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Journal ArticleDOI

A Comprehensive Revision of the US Monetary Services (Divisia) Indexes

01 Sep 2011-Federal Reserve Bank of St Louis Review (Federal Reserve Bank St Louis)-Vol. 93, Iss: 5, pp 325-358

AbstractThe authors introduce a comprehensive revision of the Divisia monetary aggregates for the United States published by the Federal Reserve Bank of St. Louis, referred to as the Monetary Services Indexes (MSI). These revised MSI are available at five levels of aggregation, including a new broad level of aggregation that includes all of the assets currently reported on the Federal Reserve's H.6 statistical release. Several aspects of the new MS] differ from those previously published. One such change is that the checkable and savings deposit components of the MSI are now adjusted for the effects of retail sweep programs, beginning in 1994. Another change is that alternative MSI are provided using two alternative benchmark rates. In addition, the authors have simplified the procedure used to construct the own rate of return for small-denomination time deposits and have discontinued the previous practice of applying an implicit return to some or all demand deposits. The revised indexes begin in 1967 rather than 1960 because of data limitations.

Summary (5 min read)

Introduction

  • The authors introduce a comprehensive revision of the Divisia monetary aggregates for the United States published by the Federal Reserve Bank of St. Louis, referred to as the Monetary Services Indexes (MSI).
  • Several aspects of the new MSI differ from those previously published.
  • Some assets, including currency and checkable bank deposits, are innately medium of exchange—that is, usable in the purchase and sale of goods and services— while others cannot be used until converted to medium of exchange.
  • Abstracts, synopses, and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.

THE MACROECONOMICS OF MONETARY AGGREGATION

  • This article discusses how to construct monetary index numbers (Divisia monetary aggregates) for the United States.
  • A complementary, but alternative, line of thought argues that (i) the concept of a monetary aggregate in macroeconomics is unnecessary and misleading and (ii) models should focus on the functions of financial assets, including as a medium of exchange and an intertemporal store of value.
  • LOUIS REVIEW 2 Throughout this analysis, the term “monetary assets” refers to those financial assets that can provide “monetary services” during the period—that is, they can serve as a medium of exchange.
  • In such models, most financial assets are treated as near-perfect substitutes; the role of the transaction costs entailed in exchanging an asset that does not furnish medium of exchange services for one that does is secondary, such that even mortgage-backed securities furnish medium of exchange (that is, monetary) services.

THE ROLE OF THE FEDERAL RESERVE BANK OF ST. LOUIS

  • The Federal Reserve Bank of St. Louis has published monetary index numbers (initially referred to as Divisia monetary aggregates and, later, as Monetary Services Indexes [MSI]) for two decades, beginning with Thornton and Yue (1992) and continuing with Anderson, Jones, and Nesmith (1997a,b,c) and Anderson and Buol (2005).
  • MSI-ALL is constructed over all assets currently reported on the Federal Reserve Board’s H.6 statistical release (the components of M2 plus institutional money market mutual funds [MMMFs]) and is the broadest level of aggregation that currently can be constructed from available data.
  • The authors also improved measures of savings and small time deposit rates in the Regulation Q era; as a consequence, the start date of the MSI has been changed from 1960 to 1967.
  • The alternative benchmark rate is the larger of their preferred benchmark rate and the Baa bond yield.
  • The next section provides a brief over - FEDERAL RESERVE BANK OF ST.

MONETARY AGGREGATION AND INDEX NUMBER THEORY

  • This section briefly reviews the economic theory of monetary aggregation.
  • Readers interested primarily in the data may skip this section without loss of continuity; readers seeking a more comprehensive survey might consult Anderson, Jones, and Nesmith (1997b).
  • The user cost of a monetary asset, defined as the interest income forgone by holding a specific financial asset rather than a higher-yielding asset that does not provide monetary services, plays an essential role in monetary aggregation theory.
  • Divisia monetary aggregates are chain-weighted superlative indexes constructed over the quantities and user costs of selected sets of monetary assets.
  • The earliest Divisia aggregates for the United States were constructed at the Federal Reserve Board through the mid-1980s by Barnett, Offenbacher, and Spindt (1981) and, later, by Farr and Johnson (1985), who introduced the descriptive label “Monetary Services Indexes.”.

Background

  • Barnett (1978, 1980) developed Divisia monetary aggregates from aggregation and index number theory; see Barnett and Serletis (2000) for a comprehensive overview.
  • When optimizing in period t, currentperiod real money balances, mn,t, are multiplied in the lifetime budget constraint by πn,t = p*t un,t, where Consequently, πn,t is the user cost for mn,t.7 Usually, πn,t is referred to as the “nominal user cost” and un,t as the corresponding “real user cost” (Barnett, 1987, p. 118).
  • In an alternative derivation, Donovan (1978, pp. 682-86) obtained the same expression by applying the user cost formula for a durable good to interest-bearing monetary assets.
  • In the present context, monetary assets are weakly separable from the other goods and services included in the utility function if where U is strictly increasing in V (see Varian, 1983, p. 104).
  • Specifi - cally, the MSI are based on the superlative Törnqvist-Theil formula.

The MSI and Their Dual User Cost Indexes

  • The published St. Louis MSI are constructed from nominal rather than real monetary asset quantities and, in that sense, are nominal monetary index numbers; corresponding real MSI can be obtained by dividing the nominal MSI by a price index.
  • The real user cost indexes can be multiplied by a price index to obtain corresponding nominal user cost indexes.
  • Thus, the purchase price of a real dollar of the monetary asset is p*t and the sale price of a real dollar of the asset one period later is p*t+1.
  • A number of studies have applied tests of these conditions to determine if specific groupings of monetary assets are weakly separable.

MSI p

  • Not exclusively, on aspects of the MSI that differ substantively from their earlier work (Anderson, Jones, and Nesmith, 1997c).
  • The authors caution readers that this section is necessarily detail oriented, but understanding the details, though sometimes tedious, is essential if the MSI are to be used intelligently in economic research and policymaking.

Aggregation Levels, Components, and Segments

  • The revised St. Louis MSI introduced in this article are monthly data beginning in January 1967; when this paper was written, the most recent available data were for May 2011.
  • More specifically, MSI-M2M is defined over the components of MSI-M2 except small-denomination time deposits, and MSI-MZM is defined over the components of MSI-M2M plus institutional MMMFs (equivalently, it includes all components of MSIALL except small-denomination time deposits).
  • Readers should note that the number of components included in the MSI varies from month to month due to data availability.
  • Exam - ples of newly available data that increased the number of components include retail MMMFs (February 1973), institutional MMMFs (January 1974), other checkable deposits (OCDs) at com- 330 SEPTEMBER/OCTOBER 2011 FEDERAL RESERVE BANK OF ST.
  • This follows from the fact that the expenditure shares add up to 1.

Retail Sweep Adjustment

  • Retail sweep programs at depository institutions began in January 1994.
  • Growth of M1 deposits has been depressed for a number of years by these programs, which shift—or ‘‘sweep’’— balances from household transactions accounts, which are subject to reserve requirements, into savings accounts, which are not.
  • Nevertheless, Federal Reserve Board staff estimate the amounts each month, and their estimates are available publicly on the St. Louis Fed’s website.
  • 16 Figure 2 plots MSI-M1 against a comparable index constructed over components not adjusted for retail sweeping; failing to adjust for the effects of retail sweeps causes significant understatement of MSI-M1.17 14 See http://research.stlouisfed.org/aggreg/swdata.html.
  • Measurement of the benchmark rate is addressed in the next section.

Benchmark Rates

  • The theory of monetary aggregation assumes that there exists a benchmark asset that furnishes no monetary services—that is, an asset that is used only to transfer wealth from period to period.
  • Long-term bond yields are often used as benchmark rates, but this approach is somewhat problematic….
  • The authors construct MSI using a benchmark rate equal to the upper envelope plus a constant (that is, not time-varying) liquidity premium of 100 basis points, which they refer to as their “preferred” benchmark rate.
  • On the other hand, adding just 152 basis points (rather than 200 basis points) to the 6-month Treasury bill rate is sufficient to produce a benchmark rate that exceeds the upper envelope in all but two months over this period.
  • Figure 3 compares year-over-year growth rates for MSI-ALL using the two benchmark rates.

Own Rates of Return

  • The MSI require estimates of the user costs of each component, which are derived from the spread between the benchmark rate of return and the component’s own rate of return.
  • The prohibition of interest on demand deposits distorts the pricing of transaction deposits and associated bank services.
  • Available data include monthly figures for deposit own rates published between 1983 and 1997 by the Federal Reserve Board in a supplementary table (Monthly Survey of Selected Deposits [FR2042]) to the H.6 statistical release.
  • In 1957 and 1962, when market interest rates rose near or above the ceiling rates on savings deposits, these ceilings were raised….
  • For January 1967 –May 1978, the authors set the own rate for smalldenomination time deposits at thrift institutions equal to the own rate on deposits at commercial banks plus the difference between the corre - sponding interest rate ceilings.

Long-Run and Short-Run Growth

  • Figure 8 shows both month-to-month and year-over-year MSI growth.
  • Generally speaking, movements in the five MSI are similar.
  • Figure 9 depicts growth of MSI during four selected decade-long periods.
  • MSI growth slowed during 1969 as Federal Open Market Committee (FOMC) policy tightened, with decreases during 1970 in the levels of MSI-M2M and MSI-MZM.
  • Panel D includes the 2001 recession/recovery, the subsequent housing boom and financial crisis, and the Federal Reserve’s credit-easing policies during 2008 and its 2009-11 quantitative easing policies.

Method of Aggregation Versus Scope of the Aggregate

  • This section compares and contrasts the MSI with each other and monetary aggregates constructed by summation of the dollar amounts of the included assets; the latter are denoted as “SUM-M1” and so on.
  • SUM-M2M, SUM-MZM, and SUM-M2 are identical to the monetary aggregates available through FRED.31 SUM-M1 is not the same as the Federal Reserve’s M1 aggregate because it is retail-sweep adjusted to be comparable with MSI-M1.32 SUM-ALL is identical to SUM-M2 plus institutional MMMFs, which are also available through FRED.
  • With respect to the former, monetary aggregates produced by the Federal Reserve’s Board of Governors are summation aggregates:.
  • From the standpoint of monetary aggregation/index number theory, the two issues are related since superlative index numbers should be constructed over groups of monetary assets that are weakly separable.
  • Figure 10 shows a scatterplot matrix of monthto-month percentage growth rates of the five MSI; correlations between the MSI are shown in the 346 SEPTEMBER/OCTOBER 2011 FEDERAL RESERVE BANK OF ST.

SUMMARY AND CONCLUSIONS

  • Valuable resources to empirical economists interested in the role that money plays in the economy.
  • The authors also introduce a new benchmark rate, defined as the largest rate in a set of rates that includes the own rates of the components of the broadest index and yields on selected short-term money market rates (the upper envelope) plus a modest liquidity premium.
  • A major problem with the official M1 monetary aggregate is, of course, retail sweeping of transaction deposits.
  • As Lucas (2000, pp. 270-71) has argued, “I share the widely held opinion that M1 is too narrow an aggregate for this period [the 1990s], and I think that the Divisia approach offers much the best pros pects for resolving the difficulty.”.
  • On the other hand, growth rates of MSI-M2 and MSI-ALL diverged much more than usual in 2010, suggesting that MSI-M3 might have contained some additional information in recent years.

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FEDERAL RESERVE BANK OF S T
.
LOUIS
RE V I EW
SEPTEMBER
/
OCTO B E R
201 1 325
A Comprehensive Revision of the
U.S. Monetary Services (Divisia) Indexes
Richard G. Anderson and Barry E. Jones
The authors introduce a comprehensive revision of the Divisia monetary aggregates for the
United States published by the Federal Reserve Bank of St. Louis, referred to as the Monetary
Services Indexes (MSI). These revised MSI are available at five levels of aggregation, including a
new broad level of aggregation that includes all of the assets currently reported on the Federal
Reserve’s H.6 statistical release. Several aspects of the new MSI differ from those previously pub-
lished. One such change is that the checkable and savings deposit components of the MSI are now
adjusted for the effects of retail sweep programs, beginning in 1994. Another change is that alter-
native MSI are provided using two alternative benchmark rates. In addition, the authors have sim-
plified the procedure used to construct the own rate of return for small-denomination time deposits
and have discontinued the previous practice of applying an implicit return to some or all demand
deposits. The revised indexes begin in 1967 rather than 1960 because of data limitations.
(JEL C43, C82, E4, E50)
Federal Reserve Bank of St. Louis Review, September/October 2011, 93(5), pp. 325-59.
financial assets selected by consumers and firms
may be separated into two groups. Some assets,
including currency and checkable bank deposits,
are innately medium of exchange—that is, usable
in the purchase and sale of goods and services—
while others cannot be used until converted to
medium of exchange.
1
Generally, monetary assets
that differ in terms of their potential usefulness
as medium of exchange also differ in their own
rates of return. Barnett (1980) developed the
concept and theory of monetary index numbers,
Money is necessary to the carrying on of trade.
For where money fails, men cannot buy, and
trade stops.
—John Locke, Further Considerations
Concerning Raising the Value of Money
(1696, p. 319; quoted by Vickers, 1959)
M
oney plays a crucial role in the econ-
omy because the purchase and sale of
goods and services is settled in what
economists refer to as “medium of exchange.”
Forward-looking consumers and firms determine
their desired quantities of medium of exchange
at approximately the same time as they (i) form
expectations of future income and expenditure
and (ii) make decisions regarding desired quan-
tities of financial and nonfinancial assets. The
1
There are exceptions, of course. Bank checks, for example, are not
accepted by all merchants. Even for currency, there are exceptions
(see Twain, 1996). More seriously, currency issued by a sovereign
country often is not accepted in other countries; for a discussion
of monetary index numbers defined across currencies, see Barnett
(2007).
Richard G. Anderson is an economist and vice president at the Federal Reserve Bank of St. Louis and visiting professor, Management School,
University of Sheffield (U.K.). Barry E. Jones is associate professor of economics at Binghamton University–State University of New York. The
authors thank Yang Liu and Esha Singha for research assistance and Barry Cynamon, Livio Stracca, and Jim Swofford for helpful comments
on an earlier draft. Anderson thanks the research department of the Federal Reserve Bank of Minneapolis for their hospitality during the com-
pletion of this analysis. Jones thanks the Federal Reserve Bank of St. Louis and the department of economics at Lund University for their
hospitality during several visits.
©
2011, The Federal Reserve Bank of St. Louis. The views expressed in this article are those of the author(s) and do not necessarily reflect the
views of the Federal Reserve System, the Board of Governors, or the regional Federal Reserve Banks. Articles may be reprinted, reproduced,
published, distributed, displayed, and transmitted in their entirety if copyright notice, author name(s), and full citation are included. Abstracts,
synopses, and other derivative works may be made only with prior written permission of the Federal Reserve Bank of St. Louis.

which he referred to as “Divisia monetary aggre-
gates.” Divisia aggregates measure, in a method
consistent with intertemporal microeconomic
theory, the aggregate flow of monetary services
derived by consumers and firms from a collec-
tion of monetary assets with different character-
istics and different rates of return. Underlying
Divisia monetary aggregates is the concept of the
user cost of a monetary asset, which is a func-
tion of the interest forgone by holding a specific
asset rather than an alternative asset that does
not provide any monetary services and earns a
higher rate of return (referred to as the “bench-
mark rate”). The close connection in microeco-
nomic theory between monetary index numbers
and agents’ anticipated income and expenditure
suggests that monetary index numbers should
be more closely related to economic activity than
conventional simple sum monetary aggregates
(see, for example, Hancock, 2005; Barnett and
Chauvet, 2011; Barnett, forthcoming).
THE MACROECONOMICS OF
MONETARY AGGREGATION
This article discusses how to construct mon-
etary index numbers (Divisia monetary aggregates)
for the United States.
2
For the most part, we do
not address when or why such measurement and
aggregation might be desirable, which is contro-
versial to some extent among macroeconomists.
The extant principal body of current macroeco-
nomic analysis widely uses the concept of an
aggregate measure of money and distinctly sepa-
rates “money” from other assets, financial and
nonfinancial.
3
Typically, macroeconomists define
“moneyas financial assets that either are medium
of exchange or convertible to medium of exchange
at de minimus cost. Demand for such assets is
motivated in a macroeconomic model by either
cash-in-advance or shopping-time constraints or
a money-in-the-utility (or production) function
specification.
4
Models differ, however, regarding
whether a household or firm might replenish a
depleted stock of money during the current period
by selling (or using as collateral) its nonmonetary
assets. If such a mechanism is permitted, the cor-
rect definition of a monetary aggregate for macro-
economic analysis depends on assumptions
regarding the liquidity of those assets that are not
medium of exchange.
A complementary, but alternative, line of
thought argues that (i) the concept of a monetary
aggregate in macroeconomics is unnecessary and
misleading and (ii) models should focus on the
functions of financial assets, including as a
medium of exchange and an intertemporal store
of value. Monetary aggregates, for example, have
no role in the class of recent search-based macro-
economic models that Stephen Williamson and
Randall Wright have labeled “New Monetarist
economics.”
5
Although the exchange of goods
and services is fundamental in such models, the
role of an asset as a medium of exchange is unim-
portant because the models (implicitly or explic-
itly) assume a transformation technology such
that (almost) any asset can fulfill the functional
role of medium of exchange—that is, all assets
are liquid. For example, Williamson and Wright
(2010, p. 294) write:
Note as well that theory provides no particular
rationale for adding up certain public and pri-
vate liabilities (in this case currency and bank
deposits), calling the sum money, and attach-
ing some special significance to it. Indeed,
there are equilibria in the model where cur-
rency and bank deposits are both used in some
of the same transactions, both bear the same
rate of return, and the stocks of both turn over
once each period. Thus, Friedman, if he were
alive, might think he had good reason to call
the sum of currency and bank deposits money
and proceed from there. But what the model
tells us is that public and private liquidity play
Anderson and Jones
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2
Throughout this analysis, the term “monetary assets” refers to those
financial assets that can provide “monetary services” during the
period—that is, they can serve as a medium of exchange. Some
assets (currency, checkable deposits) are immediately medium
of exchange. Other assets have the standby capability to act as
medium of exchange if there exist markets that allow the assets to
be exchanged for medium of exchange when need be, either by
means of a sale or use as collateral.
3
Walsh (2010) is a comprehensive recent textbook treatment.
4
A classic analysis is King and Plosser (1984).
5
Williamson and Wright (2010, 2011).

quite different roles. In reality, many assets are
used in transactions, broadly defined, includ-
ing Treasury bills, mortgage-backed securities,
and mutual fund shares. We see no real pur-
pose in drawing some boundary between one
set of assets and another, and calling members
of one set money.
New Monetarist-style models seek to illustrate
how a demand for monetary services arises as a
result of optimizing behavior by households and
firms. To do so, generally speaking, the models
assert that a shortage of medium of exchange is
costly in the sense that trades do not occur that
otherwise would be Pareto welfare-improving.
In such models, most financial assets are treated
as near-perfect substitutes; the role of the trans-
action costs entailed in exchanging an asset that
does not furnish medium of exchange services
for one that does is secondary, such that even
mortgage-backed securities furnish medium of
exchange (that is, monetary) services.
In a related recent analysis that addresses
neither the wisdom nor the necessity of monetary
aggregation, Holmström and Tirole (2011) ask if
transaction costs and “sudden stops” in financial
markets explain why households and firms choose
to hold larger quantities of highly liquid assets
than is suggested by models with de minimus
asset-market transaction costs. They note: “While
some forms of equity, such as private equity, may
not be readily sold at a ‘fair price,’ many long-
term securities are traded on active organized
exchanges…liquidating one’s position…can be
performed quickly and at low transaction costs”
(p. 1). Their analysis implies that not all financial
assets are perfect substitutes due to the risks that
(i) market trading might suddenly halt, (ii) differ-
ential user costs can arise in the solution to the
optimization problem facing households and
firms, and (iii) such differential user costs reflect
the differing amounts of monetary services fur-
nished by the assets.
THE ROLE OF THE FEDERAL
RESERVE BANK OF ST. LOUIS
The Federal Reserve Bank of St. Louis has
published monetary index numbers (initially
referred to as Divisia monetary aggregates and,
later, as Monetary Services Indexes [MSI]) for
two decades, beginning with Thornton and Yue
(1992) and continuing with Anderson, Jones,
and Nesmith (1997a,b,c) and Anderson and Buol
(2005). Publication of the most recent series was
suspended in March 2006 when certain necessary
data became unavailable.
In this paper, we introduce a comprehensive
revision of the MSI constructed at five levels of
aggregation: MSI-M1, MSI-M2, MSI-M2M, MSI-
MZM, and MSI-ALL. MSI-M1 and MSI-M2 are
constructed, respectively, over the same compo-
nents included in the Federal Reserve Board’s
M1 and M2 monetary aggregates. MSI-ALL is con-
structed over all assets currently reported on the
Federal Reserve Board’s H.6 statistical release
(the components of M2 plus institutional money
market mutual funds [MMMFs]) and is the broad-
est level of aggregation that currently can be con-
structed from available data. Finally, MSI-M2M
and MSI-MZM are zero-maturity indexes (i.e.,
they exclude small-denomination time deposits).
One change to the indexes is the adjustment of
checkable and savings deposit components of
the MSI for the effects of retail sweep programs,
beginning in 1994.
Several changes have been made to the user
costs of the components. Among these, we dis-
continued the previous practice of assigning an
implicit return to some or all demand deposits
and simplified the procedure used to construct
the own rate for small-denomination time deposits.
We also improved measures of savings and small
time deposit rates in the Regulation Q era; as a
consequence, the start date of the MSI has been
changed from 1960 to 1967. Finally, the MSI are
now constructed using two different benchmark
rates. Our preferred benchmark rate is the maxi-
mum taken over the own rates of the components
of MSI-ALL and a set of short-term money market
rates (referred to in the literature as the “upper
envelope”) plus a small liquidity premium. The
alternative benchmark rate is the larger of our
preferred benchmark rate and the Baa bond yield.
Previous practice had been to simply include the
Baa bond yield in the upper envelope.
The remainder of the paper is organized as
follows. The next section provides a brief over -
Anderson and Jones
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201 1 327

view of the theory behind the MSI. We then
describe the MSI and their changes relative to
Anderson, Jones, and Nesmith (1997c). Next, we
examine the empirical properties of the MSI,
emphasizing the time-series behavior of the
indexes. The final section offers some conclusions.
MONETARY AGGREGATION AND
INDEX NUMBER THEORY
This section briefly reviews the economic
theory of monetary aggregation. Readers interested
primarily in the data may skip this section with-
out loss of continuity; readers seeking a more
comprehensive survey might consult Anderson,
Jones, and Nesmith (1997b).
The user cost of a monetary asset, defined as
the interest income forgone by holding a specific
financial asset rather than a higher-yielding asset
that does not provide monetary services, plays
an essential role in monetary aggregation theory.
Divisia monetary aggregates are chain-weighted
superlative indexes constructed over the quanti-
ties and user costs of selected sets of monetary
assets. The earliest Divisia aggregates for the
United States were constructed at the Federal
Reserve Board through the mid-1980s by Barnett,
Offenbacher, and Spindt (1981) and, later, by Farr
and Johnson (1985), who introduced the descrip-
tive label “Monetary Services Indexes.”
6
Background
Barnett (1978, 1980) developed Divisia mone-
tary aggregates from aggregation and index num-
ber theory; see Barnett and Serletis (2000) for a
comprehensive overview. The basic ideas can be
illustrated with a simple money-in-the-utility
function model. In each period t, a representative
consumer is assumed to maximize lifetime utility:
where c
s
denotes a vector of quantities of a set of
nonmonetary goods and services and m
s
denotes
β
s t
s t
s s
u
=
( )
c m, ,
a vector of real stocks of a set of monetary assets.
The budget constraints are given by
for all s t, where b
s
denotes the real stock of a
benchmark asset that does not enter into the util-
ity function, Y
s
represents nominal income not
due to asset holdings, p
*
s
is a price index used to
convert nominal stocks to real terms, p
s
is the
price vector for the nonmonetary goods and serv-
ices, R
s
is the nominal rate of return on the bench-
mark asset, and r
n
,s
is the nominal own rate of
return (possibly zero) for the nth monetary asset.
The user cost of each monetary asset is
derived from the above maximization. Barnett
(1978) derived the formula for the user cost of a
monetary asset by combining individual-period
budget constraints into a single lifetime budget
constraint. When optimizing in period t, current-
period real money balances, m
n,t
, are multiplied
in the lifetime budget constraint by
π
n,t
= p
*
t
u
n,t
,
where
Consequently,
π
n,t
is the user cost for m
n,t
.
7
Usually,
π
n,t
is referred to as the “nominal user
cost” and u
n,t
as the corresponding “real user cost”
(Barnett, 1987, p. 118). In an alternative derivation,
Donovan (1978, pp. 682-86) obtained the same
expression by applying the user cost formula
for a durable good to interest-bearing monetary
assets.
8
Diewert (1974, p. 510) did the same for
non-interest-bearing assets.
p c
s
s s s s s s
s n s n s
p b R p b
p m r
= +
( )
+ +
( )
1
1
1 1
1
1
*
*
*
, ,
+
=
p m Y
s n s
n
N
s
*
,
1
u
R r
R
n t
t n t
t
,
,
.=
+1
Anderson and Jones
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6
Divisia money measures for the United Kingdom have been main-
tained by the Bank of England since the early 1990s (see Fisher,
Hudson, and Pradhan, 1993, and Hancock, 2005).
7
More generally, when optimizing in period t, the (discounted)
user cost for m
n,s
s t+1 is given by
See Barnett (1978) for further discussion. Diewert (1974) provides
analogous expressions for durable goods.
8
The user cost of a durable good is the difference between the pur-
chase price of a unit of the good and the present value of the sale
price one period later (adjusted for depreciation). Donovan’s argu-
ment is as follows: Holding p
*
t
dollars of a monetary asset in period
t is equivalent to holding one real dollar of the monetary asset.
p
R r
R R R
s
s n s
t t s
*
+
( )
+
( )
+
( )
+
,
.
1 1 1
1

A key property in aggregation and index
number theory is weak separability. In the present
context, monetary assets are weakly separable
from the other goods and services included in
the utility function if
where U is strictly increasing in V (see Varian,
1983, p. 104). Under weak separability, utility
maximization in period t implies that the vector
of real money balances, m
t
, chosen in that period
maximizes the sub-utility function, Vm, subject
to the budget constraint, π
t
.
m = π
t
.
m
t
, where π
t
is a vector of nominal user costs.
9
Chain-weighted superlative indexes con-
structed from data on the quantities of monetary
assets and their user costs can be used to measure
how Vm
t
evolves over time; here, we provide
an overview (see the appendix for details). Specifi -
cally, the MSI are based on the superlative
Törnqvist-Theil formula. The chain-weighted
Törnqvist-Theil monetary quantity index is
where
is the expenditure share for the nth monetary
asset for period t. The index has the attractive
property that its log difference is a weighted aver-
age of the log differences of its components:
u U Vc m c m, , ,
( )
( )
V V
m
m
t t
n t
n t
n
N
w w
n t n t
=
=
+
1
1
1
2
1
,
,
, ,
,
w
m
m
n t
n t n t
i t i t
i
N
,
, ,
, ,
=
=
π
π
1
Barnett (1980) interpreted the Törnqvist-Theil
index as a discrete-time approximation of the
continuous-time Divisia index, which is the origin
of the term Divisia monetary aggregate. As he
emphasized, in continuous time the Divisia index
is exact for any linearly homogeneous utility
function.
10
The MSI and Their Dual User Cost
Indexes
The published St. Louis MSI are constructed
from nominal rather than real monetary asset
quantities and, in that sense, are nominal mone-
tary index numbers; corresponding real MSI can
be obtained by dividing the nominal MSI by a
price index. We also publish real user cost indexes
for the various MSI that are suitable for use in
empirical work as the opportunity costs of those
MSI. The real user cost indexes can be multiplied
by a price index to obtain corresponding nominal
user cost indexes. This is analogous to the rela-
tionship between real and nominal user costs of
individual monetary assets as discussed above.
Specifically, let p
t
*
denote a price index, and
let M
n,t
and m
n,t
denote the nominal and real
quantities, respectively, of the nth monetary
asset—that is, m
n,t
= M
n,t
/p
t
*
. Let u
n,t
be the corre-
sponding real user cost, which does not depend
on the price index. The corresponding nominal
user cost is
π
n,t
=p
t
*
u
n,t
. The published nominal
MSI are constructed using nominal monetary
asset quantities as follows:
ln ln
ln
,
,
,
V V
w w
m
t t
n
t n t
n
N
n
t
( )
( )
=
+
( )
=
1
1
1
2
( )
ln .
,
m
n
t 1
Anderson and Jones
FEDERAL RESERV E B A N K OF ST
.
LOUIS
RE V I EW
SEPTEMBER
/
OCTO B E R
201 1 329
Thus, the purchase price of a real dollar of the monetary asset is
p
*
t
and the sale price of a real dollar of the asset one period later is
p
*
t+1
. If the asset earns interest, holding p
*
t
dollars of the asset for
one period results in p
*
t
1 + r
n,t
/p
*
t+1
real dollars of the asset one
period later. Consequently, the user cost of the monetary asset is
9
Barnett (1982) emphasizes weak separability in choosing the
components of a monetary aggregate. Varian (1982, 1983) derived
necessary and sufficient conditions for a dataset to be consistent
with utility maximization and weak separability. A number of
studies have applied tests of these conditions to determine if spe-
cific groupings of monetary assets are weakly separable. For recent
examples, see Jones, Dutkowsky and Elger (2005), Drake and
Fleissig (2006), and Elger et al. (2008).
p p
p r
p R
p
R r
R
t t
t n t
t t
t
t n t
t
* *
*
*
*
+
( )
+
( )
=
+
=
+
+
1
1
1
1
1
,
,
ππ
n t,
.
10
If m
t
maximizes Vm subject to the budget constraint π
t
.
m =
π
t
.
m
t
for all t and Vm is linearly homogeneous, then in the
continuous-time case
which corresponds to the continuous-time Divisia quantity index
(see Barnett, 1987, p. 141).
d V
dt
d V
dt
w
d m
dt
t
t
n t
n
N
n t
ln
ln
ln
,
,
( )
=
( )
( )
=
( )
=
m
,
1

Citations
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Posted Content
Abstract: This essay articulates the principles and practices of New Monetarism, our label for a recent body of work on money, banking, payments, and asset markets. We first discuss methodological issues distinguishing our approach from others: New Monetarism has something in common with Old Monetarism, but there are also important differences; it has little in common with Keynesianism. We describe the principles of these schools and contrast them with our approach. To show how it works, in practice, we build a benchmark New Monetarist model, and use it to study several issues, including the cost of inflation, liquidity and asset trading. We also develop a new model of banking.

98 citations


Journal ArticleDOI
Abstract: The Center for Financial Stability (CFS) has initiated a new Divisia monetary aggregates database, maintained within the CFS program called Advances in Monetary and Financial Measurement (AMFM). The Director of the program is William A. Barnett, who is the originator of Divisia monetary aggregation and more broadly of the associated field of aggregation-theoretic monetary aggregation. The international section of the AMFM web site is a centralized source for Divisia monetary aggregates data and research for over 40 countries throughout the world. The components of the CFS Divisia monetary aggregates for the United States reflect closely those of the current and former simple-sum monetary aggregates provided by the Federal Reserve. The first five levels, M1, M2, M2M, MZM, and ALL, are composed of currency, deposit accounts, and money market accounts. The liquid asset extensions to M3, M4-, and M4 resemble in spirit the now discontinued M3 and L aggregates, including repurchase agreements, large denomination time deposits, commercial paper, and Treasury bills. When the Federal Reserve discontinued publishing M3 and L, the Fed stopped providing the consolidated, seasonally adjusted components. Also the Fed no longer provides the interest rates on the components. With so much of the needed component quantity and interest-rate data no longer available from the Federal Reserve, decisions about data sources needed in construction of the CFS aggregates have been far from easy and sometimes required regression interpolation. This paper documents the decisions of the CFS regarding United States data sources at the present time, with particular emphasis on Divisia M3 and M4.

89 citations


Posted Content
Abstract: Over the last twenty-five years, a set of influential studies has placed interest rates at the heart of analyses that interpret and evaluate monetary policies. In light of this work, the Federal Reserve's recent policy of "quantitative easing," with its goal of affecting the supply of liquid assets, appears to be a radical break from standard practice. Alternatively, one could posit that the monetary aggregates, when measured properly, never lost their ability to explain aggregate fluctuations and, for this reason, represent an important omission from standard models and policy discussions. In this context, the new policy initiatives can be characterized simply as conventional attempts to increase money growth. This view is supported by evidence that superlative (Divisia) measures of money often help in forecasting movements in key macroeconomic variables. Moreover, the statistical fit of a structural vector autoregression deteriorates significantly if such measures of money are excluded when identifying monetary policy shocks. These results cast doubt on the adequacy of conventional models that focus on interest rates alone. They also highlight that all monetary disturbances have an important "quantitative" component, which is captured by movements in a properly measured monetary aggregate.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

85 citations


Posted Content
Abstract: The Center for Financial Stability (CFS) has initiated a new Divisia monetary aggregates database, maintained within the CFS program called Advances in Monetary and Financial Measurement (AMFM). The Director of the program is William A. Barnett, who is the originator of Divisia monetary aggregation and more broadly of the associated field of aggregation-theoretic monetary aggregation. The international section of the AMFM web site is a centralized source for Divisia monetary aggregates data and research for over 40 countries throughout the world. The components of the CFS Divisia monetary aggregates for the United States reflect closely those of the current and former simple-sum monetary aggregates provided by the Federal Reserve. The first five levels, M1, M2, M2M, MZM, and ALL, are composed of currency, deposit accounts, and money market accounts. The liquid asset extensions to M3, M4-, and M4 resemble in spirit the now discontinued M3 and L aggregates, including repurchase agreements, large denomination time deposits, commercial paper, and Treasury bills. When the Federal Reserve discontinued publishing M3 and L, the Fed stopped providing the consolidated, seasonally adjusted components. Also the Fed no longer provides the interest rates on the components. With so much of the needed component quantity and interest-rate data no longer available from the Federal Reserve, decisions about data sources needed in construction of the CFS aggregates have been far from easy and sometimes required regression interpolation. This paper documents the decisions of the CFS regarding United States data sources at the present time, with particular emphasis on Divisia M3 and M4.

81 citations


Cites background or methods from "A Comprehensive Revision of the US ..."

  • ...See Anderson and Jones (2011). But since the Federal Reserve no longer provides its former broad aggregates, M3 and L, the CFS is now maintaining the broad aggregates, Divisia M3 and Divisia M4, where M4 is similar to the Fed’s former broadest aggregate, L....

    [...]

  • ...We acquired that interest rate from the MSI component spreadsheet provided to us by Richard Anderson for the paper Anderson and Jones (2011). After 1987 the rate or return on interest-bearing checking accounts is from the Bank Rate Monitor Survey....

    [...]

  • ...Louis Fed for the paper, Anderson and Jones (2011). From 1986 to 1991, that data set is also used to acquire the average monthly interest-rate paid on savings deposits....

    [...]

  • ...Anderson and Jones (2011) and Anderson, Jones, and Nesmith (1997) investigated the possibility of assigning a non-zero own rate to demand deposits and proposed alternative methods, originally suggested by Barnett and Spindt (1982), Farr and Johnson (1985), and Thornton and Yue (1992). In these imputation procedures, household and business demand-deposits are separated....

    [...]

  • ...We acquired that interest rate from the MSI component spreadsheet provided to us by Richard Anderson for the paper Anderson and Jones (2011)....

    [...]


Journal ArticleDOI
Abstract: King et al. (1991) evaluate the empirical relevance of a class of real business cycle models with permanent productivity shocks by analyzing the stochastic trend properties of postwar U.S. macroeconomic data. They find a common stochastic trend in a three-variable system that includes output, consumption, and investment, but the explanatory power of the common trend drops significantly when they add money balances and the nominal interest rate. In this paper, we revisit the cointegration tests in the spirit of King et al., using improved monetary aggregates whose construction has been stimulated by the Barnett critique. We show that previous rejections of the balanced growth hypothesis and classical money demand functions can be attributed to mismeasurement of the monetary aggregates.

62 citations


Cites methods from "A Comprehensive Revision of the US ..."

  • ...It is to be noted that in this paper we do not report evidence using the St. Louis Fed s Divisia monetary aggregates, called MSI (monetary services indices), the new vintage of which is documented in Anderson and Jones (2011)....

    [...]

  • ...In particular, J-B is the Jarque-Bera (1980) test statistic distributed as a (2)(2) under the null hypothesis of normality and LM is a multivariate test statistic distributed as a 2 with K(2) degrees of freedom (where K is the number of endogenous variables in the VAR) under the null hypothesis of no serial correlation....

    [...]


References
More filters

Journal ArticleDOI
Abstract: The paper rationalizes certain functional forms for index numbers with functional forms for the underlying aggregator function. An aggregator functional form is said to be ‘flexible’ if it can provide a second order approximation to an arbitrary twice diffentiable linearly homogeneous function. An index number functional form is said to be ‘superlative’ if it is exact (i.e., consistent with) for a ‘flexible’ aggregator functional form. The paper shows that a certain family of index number formulae is exact for the ‘flexible’ quadratic mean of order r aggregator function, (Σ i Σ j a ij x i r 2 x j r 2 ) 1 r , defined by Den and others. For r equals 2, the resulting quantity index is Irving Fisher's ideal index. The paper also utilizes the Malmquist quantity index in order to rationalize the Tornqvist-Theil quantity indexin the nonhomothetic case. Finally, the paper attempts to justify the Jorgenson-Griliches productivity measurement technique for the case of discrete (as opposed to continuous) data.

2,220 citations


"A Comprehensive Revision of the US ..." refers background in this paper

  • ...38 Both the Törnqvist-Theil and Fisher ideal quantity indexes have also been shown to have attractive properties even if the utility function is not linearly homogeneous (see Diewert, 1976a,b, and Diewert, 1993, pp. 211-13)....

    [...]

  • ...Diewert (1976a) defined the concepts of exact and superlative indexes, which Barnett (1980) applied to monetary data.37 In this context, the real stocks of a set of monetary assets act as quantities paired with their corresponding user cost prices....

    [...]

  • ...Diewert (1976a) proved that the quadratic mean of order r quantity and price indexes is superlative for all r....

    [...]

  • ...Diewert (1976a) also defined exact and superlative price indexes....

    [...]


Book
27 Oct 1998
Abstract: Part 1 Empirical evidence on money and output: introduction some basic correlations estimating the effect of money on output summary. Part 2 Money in a general equilibrium framework: introduction the Tobin effect money in the utility function summary appendix - the MIU approximation problems. Part 3 Money and transactions: introduction shopping-time models cash-in-advance models other approaches summary appendix - the CIA approximation problems. Part 4 Money and public finance: introduction bugdet accounting equilibrium seigniorage optimal taxation and seigniorage Friedman's rule revisited nonindexed tax systems problems. Part 5 Money and output in the short run: introduction flexible prices sticky prices and wages a framework for monetary analysis inflation persistence summary appendix problems. Part 6 Money and the open economy: introduction the Obstfeld-Rogoff two-country model policy coordination the small open economy summary appendix problems. Part 7 The credit channel of monetary policy: introduction imperfect information in credit markets macroeconomic implications does credit matter? summary. Part 8 Discretionary policy and time inconsistency: introduction inflation under discretionary policy solutions to the inflation bias is the inflation bias important? do central banking institutions matter? lessons and conclusions problems. Part 9 Monetary-policy operating procedures: introduction from instruments to goals the instrument-choice problem operating procedures and policy measures problems. Part 10 Interest rates and monetary policy: introduction interest-rate rule and the price level interest rate policies in general equilibrium models the term structure of interest rates a model for policy analysis summary problems.

2,049 citations


Journal ArticleDOI

1,069 citations


"A Comprehensive Revision of the US ..." refers methods in this paper

  • ...Varian (1982, 1983) derived necessary and sufficient conditions for a dataset to be consistent with utility maximization and weak separability....

    [...]

  • ...These figures subsequently are replaced with published data as they become available....

    [...]


Journal ArticleDOI
Abstract: In a monetary economy, it is in everyone’s private interest to try to get someone else to hold non-interest-bearing cash and reserves. But someone has to hold it all, so these efforts must simply cancel out. All of us spend several hours per year in this effort, and employ thousands of talented and highly-trained people to help us. These person-hours are simply thrown away, wasted on a task that should not have to be performed at all.

776 citations


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569 citations


"A Comprehensive Revision of the US ..." refers background in this paper

  • ...Diewert (1976a) defined the concepts of exact and superlative indexes, which Barnett (1980) applied to monetary data.37 In this context, the real stocks of a set of monetary assets act as quantities paired with their corresponding user cost prices....

    [...]

  • ...Barnett (1980) developed the concept and theory of monetary index numbers, Money is necessary to the carrying on of trade....

    [...]

  • ...…of its components: u U Vc m c m, , ,( ) ≡ ( ) V V m mt t n t n tn N w wn t n t = ∏− −= + − 1 11 2 1 , , , , , w m m n t n t n t i t i ti N, , , , , = =∑ π π1 Barnett (1980) interpreted the Törnqvist-Theil index as a discrete-time approximation of the continuous-time Divisia index, which is…...

    [...]

  • ...Barnett (1978, 1980) developed Divisia monetary aggregates from aggregation and index number theory; see Barnett and Serletis (2000) for a comprehensive overview....

    [...]


Frequently Asked Questions (1)
Q1. What have the authors contributed in "A comprehensive revision of the u.s. monetary services (divisia) indexes" ?

The authors introduce a comprehensive revision of the Divisia monetary aggregates for the United States published by the Federal Reserve Bank of St. Louis, referred to as the Monetary Services Indexes ( MSI ). These revised MSI are available at five levels of aggregation, including a new broad level of aggregation that includes all of the assets currently reported on the Federal Reserve ’ s H. 6 statistical release. In addition, the authors have simplified the procedure used to construct the own rate of return for small-denomination time deposits and have discontinued the previous practice of applying an implicit return to some or all demand deposits.