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Federal Reserve Bank of Cleveland
Economic Review




ISSN 0013-0281

Spring 1983

Economic Review is published quarterly by
the Research D epartm ent of the Federal
Reserve Bank of Cleveland, P.O. Box 6387,
Cleveland, Ohio 44101. Telephone: (216)
579-2000. Editor: Patricia Phares Wren.
Graphics: Mike Whipkey. Typesetting:
Sally C hunat.
Opinions stated in the Economic Review are
those of the authors and not necessarily
those of the Federal Reserve Bank of Cleve­
land or of the Board of Governors of the
Federal Reserve System.
M aterial may be reprinted provided th at
the source is credited. Please send copies of
reprinted m aterials to the editor.




Spring 1983
Federal R eserve Bank of Cleveland

Economic Review




C o n ten ts
Money Demand: Cash Management
and Deregulation ............................... 2
Over the past decade cash management has
become increasingly sophisticated, signifi­
cantly affecting the use of financial in stru ­
ments for conducting transactions. Econo­
mist John Carlson describes how the new
methods affect the demand for money and
the implications of deregulation for this
process. After reviewing empirical studies
of money demand, he presents evidence of
another kind of change in the relationship
between money and income. In the context
of the conventional model, Carlson finds a
sizable shift in the speed of adjustm ent of
cash balances to desired levels. Although
the shift is consistent w ith the cashmanagement process, other interpretations
are identified and discussed.

Divisia Monetary Aggregates: Would
They Be More Palatable than the
Traditional Simple-Sum Stews? ... 17
T he traditional simple-sum approach to
m onetary aggregation inefficiently mea­
sures the total flow of medium-of-exchange
(MOE) services in the economy. The trad i­
tional approach is inefficient because it
treats financial assets dichotomously—
either totally including or totally excluding
assets from the aggregate being con­
structed. Divisia aggregates provide, at
least on the theoretical level, a more effi­
cient approach. Through the rental prices
of financial assets, Divisia aggregates pos­
sess a MOE therm om eter—a therm om eter
th a t can register an infinite num ber of
degrees in the MOEness provided, at the
margin, by financial assets. By taking
better account of the many different
degrees of marginal MOEness across v ar­
ious assets, Divisia aggregates could pro­
vide a more precise m easure of the total
flow of MOE services in the economy.

Money Demand:
Cash Management and
Deregulation
by John B. C arlson

I.

Introduction

stability suggested that the level of money
balances provided reliable information con­
cerning the current level of economic activity,
he relationship of money to economic
which is not observable until several months
activity is one of the most closely stud­
after the fact. More importantly, functional
ied relationships in economics. Prior to 1974,
stability suggested that monetary aggregates
there seemed to be consensus about the stabil­
might serve as readily observable targets.
ity of an empirical form of this relationship,
Monetary policymakers could aim at these
known as the m oney-dem and function. The
targets to promote price stability, economic
basic theoretical underpinnings of this function
growth, and high employment. In fact, during
are the models of Baumol (1952) and Tobin
the 1970s monetary aggregates evolved as the
(1956), who treat money as an asset that is held
primary targets of monetary policy. Ironically,
primarily for transactions purposes. As esti­
as the role of the narrow money measures
mated, the money-demand function includes a
grew in importance, their relationship to
positive relationship to income and a negative
income became less stable.1 Specifically,
relationship to interest rates with partial
between the mid-1970s and late 1981, M-l
adjustment of money balances (measured as
grew on average at a much slower rate than
M-l) to desired levels in the short run. While
any of the money-demand functions would
many variations on the basic model were esti­
have predicted for the existing levels of inter­
mated, almost every specification was reported
est rates and income. The literature suggests
as functionally stable before the mid-1970s.
that the shortfall in money demand occurred
That is, the estimated parameters linking
in two episodes: one in the period 1974-76, and
money to income and interest rates did not
another around 1980-81. The second episode
change significantly over time.
may be obscured in part by deregulation, par­
The stability of the relationship of money to
ticularly the introduction of interest-bearing
income and interest rates had important
checking accounts for households.
implications for monetary policy. Functional
The breakdown in the money-demand func­
tion has been viewed in two (but not mutually
exclusive) ways. One view holds that the insta­
Economist John B. Carlson does research in monetary theory
bility of money demand results from a mea-

T

and monetary policy fo r the Federal Reserve Bank of Cleve­
land. Mike Bagshaw, Kim Kowalewski, Dick Porter, and Ed
Stevens provided insightful comments on drafts of this article,
and Dick Mugelprovided excellent research assistance.




1. For a comprehensive survey of money demand and the
stability problem, see Judd and Scadding (1982).

Federal Reserve Bank of Cleveland
surement problem. Financial innovations, such
as overnight repurchase agreements (RPs) and
money market mutual funds (MMMFs), are not
included in M-l but are close substitutes for
assets in M-l. Because these assets are not
included, their growth has depressed the
growth of M-l relative to its historical relation­
ship to income and interest rates. Initially, the
solution seemed simple: just add the new sub­
stitutes to M-l. Their tremendous growth since
1979, however, suggested that these assets had
qualities making them suitable to serve both as
transactions balances and investment media.
The measurement view has led to research on
methods obtaining an index of transactions
services from a broad class of assets.2
The other view of money-demand instability
emphasizes the consequences of developments
in cash-management technology and deregula­
tion. Rather than focusing on new assets aris­
ing from financial innovation, this second
approach analyzes from a microeconomic per­
spective the effects of developments on the
opportunity cost of cash balances. The demand
for money has been reduced, in principle,
because it has become cheaper to economize
systematically on money balances. Explicit
behavioral models suggest alternative specifica­
tions of money demand. These specifications
are used to estimate the impact of indirect mea­
sures of cost and support the role of cash man­
agement in explaining the shortfalls in M-l.
This article describes the fundamental ways
in which new cash-management practices affect
the level of cash balances. Part III of this article
reviews some empirical studies of these effects.
Part IV presents an empirical finding that raises
questions about money demand not addressed in
previous studies of cash management. In the
context of the conventional money-demand
regression, this study finds a sharp increase in
the speed of adjusting cash balances to desired
levels. While this change may be consistent
with the cash-management process, it may also
be explained by alternative hypotheses. To the
2. For example, see Barnett (1980); B arnett, Offenbacher,
and Spindt (1981); Spindt (1983); and Zupan (1983).



3

extent that this result reflects a money-demand
effect, it has important implications for mone­
tary control. Specifically, the result suggests
that, in the short run, the responsiveness of M-l
to changes in opportunity cost is much stronger
than was previously thought.

II. The Cash-M anagem ent
P rocess
ash management—the control of pay­
ments, receipts, and any resulting trans­
actions balances—has become increasingly
sophisticated over the past decade.3 High inter­
est rates have made it feasible for many firms to
invest in information and forecasting systems
that accelerate the collection of receivables and
reduce uncertainty about the timing of receipts
and clearing of disbursements. Recent develop­
ments in computer and communications tech­
nology have sharply reduced the costs of these
systems, thereby increasing their rates of
return. Declining costs of funds transfers have
reduced the costs of concentrating receipts in
one account. Investing collected balances in
larger denominations enables balance holders to
reduce average investment costs by spreading
fixed costs over a larger volume.
The development of markets for immediately
available funds (IAFs), such as overnight RPs,
and other very liquid assets, such as MMMFs,
has facilitated the growth of more intensive
cash management. There are now investment
opportunities for periods as short as one day,
making profitable cash-management techniques
that free funds only temporarily. Because of
new, high-yielding, short-term assets, particu­
larly MMMFs, it is worthwhile for households
and small-to-medium size firms to manage their
own demand-deposit balances more carefully.

Effects of Cash M anagement
Porter, Simpson, and Mauskopf (1979) stud­
ied the role of more intensive cash management
3. See Carlson (1982) for a description of the more popular
cash-management techniques.

4

Economic Review □ Spring 1983

in explaining the first episode of money-demand
shortfall. Essentially, they identified three fun­
damental elements of this process: declining
information costs, reduced uncertainty regard­
ing cash flow, and reduced costs of funds
transfers. They stressed the incentives that
high market rates of interest create for manag­
ers to implement available cash-management
techniques. The cash-management process has
reduced the cost of shifting in and out of assets
yielding market rates of interest, increasing the
opportunity cost of holding transactions de­
posits not yielding market rates. Thus, a prox­
imate impact of more intensive cash manage­
ment has been to reduce the demand for
transactions balances.
Other effects of cash management are spe­
cific to the basic types of cash-management
techniques being adopted. Observing these
effects may give clues to the intensity of cashmanagement practices and hence the impact on
money demand. One important effect is shown
by controlled disbursem ent, a payment
technique adopted by many large corporations.
Controlled disbursement allows a firm to con­
trol the funding of its disbursement account so
that, for a given day, the firm need not deposit
funds in excess of the clearings against such an
account for that day. Because it is not known
what the clearings will be on the next day,
excess funds are freed for only one day; hence,
investment opportunities are limited to the
market for overnight instruments, e.g., the RP
and Eurodollar markets. Although funds may
be released for only one day, average balances
may be reduced permanently, in some cases to
zero. Fixed transactions costs make this
arrangement feasible only for firms with large
disbursements (e.g., $1 million or more). The
RP market accelerated sharply during the first
wave of cash management when disbursement
techniques were being adopted by many of the
largest firms.
Techniques that tend to accelerate receipts,
on the other hand, tend to release funds for
broader investment opportunities. An example
of this technique is the use of lock boxes. The
lock-box sy stem enables businesses to decen­



tralize the processing and collection of their
receipts, locating this function near the source
of payment. The firm receives payment earlier
by eliminating mailing time (mail float) and
may obtain earlier availability of funds by
reducing the collection time once the payment
enters the banking system (bank float).4
The key implication of these practices is that
released balances become “permanently” avail­
able. That is, users of these techniques are not
confined to invest these funds in IAFs, but may
use them for any purpose. The lock-box system
is often a profitable arrangement for
intermediate-size firms not large enough to
take advantage of disbursement techniques. It
is largely this class of firms that became eligi­
ble for cash-management services when short­
term rates peaked in 1981. Unfortunately, there
is no close correspondence between the bal­
ances made available for investment and
growth in any one set of short-term instru­
ments to corroborate empirical significance of
this technique.
Cash management by small businesses and
households, on the other hand, is typically
limited to the use of financial assets as a buffer
for the variability of cash flow created by the
lack of synchronization between receipts and
expenditures. Historically, direct investment of
cash balances has been inhibited by the round
lot (or size) requirements of the investment and
by transactions costs. Treasury bills, for
example, are sold only in lots of $10,000 or
more and are not redeemable before they
mature; hence, if the funds are needed, the sale
of the bill would involve a cost. Innovations
such as MMMFs pool funds of many investors
4. The reduction in the aggregate money supply results
from the elimination of mail float, which has never been
subtracted from demand deposits. The impact of the reduc­
tion of mail float on the money supply depends on the behav­
ior of the draw ers of the checks. If the draw ers were for­
merly successful in exploiting mail float, then money bal­
ances are not affected because the draw ers actually had
been using the balances and need to hold additional balances
to offset the decline in mail float. On the other hand, if the
draw ers considered the funds extinguished at the time the
checks were w ritten, then the impact on demand-deposit
balances equals the am ount of mail float eliminated.

Federal Reserve Bank of Cleveland
and thereby reduce denomination requirements
and transactions costs for any one investor.
Their development has facilitated more effi­
cient cash management by small-balance
holders. Increased cash management by small
businesses and households also has contributed
to the explosive growth of MMMFs since 1979.
Thus, the MMMF growth can be viewed as
both a cause and an effect of the cashmanagement process.
Because MMMFs are also attractive as a
store of value, they have lured funds from
nontransactions sources.5 The MMMF explo­
sion also reflects factors other than cashmanagement usage, e.g., cyclical buildup of
precautionary balances. Thus, it is not likely
that the impact of the cash-management pro­
cess is mirrored in any simple sum of assets
not included in M-l. This raises doubts about
using alternative, broader measures (simplesum) of transactions balances to remedy the
shortfall problem. Nevertheless, monitoring
growth in assets linked to cash management
may be useful in anticipating effects on tran s­
actions balances. The growth of money
market instrum ents, such as MMMFs, indi­
cates a broadening of the scope of cash man­
agement over time. The second wave of cash
management involved more participants as
techniques became attractive to smaller busi­
nesses and households.

Deregulation
and Cash Management
Since the early 1970s the financial industry
has faced a large number of regulatory
changes, most of which have led to a less re­
strictive financial environment. Deregulation
has important implications for cash manage­
ment, particularly for households and small
businesses. Because these deposit holders typi­
cally maintain relatively small average bal­
ances, their investment opportunities have
5. A more extensive analysis of the impact of MMMFs is
found in Dotsey, Englander, and Partlan (1981-82).



5

been limited. Deregulation has expanded such
opportunities and reduced the investment costs
for the small-balance holder.
Assets created under deregulation can serve
both as complements and as substitutes for
cash-management techniques. By reducing
investment costs, new nontransactions
accounts—such as money market certificates
(MMCs), small-savers certificates (SSCs), and
money market deposit accounts (MMDAs)—
have increased incentives to economize on
transactions balances not bearing interest or
subject to interest-rate ceilings. Thus, de­
regulation has served to complement more effi­
cient cash management, especially during peri­
ods of high interest rates and effective
interest-rate ceilings.
The new interest-bearing transactions
assets, on the other hand, have reduced incen­
tives for adopting new cash-management prac­
tices. Many households do not have sufficient
funds to maintain the minimum requirements
of the most convenient investment opportuni­
ties (e.g., $1,000 for most MMMFs and $2,500
for MMDAs). Prior to interest-bearing checking
accounts, cash management for many smallbalance holders could be characterized chiefly
by going to the bank to transfer excess transac­
tions balances into a passbook savings account.
These over-the-counter transfers involved
obvious fixed costs and seemed worthwhile
only when the amount of funds transferred
was relatively large. The advent of negotiable
order of withdrawal (NOW) and automatic
transfer service (ATS) accounts and credit
union share drafts (CUSDs) meant that trans­
actions balances could earn interest without
the “shoe leather” costs. The new accounts
reduced incentives for such transfers, espe­
cially since the explicit yield on these accounts
has been only about 25 basis points less than
on passbook savings. Parke and Taubman
(1982) estimate that in the first five months of
1981 approximately 7 percent of the funds flow­
ing into NOWs came from savings deposits
held by the same institution where a NOW
account was opened. This suggests that some
NOWs were opened for savings and hence

6

Economic Review □ Spring 1983

served to substitute for a common cashmanagement practice of households.
In providing for assets that complement cash
management, deregulation raises the opportu­
nity cost of holding transactions balances and
hastens the cash-management process. To the
extent that these assets are priced attrac­
tively, they enhance cash-management prac­
tices and thereby could reduce the demand for
transactions balances. Conversely, by autho­
rizing instrum ents that substitute for cash
management, deregulation lowers the oppor­
tunity cost of these balances and could limit
or even reverse the impact of the cash man­
agement process. The net impact on money de­
mand also depends on the relative prices (or
perhaps the perception of these prices) of the
new instrum ents.

III. Empirical Forms of the
Cash-M anagem ent H ypothesis

One justification for using the previous
peak in interest rates is that there might be
an awareness threshold th at is related to
interest rate peaks and once the previous
peak has been surpassed more attention is
draw n to the opportunity cost of holding
money balances and to the profitability of
investing in new techniques. Or, alterna­
tively, if interest rate peaks imply a higher
level of rates in the future than prevailed in
the p ast—as would be the case, for example,
if rates followed a random walk—then
firms might be willing to undertake
investm ents in new money management
techniques th at were previously judged
unprofitable. In essence, this approach sug­
gests th at once a past peak has been su r­
passed, investm ents are made in new
money management techniques that lead to
a more perm anent effect on money demand,
even after m arket rates have dropped below
the previous peak. T hat is, once the fixed
costs of an investm ent are borne, it remains
in place and is not discarded even though
rates have declined.
The relationship between peaks in inter­
est rates and the subsequent impact on
cash management, and thereby money
demand, may be lengthy and somewhat var­
iable for a num ber of reasons. If the th re­
shold effects are large, the new investm ents
to be undertaken may be more sizable than
otherwise and take a longer time to imple­
ment. Such episodes may also spur the
development of new technologies, new
research and development efforts and the
promotion of new practices by the suppliers
of cash management services. Bringing the
new technology in line—learning by doing—
takes time as does recruiting the skilled
labor force to operate it. Finally, it takes
time before the new technology is diffused
throughout the industry.

he cash-management hypothesis
essentially views the money-demand
shortfall as a consequence of incomplete speci­
fication of the money-demand function. A
“complete” form, in principle, would include
the return on investment (or profitability) of
cash-management techniques to determine the
level of money balances, particularly
noninterest-bearing transactions deposits.
Because profitability of cash management is so
closely linked to transactions costs, a measure
of these costs alone might capture the effects of
cash management.
Several studies have attempted to estimate
the effects of cash management indirectly.
Enzler, Johnson, and Paulus (1976) and Quick
and Paulus (1977) use past peaks of interest
rates as a proxy for the incentive to adopt new
The particular ratchet variable used by Simp­
cash-economizing methods. Building on this
son and Porter is given by:
approach, Simpson and Porter (1980, pp. 17980) propose a more flexible proxy variable,
also with a ratchet property, to represent the
perceived profitability of investment in cash
management:

T




Federal Reserve Bank of Cleveland
where
ri = the five-year Treasury bond rate
(chosen to be the relevant oppor­
tunity cost of evaluating a cashmanagement investment),
( )+ = the non-negative values, and
S{ = the cumulative sum of the non­
negative deviations of rt from its
12-period moving average.
This approach differs from that of Quick and
Paulus by using a moving average of the op­
portunity cost rather than a past peak. Hence,
the Simpson-Porter approach is somewhat
more flexible, ratcheting up more continuously
both before and after new peaks in the oppor­
tunity cost.
Simpson and Porter include the ratchet vari­
able in several different money-demand regres­
sions, each a special case of the following
equation:
3

(2) In (M/P) = /30 +
2

X

j8y In riH
5

where
M /P r1 r2 =
y =
g =

real M-l balances,
three-month T-bill rate,
commercial bank passbook rate,
real GNP, and
one of three functions of S:
St, St x In (St), or S f .

The regressions are estimated over the periods
1955:IQ through 1974:IIQ and 1955:IQ through
1980:IIQ, using a Schiller-lag technique. The
results are then compared with the standard
specifications of money demand, which do not
account for the effects of cash management.
Simpson and Porter find equations that include
the ratchet variable overall are superior to
those that do not, particularly on the basis of
post-sample forecasting performance since
1974. For example, the mean forecast errors of
all the alternative cash management specifica­
tions are at least as small as the lowest mean



7

forecast error of the standard specifications
estimated. The mean error of the best cashmanagement equation is less than one-half the
mean error of the best of the standard forms.
Thus, their approach offers at least some mea­
sure of improvement on the standard form.
More recently Porter and Offenbacher (1982)
have pursued the idea that what is truly rele­
vant about the effect of cash management (on
money demand) is captured sufficiently in
transactions costs or the “brokerage fee.”
Based on the analytical results of the Miller
and Orr (1966) transactions model, Porter and
Offenbacher derive indirect estimates of the
brokerage fee. Essentially, the Miller-Orr model
explains the levels of both average money bal­
ances and “financial debits” in terms of bro­
kerage fees, the variability of cash flows, and
the opportunity cost of money. These relation­
ships are used to solve for two measures of
brokerage fees, one in terms of financial turn­
over (the ratio of average money balances to
debits) and the other in terms of debits. When
these proxies for transactions costs are added
to the standard money-demand function, evi­
dence of money-demand shortfall diminishes
significantly. While the approach must over­
come some obstacles in estimation (too lengthy
to discuss here), it builds on the well-defined
theories of Baumol, Tobin, and Miller and Orr.
Kimball (1980) proposes another approach for
estimating the impact of cash management. He
posits that, because most cash-management
techniques involve the use of wire transfers,
the number of wire transfers can be used as a
proxy variable to estimate the impact of cashmanagement techniques on money balances.
Kimball finds that respecification of the rela­
tionship between money and transactions to
include the number of wire transfers greatly
reduces money-demand forecast errors in the
post-1974 period using annual data.
Dotsey (1983) also uses wire-transfer data as
a proxy for cash-management effects, finding
that this measure performs well relative to
other proxies in an annual model. He analyzes
the influence of six different proxies on the
demand for demand deposits, since it is largely

8

Economic Review □ Spring 1983

this component of M-l that seems to be most
affected by cash management. The proxies are
divided into two classes: measures representing
the equilibrium level of demand deposit econ­
omization and measures for technological inno­
vation. The first class includes the number and
real value of electronic funds transfers (EFTs)
and the ratio of demand-deposit debits to con­
sumption. Like Kimball, Dotsey argues that
EFT usage is directly related to most of the
major cash-economizing techniques adopted in
the mid-1970s—lock boxes, cash concentration,
and zero balancing. The ratio of debits to con­
sumption reflects the increase in financial
transactions relative to spending.
The proxies for technological innovation
include the real price of office computing and
accounting equipment, a Simpson-Porter
ratchet, and a time trend. Because the price
index was adjusted for quality (hedonic), it
dropped sharply in the 1970s. It was assumed
that the decline in the cost of this technology
represents the inducement to adopt the more
sophisticated techniques, causing demand de­
posits to decline. Lieberman (1977) initially
proposed the rationale for a time trend, i.e., the
adoption of new technology will be fairly uni­
form and proceed at a smooth rate.
Dotsey analyzes the influence of the various
proxies on the basis of three criteria: how they
affect other coefficients of money demand, the
out-of-sample predictive power, and the stabil­
ity of money demand over the whole sample
period (1920-79). The money-demand model
used takes an inventory approach originally
proposed by Barro and Santomero (1972).6
Without controlling for cash management, Dot­
sey finds that the model is not stable when the
sample period is divided at 1965. Most notably,
after 1965 the coefficient of transactions
6. T his specification differs from the conventional approach
in several distinct ways. First, the model uses consumption
rather than income as the scale variable. It also includes two
variables not found in the conventional specification: an
implicit interest rate on demand deposits and the real wage
rate. The latter variable is included as a m easure of the
value of time of cash managers. Finally, the model assum es
complete adjustm ent on average.




income (proxied by consumption) diminishes
sharply, and the coefficient of the value of time
(real wage rate) increases sharply. When each
of the cash-management proxies is included
separately and the model is re-estimated, each
has the desired effect of restoring parameter
estimates to levels comparable to estimates of
the pre-1965 sample. Of the alternatives, the
specification using the number of EFTs had the
smallest standard error of estimate (SEE). In a
comparison of one-step-ahead forecasts begin­
ning in 1966, the specification including the
number of EFTs produces the smallest forecast
root mean square error, although the predictive
power of the basic model is improved greatly
when any of the proxies is included. Finally, in
tests of functional stability, only with the
model including EFTs could the data reject the
hypothesis of instability.
Although these results suggest that the
number of EFTs is the best proxy for the effects
of cash management, it is not possible to extend
this conclusion to apply to quarterly models
without explicit comparisons using quarterly
data. The standard errors of the Dotsey regres­
sion models are much higher than those of typi­
cal quarterly money-demand regressions that
employ similar proxies for cash management.
Nevertheless, the message that seems to emerge
from empirical investigations is that the effects
of cash management are large and important
regardless of the way in which one proxies the
cash-management process.

IV. The A djustm ent of
Cash B alances

lthough some theoretical models of the
cash-management process account for
interaction among the determinants of mone
empirical forms thus far have not been as gen­
eral. Simply adding cash-management proxies
to log-linear forms of money demand implies
that cash management has no effect on the
parameters linking money to its other determi­
nants. However, as cash management has
become more broadly based over the last sev­
eral years, M-l has appeared to become more

A

Federal Reserve Bank of Cleveland

9

responsive to changes in interest rates and
income. That is, the short-run elasticities of the
determinants of money seem to have increased,
suggesting that cash holders are adjusting their
M-l balances to desired levels more quickly.
The hypothesis of higher short-run elasticities
can be examined in the context of the conven­
tional model.

ment speed depends on transactions costs.
The determinants of desired money (i.e., the
long-run equilibrium level) are based on the
theoretical underpinnings of Baumol (1952) and
Tobin (1956), who relate the demand for real
money balances to the level of real income and
“the” interest rate:

The Conventional Specification

(5)

The conventional money-demand specifica­
tion has followed a basic approach proposed by
Chow (1966) and also associated with Goldfeld
(1973). The basic feature of this approach is to
allow temporary differences between the
observed stock of money and the public’s
desired balances, a long-run equilibrium level.
The mechanism guiding adjustment of actual
money to its desired level is most frequently
defined as follows:

where

m* = a0y a ] r°2 ,
nif = money deflated by the price level,
= real income, and
rt = opportunity cost of holding money.

(4) In mt - In mt l - y(ln m* - In mt_^) ,

According to the theory, the parameter «0 is
related to transactions costs. Thus, trans­
actions costs can also affect equilibrium levels
of money. In addition, the basic theoretical
result of the Baumol model implies that the
elasticities o f^ a n d ^ (a j and «2) should equal xh
and - 1/2, respectively.
Most estimated forms include two interestrate variables, a money market rate—often the
three-month Treasury bill (rtb()—and the com­
mercial bank passbook rate (rcbj). In log form,
desired money is specified as

where

(6) In m* = In

m.

(3)

( m*
= (_ !_
mt-1 \ mt - i )

,

or equivalently in log form

m = money deflated by the price level (P),
7 = the adjustment rate, and
* = desired.
Because it is assumed that 0 < y < 1, real
money balances adjust only partially to the gap
between the desired balances—the quantity of
money demanded in the long run—and the hold­
ings of the previous period. In the absence of a
firm theoretical basis, the partial adjustment
framework is often defended on the grounds
that transactions costs inhibit complete
adjustment to equilibrium.7 That is, adjust­
7. T his rationale has been criticized, especially since the
estim ated adjustm ent rate is commonly too low to be
defended on adjustm ent costs alone. It is not the intent here
to defend the partial adjustm ent approach but to identify
further evidence of change in the conventional specification
that could be related to the cash-management process.




+ « 1 In yt + a2 In rtbt + «3 rcb( .
*
Because desired balances are not observable, m
is eliminated by substituting equation 6 into
equation 4, yielding the familiar empirical form
in terms of observed money:

(7) In mt = aQ+ a l In yt + a2 In rtb(
+ a3 In rcb( + «4 m( l ,
where
a0 =
a i- =
aA =

7 In of0,
7' a i•for i —1,3, and
(1 - 7 ).

Thus, all parameters of equation 4 and equa­
tion 6 can be identified exactly from this loglinear form.
To test for a shift in the adjustment rate, the
adjustment scheme was modified to include the

10

Economic Review □ Spring 1983

Table 1 Nonlinear Model
Estimation period: 1960:IQ to 1981:IVQa
Estim ated param eters1*
Long-run elasticities
Money
m easure0

Ratchet
variable

M-la

M-l

y

1+6

“l

a2

“3

“4

“5

SP-2

0.353
(5.18)

2.34
(2.88)

0.463
(11.75)

-0.041
(-2.68)

-0.046
(-1.48)

-0.010
(-11.43)

0.054
(5.58)

SP-1

0.200
(5.88)

2.80
(2.82)

0.671
(10.75)

-0.104
(-4.66)

-0.039
(-0.75)

-0.308
(-6.19)

0.093
(7.02)

SP-2

0.349
(5.10)

2.54
(2.85)

0.453
(11.06)

-0.041
(-2.78)

-0.045
(-1.38)

-0.006
(6.69)

0.067
(6.83)

SP-1

0.251
(6.03)

2.76
(2.74)

0.573
(11.24)

-0.076
(-4.61)

-0.042
(-0.95)

-0.186
(-4.58)

0.090
(8.53)

Implied short-run elasticities
Adjustment
rate

Income

T-bill
rate

Passbook
rate

Ratchet

Through 1979:IIIQ
After 1979:IIIQ

0.353
0.826

0.163
0.382

-0.014
-0.034

-0.016
-0.038

-0.004
-0.008

SP-1

Through 1979:IIIQ
After 1979:IIIQ

0.200
0.561

0.134
0.377

-0.021
-0.058

-0.008
-0.022

-0.062
-0.173

SP-2

Through 1979:IIIQ
After 1979:1IIQ

0.349
0.888

0.158
0.403

-0.014
-0.037

-0.016
-0.040

-0.002
-0.005

SP-1

Through 1979:IIIQ
After 1979:IIIQ

0.251
0.692

0.144
0.396

-0.019
-0.052

-0.010
-0.029

-0.047
-0.129

Money
m easure c

Ratchet
variable

M-la

SP-2

M-l

Period

a. The model was estimated using “Program for Computation,” IBM version 9.
b. /-Statistics are in parentheses.
c. This variable was measured on an end-of-period basis as an average of the two months surrounding the end of
the quarter.

factor (1 + 6 DGf), where DGt is a dummy vari­
able that equals 0 prior to 1979:IVQ and 1
thereafter and <5is an additional parameter to
be estimated:
(8) In

- In

= y(l + 8DGtXIn m* - In mt l ).

The desired money-demand specifications
examined include a cash-management proxy.
Two variables were used, both based on the
Simpson-Porter ratchet formula. The first (SP1) was a simple linear version proposed in Simp­



son and Porter (1980), i.e., equation 1. The
second ratchet (SP-2) was also in linear form but
was initiated in 1970 and assumed a shorter lag
length (four quarters), making it more flexible
than the former.8 All equations included a
8. Money demand appeared stable prior to 1970. There is
little evidence to suggest intensive adoption of techniques
th at were permitted by developments in information and
communications systems during the 1970s. T hus, if the
ratchet is in fact a relevant proxy variable for the waves of
cash management in the 1970s, it should not be effective
before then.

Federal Reserve Bank of Cleveland

Table 2 T est of Complete A djustm ent3
After 1979:IIIQ; Ho: y(l + 8) = 1
Money
m easure

Ratchet
variable

M-la

SP-2
SP-1

0.91
2.88

No
Yes

M-l

SP-2
SP-1

0.53
1.74

No
Yes

Reject null
/-Statistic hypothesis'3

a. This test was based on results of large sample theory
presented by Rao (1973, pp. 386-9). The estimated
variance of y (l + 8) is given by
ou (1 + 8)2 + 2 a12 y (l + 5) + a22 y 2.

b. One-tailed test with 0.05 acceptance level.

dummy variable (D1) to test for an intercept
shift in mid-year 1974.9
(9) In m* = In « 0 + a j In yt + « 2 In rtb(
+ «3 In rcbt + «4 SP( + a 5 D l,.
Modifying the conventional framework to
test for a change in the adjustment rate poses
some problems for estimation. Specifically,
substitution of equation 9 into equation 8 does
not yield a linear form that allows identification
of the parameters of the model; hence, non­
linear methods were employed to estimate the
parameters of both equations directly.
Estimation results for two measures of
money, M-l and M-l adjusted for NOWs (M-la),

9. T his variable was included to examine w hether the
cash-management proxy accounted for all the unexplained
shifts in the conventional equation. Hafer and Hein (1979)
found that before 1979 the stability of the conventional
equation could be restored if the regression accounted for
an intercept shift between 1974:IQ and 1974:IIQ. Al­
though the dumm y variable reported in table 1 assumes
that the shift occurred between 1974:IIQ and 1974:IIIQ,
the Hafer-Hein shift variable was also examined. The
results were not significantly affected. The choice of
which dummy variable to report was based on which
equation fit the data better.




11

are shown in table l .10 The results indicate a
large change in the rate of adjustment that is
statistically significant for all specifications.11
Adjustment rates jump about two and one-half
times after 1979:IIIQ. For the M-la measure,
this implies an adjustment rate as high as 0.89
in the latter period. The data do not reject the
hypothesis that, after 1979, the adjustment rate
is statistically equal to 1 in two equations exam­
ined (see table 2). In these equations lagged
money is no longer a relevant explanatory vari­
able. This clearly creates a new puzzle for the
partial adjustment approach to money demand.
Table 3 shows the same basic specifications
estimated for a sample ending in 1979 before the
apparent shift. Because all parameters of this
model could be identified from the parame­
ters of a linear form, they were estimated in
the linear form, using a maximum likelihood
iterative routine that corrected for serial corre­
lation. The short-run elasticity estimates are
comparable with those in table 1. An interest­
ing result is that the marginal significance of
the cash-management proxies increased over
the longer sample periods, indicating that the
ratchet proxy was no less useful during the
second wave of cash management.12
The evidence of quicker adjustment would

10. The adjustm ent method followed partly the approach
in Lindsey et al. (1981). Prior to 1981, the adjusted series is
constructed as if interest-bearing checkable accounts—
ATS and NOW accounts—were not perm itted. Specifically,
one-third of other checkables was excluded. Unlike Lind­
sey etal., this approach did not attem pt to adjust for the
impact of savings accounts for businesses and state and
local governm ents. For fu rth er details, see Lindsey etal.
(1981, table 10, fn. 2). Beginning in 1981, the change in
shift-adjusted M-1B was added to the base of the adjusted
series. A djustm ent for 1981 followed precisely the ap­
proach implicit in the reported data.
11. A wider variation in specifications was examined than
reported in this article. The main result of a statistically
significant shift in the adjustm ent rate was robust across
all specifications.
12. Nevertheless, it is difficult to justify how the cashmanagement proxy fits into the partial adjustm ent
framework.

12

Economic Review □ Spring 1983

Table 3 Linear Model
Estimation period: 1960:IQ to 1979:IVQa
Short-run elasticities
Money
m easureb

Ratchet
variable

Adjustment
rate

Income

T-bill
rate

Passbook
rate

Ratchet
variable

Intercept
shift

M -la

SP-2

0.316
(10.78)

0.156
(6.09)

-0.016
(-4.18)

-0.017
(-1.47)

-0.004
(-3.53)

0.015
(3.29)

SP-1

0.169
(17.86)

0.124
(5.49)

-0.023
(-6.51)

-0.007
(-0.636)

-0.059
(-2.42)

0.017
(3.85)

SP-2

0.334
(9.76)

0.162
(5.97)

-0.016
(-3.91)

-0.019
(-1.59)

-0.003
(-3.06)

0.017
(3.58)

SP-1

0.206
(15.58)

0.138
(5.84)

-0.021
(-6.20)

-0.010
(-0.93)

-0.060
(-2.48)

0.019
(4.07)

M -l

a. /-Statistics are in parentheses.
b. This variable was measured on an end-of-period basis as an average of the two months surrounding the end of
the quarter.

seem easy to rationalize from the cashmanagement view. It could simply reflect
lower transactions costs. But if this hypothesis
were true, one would expect to find other sys­
tematic changes in the adjustment rate as
transactions costs have declined relative to the
opportunity cost of money in recent years.
Several additional specifications were esti­
mated to test whether the speed of adjustment
had changed around 1974 or whether it was
systematically related to the Simpson-Porter
proxies of cash management. No evidence of
such effects was found.
The absence of such effects in the earlier
period could reflect the limited scope of the
cash-management process then. As indicated
above, the dominant effects of cash manage­
ment seemed to be reflected largely by the sig­
nificant development of the market for IAFs.
This suggested that the cash-management pro­
cess could be characterized adequately by large
firms learning to conduct transactions with
fewer (in some cases zero) demand deposits,
with the result mirrored in the growth of IAFs.
The adjustment rates of large firms were prob­
ably close to one (within three months) before



the advent of the new technology.13 Thus, these
techniques probably did little to change average
speed of adjustment in the aggregate. The cashmanagement process then would affect only the
long-run, or “desired,” level of M-l balances dur­
ing the first wave.
Although many innovations suitable to a
broader scope of cash holders were available
during the first wave, the extent of their adop­
tion was limited—perhaps by information
costs. The availability of MMMFs, for example,
which were introduced in 1973, sharply
reduced investment costs for small-balance
holders. However, MMMFs grew to only $3.5
billion by the mid-1970s. As interest rates
began to rise in the late 1970s, the advantages
of MMMFs as an investment vehicle became
widely known. MMMF growth exploded, reach­
ing a level over $230 billion by the end of 1982.
13. When examining alternative proxies for cashmanagement effects, Porter and Offenbacher (1982) use a
measure of nonfinancial business demand deposits as a
dependent variable in their regressions. They find th at the
lagged value of this variable was not statistically signifi­
cant when added to the equation; hence, adjustm ent rates
of corporate cash holders appear to be close to one.

Federal Reserve Bank of Cleveland
Because MMMFs were clearly being used by a
broader scope of cash holders—particularly
those with fewer investment opportunities—it
is likely that widespread usage facilitated
faster adjustment to desired M-l levels in addi­
tion to affecting the desired level. A consumer
who needed $10,000 to invest in a Treasury bill
in 1974 (most consumers were unaware of
MMMFs at that time) learned by the late 1970s
that a share of this investment could be bought
for as little as $500. Household balances now
need not accumulate for as long before average
adjustment costs are low enough to make a
financial transaction. Since the previously high
transactions costs for small-balance holders
probably accounted for the slow adjustment
speed of total balances, the widespread partici­
pation of households in the second wave of cash
management suggests their transactions costs
had been reduced sharply.

Other Qualifications
Evidence of a change in the short-run rela­
tionships among the variables included in the
money-demand function appears substantial.
However, the structural interpretations must
be qualified. Recent critiques of the conven­
tional money-demand function suggest alterna­
tive explanations that are especially relevant in
light of the October 6, 1979, change in operat­
ing procedure—the procedure the Federal
Reserve uses to control the money supply.
Goodfriend (1983) illustrates one way a
change in operating procedure could affect the
estimates of the parameters of the conventional
money-demand function. Specifically, Good­
friend offers an interpretation of the conven­
tional function that does not rely on a partial
adjustment rationalization. Instead, he posits
that money demand adjusts completely each
period to appropriate current interest-rate and
transactions variables that in turn are gener­
ated by independent first-order autoregressive
processes. He shows that if the regressors are
not measured correctly, the coefficient on
lagged money is positive, even though lagged
money plays no role in the true money-demand



13

function. Lagged money enters significantly
because, under the hypothesis, it helps to pre­
dict money. Goodfriend also shows that each of
the coefficients in the conventional moneydemand regression is a function of all the
parameters in true money-demand models and
all the regressor-generating process parame­
ters. Thus, to the extent the change in operat­
ing procedure implies a change in the processgenerating interest rates, it could produce a
change in the estimated coefficient of the
lagged dependent variable, which under the
hypothesis does not imply a change in the
adjustment rate.14
The coincidence of a change in operating
procedure and a stronger short-run association
between changes in money income and interest
rates also raises questions about the exogeneity
of interest rates. A common criticism of the
conventional approach is that it assumes inter­
est rates are independent of money. Under the
new operating procedure, if interest rates sys­
tematically respond to changes in money, the
relationship between interest rates and income
is simultaneous, and the methods typically
used to estimate the model are not appropriate.
A popular defense for assuming the exoge­
neity of interest rates was based on the conten­
tion that the Federal Reserve pegged interest
rates in the short run. Thus, the Fed had to
supply the quantity of money demanded. The
perfectly elastic supply curve implied that
money was endogenous—not interest rates.
Under the operating procedure implemented
between October 1979 and mid-1982, changes
in money were not fully accommodated at a
pegged interest rate. Deviations of money from
target led to an automatic impact on the federal
funds rate in the same direction. As money
moved above (below) its target path, interest
rates tended to increase (decrease).

14. T his insight was brought to my attention by Dick Por­
ter. Although Goodfriend’s hypothesis provides a basis for
the shift observed above, it is not an unambiguous implica­
tion. T h at is, unless the regressor-generating processes are
known, it is not possible to identify the direction or magni­
tude of the effect.

14

Economic Review □ Spring 1983

The parameter estimates in table 1 indicate
that the short-run elasticity of the Treasury bill
rate was significantly higher after the change in
the operating procedure, i.e., more like that of a
demand curve than a supply curve. This elastic­
ity is more negative than for any short-run
interest-rate elasticities reported in a recent
survey of the literature.15 To the extent simul­
taneity was a problem before 1979, it would
seem to be less so afterward. Nevertheless, little
solace should be taken in these results, as the
simultaneity problem is still an open issue.16
Finally, other shortcomings of the conven­
tional model also could account for an “appar­
ent” change in the adjustment rate. Brayton,
Farr, and Porter (1983) present evidence that
the response of transactions balances to their
opportunity cost increases with the level of
interest rates. This implies that the conven­
tional approach, which restricts this elasticity
to be constant, would have underpredicted the
M-l impact of interest-rate changes since
1979—a period when interest rates have been
historically high. Because the partial adjust­
ment framework restricts the adjustment pat­
tern of money holdings to be the same with
respect to all determinants of money, it is con­
ceivable that the estimated shift in adjustment
rate inappropriately reflects the nonlinearity in
the interest-rate elasticity.17

V.

Som e C oncluding R em ark s

lthough it is difficult to assess the
precise impact of cash management on
M-l, the results of a variety of studies indicate
that the impact is large and cannot be ignored.
Furthermore, it is evident in the conventional
money-demand framework that the parameter
15. See Judd and Scadding (1982).
16. To be comparable w ith the results of Brayton, Farr,
and Porter, it would be necessary to investigate this issue
in the context of their framework.
17. For an excellent discussion of the intractable nature of
the sim ultaneity problem in money demand, see Cooley and
LeRoy (1981).



estimates linking money with income and
interest rates (contemporaneously) have
changed significantly since 1979. Interpreted in
this context, the evidence implies that cash
managers are adjusting their balances to
desired levels more quickly than before. To the
extent M-l is more responsive to changes in its
opportunity cost, closer monetary control need
not imply greater interest-rate volatility. But,
this article also questions the basis of the con­
ventional model. Qualified interpretations are
presented to highlight important empirical
issues in need of closer examination.
Attempts to study this issue more closely are
likely to be obscured by continued deregulation.
It has been argued that new interest-bearing
assets have reduced the opportunity cost of
holding transactions balances. If the yields of
the new instruments are market-determined
and parallel the yields of other short-term
assets, then small-balance holders may find
little incentive to manage these balances so
closely. This implies that adjustment rates of
this class of cash holder could decline. Further­
more, the stronger the covariability between
yields on transactions and nontransactions
assets, the more difficult it would be for the
Federal Reserve to affect the opportunity cost
of transactions balances, especially after 1986
when NOW rates will be decontrolled. Thus,
although M-l may respond more quickly to
changes in opportunity cost, the Federal
Reserve may not be able to take advantage of
this in a demand-oriented procedure for mone­
tary control.

R e fer en ce s
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___ , Edward K. Offenbacher, and Paul A.
Spindt. “New Concepts of Aggregated
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(May 1981), pp. 497-505.

Federal Reserve Bank of Cleveland
___ , Paul A. Spindt, and Edward K. Offen­
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NBER Conference Paper 122, National
Bureau of Economic Research, Cambridge,
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Barro, Robert J., and Anthony M. Santomero.
“Household Money Holdings and the
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“Alternative Money Demand Specifications
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Demand,” American Economic Review,
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15

Enzler, Jared, Lewis Johnson, and John Paulus.
“Some Problems of Money Demand,” Brook­
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261-80.
Goldfeld, Stephen M. “The Demand for Money
Revisited,” Brookings Papers on Economic
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3:1976, pp. 683-730.
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1982), pp. 11-16.
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16

Economic Review □ Spring 1983

Lindsey, David, etal., “Monetary Control
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D ivisia M onetary Aggregates:
Would They Be More Palatable
than the Traditional Sim ple-Sum Stew s?
by M ark A. Z upan

I.

Introduction

indirectly by either changing reserve require­
ments, altering the discount rate, or conducting
open-market operations. Finally, the construc­
he Federal Reserve System constructs
tion of meaningful monetary aggregates is in
and attempts to control the monetary
aggregates M-l, M-2, M-3, and L. Empirical itself a problematic exercise, since financial
assets differ in their individual relationships to
evidence suggests that variations in these
ultimate policy goals. Properly mixing together
aggregates can be related to variations in vital
a
selected group of financial assets to obtain a
economic conditions such as the unemployment
useful
monetary measure is thus no piece of
rate, national output, and the rate of inflation.
cake. It has become an even more difficult
Regulating monetary aggregates to attain
exercise of late, with the rapid proliferation in
employment, output, or inflation goals, how­
types of financial assets.
ever, is difficult. The difficulty arises from four
The first three problems associated with the
factors. First, the achievement of one objective,
regulation
of monetary aggregates are quite
such as a suitable level of employment, may be
important.
This article, however, focuses on
inconsistent with the achievement of another
the
issue
of
constructing meaningful monetary
objective, such as a desired rate of inflation.
aggregates
by
analyzing an alternative to the
Second, the relationships between the mone­
measures
currently
used by the Federal Re­
tary aggregates and specific economic objec­
serve
System—Divisia
monetary aggregates.
tives are not necessarily stable and can shift in
Although
several
articles
on Divisia aggregates
unforeseen ways. Third, the Federal Reserve
have
been
published
recently
(see Barnett 1978,
System’s control of the monetary aggregates is
1980a,
1980b,
and
1981),
the
nature
and poten­
indirect and incomplete. In attempting to influ­
tial
usefulness
of
such
alternative
measures
are
ence the growth of monetary aggregates, that
probably
not
widely
known.
To
spread
the
is, the Federal Reserve System must operate
news, this article presents a simple characteri­
zation
of Divisia aggregates. A “beginner’sMark A. Zupan is a doctoral candidate in economics at the
Massachusetts Institute of Technology. The author would like
level” explanation should help a wider audience
to thank Mike Bagshaw, William Barnett, John Carlson, W.
to (1) evaluate the merits, as well as demerits,
Erwin Diewert, Milton Friedman, Bill Gavin, Roger Hinderof Divisia aggregates and (2) decide whether
liter, Kim Kowalewski, Mark Sniderman, Paul Spindt, Ed
such measures could improve both the Federal
Stevens, and Jim Winner for helpful comments, corrections,
Reserve System’s policy performance and the
and suggestions. Kathy Begy and Rose Dombo provided
greatly appreciated secretarial assistance.
public’s understanding of monetary policy.

T




18

Economic Review □ Spring 1983

II. In sid e th e F ed K itchen T oday

Fluctuations in MMMF holdings can conse­
quently indicate changes in the national out­
put, employment level, and inflation rate.
n recent years monetary policymakers
Second, it is not always easy to determine
have emphasized the control of M-l, a
monetary aggregate whose ingredients include “where” (i.e., in which level of aggregate) a
particular financial asset belongs. This fact has
financial assets that can be transferred directly
been highlighted in recent years by the appear­
to other parties in making payments. In other
ance of financial assets, e.g., negotiable order of
words, M-l is a transactions aggregate consist­
withdrawal (NOW) accounts, Super-NOWs,
ing of financial assets that more fully provide
and money market deposit accounts (MMDAs).
medium-of-exchange (MOE) services than do
Such new assets have blurred the former dis­
other financial assets. The emphasis on con­
tinction between M-l level and M-2 or highertrolling M-l reflects a large body of historical
level assets. The inability to ascertain precisely
evidence showing a short-run relation between
the extent to which particular assets provide
this MOEness measure and the level of eco­
MOEness suggests a certain “fuzziness” with
nomic activity and a strong long-run relation
regard to the traditional monetary aggregates
between the growth of this MOEness measure
and points to why monetary policymakers have
and the rate of inflation.
begun to pay more attention to movements in
As shown in table 1, M-l is formed by taking
M-2 and M-3—even though these higher-level
a simple sum of its ingredients. Successively
aggregates historically have been less reliable
higher-level aggregates (M-2, M-3, and L—in
indicators and more difficult to control.
that order) are constructed by adding to the
M-l “base” sets of financial assets that appear
While paying attention to higher-level aggre­
to provide MOE services less fully. To construct
gates may serve to increase the efficacy of
M-2, for example, the Federal Reserve System
monetary policymaking, recent research in
stirs such additional ingredients as savings and
index-number theory (Barnett 1982) suggests
small-denomination time deposits, repurchase
that the current method of “drawing and quar­
agreements (RPs), overnight Eurodollars, and
tering” financial assets is still an inefficient
general purpose and broker/dealer money
way to report and use information about the
market mutual funds into the M-l stew—
total flow of MOE services in the economy. To
ingredients considered to provide MOE services
the extent that the usefulness of monetary
less completely than the assets in M-l.
aggregates lies in their ability to measure the
Although M-l has received primary empha­
total flow of MOE services in the economy, the
sis, monetary policymakers have also devoted
inefficiency of the traditional measures is read­
some attention to the higher-level traditional
ily understood. This inefficiency derives from
aggregates. There are two valid reasons for
the fact that simple sums are taken of all
this. First, financial assets not included in M-l
financial assets belonging to particular aggre­
can still be used, to some extent, by transactors
gates to obtain values for those aggregates.
to finance expenditures. The expected relation
Reliance on simple sums carries with it the
between money and economic activity thus
implicit assumption that the relevant assets
need not be restricted to M-l ingredients. While
being mixed together are perfect substitutes as
funds held in a savings account, for example,
far as providing MOEness. Such an assumption
cannot be directly transferred to a retailer to
leads to inaccurate aggregate measures to the
purchase an appliance, a simple withdrawal
degree that the assets being mixed together are
can convert the savings funds into a transac­
nonhomogeneous with regard to the provision
tions medium. Although money market mutual
of MOEness.
funds (MMMFs) do not appear to supply MOE
In the case of the traditional aggregates, the
services as fully as currency, MMMFs still can
information loss attendant to simple-sum mix­
provide a certain amount of MOE services.
ing increases with the breadth of the aggregate.

I




Federal Reserve Bank of Cleveland

Table 1

M onetary Aggregate Ingredients

As of January 1983; seasonally adjusted unless otherwise noted

Aggregate

Ingredient

M -l:

Currency held by the public
Travelers’ checks

M-2:

4.1

(cont.)

239.4

Other checkable bank and
thrift deposits, including
credit union share drafts
and negotiable order of
withdraw al (NOW),
Super-NOW, and auto­
matic transfer service
(ATS) accounts

104.5

M-l

M-3:

M-2

$ 4 8 2 .1

Money market deposit
accounts (MMDAs)3

189.1

$116.7

$ 2 ,0 1 0 .0
310.7

Institutions-only
MMMFs3

46.1

Term RPs at commercial
banks and thrift
institutions3

40.6

482.1

Total M -3C
L:

Amount,
billions
of dollars

2,010.0

Large-denomination
time deposits at all
depository institutions

1132.5

Overnight Eurodollars
held by U.S. residents
(other than banks) at
Caribbean branches of
Federal Reserve System
member institutions3

Money market m utual
funds (MMMFs)—
general purpose and
broker/dealer3

Total M-2

Savings and smalldenomination time
deposits at all deposi­
tory institutions

Overnight repurchase
agreements (RPs) at com­
mercial banks3

Ingredient

Aggregate

$134.2

Demand deposits at com­
mercial banks and mutual
savings banks

Total M -l
M-2:

Amount,
billions
of dollars

M-3

$ 2 ,4 0 3 .3
2,403.3

U.S. savings bonds
Treasury bills and other
liquid Treasury securities

68.1
219.3

Bankers acceptances
40.1

7.2

Commercial paper

45.3
113.5

Term Eurodollars held by
U.S. residents (other
than banks)3

Total L

81.2

$ 2 ,9 3 0 .7

SOURCE: Board of Governors of the Federal Reserve System,
a. Not seasonally adjusted.
b. M-2 differs from the sum of components through a consolidation adjustm ent that represents the estimated amount
of demand deposits and vault cash held by thrift institutions to service time and savings deposits.
c. M-3 differs from the sum of components by a consolidation adjustm ent th at represents the estimated amount of
overnight RPs held by institutions-only MMMFs.




19

20

Economic Review □ Spring 1983

The broader traditional aggregates consist of
less (MOE) homogeneous assets than the nar­
rower aggregates.1 Even the narrower aggre­
gates, however, lose some information in the
stirring—provided that the assets constituting
these aggregates are not perfect substitutes
with respect to the provision of MOE services.
The inefficiency of traditional aggregates can
be partially avoided by focusing on individual
financial assets rather than on the current
aggregates. For example, the econometric
models used by the Federal Reserve estimate
relationships between individual financial
assets (i.e., currency, demand deposits, etc.)
and key economic variables. Reliance on such
individual relationships in effect provides a
vehicle for unequally weighting the compo­
nents of a traditional monetary aggregate when
simulating the results of shocks to the econ­
omy. Unfortunately, however, individual econ­
ometric relationships cannot always be relied
on. In the case of new financial assets, such as
MMDAs, there are simply not enough observa­
tions or “data points” to permit econometric
estimation. In the case of established financial
assets, econometric relationships may not
remain stable when new assets are invented or
monetary regulations are altered.
Because of the occasional problems in relying
on individual econometric relationships, poli­
cymakers have continued to search for alterna­
tive means of avoiding the inefficiency of the
traditional monetary aggregates. Divisia mea­
sures are being discussed more and more, pre­
cisely because it has been claimed that they
1. To some degree, the inefficiency of the traditional
simple-sum method could be mitigated if the monetary
aggregates consisted of the following four categories of
financial assets: M-l; assets in M-2 but not in M-l; assets in
M-3 but not in M-2; and assets in L but not in M-3. This
alternative categorization would avoid the information loss
inherent in the current procedure of mixing progressively
more disparate financial assets into the M-l base. Reliance
on the four financial asset categories, however, would still
not afford a means for dealing with cases where financial
assets within a particular asset category were not perfect
MOE substitutes. Nor would it provide a gauge of the
extent to which assets located in different asset categories
were imperfect MOE substitutes.



provide a better means for estimating the total
flow of MOE services in the economy.

III. H ow D iv isia M ea su re s
M easu re th e F low of MOE S e r v ic e s

ivisia aggregates assume that the value
of MOE services provided, at the
margin, by each financial asset can be directly
and quite easily ascertained. In essence, Divisia
aggregates presume that financial assets can be
measured with a MOE thermometer (see figure
1). The higher the MOE “temperature” of an
asset, the greater the value of MOE services
provided, at the margin, by the asset; and thus
the farther up the asset registers on the MOE
thermometer. Assets that are relatively more
acceptable, divisible, liquid, and reversible
would thus register higher (i.e., farther up) on
the MOE thermometer—assuming that such
characteristics were all positively related to the
marginal MOEness of an asset.2
To determine an asset’s MOE temperature,
Divisia measures rely on the “rental price” of
the asset. The rental price of an asset is equal
to the difference between the return on the
asset and the return on a “benchmark” asset
serving primarily as a store of value (SOV) and
providing essentially no MOE services (e.g.,
Moody’s Baa bonds). If the annual return on
currency were 0 percent while the return on
Moody’s Baa bonds (the benchmark asset) were
14 percent, the rental price of currency would
equal 14 percent (14 percent minus 0 percent).
Given such a rental price, currency would reg­
ister 0.14 on the MOE thermometer. The MOE
temperature of currency would increase in this
hypothetical situation if either the return on

D

2. Also assum ing all other things are equal—notably the
supply curves of the various assets. This latter assum ption
is im portant, since the am ount of MOE services provided,
at the margin, by any asset is determined by the intersec­
tion of the asset’s supply and demand curves. C haracteris­
tics such as acceptability, divisibility, and reversibility all
affect the magnitude of an asset’s demand curve—they act
as shift param eters.

Federal Reserve Bank of Cleveland

currency fell or the return on Moody’s Baa
bonds rose.
The assumption that rental prices reflect the
amount of MOE services individuals or busi­
nesses derive, at the margin, per dollar of an
asset held is not unrealistic if assets provide
only two services (MOE and SOV).3 The
lower the return on a particular financial
asset, the greater the opportunity cost of hold­
ing the asset in terms of the return that could
be earned if the benchmark, primarily SOV,
asset were held instead. A higher opportunity
cost quite plausibly implies that rational indi­
viduals and businesses must be obtaining a
greater amount of MOE services, at the m ar­
gin, per dollar of the particular financial asset
being held.
If rental prices accurately reflect the margi­
nal MOEness of financial assets, reliance on
such rental prices would appear to offer sev­
eral benefits. First, rental prices can be
straightforwardly and inexpensively calcu­
lated. Precise data on the returns of most
3. The value of MOE services provided, at the margin, by
an asset will not equal the value of MOE services provided
by infram arginal holdings of the asset. Specifically, if
demand curves for an asset slope downward, the value of
MOE services provided by infram arginal holdings will
always be higher than the value of MOE services provided
by marginal holdings of the asset.



21

assets are readily available—on a daily basis,
in fact. No econometric relationships between
individual assets and key economic variables
would have to be estimated.
Second, rental prices would allow for an infi­
nite number of gradations or degrees in the
marginal MOEness of financial assets. This
contrasts with the current simple-sum
approach, which essentially assumes that there
are only four degrees of marginal MOEness,
i.e., a financial asset can register at any one of
only four levels on the MOE thermometer.4 By
not having to pour financial assets into just
four MOEness pots, rental prices would allow
Divisia aggregates to avoid the information loss
inherent in the current simple-sum procedure.
The traditional aggregates, for example, treat
NOW accounts and currency as if they register
“close enough” on the MOE thermometer (both
are assigned to an M-l MOEness pot). Rental
prices, however, would permit a much finer
distinction to be drawn between NOW accounts
and currency. Indeed, to the extent that NOW
accounts and currency register farther apart on
the MOE thermometer (i.e., have more dispar­
ate rental prices), reliance on rental prices
would eliminate some of the fuzziness of the
current simple-sum measures of MOEness.
Third, rental prices would also provide a rel­
atively simple mechanism for ascertaining the
precise difference in the MOE temperatures of
various assets, i.e., for ascertaining the differ­
ence in the amount of MOEness provided, at
the margin, by different assets. In comparison,
the current simple-sum approach does not have
an easy method of determining the temperature
difference between any two of the four pre­
sumed degrees of MOEness. As a result, there
is no direct information-preserving means for
estimating the aggregate amount of MOE ser­
vices provided across all assets. This is trou­
blesome to the extent that a significant number
4. The four categories of MOEness under the current
simple-sum system consist of those assets belonging to M-l;
M-2 but not M-l; M-3 but not M-2; and L but not M-3. The
first of these categories would register farthest up on the
MOE thermom eter. Succeeding categories would register
progressively closer to zero on the thermometer.

22

Economic Review □ Spring 1983

of MOE services may be provided by financial
assets located at degrees other than the M-l
degree of MOEness. Even though MMMFs
have low marginal MOEness values, for exam­
ple, the sheer size of MMMF holdings may
ensure that transactors derive a sizable amount
of MOE services from this non-M-1 asset.
The specific manner in which rental prices
are used to construct Divisia aggregates is out­
lined in detail in the appendix. In essence,
however, Divisia measures take a weighted
average of growth rates of ingredient assets to
determine the growth rate in the flow of MOE
services provided by any designated set of
assets. The weights assigned to growth rates
of ingredient assets are “expenditure-share”
weights. The weight assigned to an asset’s
growth rate, in other words, depends on the
share of the total expenditure by asset holders
on MOEness that is accounted for by that
asset. Suppose, for example, that (1) there
were only three financial assets—currency,
demand deposits, and Moody’s Baa bonds (the
benchmark SOV asset); (2) the returns on cur­
rency, demand deposits, and Moody’s Baa
bonds were 0 percent, 5 percent, and 10 per­
cent, respectively; and (3) the quantities of
currency, demand deposits, and Moody’s Baa
bonds in the economy were $1 million, $20 mil­
lion, and $5 million, respectively. The relevant
rental prices in this particular situation thus
would be 0.1 for currency (10 percent minus 0
percent equals 10 percent), 0.05 for demand
deposits (10 percent minus 5 percent equals 5
percent), and 0.0 for Moody’s Baa bonds (10
percent minus 10 percent equals 0 percent).
The total expenditure made by transactors for
MOEness would be obtained by multiplying
the quantities of assets held by their respective
rental prices and then by summing the multi­
plied asset quantities as follows:
[(0.1)($1 million) + (0.05)($20 million)
+ (0.0)($5 million)] = $1.1 million.
Of the total expenditure on MOEness, the
shares accounted for by the individual assets
would be:



(1) [(0.1)($1.1 million)]/($l million) = l / l l
for currency;
(2) [(0.5)($20 million)]/($l.l million) = 10/11
for demand deposits; and
(3) [(0.0)($5 million)]/($l.l million) = 0/11
for Moody’s Baa bonds.
It is these shares that would be used by a
Divisia aggregate to determine the weights
assigned to the growth rates of the three
respective assets, and thereby to determine the
growth rate in the MOE services provided by
the three assets as a whole.5
While the weights assigned by Divisia aggre­
gates to growth rates of ingredient assets
depend on the expenditure shares of the assets,
the current simple-sum aggregates weight
growth rates of component assets by their
respective “quantity shares.” The simple-sum
aggregates, in other words, weight the growth
rate of any relevant asset by the share of the
total quantity of asset holdings within the
aggregate that is accounted for by that asset.
To compare the different weighting schemes
used by simple-sum aggregates, suppose that in
the preceding hypothetical example monetary
policymakers decided that only currency and
demand deposits were relevant to the construc­
tion of M-l. Such a decision essentially would
imply that the quantities of currency and
demand deposits would be multiplied by unity
(since these two types of assets were deemed to
belong to M-l), while the quantity of Moody’s
Baa bonds would be multiplied by zero (since
this asset was deemed not to belong to M-l)
when computing the total quantity of M-l asset
holdings. The total quantity of M-l asset hold­
ings would thus be:
[(1.0)($1 million) + (1.0)($20 million)
+ (0.0)($5 million)] = $21 million.
To determine the growth rate of MOE services
provided by M-l assets, the simple-sum
approach would assign the following quantityshare weights to component assets:
5. See the appendix for a detailed recipe.

Federal Reserve Bank of Cleveland
(1) [(1.0)($1 million)/($21 million)] = 1/21
for currency;
(2) [(1.0)($20 million)/($21 million)] = 20/21
for demand deposits; and
(3) [(0.0)($5 million)/($21 million)] = 0/21 for
Moody’s Baa bonds.
The preceding comparison highlights the
crucial difference between the weighting
schemes employed by Divisia and simple-sum
aggregates to determine the growth rate in the
MOE services provided by any designated set of
assets. The expenditure-share weights em­
ployed by Divisia aggregates rely on both the
quantities and rental prices of assets. The
quantity-share weights used by simple-sum
aggregates, however, rely on just the quantities
of the relevant assets—where the “relevance”
of any asset to the particular simple-sum
MOEness aggregate being constructed must be
decided on a 0/1 basis by monetary policy­
makers.6 Provided that rental prices are accu­
rate indicators of marginal MOEness, the tradi­
tional simple-sum approach produces fuzzier
aggregates. This is because the traditional
simple-sum approach ignores the MOEness
information contained in rental prices; the tra­
ditional aggregates do not rely on the many
degrees of marginal MOEness that could be
identified by a MOE thermometer. When an
asset falls into one of the degrees of MOEness
6. The problems inherent in such a dichotomous approach
are analogous to the difficulties encountered by analysts at­
tempting to determine the breadth of a market on a 0/1 basis.
A market-concentration measure is based on a market that
includes all commodities deemed to be close substitutes for the
good under consideration (and thus given a weight of unity).
The market excludes all commodities not considered to be
close substitutes (commodities that are consequently given a
weight of zero). Because a practical “middle ground” has not
been developed between unity and zero, it is necessary to con­
sider market-power measures defined over various levels of
market breadth (e.g., either including or excluding fresh lemon
juice in the case of Borden’s ReaLemon; either including or
excluding recycled aluminum in the case of Alcoa). Such con­
sideration is often subject to a great deal of controversy since
whether an additional substitute is stirred into the market
often significantly affects the measure of a firm’s market
power (e.g., note antitrust cases such as DuPont, Brown Shoe,
Von’s Grocery, Bethlehem Steel, Alcoa, and ReaLemon).




23

between the four traditional levels, the asset
must be reassigned by policymakers to the
nearest of the four levels. Such a reassignment
dissipates information about the flow of MOE
services along the way.7
In addition to providing details on the con­
struction of Divisia aggregates, the appendix
also describes several other alternative mone­
tary aggregate recipes that depend centrally
on rental prices when weighting component
asset growth rates. While the particular
manner in which Divisia and these alternative
aggregates rely on rental prices differs, all
assume that rental prices reflect the marginal
MOEness of financial assets. Divisia aggre­
gates have been singled out for attention in
the academic press because it has been
mathematically shown that they supply a
more accurate measure of the flow of MOE
services provided by a given set of financial
assets than do the other alternatives.8

IV. Cooking a la Divisia:
W hat Can Go Right
deally, there would be only one Divisia
aggregate. Such an aggregate would be
constructed across the entire set of financial
assets in the economy. If rental prices correctly
reflected the marginal MOEness of financial
assets, the Divisia aggregate would yield one
major advantage—a better approximation of
the total flow of MOE services in the economy.
The approximation afforded by a Divisia
aggregate would be more useful to the extent
that (1) MOEness is a more reliable indicator of
vital economic conditions; (2) the flow of MOE
services is more easily controllable by mone­
tary policymakers; (3) greater heterogeneity

I

7. At a theoretical level, the only case in which a simplesum aggregate would provide as much information as a
Divisia aggregate would be if the rental prices of all rele­
vant non-benchm ark assets were identical. In this par­
ticular case, a Divisia aggregate “collapses” to the simplesum aggregate.
8. See, for example, Barnett (1980a).

24

Economic Review □ Spring 1983

exists in financial asset MOEness—
heterogeneity that is accurately reflected in
rental prices; (4) substitutions occur between
financial assets; and (5) a Divisia aggregate can
be integrated into the policymaking process.9
A Divisia aggregate would be particularly
useful when substitutions occurred between
financial assets—substitutions induced by
changes in government regulations or financial
technology (e.g., the appearance of new assets
or changes in the ability of existing assets to
provide MOE services). Substitutions would
not undercut the ability of a Divisia aggregate
to keep track of the total flow of MOE services
in the economy.10 This is because a Divisia
measure relies on a simple method for deter­
mining the marginal MOEness of assets. In the
face of substitutions between financial assets,
the rental prices of existing assets would merely
have to be observed to account for any changes
in marginal MOEness. In addition, the margi­
nal MOEness of new assets could be determined
quickly by calculating the rental prices of the
new assets.
9. Although the Federal Reserve System monitors the total
flow of MOE services, it is conceivable th at the flow of
SOV services might better indicate changes in key eco­
nomic variables. In the case of nominal national income,
partial evidence against this possibility is provided by the
fact that the narrow er a traditional aggregate, the better
the explanation of fluctuations in national income provided
by th at aggregate (see Berkman 1980). A further test might
involve examining the explanatory power (with respect to
fluctuations in nominal national income) of the four catego­
ries of current financial assets: M-l; assets in M-2 but not
in M-l; assets in M-3 but not in M-2; and assets in L but
not in M-3. Focusing on MOE services would gain greater
support if the categories of assets th at appear to provide
MOE services more fully better explained fluctuations in
nominal national income. It is also conceivable th at aggre­
gates combining information on MOE and SOV services are
most indicative of changes in key economic variables. To
test this hypothesis, it would be necessary to test the com­
parative explanatory power of different “mixes” of MOE
and SOV services relative to aggregates that focus on either
MOE or SOV services.
10. This is true, provided th at rental prices continue to
reflect the marginal MOEness of financial assets; see the
discussion in the following section on the third drawback of
a Divisia aggregate.



For a number of reasons, substitutions
between financial assets prove much more
troublesome for the traditional aggregates.
First, the current simple-sum measures must
generally rely on econometric relationships to
determine the MOEness of an asset—i.e., to
determine into which MOEness pot an asset
should be stirred. Second, econometric relation­
ships may be either unstable or impossible to
estimate in the face of substitutions between
financial assets. As noted before, reliance on
econometric relationships is impossible in the
case of a new asset or a change in the ability of
an existing asset to provide MOE services—
there simply are not enough data observations.
As a result, the traditional aggregates must
utilize some other less dependable criterion for
determining the MOEness of a new or altered
financial asset—a factor that makes it harder
for the traditional aggregates to track the flow
of MOE services in the economy. Third, the
traditional approach assumes that there are
only four MOEness pots and that when calcu­
lating the MOE services in any of the four pots,
an asset either belongs or does not belong to the
pot. There is no middle ground between unity
(including the asset in the pot) and zero
(excluding the asset). The many degrees of
marginal MOEness afforded by a MOE ther­
mometer are thus set aside in favor of the more
rough “0/1” cut. This potentially can produce
sizable changes in the level of a traditional
aggregate if an important asset (important in
the sense that the holdings of the asset in the
economy are large) switches from unity to zero
or vice versa.
The relative ease with which a Divisia
aggregate deals with substitutions between
financial assets will be of greater value the
more frequent or substantial are the substitu­
tions. Consequently, periods of financial inno­
vation, regulatory modification, and high and
variable returns on financial assets all should
increase the attractiveness of a Divisia aggre­
gate. This partially explains why Divisia mea­
sures have received greater attention in the
past few years.

Federal Reserve Bank of Cleveland

25

MOE services provided by the asset, at the
margin, per asset dollar.12
The second drawback of a Divisia aggregate
is
that it may not be possible to ascertain accu­
V. W hat Can Go W rong
rate rental prices even if all financial asset
characteristics are positively related to margi­
here are three principal drawbacks
nal MOEness and negatively related to a finan­
associated with a Divisia aggregate.
cial asset’s return rate. This is the case if pub­
First, the extent to which an asset’s return lished information on the return rates of
differs from the return on a primarily SOV
financial assets is incorrect—if an asset’s
asset may not entirely reflect the value of MOE
implicit return differs from its explicit return.
services provided, at the margin, by the asset.
Some regulations, for example, force transac­
Among other characteristics, differences in the
tors to pay a specific rental price for certain
returns on financial assets depend on the
financial assets (e.g., demand deposits). If such
extent to which assets are divisible, liquid, and
price floors are effective, sellers of the regu­
reversible. The fact that an asset’s return
lated assets may attempt to lure buyers by
depends on many characteristics, however,
lowering the implicit price of their products
need not pose a problem for a Divisia aggregate
(provided that the implicit price remains above
if asset characteristics are “reducible” to a twothe cost of producing the asset). Constrained to
dimensional scale, i.e., if the characteristics of
offer no more than 5.25 percent interest on
financial assets can all be “lined up” by a MOE
NOW accounts, for example, banks may
thermometer. This is the case if the extent to
decrease the implicit price of NOW accounts to
which an asset possesses characteristics such
buyers by offering free toasters, free checking,
as divisibility, liquidity, and reversibility is pos­
or more branch offices. To the extent that
itively related to the marginal MOEness of the
banks engage in such actions, the reported
asset and is negatively related to the asset’s
return of 5.25 percent on NOW accounts would
rate of return. Under these circumstances
be incorrect—the actual, implicit return to pur­
rental prices would be accurate measures of
chasers of demand deposits would be higher.
marginal MOEness. The rental price of each
If the reported return on a financial asset is
distinquishable asset with a unique bundle of
incorrect, one solution would be to calculate the
characteristics would measure, in summary
asset’s implicit return. This is difficult, how­
form, the value of MOE services provided, at
ever. In the case of demand deposits, Barnett
the margin, by the asset.
and Spindt (1982) assume that the implicit
Although many asset characteristics are
return is 40 percent of the “competitive rate”
directly related to an asset’s marginal MOE­
(e.g., the rate of return on a primarily SOV
ness and inversely related to an asset’s rate of
asset), even though the explicit return on
return, some asset characteristics may affect
demand deposits is constrained by law to be
an asset’s return rate but may be unrelated to
zero. Barnett and Spindt base their assumption
the value of MOE services provided, at the
on the fact that firms own about 40 percent of
margin, by the asset.11 If such characteristics
were present, rental prices would be inaccu­
12. Another method for avoiding such a problem would
rate measures of marginal MOEness. It
involve calculating a “subset” or “baby” Divisia across all
would be necessary to adjust an asset’s
assets whose rental prices are accurate—i.e., whose rental
prices reflect only marginal MOEness. T his method would
return rate for the presence of such charac­
avoid
the difficulty of attem pting to adjust financial asset
teristics and then to estimate the amount of

T

11. Porter and Offenbacher (1982) argue that portfolio risk­
iness is such a characteristic.



retu rns when estim ating the total flow of MOE services in
the economy. It would do so, however, at the cost of ig­
noring the flow of MOE services provided by the “incor­
rect” assets.

26

Economic Review □ Spring 1983

all demand deposits. Since firms have ready
access to assets earning competitive returns,
Barnett and Spindt argue that firms must earn
enough implicit interest on demand deposits to
make holding such assets worthwhile.
The extent to which the second drawback of
a Divisia aggregate should be considered worri­
some depends, of course, on the amount of
financial asset holdings that have implicit
returns differing from explicit returns for regu­
latory reasons. Historically, demand deposits
and savings and small-denomination time de­
posits have been the major financial assets for
which regulations have caused implicit returns
to deviate from reported returns. To the extent
that the Depository Institutions Deregulation
and Monetary Control Act of 1980 is decontrol­
ling the financial industry, the second draw­
back of a Divisia aggregate will recede and a
Divisia aggregate will become a more accurate
indicator of the total flow of MOE services in
the economy.
The third drawback of a Divisia aggregate
stems from the possibility that, while accurate
rental prices may be obtainable, they may not
be equilibrium prices. The construction of a
Divisia aggregate depends fundamentally on
the assumption that markets for every “ingre­
dient” asset are in equilibrium. If this were
not the case, estimated rental prices would
represent “way stations” on the path to equi­
librium prices. To the extent that rental prices
for various financial assets did not follow
analogous paths, reliance on such prices then
would not accurately indicate changes in the
equilibrium flow of MOE services supplied by
a designated set of financial assets. The longer
it took financial asset markets to attain equilib­
rium, and the more dissimilar were the dis­
equilibrium paths followed by different rental
prices of assets, the more wary one would have
to be in utilizing a Divisia aggregate.
Besides the three major drawbacks asso­
ciated with a Divisia aggregate, it has some­
times been claimed that it would be difficult to
integrate a Divisia aggregate into the policy­
making process. This is unlikely to be an over­
whelming problem, however, since reliance on



a Divisia aggregate need not affect the manner
in which the Federal Reserve System effects
monetary policy (i.e., via changes in reserve
requirements, changes in the discount rate, or
open-market operations). As long as policymak­
ers recognize that tightening actions reduce the
flow of MOE services in the economy, they can
use a Divisia measure as a policy guide. For all
intents and purposes, the choice between rely­
ing on a Divisia aggregate or on the traditional
measures is separable from actual monetary
policymaking. A Divisia aggregate would
merely serve as an indicator—hopefully as a
better indicator than the traditional
aggregates—of the total flow of MOE services
in the economy and of the effect of monetary
policymaking on this flow.
It must be stressed that the choice between
Divisia and simple-sum aggregates is not an
either/or choice. Reliance on Divisia aggre­
gates, that is, would not necessitate the dis­
carding of traditional aggregates. Indeed, even
if Divisia aggregates became the primary indi­
cators of the total flow of MOE services in the
economy, the traditional aggregates might still
prove valuable in certain cases.13 The choice
between Divisia and simple-sum aggregates is
rather a choice of whether Divisia aggregates
should be included in the information-set menu
used by policymakers—whether such aggre­
gates would enhance the ability of policymak­
ers to track and regulate the total flow of MOE
services in the economy.
More fundamental questions concerning both
Divisia and simple-sum aggregates include the
desirability of monitoring the total flow of
MOE services in the economy and the ability
of the Federal Reserve System to regulate this
total flow. While a full discussion of such
“deeper” issues is beyond the purposes of this
article, they are forests that should not be lost
sight of. The desirability of monitoring MOE
services, for example, stems from the pre­
sumption that movements in the total flow of
13. For one situation where traditional aggregates might
prove helpful, see the second mathem atical draw back to
Divisia aggregates noted in the appendix.

Federal Reserve Bank of Cleveland
MOE services are closely related to changes in
the ultimate goals of policy, such as the
employment level, national output, and rate of
inflation. It well may be, however, that there
are more accurate indicators than the flow of
MOE services when it comes to monitoring the
ultimate goals of policy—indicators more
highly related to key economic variables.14 It
may also be true that there are indicators that
are easier to regulate and use to attain ulti­
mate policy goals.

VI. The Theory May Be Fine
. . . But Will It Fly?
mpirical evidence on the ability of
Divisia aggregates to provide informa­
tion about key economic conditions is just
beginning to surface. The research to date has
generally compared the traditional aggregates
(M-l, M-2, M-3, and L) with corresponding
Divisia measures constructed across the com­
ponent assets of the traditional aggregates
(Divisia M-l, Divisia M-2, Divisia M-3, and
Divisia L). One can make four observations
about the findings to date (best summarized in
Barnett 1982). First, higher-level Divisias (the
M-2, M-3, and L Divisias) consistently outper­
form their simple-sum counterparts. Divisia
M-3, that is, typically provides more informa­
tion than simple-sum M-3 about such economic
conditions as the growth rate of personal
income, the unemployment rate, and the rate of
change of prices. Second, while Divisias gener­
ally outperform their simple-sum counterparts
at higher levels of aggregation, both Divisia and
simple-sum M-l provide comparable indications
of economic conditions. This suggests that the
manner in which the traditional M-l aggregate
mixes together ingredient assets may not be too
far off the mark. Third, among all aggregates
considered (both traditional and Divisia),
Divisia L generally is the most informative
measure. Divisia L consistently explains more
of the variance in the inflation, unemployment,

E

14. See footnote 9.



27

and output levels than any of the traditional
aggregates as well as any of the other Divisia
aggregates. The only case in which Barnett
(1982) finds a simple-sum measure to be the
most informative aggregate is in explaining the
variance in the rate of unemployment among
males over the age of 25.15
Finally, Divisia aggregates partially explain
some puzzles that have cropped up in recent
investigations of financial asset markets.
Divisia aggregates, for instance, may help to
account, at least partially, for the breakdown of
the traditional money-demand equations in the
1970s. In the face of high and volatile interest
rates, money-demand equations for the tradi­
tional aggregates no longer appeared to be sta­
ble and began persistently to overpredict the
growth rate of money demand. The results of
Porter and Offenbacher (1982) and Barnett
(1982) suggest that this instability may result
from the inaccuracy of traditional aggregates in
measuring the flow of MOE services provided
by a given set of financial assets. These inac­
curacies are accentuated by periods of higher
and more volatile asset returns. Porter and
Offenbacher find that the demand for Divisia
money aggregates is relatively more stable than
the demand for traditional money aggregates.16
Porter and Offenbacher also find that, among
all aggregates considered, the demand for
Divisia L is most stable.
In addition to partially explaining the recent
breakdown in the money-demand equations of
the traditional aggregates, Divisia measures
also afford some insights on the trend in
simple-sum “multipliers” over the 1970s. A
monetary aggregate multiplier consists of the
ratio of a monetary aggregate to the monetary
base (total currency in the hands of the public
15. In several of the differently specified models examined
econometrically, the traditional M-2 measure provides more
explanatory power than any of the other aggregates.
16. Porter and Offenbacher confirm this after first
accounting for the possibility th at the demand for money
may have shifted inw ard because of technological
reasons—computer and telecommunications innovations as
well as new cash-management procedures such as sweep
accounts and remote disbursem ent.

28

Economic Review □ Spring 1983

Table 2 D ivisia and Sim ple-Sum M-2
October 1979 — May 1980
Monthly level
Date

Annual growth
rate, percent

Divisia
M -2

Simplesum M-2

Divisia Simple M-2 sum M-2

226.4
225.8
224.8
225.2

263.6
264.9
266.1
267.6

-3.1
-5.0
2.3

5.8
5.3
7.1

225.3
225.5
225.1
223.3
223.7

269.2
271.4
272.6
271.9
274.2

0.5
1.0
-2.2
-9.5
2.3

6.8
10.0
5.4
-3.1
10.2

19 7 9
September
October
November
December

—

—

1980
January
February
March
April
May

SOURCE: Barnett and Spindt (1982). Figures are sea­
sonally adjusted, with January 1969 = 100.

plus the vault cash of commercial banks plus
commercial bank deposits with the Federal Re­
serve System). Money multipliers are useful in
that they allow policymakers to predict the
effect of a given change in the rather narrow
monetary base on the flow of MOE services
provided by a much broader set of financial
assets in the economy. Stable money multipli­
ers consequently permit policymakers more re­
liable control of the flow of MOE services in the
economy via regulation of the monetary base.
During the 1970s the multipliers for the tra­
ditional aggregates were not stable; the multi­
plier for M-l decreased, while the M-2, M-3, and
L multipliers increased. Barnett and Spindt
(1982) argue that the rising interest rates of the
1970s caused substitutions out of assets with
high marginal MOEness into assets with low
marginal MOEness, thereby producing the
observed changes in the traditional multipliers.
Compared with the simple-sum multipliers, the
higher-level Divisia multipliers (the multipliers
for Divisia M-2, Divisia M-3, and Divisia L)
were much more stable in the 1970s.
Policymakers should be encouraged by the
apparent greater stability of higher-level
Divisia multipliers. Such stability suggests



that the relationship between the monetary
base and the flow of MOE services in the econ­
omy is more predictable than the corresponding
simple-sum multipliers would indicate. The
possibility that higher-level Divisia aggregates
could enhance the controllability of the flow of
MOE services in the economy is further sup­
ported by the fact that the variations that do
exist in the multipliers for the Divisia aggre­
gates are strongly (negatively) correlated with
interest rates, whereas variations in interest
rates explain an insignificant part of the
movements in simple-sum multipliers (see Bar­
nett and Spindt 1982). Cyclical variations in
Divisia multipliers, in other words, are more
predictable than the cyclical variations in tradi­
tional multipliers.
With regard to actual information provided
about recent monetary policymaking, the
Divisia aggregates sometimes provide a very
different picture about MOE services growth
than do their simple-sum counterparts. Follow­
ing the Federal Reserve System’s move away
from controlling interest rates and toward con­
trolling money-supply growth in October 1979,
Divisia M-2 suggests much more restrictive
monetary policymaking than does traditional
M-2. Between September 1979 and May 1980,
Divisia M-2 grew at an average rate of around
-1.7 percent, whereas simple-sum M-2 grew at
an average rate of 5.9 percent over the same
period (see table 2).17
Over 1981 and 1982, the higher-level Divisia
aggregates also indicate slower MOE services
growth than their simple-sum counterparts.
Between the fourth quarter of 1980 and the
fourth quarter of 1981, Divisia M-2 grew 1.4
percent, while simple-sum M-2 increased 9.4
percent. Between the fourth quarter of 1981
and the fourth quarter of 1982, Divisia M-2
rose 2.4 percent, while simple-sum M-2
climbed 12.1 percent.18
17. D uring the sam e period, changes in the prim ary tradi­
tional aggregate (termed M-1B at the time) correspond
quite well w ith changes in its Divisia counterpart. Divisia
M-1B grew by 2.1 percent, while simple-sum M-1B grew by
1.4 percent.

Federal Reserve Bank of Cleveland
The latest Divisia figures indicate that the
recent upswing in MOE services growth may
not be as dramatic as the simple-sum aggre­
gates would suggest. During the first quarter
of 1983, simple-sum M-l and simple-sum M-2
rose 14 percent and 20.3 percent, respectively.
Divisia M-l and Divisia M-2, however, grew
only 10.6 percent and 3.6 percent, respec­
tively.19 Thus, the recent money-supply bulge
does not appear to be so large when viewed
from the Divisia perspective. This suggests
that monetary policymakers should be wary
about constricting the total flow of MOE ser­
vices in the face of the apparent bulge. It also
suggests that fears about reigniting inflation­
ary fires may be less well-founded than the
traditional aggregates seem to indicate.

VII. C onclusion
he current simple-sum approach to
monetary aggregation treats financial
assets dichotomously—either including or
excluding individual assets from the aggregate
being constructed. Such a dichotomous scheme
is inefficient for two reasons. First, financial
assets included in a particular aggregate are
not perfect substitutes as far as medium-ofexchange (MOE)ness goes. Second, financial
assets excluded from a particular aggregate are,
to some extent, substitutes for the assets
included in the aggregate. While the Federal
Reserve System attempts to avoid the ineffi­
ciency of the traditional monetary aggregates
by estimating econometric relationships
between individual financial assets and key
economic indicators, such econometric relation­

T

18. Over the same periods, Divisia and simple-sum M-l
tracked similarly. Between the fourth quarter of 1980 and
the fourth qu arter of 1981, Divisia M-l grew 6.5 percent,
while simple-sum M-l rose 5.1 percent. Between the fourth
q u arter of 1981 and the fourth q u arter of 1982, Divisia
M-l increased 8.2 percent, while simple-sum M-l grew
10.4 percent.
19. W hereas the previous percentages were based on
1969 = 100, the most recent figures treat 1982 as the base,
i.e., 1982 = 100.



29

ships are not always stable over time; nor are
they always estimable.
Divisia aggregates provide an alternative
means of avoiding the inefficiency inherent in
the traditional aggregates by focusing on the
information contained in the rental prices of
financial assets, rental prices being the differ­
ence between an asset’s return and the return
on a benchmark store-of-value (SOV) asset that
is likely to provide very few MOE services.
Through rental prices, Divisia aggregates pos­
sess a MOE thermometer—a thermometer that
measures the amount of MOE services pro­
vided, at the margin, by various assets. Such a
thermometer allows Divisia aggregates to
account for many more degrees of marginal
MOEness than does the dichotomous approach
employed by the traditional aggregates.
If rental prices were accurate measures of
the MOE services provided, at the margin, by
an asset, they would offer an attractive sub­
stitute for econometric estimation. Rental
prices could provide a measure of an asset’s
marginal MOEness with only one data or ob­
servation point. This would be particularly
helpful in the case of a new financial asset or
in the case of changes in the marginal MOE­
ness of existing financial assets. The ability of
Divisia aggregates to deal with such situa­
tions partially explains the current appeal of
Divisia measures.
While Divisia measures could, in theory,
provide better approximations of MOE service
flows, Divisias do not offer a foolproof recipe.
The dangers of relying on Divisia aggregates
stem primarily from the fact that rental prices
may not be accurate marginal MOEness indica­
tors. Such would be the case if the implicit
return on an asset differed from the explicitly
reported return; or, if an asset’s rental price
reflected a characteristic of the asset unrelated
to the amount of MOE services provided, at the
margin, by the asset; or, if an asset’s rental
price were not an equilibrium rental price.
Whether these dangers are sufficient to w ar­
rant keeping Divisia aggregates off the infor­
mation-set menu of monetary policymakers is
in need of greater examination. The limited

30

Economic Review □ Spring 1983

empirical evidence does suggest that Divisia
measures might offer a better approximation of
the total flow of MOE services in the economy.
The relationships between Divisia aggregates
and key policy goals, such as the rate of infla­
tion, unemployment level, and national output,
appear to be stronger than the analogous rela­
tionships between traditional simple-sum
aggregates and key policy goals. The evidence
also suggests that Divisia aggregates might, in
addition to providing a more informative MOE
services measure, offer monetary policymakers
an additional layer of icing. To the extent that
Divisia multipliers are more stable and predict­
able, Divisia aggregates might improve the abil­
ity of monetary policymakers to regulate the
total flow of MOE services in the economy
through changes in the monetary base.

A p p en d ix

T he D ivisia R ecip e

Divisia aggregates are constructed via the
following formula:

'/>
j=

i

In {A.) - In (A.t j)
Z l* r ,
■j=l

where
Dt = Divisia measure (the Tornqvist-Theil
discrete time approximation) of the
growth in the MOE services provided
by a set of ;=1, 2 . . . N different
assets between time /- I and time /;



A *7-1

RP it-l

amount of the zth financial asset at
time /;
amount of the *th financial asset at
time /- l;
rental price of the *th financial asset
at time /; and
rental price of the i‘th financial asset
at time t- l.

As shown in equation 1, the Divisia measure of
MOE services growth is derived by taking a
weighted sum of the growth rates (as measured
in natural log terms) of individual financial
assets—where the weight on the ith asset
equals the average of (1) the fraction of total
transactor expenditure for MOE services
devoted to the *th asset at time t and (2) the
fraction of total transactor expenditure for
MOE services devoted to the *'th asset at
time t- l.
Whereas equation 1 is a Divisia measure of
the growth rate of MOE services between two
different points in time, the actual level of a
Divisia aggregate at any particular point in
time is derived by setting the amount of MOE
services provided by a set of financial assets
equal to an arbitrary number (e.g., 100.0) for a
given time (e.g., 1969). Then the equation 1
formula is used to determine the level of the
Divisia aggregate for points in time other than
the reference time point (i.e., 1969).
Four Divisia aggregates are currently esti­
mated on a monthly basis by the Federal Re­
serve System and are available to the general
public on request. The four Divisias—Divisia
M-l, Divisia M-2, Divisia M-3, and Divisia L—
are calculated across the financial assets span­
ning the traditional aggregates M-l, M-2, M-3,
and L, respectively.
In addition to Divisia aggregates, reliance on
rental prices allows for the construction of
several other measures of the total flow of MOE
services provided by a set of financial assets.
Among these alternative measures are Laspeyres, Paasche, and money-income aggregates.
Laspeyres aggregates are obtained via
the formula:

Federal Reserve Bank of Cleveland

r~

i 1—
s

^ u a u- 1
A U-1

(2) L , = X

s~

-

2 (W y ^ , )
J
J L«=i
(4) M I = =1

1

I

2/=1( ^ , 7 - . ) <Av>
N

where P( is the Paasche measure of the growth
in the MOE services provided by a set of j - 1,
2 . . . N different assets, and all other symbols
are as before.
Money-income aggregates are derived via
the formula:

1

l

~N

31

J

J= i

- 1

,

<A,.i
j= 1

Xi=i (Rpj

1

1 <ray(VP A
(A<>

-

i
i=i

(& > }< *,.)

j'=i
i

(RP>) w ;

2 (RPi)(A,i- )
j= i




- 1,

....

>
>

(RP,)(A,)

(3) />, = 2

1

1

where L ( is the Laspeyres measure of the
growth in the MOE services provided by a set
of j - 1, 2 . . . N different assets, and all other
symbols are as before.
Paasche aggregates are constructed via
the formula:

where M / is the money-income measure of the
growth in the MOE services provided by a set
o f/= l,2 . . . N different assets, and all other
symbols are as before.
Although the three alternative measures
presented here provide good approximations of
changes in the total flow of MOE services and
may closely parallel the behavior of a Divisia
measure, the Divisia measure is preferred to
any of the three alternatives on a priori theoreti­
cal grounds (Diewert 1976). Despite the fact that
Divisias fall within Diewert’s class of superla­
tive index numbers, two mathematical prob­
lems remain with a Divisia aggregate. First, a
Divisia index based on equation 1 (the
Tornqvist-Theil approximation) is a line inte­
gral whose value depends on the time path over
which it is evaluated (Usher 1974). While in con­
tinuous time, the Divisia index always provides
an exact measure of the change in the total flow
of MOE services in the economy (Hulten 1973;
Barnett, Spindt, and Offenbacher 1981b), the
Tornqvist-Theil discrete time approximation of
a Divisia index may not always be exact.
Second, when a new asset is introduced, its
initial growth rate is equal to infinity if no
adjustments are made to the equation 1 Divisia
formula. This inappropriately makes the
Divisia measure of the growth rate in the MOE
services flow also equal to infinity. To correct
for this possibility, the Federal Reserve System
computes Divisia aggregates according to a

32

Economic Review □ Spring 1983

Fisher Ideal index formula during the initial
months of a financial innovation ideal—with
the rental price of the new asset being assigned
a “reservation” price in the period immediately
preceding its innovation. See Barnett (1983) for
details on the Fisher Ideal formula.

R eferen ces
Barnett, William A. “The User Cost of Money,”
Economics Letters, vol. 1 (1978), pp. 145-49.
_____ “Economic Monetary Aggregates: An
Application of Index Number and Aggrega­
tion Theory,” Journal of Econometrics, vol.
14, no. 1 (September 1980), pp. 11-48.
_____ “Economic Monetary Aggregates:
Reply,” Journal of Econometrics, vol. 14, no.l
(September 1980), pp. 57-59.
_____ Consumer Demand and Labor Supply:
Goods, Monetary Assets, and Time. Amster­
dam: North-Holland, 1981a.
_____ “The New Monetary Aggregates "Journal
of Money, Credit and Banking, vol. 13, no. 4
(November 1981b), pp. 485-89.
_____ “The Optimal Level of Monetary Aggrega­
tion,” Journal of Money, Credit and Banking,
vol. 14, no.4, pt. 2 (November 1982), pp. 687-710.
_____ “New Indices of Money Supply and the
Flexible Laurent Demand System,” Journal of
Business and Economic Statistics, vol. 1, no. 1
(January 1983), pp. 7-23.
____ , and Paul A. Spindt. “The Velocity
Behavior and Information Content of Divisia
Monetary Aggregates,” Economics Letters,
vol. 4 (1979), pp. 51-57.
____ , and Paul A. Spindt. “The Information
Content of Divisia Monetary Quantity In­
dices,” Special Studies Paper 146, Board of
Governors of the Federal Reserve System,
Washington, DC, August 1980.



------ , and Paul A. Spindt. “Divisia Monetary
Aggregates: Their Compilation, Data, and
Historical Behavior,” Staff Studies Paper
116, Board of Governors of the Federal
Reserve System, Washington, DC, May 1982.
____ , Paul A. Spindt, and Edward K. Offenbacher. “Empirical Comparisons of Divisia
and Simple Sum Monetary Aggregates,”
NBER Conference Paper 122, National
Bureau of Economic Research, Cambridge,
MA, August 1981a.
____ , Paul A. Spindt, and Edward K. Offenbacher. “The New Divisia Aggregates,” Pro­
cessed, University of Texas at Austin and
Board of Governors of the Federal Reserve
System, 1981b.
Berkman, Neil G. “The New Monetary Aggre­
gates: A Critical Appraisal,” Journal of
Money, Credit and Banking, vol. 12, no. 2, pt.
1 (May 1980), pp. 135-54.
Diewert, W. Erwin. “Exact and Superlative
Index Numbers,” Journal of Econometrics,
vol. 4, no. 2 (May 1976), pp. 115-45.
Hulten, Charles R. “Divisia Index Numbers,”
Econometrica, vol. 41, no. 6 (November 1973),
pp. 1017-1025.
Porter, Richard D., and Edward K. Offenbacher.
“Financial Innovations and the Measurement
of the Money Supply,” Unpublished paper for
Conference on Financial Innovations, Federal
Reserve Bank of St. Louis, October 1982.
Tinsley, Peter A., Paul A. Spindt, and Monica E.
Friar. “Indicator and Filter Attributes of
Monetary Aggregates: A Nit-Picking Case for
Disaggregation,” Journal of Econometrics, vol.
14, no. 1 (September 1980), pp. 61-91.
Usher, D. “The Suitability of the Divisia Index
for the Measurement of Economic Aggre­
gates,” Review of Income and Wealth, series
20, no. 3 (September 1974), pp. 273-88.

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Social Security: Issues and Options
Soil Conservation: Market Failure
and Program Performance
Issues in the 1983 Auto-Sales Outlook
Loan Quality of Bank Holding Companies
Economic Outlook for 1983
Exchange Rates and U.S. Prices
Velocity and Monetary Targets
The Mythology of Domestic Content



Author(s)

D ate

Paul R. Watro
John B. Carlson
Michael F. Bryan

1/11/82
4/05/82
4/19/82

Paul R. Watro

5/03/82

Gerald H. Anderson
John B. Carlson
Gary Whalen
Daniel A. Littman
Michael F. Bryan
K.J. Kowalewski
Amy L. Kerka and
Owen F. Humpage
Gerald H. Anderson
Owen F. Humpage
Amy Kerka
Paul Gary Wyckoff
Michael F. Bryan
Gary Whalen
Paulette Maclin and
Joanne Bronish
Gerald H. Anderson and
Owen F. Humpage
William T. Gavin
Michael F. Bryan

5/17/82
5/31/82
6/14/82
6/28/82
7/12/82
7/26/82
10/04/82
10/18/82
11/01/82
1/10/83
1/24/83
3/07/83
3/21/83
4/04/83
4/18/83
6/06/83
6/20/83