growth, so that it seems that money
grow th is no longer controllable by the growth
195
Figure 10
Recursive Estimate of the Coefficient of the Reserves Growth in
Equation 16
Figure 11
Dynamic Ex Ante Forecast of Inflation, Using Lagged Resources
Growth as Input (Equation 12)
■
MARCH/APRIL 1994
196
Figure 12
Recursive Estimate of the Coefficient of Lagged Reserves Growth
in Equation 12
o f reserves. Th e control equations involving the
grow th o f reserves w ere described in the se
cond flo w chart, shown here again:
X < ----- DX = (A+BC)X + (Bb)z
+ (Be" + e ') < -------------------z
intermediate target
control variable
A direct test o f controllability is equations 12
and 13, in the surrogate system, estimated in
Table 2, columns three and four:
Call this the control system. The next two
sections show that the controllable growth o f
reserves may be a good intermediate target for
the rate o f inflation. The subsequent section
shows that the short-term Treasury bill rate,
which may be controllable, has no informational
content; it is neither an indicator nor an inter
mediate target. Interest rate targeting, which
has had disastrous results both in the Great
Depression and the pre-1979 periods, is to be
avoided at all costs.
(12) ir(t) = b ’ + b 'J U (t-l) + b 'j j f t - l )
0
+ b'3 z ( t - l ) + e ;
H K + K = 2; b: < (>
„:
(13) U(t) = a' + a [ U ( t - l ) + a 'M t-1 )
+ a'3 z ( t - l ) + e ;
H0 a' + a' = 0; a'3 < 0
:
31We did not use the growth of the adjusted monetary base
as the control variable for two reasons. First, it failed to
satisfy the neutrality requirement. Second, it is not a relia
ble control over the growth of M1 due to the significant var
iations in the currency ratio. See Garfinkel and Thornton.
FEDERAL RESERVE BANK OF ST. LOUIS
The Grow th o f Adjusted R eserves
Is A n Interm ediate Target3
1
In the control system, the control input is z
the growth o f adjusted reserves. This variable is
197
clearly controllable.3 W e evaluate w hether the
2
control system is structurally stable and policyrule-invariant, w hen there have been changes in
Federal Reserve operating procedures and policy,
and financial market deregulation. Table 2,
columns three and four, and the subsequent
analysis show that the control system is quite
significant fo r the inflation rate but less so for
the unemployment rate.
The Inflation Equation in the S M
M o d e l with the Grow th o f Adjusted
R eserves
The inflation equation is 12. The rate o f infla
tion rises when (1) real reserves rise, the growth
o f reserves exceeds the current rate o f inflation,
or (2) when the labor market is tight, the unem
ployment rate is below its equilibrium rate. In
the steady state, the rate o f inflation w ill rise by
the same amount as the rise in the growth o f
reserves. Real reserves converge to a constant.
This is the neutrality hypothesis b'2*b'3 = 1 in
12. The second factor states that the coefficient
o f the lagged unemployment rate is negative.
from Table 2, column three, denoted INFRES.
The large deviations fo r the 1977-80 period are
corrected by 1986; and the model is back on
track. Second, Figure 12 displays the structural
stability in a clear and dramatic way. It is a
recursive estimate o f coefficient b'3 which relates
the effect o f a change in z ( t - l ) the grow th o f
reserves in year t - 1 upon ir(t) the rate o f infla
tion in year t, given the initial values o f unem
ployment and inflation. This coefficient is fairly
stable, despite the changes in policy regim e over
the period. The conclusion is that the grow th o f
adjusted reserves is an intermediate target for
achieving price stability, within the context o f
the dynamic equation.
The U n em p loym en t Rate Equation
with the Grow th o f Adjusted
R eserves
Table 2, column three, is consistent w ith these
hypotheses. Each coefficient is significant and
has the hypothesized sign.3 The Adj. R-SQ=0.78.
3
The neutrality hypothesis is confirmed. It is
seen w ith a Wald test that the sum o f the co effi
cients o f the inflation and growth o f reserves is
not significantly different from unity: prob lb ' +
b'3 = 1] = prob [0.92 + 0.16 = 1] = 0.44.
The inflation equation is not sufficient to an
swer the question: H ow can the central bank
achieve price stability and "prom ote sustainable
growth?” The reason is that the inflation rate is
affected by the state o f the unemployment rate
as well as by its past history and the grow th o f
reserves. Attempts to reduce the rate o f infla
tion by varying the grow th o f reserves w ill af
fect, in the medium run, the unemployment
rate. In turn, the unemployment rate w ill affect
the inflation rate. Another dimension to this
problem concerns w hether m onetary policy can
also affect, in the medium run, the unemploy
ment rate, and w hat w ill be the consequences
fo r the rate o f inflation?
W e show in several ways that this equation is
structurally stable and policy-invariant. First,
Figure 11 compares the actual rate o f inflation
w ith a dynamic ex ante forecast derived
We turn to equation 13 in Table 2, column
four, to see to what extent the growth o f reserves
affects the unemployment rate. Table 3, column
four, is consistent with several hypotheses. First,
32We believe that the growth of reserves is controllable and
has not been an endogenous variable, even in the 1979-82
period when there was fairly explicit interest rate targeting.
If the growth of reserves were endogenous, then it should
be responding to the growth of nominal GDP and the value
of the Treasury bill rate. A rise in the growth of nominal
GDP, given the Treasury bill rate, should increase the de
mand for reserves and induce a greater supply. Similarly,
given the growth of nominal GDP, a decline in the Treasury
bill rate should induce a decline in the growth of reserves
to force the treasury bill rate up to a desired level. We exa
mined the issue of whether the growth of reserves
(DRES=z) has been an endogenous variable by regressing
it upon the lagged growth of nominal GDP [DNGDP(-1)]
and the lagged Treasury bill rate [TB3(-1)], to avoid a
simultaneous equation problem. The sample period is
1959-92. The dummy variable (DUM) was set at DUM=1
during the 1979-82 period, and DUM=0 otherwise. We
constructed two variables, DUM*DNGDP and DUM*TB3, to
highlight the short period of interest rate targeting. The
regression equation was
(14) DRES = 5.13 -0.25 7 DNGDP(-1) + 0.40TB3(-1)
(t-stat)
(2.7)
(-1-09)
(1.3)
-0.48'DUM'DNGDP(-1) + 0.118DUM'TB3(-1)
(-0.77)
(0.22)
ADJ R-squared = 0.00. No coefficient is significant and
there is no evidence that the growth of reserves has been
an endogenous variable in any significant way during the
period 1959-92.
33There is no evidence of either serial correlation (LM test
prob=0.18) or heteroskedasticity (ARCH test prob=0.49).
The Ramsey RESET test of whether there are omitted vari
ables, incorrect functional form or correlation between the
regressors and the error term indicates that the probability
that there is no specification error is 0.38.
MARCH/APRIL 1994
198
Figure 13
Dynamic Ex Ante Forecast of the Unemployment Rate, Using
Lagged Resources Growth as the Input (Equation 13)
Figure 14
Recursive Estimate of the Coefficient of Lagged Reserves Growth
in Equation 13
FEDERAL
http://fraser.stlouisfed.org/ RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
199
each coefficient has the correct sign and is sig
nificant at the 1 percent level; and the R2= 0.71.3
4
Second, the neutrality hypothesis is confirmed.
W hen reserves rise at the same rate as the rate
o f inflation, there is no effect upon the unem
ployment rate, which would then converge to its
equilibrium rate. Hence, a' + a' = 0, that is, the
coefficients o f inflation and the grow th o f
reserves sum to zero. Using a Wald test, the
Prob /a'+a' = 07 = Probl0.23 - 0.13 = 0] = 0.23,
thereby confirm ing the neutrality hypothesis.
makes any economic sense, the interest rate
should be a significant input into the dynamic
inflation and unemployment rate equations,
either by itself [6 = 0] or as additional inform a
tion [6 = 1] to the grow th o f M2, in equations
(12.1) and (13.1).
(12.1) -reft) = Cj + c2U ( t - l ) + c3i r ( t - l )
+ 6c4 ( t - l ) + c j j f t - l ) + e
n
(13.1) U(t) = c; + c'2U ( t - l ) + c'3i r ( t - l )
Third, the explanatory pow er o f this equation
is much less satisfactory than the inflation equa
tion w here the input is the growth o f M2. In
Figure 13, the actual unemployment rate is com
pared w ith a dynamic ex ante simulation o f the
value implied by the coefficients in lable 2,
column four, w here the lagged dependent varia
ble is the previously predicted value. The fo re
cast predicts basic trends but gives misleading
predictions o f the level o f the unemployment
rate.
Fourth, Figure 14 plots the recursive estimate
o f the coefficient a'3 < 0 o f the lagged growth
o f reserves. The absolute value o f this co effi
cient has been diminishing over the sample
period.3 A possible reason fo r the decline in im
5
portance o f the grow th o f reserves in the unem
ployment equation may be that the growth o f
reserves has becom e a less important deter
minant o f money grow th (Figure 13) in a period
w hen the non-M l component o f M2 has become
more important.
The Treasury Bill Rate is N o t an
Interm ediate Target: It Adds N o
Useful In form a tion
The Federal Reserve has revived the issue o f
interest rate targeting, w here the Treasury bill
rate is an intermediate target. Is there evidence
to support interest rate targeting? Th e Treasury
bill rate, denoted
is controllable. Hence, it
should be used to evaluate interest rate target
ing. The surrogate dynamic SM model implied
equations 12 and 13. I f interest rate targeting
34There is no evidence of serial correlation (LM test
prob=0.72) nor of heteroskedasticity (ARCH test
prob=0.64). According to the RESET test, there is no evi
dence of misspecification (RESET test prob=0.12).
35l do not have an explanation why the coefficient a3< 0 in
Figure 9 is stable, but a'3<0 is not in Figure 14.
+ 6c'4 i . ( t - l ) + c U J t-1 ) + e'
i
Since the rate o f inflation is a regressor, a rise
in the nominal interest rate in the regression
corresponds to a rise in the observed real rate.3
6
Table 5 describes the results o f such a test.
Column one is the inflation equation, which just
uses the Treasury bill rate as a control [6 = 0].
It is seen that the coefficient o f the Treasury bill
rate is not significant. It contains no additional
information about what w ill happen to inflation.
Column tw o adds the growth o f M2 as an input
[6 = 1], The grow th o f M2 is highly significant
(as it was in Tkble 2), and the Treasury bill rate
remains insignificant. The conclusion here is
that adding the Treasury bill rate adds no in for
mation about what w ill happen to inflation.
Columns three and fou r concern the unem
ployment rate. In column 3 [6 = 0], the results
are bizarre. The coefficient o f the nominal in
terest rate is not significant at the 5 percent
level, and the coefficient o f inflation is not sig
nificant. Given the nominal interest rate, a rise
in the rate o f inflation corresponds to a decline
in the real rate o f interest. This should lower
the unemployment rate, but it does not. Th ere
fore, it would appear that real interest rate tar
geting is not promising. In column four, w e add
the rate o f M2 grow th [6 = 1]. The results turn
sensible fo r everything but the Treasury bill
rate, which continues to remain insignificant.
The conclusion is that the Treasury bill rate at
( t - 1 ) adds absolutely no information to what is
obtained from the results in 'lable 2.
use estimates of anticipated inflation that cannot be objec
tively justified. It is not clear whether the spread between
the bond rate and Treasury bill rate is a more or less ac
curate measure of anticipated inflation than is the recent
ex post inflation. In either case, the onus of finding the
true ex ante real rate is upon the advocates of interest rate
targeting.
36lf there is real interest rate targeting, the only available in
formation concerns observed, not anticipated, rates of infla
tion. It requires prescience for the monetary authority to
MARCH/APRIL 1994
200
Table 5
Inflation and Unemployment Rate Equations_________________
liti-D
1.99 [0.02]
1.39
U(t) 16= 1
1
-0 .2 4 [0.12]
-0 .3 9
s
16=01
II
tW
t
Equation 13.1
oi;
ii
Equation 12.1
Variable
Constant
U ( t-l)
■K(t-l)
ilt-1 )
[0.12]
1.27 [0.05]
1.89
[0.00]
[0.018]
0.56 [0.00]
0.72
[0.00]
0.226 [0.01]
0.95 [0.00]
0.858 [0.00]
0.12 [0.18]
-0 .0 5 9 [0.61]
-0 .0 0 8 [0.94]
0.15 [0.07]
0.079 [0.27]
-0 .2 2
[0.00]
Note: Sample period is 1958-92. N=35. The two-tail significance is shown in brackets.
The Transm ission M echanism
Th ere is a good reason w hy the Treasury bill
rate is neither an indicator nor an intermediate
target. This concerns the transmission mechan
ism. Aggregate investment demand depends
upon the Keynes-Tobin (/-ratio. M onetary policy
exerts its effects upon the economy through this
ratio. Keynes (1936, p. 151) explained the theory
o f the (/-ratio: "...the daily revaluations o f the
stock exchange, though they are prim arily made
to facilitate transfers o f old investments between
one individual and another, inevitably exert a
decisive influence on the rate o f investment. For
there is no sense in building up a new enter
prise at a cost greater than that w hich a similar
enterprise can be purchased; w hile there is an
inducement to spend on a new project what
may seem like an extravagent sum, if it can be
floated o ff on the stock exchange at an immedi
ate profit.”3
7
Formally, let q'.k be the market value o f k the
existing capital and let p.k be the reproduction
cost.3 Their ratio is the (/-ratio.
8
(17) q = q'.k / p.k
The portfolio balance equation 18 is that the ra
tio o f money to the market value o f capital
M/q'.k depends upon L(i) w h ere i is a vector o f
opportunity costs i= (i1
,-.,in), and element / is
.
the perhaps controllable Treasury bill rate. Solve
equation (18) fo r q=q'.k / p.k, which is associated
with portfolio balance and obtain 19. Denote
37The role of financial markets in capital formation, along
these lines, is the theme of Stein (1987, ch. 7; 1991, ch. 3).
38The period represents an inner product. Variables q\ k and
p are vectors of market prices, physical quantities and
reproduction costs, respectively. Capital and bonds are in
vector k and the weighted sum is q'.k. This is definitely in
the spirit of Keynes and Tobin.
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Federal Reserve Bank of St. Louis
m = M/p.k, the ratio o f real balances per unit o f
capital.
(18) M/q'.k = M / q pk = M/pk / q = Lti)
(19) q = [M/p.k] / L (i) = m / L(i)
M onetary policy, which changes reserves,
operates as follows in the context o f equation
19. Let there be a rise in real bank reserves,
w hich is a control variable. The higher ratio o f
reserves to deposits induces banks to purchase
financial assets, equity or debt. The greater w ill
ingness to lend induces their customers to b o r
row to purchase equity and debt. The money
stock rises. Given the vector o f expected returns
i on the n-assets, the prices o f existing assets,
real and financial, rise. This is a rise in the
Keynes-Tobin (/-ratio, the ratio o f the prices o f
existing assets (stock prices, bond prices, physi
cal plant), relative to their reproduction costs.
This encourages the production o f investment
goods and raises the excess demand fo r goods
relative to current GDP.3 This is the logic o f
9
having m in equation 19 above: It reflects the qratio effect. The rise in q = q'.k/p.k need not be
reflected in the Treasury bill rate or in any par
ticular interest rate. Changing the Treasury bill
rate without changing the grow th o f M2 has a
negligible effect upon the (/-ratio, whereas
changing the money stock has a large effect,
assuming that both are controllable. Interest
rate targeting o f the Treasury bill rate pro
vided a misleading indicator o f w hat has been
39This is not the textbook transmission mechanism, but it is
the one stressed by Keynes, Tobin and Friedman.
201
happening to the (/-ratio, or the stance o f m one
tary policy as was stressed by Friedman and
Schwartz in their account o f the Great Con
traction.4
0
CONCLUSIONS
In the long run, the GDP deflator is closely
related to the quantity o f M2 per unit o f real
GDP.4 The question examined in this paper con
1
cerns how the Federal Reserve should select
ranges fo r m onetary grow th over the coming
year to achieve a given rate o f change in the
price level in the near future. Our conclusions
w ere stated as propositions A-D at the beginning
o f the paper. Friedman does not think that the
inflation rate can be controlled finely:
"...we cannot predict at all accurately just what
effect a particular m onetary action w ill have on
the price level and, equally important, just when
it w ill have that effect. Attem pting to control
directly the price level is therefore likely to
make monetary policy itself a source o f econom
ic disturbance because o f false stops and starts
...Accordingly, I believe that a m onetary total is
the best currently available immediate guide or
criterion fo r monetary policy—and I believe that
it matters much less which particular total is
chosen than that one be chosen (1969, p. 1089)...there seems little doubt that a large change
in the money supply within a relatively short
period w ill force a change in the same direction
in income and prices...But w hen the money
changes are moderate, the other factors come
into their own. If w e knew enough about them
40One of the most vivid examples of the dangers of interest
rate targeting, inspired by Friedman and Schwartz, is
shown below, which compares 1929 with 1932. The data
are from the U.S. Department of Commerce; the appropri
ate series are noted. The first row is the S&P index (B85),
the second row is the implicit price deflator P' for fixed in
vestment (B68), the ratio of the two is an index of the
qr-ratio. The fourth row is i1, the Treasury bill rate (B83).
The variable /2 is the basic yield of 30-year corporate
bonds (B75). Variable i3 is the Manhattan real estate mort
gage rate (B78). The row labelled P is the implicit GNP
deflator (B63) and M is the money supply (B110). The aver
age annual rate of growth of P and M is in square brackets
in the 1932 column.
The movement in the treasury bill rate was a misleading
measure of the extent that the qr-ratio changed.
and about the detailed effects o f monetary
changes, w e might be able to counter these e f
fects by m onetary measures. But it is utopian
given our present level o f knowledge. Th ere are
thus definite limits to the possibility o f any fine
control o f the general level o f prices by a fine
adjustment o f m onetary change.” (p.181)
Friedman’s argument should be qualified, in
view o f the analysis in this paper. First, the
choice o f the m onetary aggregate does matter.
No aggregate has the same quality o f explana
tory power as does M2, w ithin the context o f
the dynamical system. Second, there is a serious
question w hether the grow th o f M2 is controlla
ble. From 1958 to 1975, the growth o f M2 was
controllable. The equation fo r its grow th was a
constant (which is the trend) plus the grow th o f
reserves plus an error. From 1975 to 1992, the
link betw een the grow th o f M2 and the growth
o f reserves was no longer apparent.
W hat should be the Federal Reserve’s control
policy, since the link betw een M2 grow th and
reserve grow th after 1975 is not apparent? We
concluded that:
(1) The grow th o f M2 is a good indicator within
the context o f the dynamic model. However, it is
doubtful that it is controllable in the medium run.
(2) The Federal Reserve should place greater
weight upon its control o f inflation, than upon
the attempt to fine-tune the economy, because
the inflation equation in the reduced form sys
tem has more stability and predictability than
does the unemployment equation in that system.4
2
4 See Figure 1. There is also a close long-run relation
1
between M2 and the quantity of adjusted reserves, and,
hence, a long-run relation between the GDP deflator and
the ratio of adjusted reserves per unit of real GDP. These
relationships look similar to Figure 14. However, none of
these three relationships passes the usual cointegration
tests.
42Hall (p. 278) wrote: “ I conclude that established models
are unhelpful in understanding this recession [1990-92]
and probably most of its predecessors.” Insofar as the
growth of M2 was controllable prior to 1975, the SM
dynamic model does explain the recessions. See Figure 6
above. However, after 1975 it is not clear that the growth of
M2 is controllable. Hence, the good fit in Figure 6 after
1975 does not contradict Hall.
The Great Depression Period
1932
1929
variable
26.02
6.93
S&P index
39.4
31.6
Price investment good
0.22
0.66
qr-ratio index
0.88% pa
4.42% pa
treasury bill (i1)
4.22
4.7
30 yr corp (i2)
5.75
5.92
mortgage rate (i3)
0.2[-7.67% pa]
GNP deflator P
50.6
26,419
20,689[-8.15% pa]
Money stock
MARCH/APRIL 1994
202
(3)
Friedman’s admonitions concerning fine
tuning with respect to money, which is not obvi
ously controllable, should apply to fine tuning o f
the reduced form system using the controllable
grow th o f reserves. Mathematically Friedman’s
argument is that given the uncertainty concern
ing the values o f the parameters in T&ble 2 as
reflected in their standard errors, the central
bank should be most reluctant to vary its con
trol variable in pursuing its objective o f price
stability lest grow th be adversely affected.
However, an optimal control policy in this con
text has not as yet been established.4
3
Garfinkel, Michelle, and Daniel L. Thornton. “ The Link
Between M1 and the Monetary Base in the 1980s,” this
Review (September/October 1989), pp. 35-52.
Greenspan, Alan. 1993 Monetary Policy Objectives: Summary
Report of the Federal Reserve Board. Board of Governors of
the Federal Reserve System, 1993.
Hall, Robert E. “ Macro Theory and the Recession of
1990-91,” The American Economic Review (May 1993), pp.
275-79.
Infante, E.F., and Jerome L. Stein. “ Money Financed Fiscal
Policy in a Growing Economy,” Journal of Political Economy
(April 1980), pp. 259-87.
Issing, Otmar. “ Theoretical and Empirical Foundations of the
Deustche Bundesbank’s Monetary Targeting,” Inter
economics (November/December 1992), pp. 289-300.
Keynes, J.M. The General Theory of Employment, Interest and
Money. Harcourt Brace, 1936.
REFERENCES
Barnett, W.A., E. Offenbacher and P Spindt. “ The New
.
Divisia Monetary Aggregates,” Journal of Political Economy
(December 1984), pp. 1049-85.
Beiongia, Michael T. “ Measurement Matters: Recent Results
from Monetary Economics Re-examined,” mimeo, Universi
ty of Mississippi, 1993a.
_______ . “ Consequences of Money Stock Measurement: Evi
dence from Three Countries,” presented at meetings of the
American Statistical Association, August 8-10, 1993b.
_______ , and Dallas S. Batten. “ Selecting an Intermediate
Target for Monetary Policy When the Goal is Price Stabili
ty,” Federal Reserve Bank of St. Louis Working Paper
92-008A (October 1992).
Carlson, Keith. “ Inflation, Unemployment and Money:
Comparing the Evidence from Two Simple Models,” this
Review (September 1978), pp. 2-6.
Friedman, Milton. The Optimum Quantity of Money, and Other
Essays. Aldine Publishing Co., 1969.
_______ , and Anna J. Schwartz. A Monetary History of the
United States 1867-1960. Princeton University Press, 1963.
43The reason is that the coefficients of the dynamical system
— equations 11, 12 and Table 2 (columns three and four)
— are stochastic, with significant standard errors which do
not go to zero as the sample size increases. This problem
is being studied at present by Wendell Fleming (Depart
ment of Applied Mathematics, Brown University) and the
author.
FEDERAL
http://fraser.stlouisfed.org/ RESERVE BANK OF ST. LOUIS
Federal Reserve Bank of St. Louis
Modigliani, Franco, and L. Papademos. “ Monetary Policy for
the Coming Quarters: The Conflicting Views,” Federal
Reserve Bank of Boston New England Economic Review
(March/April 1976), pp. 2-35.
_______ , a n d ________ Targets for Monetary Policy in the
Coming Year, Brookings Papers 1, (1975), pp. 141-63.
Ritter, Joseph A. “ The FOMC in 1992: A Monetary Conun
drum,” this Review (May/June 1993), pp. 31-49.
Stein, Jerome L. “ Cobwebs, Rational Expectations and
Futures Markets,” Review of Economics and Statistics
(February 1992a), pp. 127-34.
_______ . “ Price Discovery Processes,” Economic Record,
special issue (1992b).
________International Financial Markets. Blackwell, 1991.
_______ . The Economics of Futures Markets. Blackwell, 1986.
_______ . Monetarist, Keynesian and New Classical Econom
ics. New York University Press, 1982.
Thornton, Daniel L. “ Targeting M2: The Issue of Monetary
Control,” this Review (July/August 1992), pp. 23-35.
United States Department of Commerce. Long Term Economic
Growth 1860-1965. Bureau of the Census, U.S. Government
Printing Office, 1966.
203
Appendix
Use of Quarterly Data in Estimating the Dynamic
SM Model
The results in the table below indicate w hy
w e used annual data in our empirical analysis.
Inflation is measured relative to the previous
quarter, but at an annual rate. The grow th o f
M2 is measured in the same manner. The e f
fects build up over time and quarterly move
ments per se have no significance.
Consider first columns one and two, which
correspond to equations 10 and 11. In the infla
tion equation (column one) only the lagged de
pendent variable is significant at the 5 percent
level. The lagged money grow th is significant at
the 8 percent level, but the equation fails to
satisfy the neutrality constraint. Theoretically,
in an equation such as 10, regardless o f the
time span, the sum o f the coefficients o f lagged
inflation (bo= 0.75) and lagged money growth
(b3= 0.08) should sum to unity. The null hypothe
sis that b2+ b3= l has a probability level o f 0.014;
hence, the neutrality (null) hypothesis is reject
ed. In addition, there is very serious serial
correlation o f the residuals. Th e LM statistic,
using three lags, w here the null is no serial
correlation, has a probability o f 0.00. The
ARCH test rejects homoskedasticity at the 3
percent level.
Column tw o relates to equation 11. A t first
glance, the results are significant. However,
there are difficulties. First, the coefficient o f the
lagged unemployment rate (0.98) is not signifi
cantly different from unity, and the constant is
not significantly different from zero. Thus, if in
flation equals money growth, the unemployment
rate converges to zero. Second, there is serious
serial correlation o f the residuals. Using lags up
to tw o quarters, the LM test o f no serial correla
tion has a probability o f 0.00. Third, the ARCH
test o f no heteroskedasticity has a probability o f
0.00. So the unemployment equation in column
tw o fails using these diagnostics. The conclusion
is that w e cannot have confidence in the results
o f columns one and two.
Columns three and four consider tw o lags of
inflation and money growth, w here time is
measured in quarters. This means that a span of
half a year is being considered. The main
results are that nothing o f significance, other
than the effects o f its own lagged variable, is ap
parent by focusing upon quarters rather than
upon annual data. The only significant variables
in the inflation equation (column three) are the
lagged inflation rates one and tw o quarters. The
one-quarter lagged money grow th is not signifi
cant. The lagged two-quarter money grow th is
significant at the 8 percent level. So, nothing
much shows up within tw o quarters. Second, in
the unemployment rate equation (column four),
the lagged dependent variable is significant. In
flation during the previous tw o quarters is not
significant. The money growth in the previous
quarter is not significant. However, the money
grow th tw o quarters earlier is significant. Com
pare T&ble 2 in the text w ith the table above.
These are the reasons w hy w e used annual data
in the analysis in the paper.
Table A1
Inflation
it
and Unemployment U Equations (10-11)
Equation 10
Variable
Constant
U(t-1)
T (t-2 )
A t- 2 )
7T
0.91 [0.12]
-0.07 [0.50]
0.75 [0.00]
-----0.08 [0.083]
------
Equation 11
U
0.21 [0.12]
0.98 [0.00]
0.036 [0.00]
------0.032 [0.00]
------
Equation 10
7T
0.76
-0.15
0.42
0.44
0.01
0.09
[0.16]
[0.11]
[0.00]
[0.00]
[0.84]
[0.08]
Equation 11
U
0.26 [0.04]
0.99 [0.00]
0.02 [0.21]
0.03 [0.14]
-0.002 [0.86]
-0.05 [0.00]
Notes: Quarterly data. M2 Growth is the input. The sample is 1956:4-1992:4 The two-tail significance is shown in brackets.
MARCH/APRIL 1994
204
Frederic S. Mishkin
Frederic S. Mishkin is the A. Barton Hepburn professor of eco
nomics, Graduate School of Business, Columbia University. He
is also a research associate, National Bureau of Economic
Rsearch.
Commentary
j L HE TIT LE OF THE PAPER by Jerry Stein is
somewhat misleading. A m ore accurate title
would be "The Resurrection o f M2 as a M one
tary Indicator/' or "M2 Lives; Long Live M2.” The
paper is really about how w ell the M2 aggregate
functions as a m onetary indicator to guide
m onetary policy. Because the paper provides
support fo r M2 as a m onetary indicator, Jerry
concludes that the central bank can achieve
price stability. I agree w ith Jerry that the cen
tral bank can achieve price stability, but this is
not really the focu s o f the paper because, as I
discuss later, the success o f M2 as a monetary
indicator is not required fo r a central bank to
achieve the price stability objective.
THE BASIC IDEA
The basic idea behind the paper is a simple
one: A m onetary indicator may by itself convey
little information about future inflation or
unemployment—even though it is actually an
excellent indicator fo r these variables—if the
dynamic interaction between inflation and un
employment is ignored. This point may be a
simple one, but it is important nonetheless be
cause it has often been overlooked in the recent
debates about w hether the Federal Reserve
should use M2 as a m onetary indicator or tar
get. What the model in Stein’s paper shows is
that dynamic interactions betw een inflation and
unemployment im ply that the effect o f M2
FEDERAL RESERVE BANK OF ST. LOUIS
grow th on the econom y depends very much on
the current state o f the economy. If the econo
my is slack w ith high unemployment and M2
grow th rises, inflation is likely to fall at first, but
then w ill rise in the long run. Similarly, if the
economy is boom ing w ith unemployment low, a
decline in M2 grow th may be follow ed by rising
inflation at first rather than falling inflation.
The relationship betw een M2 grow th and infla
tion may thus not be very apparent, even
though there is a close relationship betw een M2
g ro w th and inflation in the long ru n as the stan
dard quantity theory o f money predicts.
Recent research which finds that M2 is a poor
m onetary indicator has looked solely at the
direct relationship betw een M2 grow th and a
particular economic variable such as inflation or
real output. Stein's analysis indicates that this
approach may be highly misleading and that,
w hen the dynamic interactions betw een infla
tion and unemployment are taken into account,
M2 comes out very w ell as an appropriate indi
cator fo r the monetary authorities. Stein’s resur
rection o f M2 has advantages over other recent
attempts to resurrect M2 as in Feldstein and
Stock (1993). They find that M2 helps predict
nominal output growth, but is not a good fo re
casting variable fo r either inflation or real out
put growth. It is not clear that the FeldsteinStock finding is all that com forting to M2 advo
cates since w e do not directly care about nomi-
205
nal output growth, but are more interested
in its components—inflation and real output
growth.
Indeed, Stein’s paper may help explain w hy
Feldstein and Stock find that M2 grow th works
w ell in forecasting nominal output growth, but
does poorly in forecasting its components. W hen
M2 grow th rises, Stein's dynamic system indi
cates that real output rises at first but this rise
does not continue, w hile inflation rises later. In
both the short and the long run, nominal out
put growth is higher when M2 grow th rises,
and this may explain the link between M2
growth and nominal output grow th that Feld
stein and Stock find. On the other hand, the
different response o f real output grow th and in
flation in the short and long runs make it hard
er to find a link between M2 grow th and real
output growth and inflation.
SOME CRITICISMS
Stein’s paper provides a useful perspective on
how to interpret the evidence on m onetary indi
cators and provides new evidence that M2 might
have a useful role as a monetary indicator. This
paper suggests that the abandonment o f M2 by
the Fed outlined in Alan Greenspan's recent tes
timony in Congress may be premature. Despite
finding value in this paper, like any good discus
sant I have to poke some holes in its arguments
and raise some criticisms.
One serious problem w ith the evidence in the
paper is that the favorable findings fo r M2
growth as a m onetary indicator only appear
with annual data. Jerry deserves to be com
mended fo r being very forthright in indicating
that M2 and his model do not fare w ell with the
quarterly data in Appendix 2. Jerry attributes
the problem with the quarterly data to the nois
iness o f this data. I continue to be quite dis
turbed, however, that the results w ith quarterly
data are so poor. A key point o f his analysis is
that it focuses on dynamic interactions. W hen
w e are interested in dynamic interactions, w e
are particularly interested in looking at data ob
served at short intervals such as a quarter be
cause data averaged over longer intervals such
as a year may not reveal much about the dy
namics. The disappointing results w ith quarterly
data are thus very troubling, because this is the
data that would seem to be m ore suited to tests
o f his model.
Another issue about the robustness o f M2 as a
monetary indicator arises w hen the paper uses
the M2 divisia index instead o f M2 in the esti
mated equations. In K. Alec Chrystal's paper in
this volume, divisia M2 tends to outperform
simple-sum M2 in the forecasting equations, and
yet Stein’s results w ith divisia M2 do not satisfy
the theoretical restrictions o f his model. Since
there are some theoretical restrictions argu
ments fo r divisia indices over simple-sum ag
gregates, the lack o f robustness o f the results
using divisia M2 is somewhat disturbing, par
ticularly because other researchers such as
Chrystal find that divisia M2 does pretty well.
I also have some problems with the paper’s
evidence on the poor forecasting perform ance
o f real interest rates in the dynamic model. The
way the effect o f real interest rates is tested is
to add one lag o f the nominal interest rate as an
explanatory variable in the regressions, which
also include one lag o f the inflation rate. A rise
in the lagged nominal interest rate is thus equiva
lent to a rise in the lagged ex-post real interest
rate in these regressions. Although the co effi
cient on the lagged nominal interest rate there
fore reflects the effect o f the lagged ex-post real
interest rate, it is the effect o f the ex-ante real
interest rate, a forward-looking variable, that is
m ore relevant to the debate on w hether real in
terest rates should be used as a m onetary indi
cator. One variable that researchers have looked
at that is meant to represent the effect o f real
interest rates is the spread between short- and
long-term interest rates. The idea is that the
long rate reflects expected inflation and so the
short-long spread tells us something about the
real short-term interest rate. The short-long
spread does pretty w ell in forecasts o f real eco
nomic activity [for example, see Hardouvelis
(1991), Bernanke and Blinder (1992) and Bernanke
and Mishkin (1992b)], and it might be w orthwhile
to look at how w ell it does in Stein’s fram ework.
I also have some questions about the paper’s
evidence on the controllability o f M2. The paper
provides evidence that the coefficient on adjust
ed reserves in an M2 regression is not signifi
cant after 1975, thus casting doubt on the
controllability o f M2 in recent years. Although
the conclusion that M2 is uncontrollable might
be correct, I think the jury is still out on this
one. Despite Stein’s evidence, M2 might be more
controllable than his evidence suggests because
there are a lot o f other factors that affect the
relationship betw een M2 and adjusted reserves
that are left out o f his regression. I f these fac
tors are predictable by the monetary authorities,
MARCH/APRIL 1994
206
then the monetary authorities might be able to
offset them and exercise far tighter control o f
M2 than Stein’s regression equation suggests.
POLICY IMPLICATIONS
The paper indicates that since M2 growth
works w ell in the dynamic model, it is a good
long-run indicator fo r inflation. In addition,
Jerry comes to the conclusion that since his
inflation equation has m ore stability than the
unemployment equation, the Federal Reserve
should focus on price stability rather than un
employment as the goal o f m onetary policy. I
strongly agree that the prim ary focus o f central
banks should be price stability rather than the
business cycle. Th e uncertain effects o f m one
tary policy on real output is one reason, as
Jerry points out. Another important reason,
however, relates to the expectations created by a
particular strategy fo r monetary policy.
Stein’s paper does not emphasize this second
reason fo r focusing on the price stability objec
tive because it does not make use o f rational ex
pectations. W hether you buy into it completely
or not, the rational expectations revolution has
taught us important lessons about the problems
that face central banks w ho attempt to manipu
late real output or unemployment. I f a central
bank tries to reduce business cycle fluctuations,
models such as Barro and Gordon (1983) indi
cate that this strategy w ill lead to high inflation
w ithout necessarily achieving any reduction in
the degree o f business cycle fluctuations. The
problem is that attempts to reduce business
cycle fluctuations destroy the credibility o f the
central bank and so create expectations that
high inflation w ill be accommodated, which
results in a self-fulfilling prophecy.
This lesson from rational expectations models
has had an important impact on the economics
profession. Most macroeconomists take the issue
o f credibility very seriously w hen discussing
monetary policy and, as a result, tend to sup
port the view that m onetary policy should focus
almost exclusively on price stability. Thus,
w hether macroeconomists are monetarist or
not, or w hether they accept the evidence in
Stein’s paper resurrecting M2 as a m onetary
indicator, they tend to agree with Stein’s view
that price stability should be the prim ary goal
o f a central bank.
The importance o f credibility and expectations
about m onetary policy suggests an important
FEDERAL RESERVE BANK OF ST. LOUIS
reason w hy m onetary targeting might be useful
fo r monetary policymakers. As Bernanke and
Mishkin (1992a) point out, targets fo r growth
rates o f monetary aggregates might help signal
the public about the long-run intentions o f a
central bank regarding inflation. Adherence to a
m onetary target may low er the public’s inflation
expectations, which helps keep inflation from
getting out o f hand. Stein’s paper lends some
support to the use o f M2 targeting in the United
States because it suggests that M2 grow th is a
good indicator fo r inflation in the long-run and,
thus, can provide an appropriate signal to the
public.
To finish my comments, I want to return to
the issue o f w hy I think the title o f Stein’s paper
is misleading. Jerry’s paper is not really about
w hether the central bank can achieve price sta
bility. It is true that having M2 be an accurate
m onetary indicator makes it easier fo r a central
bank to achieve price stability both because it
provides a m ore accurate guide to m onetary
policy and because it enables the central bank
to signal the public about its anti-inflationary
stance. However, even if M2 or any other m one
tary aggregate is a poor m onetary indicator, cen
tral banks can achieve price stability. Indeed,
this is exactly w hat w e have seen over the last
10 years in the United States.
The way I would characterize the Federal
Reserve’s strategy fo r the conduct o f m onetary
policy in recent years is that it has not made
much use o f any specific monetary indicator.
Instead, it has operated in the follow ing man
ner: W henever the economy has been getting
close to full employment o r inflation has risen,
the Fed has stood ready to slam on the brakes
by restricting reserves grow th and raising in
terest rates until inflationary pressures subside.
This strategy is not too different from nominal
GDP targeting, although the weights on real out
put grow th and inflation may not be equal as in
nominal GDP targeting.
This strategy seems to w ork pretty w ell in the
United States and in other countries as long as
the central bank pursues the follow ing rule-like
behavior: It creates expectations that when infla
tionary pressures increase, it w ill pursue tighter
m onetary policy and then lives up to these ex
pectations by actually carrying out this policy.
The outcome o f this policy in the United States
has been a low inflation rate with very little
variability. Since the success o f this policy has
not been based on the use o f any m onetary in
207
dicator, it should be clear that price stability can
be achieved without it. '[’bus, even if w e are
unable to find a satisfactory monetary indicator,
there is still a strong case fo r rule-like behavior
on the part o f the central bank to control
inflation.
_______ , and Frederic S. Mishkin. “ Central Bank Behavior
and the Strategy of Monetary Policy: Observations from Six
Industrialized Countries,” NBER Macroeconomics Annual
(1992a), pp. 183-228.
_______ , a n d ________ “ The Predictive Power of Interest
Rate Spreads: Evidence from Six Industrialized Countries,”
mimeo, Princeton University, December 1992b.
REFERENCES
Chrystal, K. Alec., and Ronald MacDonald. “ Empirical Evi
dence on the Recent Behavior and Usefulness of SimpleSum and Weighted Measures of the Money Stock,” this
Review (March/April 1994).
Barro, Robert, and David B. Gordon. “ A Positive Theory of
Monetary Policy in a Natural Rate Model,” Journal of Politi
cal Economy (August 1983), pp. 589-610.
Estrella, Arturo, and Gikas A. Hardouvelis. “ The Term Struc
ture as a Predictor of Real Economic Activity,” Journal of
Finance (June 1991), pp. 555-76.
Bernanke, Ben, and Alan Blinder. “ The Federal Funds Rate
and the Channels of Monetary Transmission,” The Ameri
can Economic Review (September 1992), pp. 901-21.
Feldstein, Martin, and James H. Stock. “ The Use of Mone
tary Aggregates to Target Nominal GDP,” NBER Working
Paper no. 4304 (March 1993).
MARCH/APRIL 1994
209
A Conference Panel Discussion
Michael J. Boskin
Michael J. Boskin is Tully M. Friedman professor of economics
and senior fellow, Hoover Institution, Stanford University. He is
also an adjunct scholar with the American Enterprise Institute.
The Role o f Rules in Monetary Policy
J . W IL L TRY TO ASSUME m y comparative ad
vantage on this panel and put a broader-brush
perspective on m onetary aggregates, interm edi
ate targets, rules versus discretion, and the re
cent history o f m onetary policy-making. Many
o f my positions have been stated in various
parts o f several o f the recent Econom ic Reports
o f the President.
A bove all, m onetary policy ought to be forwardlooking. It should be rule-like, or rules-based,
but not necessarily mechanical as in a Friedman
or Shaw fixed m oney grow th rule. Let me state
a fe w propositions that support m y position and
which a fair reading o f history w ould conclude
are sensible even though there are persons at
this conference w h o have argued contrary
propositions over time.
Th e first is that high inflation, indeed even
high and stable inflation, can carry substantial
cost to the economy. It was not uncommon in
the late 1970s and early 1980s fo r people to ar
gue that if w e could m ore or less stabilize infla
tion so that the variance was much smaller than
it had been, a high mean o f 10 or 12 percent
might be far preferable to bearing the potential
cost o f disinflation. The cost o f disinflation was
view ed as inordinately high, and indeed w e did
have a high cost, as Rick Mishkin stated, in the
recessions o f 1980 and 1981-82. But that cost,
according to any serious analysis, was far less
than the simple models that many economists
w ere using predicted, especially in terms o f lost
output. Th e costs w e re perhaps a third, and
certainly less than half, in terms o f lost real out
put than w hat had been predicted fo r the
amount o f disinflation engendered.
The cost o f inflation stems from a variety of
things but one o f the most important is that the
fiscal rules that determine our tax system are
not invariant to the rate o f inflation. W hile w e
eventually in the early '80s indexed tax brackets
fo r inflation, w e did not index the definition o f
income. W e still have historic cost depreciation.
W e still have nominal capital gains tax, tax nomi
nal interest, and allow deductions fo r nominal
interest. It is complex, but w hen you are look
ing at investment decisions, those are important.
This is part o f the reason w h y monetary policy
in the late 1970s, likely the w orst episode in the
post-World W ar II history o f m onetary policy,
was so bad. Attention was being paid to nomi
nal interest rates rather than, as difficult as
they are to measure, expected long-run real nefof-tax interest rates.
The second point I w ould make, and w ill
come back to, is that those w ho argue that in
deed m oney does m atter initially—and not just
fo r prices but fo r real output—seem to have
been correct. A tighter m onetary policy than
the Fed envisioned in the early ’80s led to that
costly (but not as costly as predicted) disinfla
tion. I think that the simple monetarist proposi
tions available at that time broke dow n w ith the
collapse o f M l velocity in the early 1980s (and
MARCH/APRIL 1994
210
again w ith the collapse o f M2 velocity in the
early 1990s).
The simplistic notions o f monetarists took a
beating, even if the fundamental tenets w ere,
and I think continue to be, m ore or less correct.
Keynesian and neo-Keynesian arguments took a
beating as w ell since w riters in the econom etric
Keynesian tradition greatly overstated what the
cost o f the disinflation w ould be in terms o f lost
output. Those w ho focused on expectations and
on credibility proved to be—and let me make
sure I am careful about this—partially correct,
in m y opinion. I think they w ere no m ore fully
correct than the monetarists w ere or than the
simple Keynesians and neo-Keynesians w ere.
All o f these schools o f thought contained ele
ments o f truth, but none was a sufficient
descriptor o f the econom y or prescriber o f eco
nomic policy. W e have learned through the
w ork o f some people at this conference and
others that some households and businesses in
deed are liquidity-constrained and do respond to
short-run cash flows. Hence, there is some
scope fo r affecting the shorter term course o f
the economy, if and w hen that proves to be
desirable, w ith discretionary policy.
Expectations certainly have been shown to
matter. A large part o f the reason that the last
decade has been substantially better than the
previous decade, in terms o f macroeconomic
perform ance and in a manner I w ill describe in
a moment, stems from the fact the Fed has
gradually built considerable credibility on reduc
ing inflation and keeping inflation low and sta
ble. Th e inflation expectations premium has
been gradually abating.
The next point I w ould make is that the eco
nomics profession ought to be quite humble
about both our ability to go from changes in
m onetary policy to short-run changes in nomi
nal GDP, and from the change in nominal GDP
to the changes in inflation and real output.
Humility is called fo r in far greater magnitude
than has been evidenced by most economists;
that w ill lead me back in a moment to the
proposition that I w ill make about nominal
GDP rules.
The w eight o f the evidence accumulated dur
ing the recent relatively successful disin fla tion first in the early '80s and later in the last few
years, from double digits dow n to the 4 to 5
percent range and, later, from that range down
to around 3 percent—suggests that after adjust
FEDERAL
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ing fo r the state o f the econom y the disinflation
was achieved in the context o f much low er un
em ployment and much less lost output than had
been expected. Some people claim that the 1970s
was just as good a decade and that despite the
long expansion in the 1980s, the grow th then
was no higher. But the 1980s w ere a period
when lots o f inflation was taken out o f the sys
tem and the previous decade was a situation in
which lots o f inflation was added to the system.
Indeed, if you step back (and I know it is hard
when you are doing technical research on a
specific subject) and look at post-W orld W ar II
history, w e w ere in this horrible situation
w here at corresponding stages o f each cycle—
the midpoint, trough or peak—inflation at that
point was getting higher and higher. And
perhaps the most remarkable thing is that not
only was inflation stabilized but that relation
ship was broken, hopefully fo r a considerable
length o f time, fo r the foreseeable future. There
w ere many people who, circa 1980, thought w e
would have, as I mentioned, not only something
close to a depression to get inflation dow n to
low levels, but that inflation w ould then start to
accelerate substantially once w e got w ell into
the next expansion.
Can w e do better? M y answer is yes. And I
w ill get to that in a second. As I said earlier,
the w orst episode was the late 1970s and I b e
lieve that there w ere several fundamental mis
takes. One was accommodation and, without
getting into personalities, I’ll just say that it
seemed to me w e had a Fed in the late 1970s
that was really not responsible. W hatever
modest impetus and modest cost-push supplyshock w e had, w hatever oil prices did, was a
tiny fraction o f the total impact on the accelera
tion o f inflation. Some people attribute up to 3
percentage points in the 13 percent rate to the
oil shock. But the inflation was basically a
m onetary phenomenon.
The Volcker disinflation o f the late 1970s and
early 1980s, if I can revert to a professor giving
grades, gets a B + or A - . It was achieved at
much less cost than anticipated despite the
severe recession, but also I think Rick Mishkin
is right that the Fed really wasn’t looking just at
m oney as velocity was collapsing. I do believe
that m onetary policy, ex post, proved to be
much tighter than the Fed had imagined and
they did want a m ore gradual disinflation
(that is one reason they don't get an A). W hether
a m ore gradual disinflation could have been
211
achieved at a low er cost is something w e w ill
never know. I give the Fed an A - fo r its policy
in the late 1980s to try and proactively head o ff
an incipient, building inflation. And this gets
back to a point several people have made that
m onetary policy has to be forward-looking.
The Fed rarely gets credit w hen it prevents
the inflation rate from going from , say, 4.5 per
cent to 6.5 percent, because people never see it
get up to 6.5 percent and then go back down
again. And so I think an A - because they prob
ably w ent a little too far. W hile they couldn’t
have foreseen the oil shock or anticipate the
size o f the defense drawdowns and other things
going on in the economy, they probably should
have done better at understanding that the
regulatory system o f financial institutions was
going to take some steam out o f the economy.
W heth er that was desirable is another story,
but I think that you can't understand m onetary
policy without also looking at the regulatory
structure o f the financial system. I would give
the Fed low er marks fo r easing too slowly and
too timidly but, to be intellectually honest, had
they eased as I thought desirable—a bit m ore
rapidly and a bit m ore aggressively
—how much o f that w ould have shown up in
output and how much o f that in slower reduc
tion in inflation is certainly an open question.
I certainly give them much higher marks than
most o f the academic economics profession—
Samuelson, Tobin, Solow, Feldstein, Friedman,
McCracken and others. Yet, by the end o f ’91 or
early '92, they got to about w h ere they should
be, and I think the Fed is pretty close to w h ere
it ought to be, although it probably w ill need to
m ove to a less accomodative policy as 1994
progresses.
W hat have they been doing? At various times,
the Fed has announced or listed in prime direc
tives that they have been looking at interest
rates, reserves, M l and M2, comm odity prices,
exchange rates, and so on. I think it is very
clear that on the Federal Open Market Commit
tee (FOMC) people are looking at different
things but that, in general, the prim ary concern
is and has been reducing inflation. They have
been somewhat opportunistic about doing that.
Th ey get concerned w hen it appears that infla
tion looks like it may accelerate or over bad
news in contemporaneous data about inflation.
It is an interesting issue how much information
that it is conveying and its potential as a leading
indicator o f future inflation. Th ey have tended
to take advantage o f opportunities to try to take
another round out o f inflation w hen that seems
desirable. W hen the econom y happens to be
slack, they tend to try to help the economy
somewhat in the short run. W hile there was
not a lot o f discussion in the last year or tw o
about price stability, there was a lot o f discus
sion o f that as the prim ary goal a fe w years
ago—they vie w their job as to try to keep infla
tion low and steady and try to avoid doing any
thing that leads to an unnecessarily large swing
in output. I echo the lender-of-last-resort, avoida-financial-panic issue. They have operated under
some big structural changes in the economy, in
cluding the declining fraction o f credit extended
by the banking system, the fact that far less of
broad m onetary aggregates is reserved against
any more, changes in the international arena
w hich leads to far m ore m obility o f capital, and
so on.
W hat I infer from all o f this is that the Fed
has to be a compass, not a w eather vane, laying
out a basic path that they are trying to achieve
fo r their policy. I think they have done that,
although at times less than clearly. In general,
they have laid out a course o f what they are
trying to achieve that has generally been fairly
reasonable, with a couple o f exceptions in the
last decade or so. It is a rules-based policy, not
one that is a fixed rule, but one that basically
lays out a policy path that is deviated from only
rarely and tem porarily, fo r contingencies that
are generally well-understood by the public to
be rare events. The basic rules-based fram e
w ork is the proper one fo r m onetary policy,
and I think it is probably the w ay to under
stand what the Greenspan Fed has been trying
to do, and perhaps the Volcker Fed up to a
point as well.
A far m ore difficult question is what do you
do about specific indicators. I personally do not
believe that M2 is a sufficient intermediate indi
cator. I don’t believe nominal GDP is either,
since w e still have the problem o f separating
out real grow th and inflation. I believe the list
o f indicators must include m ore than one sim
ple measure such as M2, or adjusted reserves,
or M l. That is not necessarily a disingenuous
intellectual exercise to th row the Congress o ff
their backs, although that may be a valuable
purpose. I think that there is information con
tained in a variety o f indicators and the Fed is
going to have to look at all o f them.
MARCH/APRIL 1994
212
Secondly, I believe that it is desirable fo r the
Fed to lay out parameters, broadly speaking,
despite Rick Mishkin’s argument that the Bun
desbank and the Swiss have often been w ay o ff
in m oney grow th targets. The Fed w ill continu
ally face episodes such as w e had in the early
'80s and the early '90s w hen relationships be
tw een reserves and rates, betw een one or
another m onetary aggregate and nominal GDP,
and among nominal GDP, real GDP and infla
tion, w ill be far less stable than they are at
other times. Nevertheless, I do believe it is
desirable fo r the Fed, in the context o f the
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Federal Reserve Bank of St. Louis
rules-based policy, to lay out w hat it is trying to
achieve and how it is trying to achieve it in a
w orld o f incomplete information, rapid structur
al change and inaccurate data. That is not a
simple task, but one the Fed has perform ed, by
any fair evaluation, quite w ell fo r the past
decade-and-a-half.
REFERENCES
Council of Economic Advisors. Economic Report of the Presi
dent. U.S. Government Printing Office.
213
Philip H. D ybvig
Philip H. Dybvig is Boatmen’s Bancshares professor of banking
and finance, Oiin School of Business, Washington University,
St. Louis. I am grateful for helpful comments from Kerry Back,
Jim Bullard, Ning Gong, Hyeng Keun Koo, Mahesh Maheswa
ran, and participants in the Conference on Monetary Ag
gregates at the Federal Reserve Bank of St. Louis. All
comments are the author’s and may not represent the position
of the Federal Reserve Bank.
What Is the Fed’s Decision Problem ?
W
■ 'H A T IS THE BEST m odel o f a piece o f
iron? I f it is to be thrown, the best m odel might
be a uniform mass o f fixed density and shape.
I f it is to conduct electricity, thinking o f the
piece o f iron as a hollow tube like a pipe that
carries water, is illuminating. For purposes o f
studying its magnetic properties, it may be best
to consider the piece o f iron as a collection o f
rigidly located magnetic dipoles that can be
aligned or not. In general, the best model de
pends on the use to which the model is put.
In an economic setting, the best economic
model is one that helps us understand the
choices made by econom ic agents. Unfortunately,
the specific nature o f the Fed's decision problem
remains obscure in most discussions o f Federal
Reserve policy. In these remarks, I look at the
Federal Reserve through the lens o f decision
theory. W hile I'm not necessarily suggesting
that the Fed must or should specify an explicit
objective function, I do think that decision theory
is nonetheless a very useful fram ew ork fo r
thinking about the economy, m onetary ag
gregates and the Fed’s policy role. This should
be a com fortable notion fo r economists, virtually
all o f w hose models are based on decision theory.
The O b je c tiv e Function
Many purely political attacks on the Fed are
posed in terms o f the objective function. None
theless, its specification is a substantive issue.
Focusing on the Fed’s role in m onetary policy,
there seems to be some consensus within the
Fed that there is a lexicographic preference to
keep inflation down, and given low inflation, to
stimulate economic growth. Separate criteria are
applied to crisis management such as the injec
tion o f cash to help illiquid specialists during a
crash. None o f this is entirely satisfactory:
Lexicographic preference fo r reducing inflation
is certainly not the ultimate objective o f the
Fed, which might ultimately seek a good out
come fo r the econom y given the complex inter
action betw een the Fed, the Congress, the rest
o f governm ent, and the rest o f the economy.
In order to achieve a good outcome, part o f
the Fed’s objective should be political survival
w ith pow ers (including independence) intact. It
seems that the lexicographic objective to keep
inflation dow n is intended to do some good in
the econom y subject to political survival and
given inherent limitations on what the govern
ment can do to help the economy. This narrow
view o f the Fed does not seem ideal, but is sur
ely better than what w ould com e under the po
litical control that w ould result from any loss o f
the Fed’s independence.
C on trol Variables
Although control variables include such things
as reserve requirements and discount w indow
policy, the most comm only used control variable
is the open market operation. I continue to be
puzzled as to w h y the Fed confines its open
m arket operations to trading only once each
day in a ve ry limited set o f securities, most
MARCH/APRIL 1994
214
often repurchase agreements in short-term
Treasuries. At the same time, the Fed seems to
be very interested in the behavior o f long rates,
apparently believing that movements in long
rates signal changes in expectations o f inflation.
In other words, the Fed is trading short-term in
struments w hile judging the success or failure
o f its actions, relative to maximizing its objective
function, by watching long-term rates. This
choice o f control variable, given the objective
function, seems puzzling. Since the Fed is not
the only econom ic actor in the econom y that
looks to long rates to think about inflation,
perhaps a better w ay to influence expectations
o f inflation is by trading long-term bonds them
selves. W h y doesn’t the Fed trade long-term
bonds? One reason often cited is, in truth, ir
relevant: Operation Tw ist in the ’60s was a bad
idea imposed on the Fed from outside and it
didn’t work. A m ore serious suggestion is that
the Fed may not be big enough to affect long
rates or, in other words, that long-term bonds
may not in fact be a feasible control variable.
The reasons w hy it may be infeasible fo r the
Fed to trade enough to m ove long rates, h ow
ever, aren't self-evident and usually are left
unstated. In addition to long-term bonds, there
are numerous other financial instruments such
as futures and options on Treasuries that might
be used as control variables. One reason fo r
considering these instruments as control varia
bles arises from the recent finance literature on
h ow price pressure—the amount prices m ove in
response to trading volum e—varies across m ar
kets. Price pressure is a lot like walking down
the demand curve as a monopolist: W hen your
early trades have a big effect on price, you get
a much less favorable price on subsequent
trades. Most agents w ho take a position with
respect to market interest rates want to mini
m ize price pressure. The Fed actually may
p refer the opposite perspective. If the Fed's m o
tive fo r trading is an attempt to change expecta
tions (say, o f future inflation) without taking on
too large a risky position, the Fed may want to
maximize (not minimize) price pressure fo r a
given level o f exposure. Trading long-term in
struments may be a feasible w ay to do so.
Constraints
W hat are the constraints faced by the Fed in
maximizing its objective function? Almost every
discussion o f Fed policymaking hinges on some
implicit constraint. If the Fed is, in fact, too
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small to m ove long rates, fo r example, then there
must be some limitation to the Fed's ability to
short T-bills and go long Treasury bonds or vice
versa; otherwise, it seems that they surely could
take positions that w ould m ove long-term rates.
It should be interesting to specify explicitly such
restrictions. Other constraints may arise from
the Fed’s charter. Does the Federal Reserve Act
constrain the amount o f risk the Fed is permitted
to absorb? It might seem not. A fter all, what is
interest rate risk to an agent w h o can always
print m oney to satisfy a claim?
Several central banks have learned the hard
w ay the limitations on their ability to influence
foreign exchange markets. The possibility o f large
losses (or even profits) seems less likely in domes
tic markets, given the printing o f m oney and
possible deferral o f paper losses. Nonetheless,
given the 1993 magnitude o f $16 billion returned
to the Treasury by the Fed, it seems that trading
gains or losses o f $5 billion could cause severe
political damage. If the Fed misjudges its capacity
to bear risk, it can cause significant damage by
being either too bold or too timid.
The In fo rm a tio n Set
W e have discussed the objective function, the
controls, and the constraints. W e cannot under
stand a decision problem w ithout knowing the
decision maker's inform ation set. In finance, w e
routinely gather a great deal o f inform ation by
m onitoring m ore or less continuously the m ar
ket prices o f securities. Macroeconomists simi
larly often m onitor high-frequency data such as
market interest rates as indicators o f expected
inflation and the level o f the stock market fo r
expectations o f economic activity. Th ere are,
how ever, many other variables that should be
considered. Option prices, such as Standard &
Poor's 100 index options and T-bond futures op
tions, may be used to infer the types and
amount o f risk people perceive in the market.
These data permit us to separate the degree o f
investors' uncertainty about the level o f future
inflation from investors’ expectations o f the level
o f inflation. This is important because it is the
degree o f uncertainty about inflation, not the
level itself, that makes planning difficult fo r
businesses using nominal contracts. Similarly,
the stock index options measure investors' uncer
tainty about the overall level o f future economic
activity.
Other data, such as information on the money
stock or unemployment, are available at an
215
intermediate frequency. These intermediate
frequency data provide some independent in for
mation beyond what is available in security
prices, although how much is really an empirical
question. And then there are the low-frequency
time series, which are very important, such as
inflation or industrial productivity.
This plethora o f variables raises the difficult
question: W hen w e can't look at 16 things at
once, how do w e summarize the information in
a w ay that is useful fo r policymaking? This is
the type o f question that is implicit in the
choice o f a m onetary aggregate or any other
policy indicator or target. In principle, w e
should not throw anything away. How ever, if
w e put too many variables in our statistical
analysis, the loss o f p ow er w ill reduce the quali
ty o f fit, especially w hen some ultimate objec
tives such as production and inflation are
available only at low frequencies. Although it
seems sensible to focus on a subset o f the avail
able data, it is unclear what should be the crite
rion fo r combining data or fo r deciding which
data to th row away and which data to retain.
This b rie f look at the Fed’s decision problem
suggests several interesting avenues fo r research.
It w ould be useful to have a careful and apoliti
cal analysis o f the Fed's objectives. W e should
quantify the Fed's constraints on trading, base
m oney creation, and risk-bearing. Empirically,
w e should have m ore w ork w ith high-frequency
data (daily and intra-day) and m ore examination
o f the Fed’s actual controls (trades) and their
direct impact on markets. It w ould be interest
ing to understand better how to aggregate lowand high-frequency data. Keeping the Fed’s deci
sion problem in mind w ill help to guide our re
search tow ard the most important policy issues.
MARCH/APRIL 1994
216
Bennett T. McCallum
Bennett T McCallum is H.J. Heinz professor of economics at
.
the Graduate School of Industrial Administration, Carnegie
Mellon University. He is also a research associate, National
Bureau of Economic Research.
Monetary Policy Without Monetary Aggregates
J L HE PAPERS PRESENTED at the conference
represent a useful step in the ongoing search
fo r im proved ways o f measuring m onetary ag
gregates. Th eir basic idea, o f w eighting com po
nents o f the aggregates by a measure o f the
extent to which they serve as media o f ex
change, should be rather appealing to anyone
w ho view s the medium-of-exchange function as
the defining characteristic o f money. And I
don’t know o f any other potential defining
characteristic (for example, the store-of-value
function) that makes any sense. So, to repeat, I
find quite promising the idea that some indices
and w eighted sums might do a better job than
the simple-sum aggregates in measuring the
quality o f money.
But w hile this type o f study seems potentially
useful fo r the purpose o f studying m oney de
mand behavior, building econom etric models
and judging the historical record, I am not en
thusiastic about the developm ent from the per
spective o f monetary targeting. The reason—as
some o f you w ill have heard me argue b e fo re—
is that I believe that there is a good w ay o f con
ducting m onetary policy that does not rely on
any targeted m onetary aggregate. Instead, it
uses as its target variable nominal GDP, or GNP,
or domestic demand, or some such measure of
aggregate nominal spending.
Th ere are several ways o f arguing that nomi
nal GDP (or whatever) is a m ore appropriate
target variable than any m onetary aggregate.
The simplest and most blatant is to just assert
that it is obvious that a central bank's main job
FEDERAL RESERVE BANK OF ST. LOUIS
is to keep total nominal spending grow ing
smoothly at a noninflationary rate. But one can
proceed m ore circumspectly by arguing instead
that from the perspective o f hitting price level
or inflation targets, on average over the next
decade or so, w e know w ith much greater ac
curacy what grow th rate o f nominal GDP w ill
do the job than w e do fo r M l or M2. And even
if the task o f developing an im proved index o f
m oney is successful, it w ill still be true that w e
w ill know w ith m ore accuracy what rate o f
grow th is needed (to deliver a chosen inflation
rate) fo r nominal GDP.
T o the foregoing one might naturally respond,
w h y not make inflation the target directly
rather than indirectly? But to this there are tw o
answers. One is that, because the price level
usually responds m ore slowly to policy actions
than does nominal GDP, a policy feedback rule
is m ore likely to generate dynamic in stabilityso-called instrument instability—if it responds to
target misses fo r the price level rather than
nominal GDP. And the second argument is that
generating a smoothed path fo r nominal GDP is
likely to result in smaller fluctuations o f real
GDP— that is, reduced cyclical variability. (I am,
o f course, aware that w e cannot be certain
about the latter, given current knowledge, and
also that it is not desirable to smooth out
responses to all types o f shocks. But I w ill stand
by the statement nevertheless.)
T o return to the issue concerning m onetary
aggregates, the only advantage that I can see
217
fo r them (as targets), relative to nominal GDP, is
that observations are available m ore often and
m ore promptly. But w e could certainly devise
other measures o f nominal aggregate spending
that w ould be available m ore frequently and
promptly. Furthermore, it is not clear that hav
ing measurements m ore frequently is terribly
important. O ver the last year or so, w e have ex
perienced quarter after quarter o f rapid M l
and base grow th at the same time as very slow
M2 growth. These aggregates w ere suggesting
either excessively loose or excessively tight
monetary policy, depending on which one you
utilized. But nominal GDP grow th chugged
along reasonably close to 5 percent (per annum)
in almost every quarter, which is just about
enough fo r 3 percent real grow th and 2 percent
inflation. So if 2 percent is the Fed's concept o f
"ze ro inflation,” which seems defensible, then
policy behavior has been just about right from a
medium-term perspective. And the point, rela
tive to the issue regarding the frequency and
promptness o f measurements, is that these vari
ous grow th rates have differed in the manner
described above fo r many months in succession.
One objection that is sometimes raised against
nominal GDP targets is that they might make it
appear to the public that the Fed is controlling
real GDP—that it is attempting a role that is
greater than is actually feasible. But I w ould not
presume that these targets w ould be publicly
announced. The role fo r targets that I have in
mind is as significant inputs that the FOMC
w ould use in making its decisions, as proposed
by Taylor (1993). Announcements are much less
important, I believe, than behavior.
Having appropriate targets is, o f course, not
the w hole story; to conduct m onetary policy
successfully it is also necessary to have a policy
feedback process—among friends I w ould call it
a "ru le”—that specifies instrument settings, that
is, settings o f a variable that the central bank
can control directly or w ith great accuracy. In
m y ow n studies,1 which have been designed to
see if a simple rule w ould succeed in hitting
nominal GNP targets w ith reasonable accuracy
in a variety o f (small) econom etric models, I
have usually used the St. Louis adjusted m one
tary base as the instrument variable. The rea
son fo r that choice is that the base’s grow th
rate provides a nice measure o f the pace at
which open market purchases (or sales) are b e
ing conducted, and if the adjusted base is used
the measure takes account o f changes in
reserve requirements as well. So it seems to be
the most natural aggregate among those that
are highly controllable —which the base is since
it appears on the Fed's ow n balance sheet and
so could be m onitored daily (and thereby kept
close to the specified values).
The other main contender fo r the role o f the
instrument variable is, o f course, the federal
funds rate (or some other short-term interest
rate). But interest rates seem quite unattractive
because a high interest rate suggests tight
money from a short-term perspective but easy
m oney from a long-term perspective. Or, as I
say to m y students, if a central bank wants in
terest rates to be low er, then it needs to raise
interest rates. That strikes me as an extrem ely
undesirable feature fo r an instrument variable.
In addition, I have tried in m y simulation w ork
to design interest rate rules and have found
that they perform much m ore poorly than ones
w ith the base instrument.2 These results, at the
quarterly frequency, are not definitive but they
are supportive o f the belief that the base is the
better instrument from a m acroeconom ic per
spective.
Most actual central banks are, o f course, ex
trem ely resistant to proposals fo r accurate base
control, on a short-term basis, and have accord
ingly been rather unreceptive to such policy
rule suggestions. One important reason fo r that
resistance, I believe, is the b elief that exerting
short-term base control w ould generate more
financial market instability and w ould also re
quire the central bank to give up its role as the
lender o f last resort. But I w ould like now to ar
gue against that belief.
There is a fairly w ell-known paper b y Goodfriend and King (1988) that emphasizes that
functioning as the lender o f last resort does not
necessarily require the provision o f discount
w indow loans; what is necessary is that the cen
tral bank makes available additional base money
at times o f financial crisis. And they argue that
this response w ould come about automatically if
interest rate smoothing w e re being practiced.
Some critics have described the Goodfriend-King
scheme as calling fo r a constant rate o f base
money grow th during times o f financial crisis,
'These include McCallum (1988, 1990, 1993a).
2See McCallum (1990, pp. 61-6; and 1993a, Section VII).
MARCH/APRIL 1994
218
but that is an entirely incorrect description o f
what their argument or proposal actually is.
Consequently, in a paper that I have very re
cently w ritten fo r a Bank o f Japan conference
(McCallum, 1993b), I have tried to follow up on
the Goodfriend-King idea by exploring the possi
bility o f using a nominal GNP targeting rule to
generate implied quarterly settings o f the m one
tary base, and then to combine that w ith a
higher-frequency rule that calls fo r w eekly ad
justments o f a federal funds rate instrument
that are designed to achieve the specified quart
erly base values. This w eekly rule can be made
to imply a lot o f week-to-week smoothing o f the
funds rate and thereby automatically to provide
lender-of-last-resort support to the financial sys
tem. But can it do that w hile simultaneously hit
ting the quarterly base settings w ith reasonable
accuracy? That is clearly an empirical question
whose answer depends upon the size o f shocks
that occur and the strength o f w eekly responses
o f the base to funds rate adjustments. But I have
begun to study that question in this new paper,
and the results obtained are quite encouraging.
http://fraser.stlouisfed.org/RESERVE BANK OF ST. LOUIS
FEDERAL
Federal Reserve Bank of St. Louis
I w ould like to conclude by expressing my
appreciation to the St. Louis Fed’s Research
Department fo r continuing their long-running
program o f searching fo r ways to im prove the
conduct o f m onetary policy.
REFERENCES
Goodfriend, Marvin, and Robert G. King. “ Financial Deregu
lation, Monetary Policy, and Central Banking,” Federal
Reserve Bank of Richmond Economic Review (May/June
1988), pp. 3-22.
McCallum, Bennett T. “ Robustness Properties of a Rule for
Monetary Policy,” Carnegie Rochester Conference Series on
Public Policy (autumn 1988), pp. 173-203.
_______ . "Targets, Indicators, and Instruments of Monetary
Policy,” in William S. Haraf and Phillip Cagan, eds., Mone
tary Policy for a Changing Financial Environment. American
Enterprise Institute, 1990, pp. 44-70.
_______ . “ Specification and Analysis of a Monetary Policy
Rule for Japan,” Bank of Japan Monetary and Economic
Studies (December 1993a).
________“ Monetary Policy Rules and Financial Stability,” un
published working paper (October 1993b).
Taylor, John B. “ Discretion Versus Policy Rules in Practice,”
Carnegie-Rochester Conference Series on Public Policy 39
(December 1993), pp. 195-214.
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