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FEDERAL RESERWE BANK
OF SAN FRANCISCO

EC O N O M IC R E V I E W

FALL 19 8 2

Opinions expressed in the Economic Review do not necessarily reflect the views of the management of
the Federal Reserve Bank of San Francisco, or of the Board of Governors of the Federal Reserve
System.

The Federal Reserve Bank of San Francisco’s Economic Review is published quarterly by the Bank’s
Research and Public Information Department under the supervision of Michael W. Keran, Senior Vice
President. The publication is edited by Gregory J. Tong, with the assistance of Karen Rusk (editorial) and
William Rosenthal (graphics).
For free copies of this and other Federal Reserve publications, write or phone the Public Information
Department, Federal Reserve Bank of San Francisco, P.O. Box 7702, San Francisco, California 94120.
Phone (415) 974-3234.

“ Money- Demand and Control"

I.
II.

Introduction and Summary

An Examination o f the Federal Reserve’s Strategy for Controlling
the Monetary Aggregates
7
John P. Judd
.. .deviations of money from its short-run path, caused by permanent disturbances to the
money and reserve markets, could be offset in a shorter period of time with relatively
small increases in interest rate volatility.

Editorial Committee:
Charles Pigott, Brian Motley, Roger Craine

III.

Dynamic Adjustment in the Demand for Money: Tests of
Alternative Hypotheses

John P. Judd and John L. Scadding
...The empirical results in this paper do not support the conventional specification of
short-run dynamics, in which observed money accommodates itself gradually to changes
in money demand. Uniformly superior results were obtained from equations in which
money demand adjusts (through changes in the price level) in response to independent
changes in the supply of money.
Editorial Committee:
Roger Craine, Michael Keran, AldenToevs

A better understanding of the public's demand for
money is important because of the impact of money
on output and prices and the central role assumptions about money demand play in the making of
monetary policy. The two articles in this Review
shed light on the inter-relationship of money demand and strategies to control the money supply. In
the first article, John Judd describes and assesses
the Federal Reserve's existing strategy for short-run
control of the monetary aggregates. In the second
article, John Judd and John Scadding establish that
independent changes in the money supply, such as
those that result from monetary control policies,
affect the behavior of money demand.
John Judd, in his article notes that, through the
middle of 1982, monetary control had improved on
an annual basis but monetary aggregates had become more volatile on a shorter term since the
Federal Reserve changed the way it controlled
money (from establishing targets for short-term interest rates to focusing on targets for bank reserves.)
The article was written prior to the major deregulation of deposit interest rates at the end of 1982. It
abstracts from issues concerning monetary variables targeted and annual numerical ranges for
monetary aggregates raised by this development to
discuss approaches to achieving whatever monetary
targets the Federal Reserve chooses.
The Federal Open Market Committee, which sets
target ranges for the growth rate of the monetary
aggregates, has followed a strategy whereby it attempts to return monetary aggregates to the target
range gradually. According to Judd, a major rationale for this practice is that much of the volatility is
believed to be self-correcting. Attempts to reduce
such variations can add unnecessarily to interest
rate fluctuation in the short-run.
Judd warns, however, that there are money supply deviations caused by persistent disturbances to
the economy that, if left unchecked, have adverse
effects on prices and GNP. Moreover, he argues that

"a larger number of unnecessary reactions (on the
part of the Federal Reserve) might be less costly to
the economy than a smaller number of large persistent monetary control errors."
Judd focuses on the size of changes in nonborrowed reserves initiated by the Fed as a measure of
the aggressiveness of monetary control actions. He
uses the Money Market model developed at the San
Francisco Federal Reserve Bank to estimate the size
of changes in short-term interest rates needed for
various rates of MI re-entry into the annual target
ranges.
A key element of the model is a provision for the
effect of bank loans on the money supply. Most
conventional models do not incorporate this relationship.
Using the San Francisco Money Market model,
Judd finds that, once the effects of a change in
nonborrowed reserves on both open market interest
rates and bank lending are accounted for, "given
changes in MI can be accomplished with smaller
changes in interest rates." Thus, the costs, as measured by increased interest rate volatility, of closer
control of MI are lower than conventional models
would suggest.
He concludes that "a more aggressive approach
(to returning monetary aggregates to target) would
reduce the incidence of persistent deviations that
have significant effects on GNP and prices. Such an
approach would also reduce the risk that the Fed
would have to resort to inducing persistent swings
in short-term interest rates to eliminate large money
deviations. Finally, a more aggressive approach
might contribute to the stability of long-term interest rates, which are especially important for the
performance of the economy."
Judd and Scadding, in their article, test alternative specifications of short-run money demand dynamics to find the one which best predicts the level
of real money balances. The two authors note that
the conventional specification' 'went seriously off
5

group share thefea.ture that money demand adjusts
with a lag to changes in the supply of money. The
specifications differ among themselves as to which
argument of the money demand function bears the
burden of adjustment-interest rates, income,
prices, or, in one case, a combination of these.
All the equations were put into the same canonical fonn and estimated \vith real money balances as
the dependent variable. The sample data used in the
estimation spanned the'period from the first quarter
of 1959 to the second quarter of 1974. The equations
thatyielded reasonable estimation results were then
used to simulate money dynamics in the period from
the third quarter of 1974 to the third quarter of 1980.
Judd and Scadding found that "money demand
equations in which prices adjust to exogenous
changes in money, interest and income outperform
equations in which money is the adjusting variable.
Equations in which money is the adjusting variable,
in tum, outperform equations where interest rates
and income are the adjusting variables,"

track" whel1 it tried to predict the shift in money
demand from 1974 to 1976, leading some observers
to question whether this was due to the conventional
assumption "thatthemoney supply is endogenous,
adjusting to exogenous changes in income and
interest rates operating through the demand for
money."
Judd and Scadding question whether the conventional assumption is appropriate for situations in
which shocks occur in the supply of money rather
than the demand for money.
They believe that the correct specification of the
short-run dynamic adjustment in the money demand
function "depends critically on which variables are
made exogenous and which endogenous." They,
therefore, study nine specifications of money demand with different adjusting and exogenous variables. The nine can, however, be grouped into two
major categories. The first includes the conventional specification and its variants, in which the quantity of money adjusts with a lag to changes in the
demand for money. Specifications in the second

John P. Judd*

I. Introduction
On October 6, 1979, the Federal Reserve changed
the way it controlled money from establishing targets for short-term interest rates to focusing on
targets for bank reserves. The new procedure was
expected to result in more interest rate volatility as
the rates were freed to respond to market forces.
The procedure was also intended to achieve better
control of the monetary aggregates. Since October

short-run control would most likely entail large
increases in interest rate volatility, which could
seriously inhibit the performance of the economy.
The present study therefore has two main purposes. The first is to describe how the reserveoriented monetary control procedure works, in
theory and in practice.** The second is to assess the
effectiveness of the new procedure as it has been
implemented. A key feature of any control procedure is how quickly it brings the quantity of money
back to a set target when deviations occur. The
evidence in this paper for 1981 through the first half
of 1982 suggests that the Federal Reserve has continued to follow procedures producing relatively
gradual re-entry to the annual target ranges that
form the basis of monetary policy. But unlike the
earlier study noted above, this study suggests that
deviations could be eliminated more rapidly without
incurring large increases in interest rate volatility.

1979, interest rate volatility has increased, and

monetary control has improved on an annual basis.
But surprisingly, the monetary aggregates became
more volatile on a short-term basis.
In February, 1981, the Federal Reserve published
results of a System study evaluating the experience
under the new control procedure. [ The study concluded that the increased volatility of the monetary
aggregates in 1980 was caused, in part, by unusually large shocks to the money and credit markets.
The largest of these shocks came from the Special
Credit Control Program implemented in the Spring
of 1980. A second conclusion was that more accurate short-run control might have been achieved by
more aggressive adjustments in the reserves targets
when the quantity of money departed from target. 2
However, the study also concluded that closer

**This paper was written in the middle of 1982,
prior to the reduction in emphasis by the FOMC on
MI targeting and the major deposit regulation that
occurred in the latter part of 1982. Thus, the monetary control procedures described and analyzed are
those that prevailed in mid-1982.
For a discussion of the issues raised by using Ml
as an intermediate target under interest rate deregulation, see John P. Judd and John L. Scadding,
"Financial Change and Monetary Targeting in the
United States," available from the authors.

*Research Officer, Federal Reserve Bank of San
Francisco. I am indebted to Adrian W. Throop for
enlightening discussions of the issues discussed
in this paper. Lloyd Dixon provided research
assistance.

II. Money and Reserve ControlProcedures
The Federal Reserve attempts to promote full
employment growth at low rates of inflation by
maintaining growth rates in certain monetary aggregates that are compatible with its objectives. Each
year the Federal Open Market Committee (FOMe)
sets annual growth-rate target ranges for the monetary (and credit) aggregates. These extend from the
fourth quarter of the previous year to the fourth
quarter of the current year. In 1982, for example,
the range for Ml is 2V2 to 5 1/2 percent (see Figure
1).3 Although ranges are specified for Ml, M2, M3
and bank credit, only those for Ml and M2 have had
much operational significance since October 1979.
These ranges represent the FOMe's goals for average annual money growth. They reflect the long-run
policy of gradually lowering the rate of inflation.
Over the past three years, the growth rate ranges for
MI have been reduced by about V2 percent each
year. The goal of this gradualist policy is to reduce
growth in money slowly enough over a number of

years that inflation is reduced with the smallest
possible adverse effects on output and employment.
In recent years, innovations in cash management
have made the job of setting appropriate annual
growth rates. for the aggregates more difficult.
These innovations have frequently suggested to policymakers that the public's demand for money is
shifting and that growth rate objectives for the
aggregates must accommodate these shifts in order
to avoid undesired affects on the economy. For
example, if the demand for money shifts down and
supply is not also lowered, interest rates will fall
and monetary policy will have been too expansionary. In 1981, the Fed essentially aimed to keep the
quantity of money as measured by Ml near the
lower boundary of the target range because the
demand for MI appeared to be shifting downward.
By mid-1982, the Fed was content to see Ml at the
top of its annual range because of a perceived upward shift in the demand for MI.

Figure 1
Monthly M1-1982
$ Billions

470
465
Actual
Short-Run Path

460
455
450
445
440
435
430
425

1981

1982
8

The purpose of this paper is not to evaluate the
Federal Reserve's attempts to achieve its macro
economic goals, but rather to assess the Fed's procedure for controlling the monetary aggregates in
the short-run. Thus, the annual growth rate objectives for MI are taken as the starting point, without
evaluating whether these were the appropriate
target ranges for achieving the Fed's macroeconomic goals.
Short-Run Monetary Paths
The Fed's monetary control procedure can be
divided into three levels. 4 The first level involves
the choice of short-run paths for the monetary aggregates (Ml and M2) by the FOMC at each of its
meetings. In the final month of each quarter, a
three-month path is chosen to cover the next quarter: e. g., on March 31, 1981 a path was chosen for
March to June (see line marked (2) in Figure 2).

These quarterly paths are sometimes revised in the
final two months of the quarter. An example of such
a revision occurred on May 18, 1981, when an Ml
path for April to June was specified-see the line
denoted (3) in Figure 2. This latter path supplanted
the original second quarter path.
The short-run paths define the FOMC's preferred
rate of re-entry to the longer-run target ranges. For
example, again consider the second quarter of 1981.
At its March 31 meeting, the Committee chose a
growth rate of 5-6 percent for MI, (plotted as 51/2
percent in Figure 2 and denoted as (2) ) beginning
from a March base that was well below the lower
boundary of the annual target range. The March
path "pointed" MI back toward its range, and
would have achieved the lower boundary of the
range within five months (by August) if it had been
maintained that long.

Figure 2

Monthly M1-1981

$ Billions

445

440

Actual
Short-Run Path

435

430

425

420

415 ............_ ......-

N
1980

J
1981

SON

The paths for 1981 and 1982 suggest that the
Committee's desired rate of re-entry to the annual
range was relatively slow. 5 Each month, the Committee sought to eliminate only a small part of the
previous month's deviation of Ml from the annual
target range. The shortest re-entry horizon in 1981
was contained in the first quarter path (denoted as
(1) in Figure I), which would have reached the
lower boundary of the annual range in early April,
about three months after the January deviation just
prior to the FOMC meeting in early February.
The path denoted 5 would have reached the lower
boundary of the annual range in four months, and
those denoted 2 and 4 would have reached the lower
boundary in 5 months. Finally, paths 6, 7 and 8,
chosen for the fourth quarter of 1981 would not have
attained the annual lower boundary by the end of
that year. Attempted re-entry in the first half of 1982
was somewhat faster. The path denoted 2 in Figure 1
would have achieved the upper boundary of the
target range in four months, while the paths denoted
as 3 and 4, reach the upper boundary in three and
two months, respectively.
The choice of a relatively slow re-entry rate apparently reflects the view that faster re-entry would
involve excessive amounts of interest rate volatility.
This point was made in the February 1981 Federal
Reseve Staff study of the new reserve control procedures. This study concluded that a faster re-entry
rate than had been used in 1980 would have provided only marginally closer month-to-month control of Ml at the expense of substantially greater
volatility in the Federal funds rate. 6

instruments. The Fed must also project reserves
held in excess of reserve requirements. These compositional changes require adjustments of the total
reserves paths to make them consistent with unchanged paths for MI and M2. These so-called
technical, or "multiplier," adjustments are made
when necessary on a week-by-week basis. The discussion in the remainder of the paper abstracts from
these technical adjustments, and focuses instead
on reserve changes designed to be consistent with
changes in the Ml and M2 paths.
The third level' of the control procedure involves
the use of a reserves instrument to achieve the
short-run paths for Ml and M2. Under certain institutional arrangements, the Federal Reserve has the
option of directly manipulating total reserves to
control money. However, this approach has not
been feasible because of the existing practice of
lagged reserve accounting (LRR). 8 This reserve accounting rule requires banks to hold an amount of
reserves in any given week based on deposits held
two weeks earlier. Banks' required reserves are
therefore predetermined in any given week. The
Fed, for its part, must supply the banking system
with enough reserves to meet the requirement. If the
Fed did not do so, it would force some individual
banks into a reserve deficiency beyond their control. Thus under LRR, the Fed is not in a position to
use total reserves as the money control instrument
on a weekly basis.
The Fed's way of dealing with this problem is to
use as its control instrument the proportion of total
reserves provided to banks through the Federal Reserve discount window. If the Fed wants to pursue a
tighter money policy, for example, it supplies fewer
reserves outright to the market through open market
operations (i. e., fewer non-borrowed reserves).
This means that banks will have to acquire a larger
proportion of their predetermined required reserves
by borrowing at the discount window. Banks, however, are reluctant to go to the discount window
because the Fed imposes restrictions on the quantity
and frequency of loans it will make to individual
banks over specified periods of time. 9 Thus, when
the Fed provides fewer non-borrowed reserves, the
Federal funds rate must rise relative to the discount
rate to induce banks to use up more of their available
credit at the discount window. Such increases in the
funds rate slow growth in money and total reserves.

Paths for the Reserve Aggregates
The second level of the monetary control procedures translates the short-run paths for Ml and
M2 into a path for total reserves over periods between FOMC meetings. These total reserve paths
are calculated by multiplying the appropriate reserve requirement ratios by projections of the various reservable liabilities of depository institutions
thought to be consistent with the paths for Ml and
M2. 7 Since the Fed imposes different reserve requirement ratios on the various components of Ml
and M2, and on instruments not in these aggregates,
the calculation of the current total reserve paths
depends on accurate estimates of movements in the
components of Ml and M2 and of other reservable

This method of monetary and reserve control is
illustrated in Figure 3. Consider first the supply of
total reserves, RS, which consists of two parts. First,
so-called nonborrowed reserves (RU) are provided
outright to the banking system when the Fed buys
open market securities (e. g., Treasury bills) from
the public and pays for the securities with bank
reserves. Because the Fed directly controls the
amount of nonborrowed reserves, this portion of
total reserves does not respond to the Federal funds
rate, and is depicted by the vertical portion ofR s.
Second, borrowed reserves (RB) are provided
when the Fed lends reserves to banks through its
discount window. As noted earlier, the quantity of
borrowed reserves will rise only if the funds rate
increases sufficiently above the discount rate to
overcome banks' reluctance to borrow. Thus banks'
demand curve of borrowed reserves is upward sloping when the funds rate is above the discount rate.
The upward sloping portion of R S represents the
sum of borrowed reserves, which respond positively to the funds rate, plus a fixed amount of
nonboITowed reserves. (Note that the kink in R S
occurs where the funds rate equals the discount rate
and borrowed reserves are zero. Up to this point,
total reserves are composed entirely of nonborrowed reserves, and thus R S is vertical.)
As noted above, banks' demand for total reserves
is predetermined in any given week under LRR.
Thus, the short-run demand for reserves, R DsR , is
vertical. However, over periods longer than two
weeks, total reserves respond to changes in the
quantity of deposits banks issue. Since a higher
funds rate restrains deposit growth, the long-run
reserves demand, R~.R' is negatively sloped with
respect to the funds rate.
Assume that point A in Figure 3 represents an
initial starting point, where total reserves (R*) and
the funds rate (iF*) correspond to the level ofMI on
its path. Now, suppose the Fed reduces its desired
level for MI. This requires a tighter policy in the
reserves market, which means a reduction in nonborrowed reserves from RU[* to RU 2 *. In the shortrun, this action raises borrowings (from RB [ to
RB 2 ) by an equal amount and raises iF to point B,
because the demand for reserves is fixed. However,
the higher funds rate restrains money growth contemporaneously, and this leads, with a two-week

Figure 3
Funds
Rate
(iF)

Funds
Rate =
Discount
Rate

RU~ RU~

R*
Total Reserves

lag, to slower growth in the demand by banks for
total reserves. Thus, over periods longer than two
weeks, the demand for reserves responds to the
funds rate and so reserves and the funds rate fall
from point B to point C.
If the Fed could predict the supply of and demand
for money and reserves with certainty, it could
always achieve its desired paths (over periods longer than two weeks) by setting nonborrowed reserves
at a level such that R S intersects the long-run reserves demand curve at the desired leveI of total
reserves. Unfortunately, neither Rdnor R S is known
with certainty. For example, unexpected shifts in
banks' reluctance to borrow affect R S. Unexpected
changes in the public's demand for Ml and bank
credit affect Rd.
Nevertheless, monetary control procedures affect the extent to which the money supply is affected
by these and other shocks. For example, lagged
reserve accounting allows money to be pushed
away from the target path to a greater extent than
does contemporaneous accounting. Under LRR,
sudden changes in the public's demand for money
affect banks' demand for reserves, and thus the
funds rate, with a lag of two weeks. Money is
therefore, more susceptible to shocks because the
interest rate changes needed to moderate deviations

of money from target are delayed. Under contemporaneous reserve accounting (CRR) (where current
reserve requirements are determined by current
deposits), these moderating interest rate changes
occur immediately, contributing to tighter monetary
control. The Federal Reserve has recently announced its intention to switch to CRR in 1984.
The operating instrument used for monetary control also has an important effect on the susceptibility
of money to shocks. In October 1979, the Fed
switched from using the Federal funds rate to using
nonborrowed reserves as its instrument of control.
The funds rate approach had the disadvantage that
unanticipated changes in the demand for money and
reserves were often accommodated by automatic
increases in the supply of reserves as the Fed held its

funds rate instrument constant. This accommodation does not occur to the same extent under present
procedures, since the Fed often holds nonborrowed
reserves constant when unanticipated changes in
money and reserves demand occur. With RU fixed,
an increase in money and total reserves demand
automatically causes borrowed reserves to rise.
Greater borrowing at the window causes the funds
rate to rise, which tends to retard the increase in
money,· leading to"a smaller monetary control error.
Some analysts argue that a total reserves instrument
would be even more effective in this regard, but this
remains a matter in dispute. 10 The Federal Reserve's
switch to CRR will at least give the System the
option of using a total reserves instrument, an option not feasible under LRR.

III. Choosing the Nonborrowed Reserve Path
Another important feature of the monetary control procedure, and the focus of this paper, is how
quickly the Fed attempts to reenter the longer run
target ranges once deviations occur: i.e. how aggressively does the Fed act to offset monetary control errors? The aggressiveness of monetary control
actions can be measured by the size of changes in
nonborrowed reserves initiated by the Fed in response to deviations of money and total reserves
from path. For example, when money overshoots
its path, nonborrowed reserves must be lowered in
order to raise the funds rate and eventually make
money fall back to its path. All else equal, the larger
the reduction in nonborrowed reserves, the more
rapidly money will go back to path.
The Fed's method of choosing nonborrowed reserves paths involves two basic elements. The first
element is the FaMe's choice of a so-called initial
borrowing assumption. In addition to choosing
paths for Ml and M2, which are translated by the
staff into a total reserves path, the FOMC also
chooses an initial borrowing "assumption" for the
interrneeting period. The total reserves path minus
the borrowing assumption is the initial nonborrowed reserves path level to be aimed for by the
Federal Reserve Bank of New York Trading Desk.
Thus when the FOMC chooses paths for Ml and M2
and an initial borrowing assumption it simultaneously chooses a nonborrowed reserves path.

At each meeting the FOMC is presented by the
staff with a menu of (usually) three short-run policy
alternati ves, typically representing possible
"tight," "easy" and "status quo" policies. Each
alternative contains a combination of paths for Ml
and M2, a borrowing assumption, and a Federal
funds rate range." The staff designs each path to be
internally consistent, that is, the staff projects that a
given level of borrowing would be necessary to
achieve the corresponding short-run Ml and M2
paths by the end of the period they cover. Thus by
construction, the nonborrowed reserves path
(which is calculated on the basis of the initial borrowing assumption) is an initial guess at the level of
nonborrowed reserves consistent with achieving the
short-run monetary aggregates paths. Since the Ml
and M2 paths typically reflect an attempt to re-enter
the annual target range gradually, so do the nonborrowed reserve paths.
The second element in the Fed's choice of a
nonborrowed reserve path involves intermeeting
adjustments of the initial nonborrowed path. Since
October 1979, the nonborrowed path has sometimes
been changed between FOMC meetings in response
to projected deviations of total reserves from path.
When total reserves have been projected to be deviating from path during control periods by a significant amount, nonborrowed reserves have sometimes been changed in the opposite direction to
12

reinforce total reserve deviations rather than offset
them. An example is in April of 1980 (during the
period of the Special Credit Controls), when nonborrowed reserves came in below their initial paths
in an intermeeting period in which total reserves
were well below path. This development reinforced
the weakness in MI and total reserves in that period,
but cushioned the declines ·in interest rates that were
occurring simultaneously. Two such reinforcing
changes occurred in nonborrowed reserves in intermeeting periods in 1980, and three occurred in
1981 13
As shown earlier, the FOMe's choice of initial
nonborrowed reserves paths represents relatively
gradual rates of re-entry to the longer-run target
ranges. However, to evaluate the reserve control
procedure as a whole, we must also take account of
the adjustments to these initial paths made in the
intermeeting periods. These latter actions serve as
mid-course corrections in response to the latest
data. They do not, however, convert gradual reentry into rapid re-entry. These mid-course corrections were designed to keep on the pre-determined
gradual short-run paths. Moreover, the sporadic use
of intermeeting adjustments suggests that they have
not been a major factor holding Ml to its short-run
paths, especially in 1981.

speed the movement of MI back to path. Assume,
for example, that total reserves are above path.
Holding the path for nonborrowed reserves at its
original level would limit the total reserves overshoot to consist of borrowed reserves. Higher borrowing would raise the funds rate and help bring MI
and total reserves back to path. The intermeeting
adjustments involve raising borrowing and the
funds rate even further, by reducing the nonborrowed reserves path from its original level, thereby
inducing MI and total reserves to move back to path
more rapidly.
These intermeeting adjustments were used more
frequently in 1980 than in 1981 and their size has
varied widely among control periods. In 1980, there
were six such adjustments ranging in size from
around 25 percent of the total reserve deviation to
around 125 percent. 12 In 1981, there were two such
adjustments, one that was larger than the total reserve deviation, and a second one that was smaller.
Fewer intermeeting adjustments were made in
1981, in part because MI and M2 often gave conflicting signals-M2 was often above its path when
Ml was below its path.
There have also been several control periods in
1980-81 when flonborrowed reserves were changed
during intermeeting periods in the same direction as
total reserve deviations. These actions tended to

IV. Rates of Re-Entry
this section examines this factor. Two other factors
will be discussed later: The relative benefits provided to the economy by more stable money market
interest rates in the short-run versus less persistent
deviations of Ml from target, and the nature of
deviations, that is, whether or not they are self
correcting.

The previous section showed that under current
operating procedures the Fed sets its nonborrowed
reserves path to be consistent with gradual rates of
re-entry of Ml and M2 to the annual target ranges.
The major argument advanced for gradual re-entry
is that it helps stabilize interest rates. Implicit in this
argument is the point that attempts to get back to the
annual target ranges more quickly would require
larger changes in interest rates. These sharp interest
rate changes, in turn, can disrupt financial flows
and weaken the performance of the economy. 14
How aggressively should policy attempt to return
Ml and M2 to the annual ranges? This is an empirical question the answer to which depends on several
factors. The first issue concerns the size of the
response in short-term interest rates elicited by the
changes in nonborrowed reserves necessary to
achieve given rates of re-entry. The remainder of

Conceptual Framework
An analysis of how much increase in interest rate
volatility will accompany faster re-entry, in part,
depends on empirical estimates of the demand and
supply relationships in the markets for money and
reserves. We have used the San Francisco money
market model to estimate the size of changes in
short-term interest rates required for various rates of
MI re-entry to the annual target ranges. The model
is a monthly structural model which describes the

behavior of banks, the nonbank public, and the
Federal Reserve in the markets for bank reserves,
deposits and bank loans. 15
The SF model contains a conventional borrowing
function in which banks' demand for borrowed reserves depends positively on the funds rates, and
negatively on the discount rate, whenever the funds
rate is above the discount rate. Thus the model's
supply of total reserves schedule looks like the one
shown in Figure 3.
In the model, banks' demand for total reserves
varies negatively with respect to the Federal funds
rate. Since banks' demand for reserves results primarily from reserve requirements, the reserve demand function reflects the response of deposits to
the Federal funds rate. The inverse relationship
between the funds rate and deposits depends mainly
on two relationships. First, arbitrage in financial
markets means that rates on longer-term money
market instruments, like commercial paper, tend to
move up and down with the federal funds rate. The
commercial paper rate represents the interest foregone from holding transactions deposits. For this
reason, increases in the paper rate induce the public
to hold fewer transactions deposits, and banks consequently need supply fewer of these deposits. This
is one way in which a higher funds rate reduces Ml
and reserves demand. It is the channel of influence
common to most money market models.
Second, bank loans act as a catalyst in another
channel of influence unique to the SF model. Banks
compete to make loans to the public by setting their
loan rates relative to rates available in direct finance
markets like those for commercial paper and corporate bonds. For any given level of GNP, the
public's demand for bank loans depends negatively
on the prime rate and positively on the commercial
paper rate. Thus, as the prime rate falls relative to
the commercial paper rate, banks issue more loans
in response to rising demand by the public. Since
the proceeds of these loans are generally paid in the
fonn of transactions deposits, increases in MI and
reserves demand are the immediate effect of loan
extensions. These newly created deposits tend to
stay in the public's portfolio of assets, and thus
affect observed MI, for up to six months, according
to the empirical estimates. 16
Changes in the funds rate affect bank loans and

Ml through the prime rate. For example, an increase in the funds rate induces a higher prime rate
because banks set their prime rates at a variable
markup over their cost of obtaining funds to lend.
Since the funds rate forms the base of those borrowing costs, the prime rate tends to move up or down
with <;urrent and lagged funds rates. Thus, if the
Federal Reserve takes actions that raise the funds
rate, this raises the prime rate. A higher prime rate
causes the supply of money to fall by lowering bank
loans. 17
The presence of bank loan effects means that
changes in nonborrowed reserves have a larger effect on Ml and a smaller effect on money market
interest rates. An increase in RU, for example,
reduces the Federal funds rate and raises MI in two
ways. First, the lower funds rate lowers the commercial paper rate, thereby raising the public's underlying demand for money. Second, higher nonborrowed reserves raise Ml via increases in bank
loans, as lower funds rates cause the prime lending
rate to fall. This added response of Ml to money
market interest rates means that given changes in
MI can be accomplished with smaller changes in
interest rates. Bank loan effects therefore have an
important implication for monetary control-the
costs of short-run control (interest rate volatility)
are less than conventional models (without bank
loan effects) would suggest.
Empirical Results

The money market model was used to estimate
the changes in the commercial paper rate needed to
eliminate given deviations of Ml from target over
different periods of time. 18 The analysis applies to
MI deviations that are persistent, in the sense that
they would not be eliminated without Federal Reserve action. The estimates are based on simulations of the estimated model. The model simulations included the assumption that the Fed changes
nonborrowed reserves by enough to eliminate specified percentages of initial Ml deviations each
month. For example, a four-month control horizon
involves eliminating 25 percent of an initial MI
deviation each month for four straight months.
Constant nominal income and a constant discount
rate were two other assumptions. It should be noted
that these simulations were not attempts to replicate

would occur with one-month control, which requires a 205 basis point change in the paper rate in
the first month following the M 1 deviation.
The large difference between the one-month and
the two-month control rules has to do with the
behavior of bank loans. Empirical evidence indicates that the public's loan demand responds to a
change in the prime rate with a lag of one month.
This presumably occurs because corporate and
other types of borrowing are controlled by spending
plans which are not revised very much at the same
time that borrowing costs change. In any event, the
lag in the response of bank loans to Fed policy
actions means that a larger interest rate change is
required for a given degree of monetary control.
These results suggest that the change in nonborrowed reserves in response to a deviation of MI
from its annual target range could be larger than it is
currently without large increases in interest rate
volatility. This finding implies that the Fed could
attempt to re-enter the range fOf MI within 2 to 3
months, rather than the 4 to 5 month horizon often
used, without significantly increasing the volatility
of the commercial paper rate.
The preceding analysis assumed that income and
prices were unaffected by Ml deviations, but removing this assumption only strengthens the case
for closer monetary control. This subject is discussed in the next section.

a sequence of nonborrowed reserves changes that
actually occurred under current procedures. Rather
they were designed for comparison purposes to indicate the interest rate consequences of alternative
rates of re-entry to the annual target ranges.
Table 1 shows the model's estimates of the interest rate consequences of alternative rates of reentry. The numbers shown are the cumulative
changes in the commercial paper rate (in basis
points) corresponding to the various control horizons also shown. For example, the three-month
horizon implies that the RU path is designed to
eliminate one-third of a $2 billion Ml deviation
each month for three months. RU is then set to hold
Ml on path for the next three months. The row
labeled three months in Table I shows that under
such a horizon, a $2 billion Ml overshoot would
imply that, in the following six months, the commercial paper rate would be 68, 107, 121, 69, 50 and
45 basis points higher than it would have been if
there had been no change in nonborrowed reserves.
In general, Table I suggests that shorter control
horizons (i.e., faster re-entry rates), require larger
cumulative changes in the commercial paper rate,
and that these larger changes must occur sooner. For
example, two-month control requires a 152 basis
point change in the paper rate by the second month
after the Ml deviation, while three-month control
requires a 121 basis point increase in the paper rate
by the third month. The most extreme variability

v. Policy Implications and Conclusions
The Federal Reserve's current approach to reserve targeting involves a relatively gradual reentry to the annual target ranges once a deviation
has occurred. According to the empirical evidence
presented in this paper the re-entry rate may be
shortened at least a few months without causing
significantly larger movements in interest rates.
However, this result by itse?f does not necessarily
justify a shortening in the control horizon. The
advisability of such a decision depends upon the
sources of disturbances to the money and reserve
markets that cause the money control errors, and an
assessment of the relative costs of interest rate volatility relative to the costs of money control errors.
An argument cautioning against a strong reaction
to deviations of total reserves from path is that many
deviations are self-correcting. To illustrate, the error term from an estimated money demand equation
is relatively large and may account for a large number of temporary MI and, therefore, total reserves
deviations. These deviations correct themselves in a
short time without Fed actions that would cause
interest rates to change. However, since it is often
very difficult to distinguish temporary from permanent disturbances, strong Fed reactions could sometimes unnecessarily induce interest rate volatility.
Nevertheless, by seeking to avoid the error of
reacting when it is unnecessary, the Fed runs the
risk of not reacting appropriately when disturbances
are persistent. It is the latter error that permits MI
deviations to persist long enough to have an undesired effect on GNP and prices. Thus, even if temporary disturbances occurred more frequently than
persistent disturbances, it might be worthwhile to
choose a faster re-entry rate. In other words, a larger
number of unnecessary reactions might be less cost1y to the economy than a smaller number of large
persistent monetary control errors.
Permanent disturbances to the market for money
often require very large persistent changes in interest rates to bring Ml back to target. For example,
assume that a sudden surge in bank loans causes MI
to accelerate above its targeted path. If this deviation were not corrected quickly enough, GNP
would also begin to accelerate. Ultimately, interest
rates would have to increase to offset both the surge

in loans and GNP. If the Fed had taken corrective
action early, it would only have had to offset the
surge in loans. This narrower task requires a smaller
and less persistent increase in short-term interest
rates.
A problem with persistent swings in short-term
interest rates is that they are likely to show up in
long-term rates. Investors can choose between buying a long-term security with a maturity equal to
their desired investment period, or a series of shortterm securities with maturities that add up to the
investment period. If the Fed were to offset an MI
control error gradually in an investment period,
short-term interest rates would rise gradually in that
same period. Investors anticipating the rise, would
then prefer to buy short-term securities in series,
re-investing each time at the expected higher shortterm rates. They would adopt this strategy unless
the yield on the long-term security also rose. On the
other hand, they would not need this inducement to
buy the long-term security if they expected the MI
control error to be offset quickly by a short, sharp
increase in short-term interest rates. In this way,
gradual re-entry to the MI paths means more persistent movements in short-term interest rates, which
in tum means that longer-term interest rates are
affected to a greater degree by monetary control
actions. These long-term interest rates are of potentially great importance because they affect business
investment and housing.
Finally, deviations of Ml from target can also
induce volatility in long-term rates if the deviations
are perceived by the public to be persistent enough
to affect inflation. A great deal of empirical evidence links higher inflation with faster growth rates
for money. Thus, when the public sees a persistent
increase in money growth, it may anticipate more
inflation. Long-term interest rates then rise because
they include a premium for inflation. This relationship between money growth and long-term rates is
especially likely to exist when the Treasury runs
large budget deficits and when Federal Reserve
credibility is low. Faster rates of re-entry to the MI
target can be a more emphatic way of showing that
Ml deviations will not persist long enough to affect
inflation.
16

would be forced to induce persistent swings in

In summary, a more aggressive approach to

short-tenn interest rates to eliminate large money

short-run monetary control most likely would re-

MI deviations

that

deviations. Finally, a more aggressive approach

have significant effects on GNP and prices. Such an

might contribute to the stability of long-tenn inter-

duce the incidence of persistent

est rates, which are especially important for the

approach would also reduce the risk that the Fed

performance of the economy.

FOOTNOTES

5. In February 1980-November 1980 M1 paths were
chosen such that on average, the FOMC sought to eliminate 29.2 percent of the previous month's error in each
current month. Peter A. Tinsley, Peter von zur Muehlen,
Warren Trepeta, and Gerhard Fries, "Money Market Impacts of Alternative Operating Procedures," New Monetary Control Procedures, Volume II, and Axilrod, February 1981, pp. B1-B4.

12. The following equations show how to calculate the
difference between the actual value taken on by nonborrowed reserves in a given control period and the initial
nonborrowed reserves path implicitly chosen by the FOMC.
(1) R = RU + RB
(2) R*= RU* + RB*
(3) RU* - RD* = + RB*
RB* + R* Fl*
where
R = total reserves
RU = nonborrowed reserves
RB = borrowed reserves
* indicates current path
"Bar" * indicates initial path chosen by FOMe.
By subtracting (2) from (i), we obtain
(4) R R* = RU - RU* + RB - RB*.
Next we solve (3) for RS', and substitute it into (4), to obtain
RU - RU*= (R R*)
(RB - RS*).
Thus, the difference between RU and the FOMC's initial
path for RU equals the total reserve deviation minus the
deviation between borrowed reserves and the FOMC's initial borrowing assumption.
An indication of these values can be obtained from data and
description in "Monetary Policy and Open Market Operations in 1980:' and "Monetary Policy and Open Market
Operations in 1981," Quarterly Review, Federal Reserve
Bank of New York, Summer 1981 and Summer 1982,
respectively.

6. See Axilrod (1981), p. A17, and Tinsley, von zur Muehlen, Trepeta and Fries (1981).

13. This occurred in the control periods ending 2/6/80,
4/23/80,2/4/81,4/1/81, and 12/23/81.

1. New Monetary Control Procedures, Federal Reserve
Staff Study-Volumes I and II, Board of Governors of the
Federal Reserve System, February 1981.
2. Stephen Axilrod, "Overview of Findings and Evaluation," New Monetary Control Procedures, Volume I, pp.
A6 and A23.
3. M1 is the sum of currency, traveler's checks, demand
deposits, and other checkable deposits. M2 is M1 plus
overnight RPs and eurodollars, non-institutional money
market funds, and saVings and small time deposits. In
1982, M2 was redefined to include retail RPs and to exclude
institutional money market funds. M3 is M2 plus large time
deposits, term RPs, and institutional money market funds.
4. See E. J. Stevens, "The New Procedure," Economic
Review, Federal Reserve Bank of Cleveland, Summer
1981, pp. 1-17, for a detailed discussion of the reserve
control procedures.

7. Fred Levin and Paul Meek, "Implementing the New
Procedures: The View from the Trading Desk," New Monetary Control Procedures, Volume II, pp. Ai-AS.

14. Axilrod (1981), p. A17.
15. See John P. Judd and John L. Scadding, "Liability
Management, Bank Loans, and Deposit 'Market' Disequilibrium," Economic Review, Federal Reserve Bank ofSan
Francisco, Summer, 1981 and "What Do Money Market
Models Tell Us About How to Implement Monetary policy?Reply," Journal of Money, Credit and Banking, November 1982, Part 2, pp.868-876. Also see Flichard G.
Anderson and Robert H. Rasche, "What Do Money Market
Models Tell Us About How to Conduct Monetary>Policy,"
Journal of Money, Credit and Banking, November 1982,
Part 2, pp. 796-828.
16. Changes in bank loans have a significant and persi~
tent impact on the monetary aggregatesbecause money IS
a buffer stock in the public's portfolio. Money acts much like
an inventory of goods in a warehous~. Such an inventory,
by its very nature, Wilt represent there§idual of a whOle set
of other decisions which, in the sho~frun cO(Jld keep the
"inventory" from its desired level. The viewof money demand as largely passive in the short-run, accommodating

8. See Warren L. Coats. "Lagged Reserve Accounting and
the Money Supply Process," "Journal of Money, Credit
and Banking, May 1976, VIII (1) pp. 167-180: Daniel E.
Laufenberg, "Contemporaneous Versus Lagged Reserve
Accounting," Journal of Money, Credit and Banking,
May 1976, VII(1), pp. 239-246.
9. See Murray E. Polakoff and William L. Silber, "Reluctance of Member Bank Borrowing: Additional Evidence:'
Journal of Finance, March 1967, pp. 88-92.
10. David Lindsey, et. al., "Monetary Control Experience
Under the New Operating Procedure," New Monetary
Control Procedures, Federal Reserve Staff Study-Volume2.
11. The funds rate range has had little operational significance, except occasionally to trigger Committee consultation when the funds rate violates the range.

itself to changes in the supply of money, reflects the transactions costs of closely managing money balances. Unanticipated inflows or outflows of funds cause inventories of
money balances in the short run to wander away from their
desired levels because it is too costly for some money
holders to monitor closely their accounts, and to make the
necessary purchases and sales of securities frequently
enough to bring money balances quickly back to their
desired levels.

folios, it may stay there for awhile. Moreover, actions of one
mon~y-holder to bring tlalancesinto line may throw other
holders out of balance. For this reason, the system as a
whole takes longer to adjust than does anyone household
or corporation.
Whether these effects are significant enough to make a
difference is a factual question. Recent empirical estimates
at this bank suggest that buffer stock effects are significant
-that the monetary aggregates can depart significantly
from levels desired by the public for up to six months at a
time; that is, an increase in bank loans causes the level of
money to depart from the public's underlying demand for
about six months.

This view does not dispute the importance of the emergence in the 1970's of sophisticated cash management
techniques and new instruments like repurchase agreements.. These developments mean that trans<;ictions costs
are now so low for sOme money holders, especially large
COrporations, thatthey hold only money bal<;inces th<;itare
consistent with their underlying demands. However, smaller and less sophisticated corporations and households
could easily hold more or less transactions balances than
they desire for an extended period of time. Most households and small corporations have relatively low money
balances on average, and actions to adjustthose balances
to desired levels may be costly relative to the benefits of
holding exactly the desired amount of money. If money,
therefore, finds its way into these "loosely" managed port-

17. The commercial paper. rate affects bank loans with a
positive sign. This rate also rises with the funds rate. This
means that theory cannot tell whether bank loans vary
positively or negatively with thEl funds rate.. However, .the
empirical results in the San Francisco model show an inverse relationship.
18. See Judd and Scadding, 1982 for empirical estimates
of the key equations used in the simulations. Other equations in the model can be obtained from the authors.

John P. Judd and John L. Scadding*

Alternative theories of the public's demand to
hold money are among the most widely tested theories in macroeconomics because the demand for
money occupies a central role in monetary policy.
The Federal Reserve conducts monetary policy by
attempting to achieve target growth rates for several
measures of money, with a large amount of attention traditionally focused on Ml, which represents
the public's holdings of currency plus checkable
deposits. If the Fed wants to lower inflation, for
example, it reduces the growth rate of Ml. But it
can do so only by inducing the public to want to hold
fewer M I balances. The conventional explanation
of how this happens, in the short-run, is that the Fed
raises interest rates on financial instruments that are
substitutes for M 1. Since altemative investments
now have a higher yield, the public chooses to hold
more of them and less money. This process affects
prices and output of goods and services because the
public's demand for these goods and services varies
negatively with interest rates. That is, increases in
these rates represent higher borrowing costs to
finance spending. By raising these borrowing costs,
efforts to slow Ml growth tend to lower output and
the growth of prices.
Both theory and evidence point to interest rates
(which measure the opportunity cost of holding
money), and either income or wealth as the major
determinants of the demand for money. The quantity of real money balances determined by these
variables defines the long-run equilibrium, or "desired," quantity of money demanded. It is generally

recognized, however, that in the short run the quantity of money actually held by the public can differ
from this long-run, or desired level. The reason for
this is that it is too costly to rearrange portfolios
constantly to keep desired and actual real money
balances the same at every point in time. Any discussion of money demand in the short run must,
therefore, specify the relationship between actual
money balances and the desired level. This is typically done by specifying a dynamic adjustment process by which actual money balances and the desired level are made equal.
The conventional assumption is that this process
of dynamic adjustment consists of the public adjusting the quantity of money it holds gradually over
time, until it is equal to the long-run demand for it.
This version of dynamic adjustment has become
almost universally accepted, despite the lack of
much research comparing it to alternative formulations. As we shall see, the conventional formulation
is a reasonable description of dynamic adjustment
when the supply of money passively accommodates
itself to changes in the demand for money. It seems
less well suited to situations in which the supply of
money can change independently of money demand
-in other words, to a world in which there can be
exogenous changes in the supply of money.
This line of criticism is not new, but it has been
largely ignored until recently. It began to receive
renewed attention when evidence emerged after
1973 that the conventional equation was going
badly off track in predicting money. I The large
cumulative overpredictions of Ml from 1974
through mid-1976 were explained as a so-called
"shift" in the demand for money associated with
rapid innovation in the financial markets that al-

*Research Officers, Federal Reserve Bank of
San Francisco. David Murray provided research
assistance.
19

an incorrect specification of short-run dynamics
"""" "n",] aflect estmlat(~S of the elasticities of
the determinants of long-run money demand, estimates that are important for predicting the impact of
money on output and prices. This consideration is
Particularly important in view of the prolonged
shifts in conventional money demand equations
since 1973, and the problems these shifts cause for
monetary policy.
Second, the form taken by short-run dynamics
has an important implication for the cost of close
short-run monetary control. As shown below, the
conventional specification implies that a small
exogenous change in money by the Federal Reserve
requires a large change in interest rates. Since the
Fed historically has considered interest rate volatility an important cost of short-run monetary control,
reliance on the conventional specification tends to
discourage precise short-run control. The alternative specifications of money demand dynamics,
which are designed to be more consistent with an
exogenous money supply, imply that the increase in
interest rate volatility resulting from efforts to control money more closely in the short run would be
smaller than typically thought.
The empirical results in this paper do not support
the conventional specification of short-run dynamics, in which observed money accommodates itself
gradually to changes in money demand. Uniformly
superior results were obtained from equations in
which money demand adjusts (through changes in
the price level) in response to independent changes
in the supply of money. Moreover, the latter equations showed significantly less instability during
1974-76 than the conventional dynamic specification. Specifically, the dynamic forecast error of the
best alternative equation was over 65 percent lower
than that of the conventional equation by the end of
this period.

lowed the public to economize on its holdings of
money balances.
This episode of financial innovation also coincided with the period in which the Federal Reserve
paid increasing attention to targeting the monetary
aggregates; i.e., to a strategy that was consistent
with providing a greater element of exogeneity in
the money supply. As a result, several alternative
dynamic formulations of short-run money demand
were proposed and tested-formulations which it
was argued were more consistent with a world in
which changes in the supply of money were an
important independent source of changes in the
observed quantity of money held by the public.
Unfortunately, it is practically impossible to
compare the performance of the different formulations in the existing literature because they were not
designed to explain the same variable 2. Some used
money as the dependent variable in their regressions, some used prices and others used interest
rates. Another reason making comparisons difficult
is that the different regressions were not estimated
over the same sample period. The purpose of this
paper is to find the best specification of short-run
money demand dynamics. Our method is to survey
the different past formulations and to provide estimates of them that are comparable. To this end we
show how the ostensibly different formulations are
actually specific cases of a general formulation for
predicting the level of real money balances. We use
this result to investigate how successful each is in
"explaining" the same variable-the level of real
money balances-over the same sample period,
1959/QI to 1974/Q2. We also investigate how successful the variants are in predicting the post1974/Q2 period, the period in which the conventional specification went seriously off track.
Finding the correct specification of short-run dynamics is an important task for two reasons. First,

I. The Conventional Specification
term of equation (2». The second is the current
period "shock" caused by changes in money demand originating in exogenous changes in interest
and income (the latter term of (2».
This interpretation is consistent with the standard
description of individual money demand in the presence of portfolio adjustment costs. Individuals take
income and interest rates as exogenous determinants of their demand for money, but because portfolio adjustment is costly, changes in these variables do not induce immediate adjustment to the
new desired level of money.

Most quarterly money demand specifications
allow for temporary differences between the observed stock of real (price deflated) money balances
in the short run, and the public's desired level of
such balances in the long run. Typically, a partial
adjustment model is used, in which the market for
money is assumed to adjust over time to restore
long-run equilibrium after it is disturbed by shocks.
This general specification raises the need to identify
the specific exogenous and endogenous variables in
the market for money. The variables causing shocks
define the exogenous variables, while the variables
which adjust to these shocks constitute the endogenous variables.
The traditional specification, as derived by
Gregory Chow, implicitly assumes that the money
supply is endogenous, adjusting to exogenous
changes in income and interest rates operating
through the demand for money. 3 This specification
assumes that the quantity of money changes in the
current quarter by some fraction of the difference
between this quarter's long-run demand and last
quarter's actual level. Money will continue to adjust
over time until the actual level equals the long-run
demand. This specification is shown in equation
(I ),
.lm,

A[m~

(i,y) - m H

Conventional Specification Problems
The Chow specification (or a close variant) has
become the almost universally accepted version of
the short-run demand function for money. In large
part, its popularity is due to an influential article by
Stephen Goldfeld, written in 1973, that demonstrated its remarkable stability over most of the
postwar period up to then. 4 This popularity has not
gone unchallenged, however, as a few authors have
argued that this specification was not necessarily a
suitable specification of the dynamics of the market
for money, whatever its merits might be as a description of individual behavior. 5 In particular,
these authors have argued that the Chow specification implies some rather peculiar dynamics of
money market adjustment when the supply curve of
money shifts (say, because of a change in monetary
policy). Thus, the unanswered question is whether
this specification is appropriate for situations in
which shocks occur in the quantity of money, rather
than in the arguments of money demand. Presumably it is this last specification that is relevant when
there are exogenous changes in the supply of
money.6
There are two potential defenses of the conventional dynamic specification. The first is that
equation (I) is a structural equation that is agnostic
about which variable is endogenous. Thus, if the
money supply were exogenous and money demand
endogenous, equation (1) simply could be rearranged to solve for whichever argument of money
demand takes the burden of adjustment. In most
large-scale macroeconomic models, for example,

(1)

where Ll denotes a change in a variable, m is real
(price-deflated) money balances, m d is desired or
equilibrium money balances, shown as a function of
its arguments-interest rates (i) and real income
(y)-and A is a parameter that measures the speed
with which real balances adjust to the desired level.
The conventional specification can be re-arranged slightly to yield an alternative interpretation,
shown in equation (2),
Llm,

A(m~_1

- mH

)

ALlm~

(Lli,Lly)

(2)

where Llm~ denotes the change in money demand,
here shown as a function of changes in interest rates
(i) and real income (y). Hence the Chow specification implicitly views the quantity of real money
balances as adjusting to two factors. The first is a
fraction (A) of the difference between desired and
actual money balances from last period (the first

the money demand function is typically used to
solve for the shorHenn rate of interest, which is
viewed as the endogenous variable that adjusts to
clear the market for money in the short-run whenever the money supply is taken as exogenous.
The problem with this defense is that the conventional specification assumes that it takes a large
change in interest rates to induce a small change in
money in the short-run. This result follows from the
partial adjustment of money to exogenous changes
in interest rates. When the equation is turned around
so that it predicts interest rates as a function of
exogenous money, it suggests that interest rates
have to overshoot their long-run levels in the shortrun in order to induce the public to accept a change
in the stock of money supplied by the Fed. 7
This result seems inconsistent with the rationale
for partial adjustment in the short run-namely,
that the costs of adjusting portfolios make it suboptimal to adjust fully. By this reasoning, when an
individual experiences an unexpected cash receipt,
he presumably does not attempt immediately to
return his cash holdings to their desired long-run
value. Instead, the costs of adjusting his portfolio
cause him to dispose of the excess cash gradually
over time. x
The same will be true in the aggregate. When
there is an exogenous increase in the supply of
money, the pressure on interest rates to change will
be relatively little in the short run as the public will
tend to hold on to the increase initially. Hence
adjustment costs do not point to the overshoot pattern of interest rates implied by the conventional
specification. Moreover, the actual behavior of interest rates does not appear to conform to the overshoot pattern either. Simulations of the Treasury bill
rate using the money demand function in the
Board's FMP (Federal Reserve-MIT-University of
Pennsylvania) model showed "spikes" that were
not present in the actual data. 9 Since the FMP
money demand function has a conventional partial
adjustment specification, these spikes can be presumed to be the product of the overshoot built into
that specification.
The second defense of the conventional partial
adjustment model argues that the stock of money
was effectively detennined by demand under the
Federal Reserve's pre-October 6, 1979 procedure of

using the federal funds rate to try to control money.
This procedure consisted of pegging short-term interest rates, or at least moving them only very gradually, in response to deviations of money from
target. 10 In order to do that, it is argued, the Federal
Reserve had to provide whatever quantity of money
the public demanded. Hence the quantity of money
was detennined by the demand for money. In such a
world, the conventional specification of money
market adjustment-which has the quantity of
money adjusting to changes in the demand for itseems appropriate.
The major theoretical assault on this position is
found in the work of Brunner and Meltzer who
argue that it fails to distinguish between money and
credit. II In a world in which there are distinct
markets for bonds (credit), as well as for money and
commodities, it is possible to have exogenous
changes in .the supply of money even when the
monetary authority pegs interest rates. Suppose, for
example, that finns decide to spend more on plant
and equipment. They may finance this desired
increase in spending by floating new bonds. Hence
the increased demand for commodities (investment
goods) is matched by an increased supply of bonds
(demand for credit). The increased demand for
credit puts pressure on interest rates to rise. To
prevent this, the monetary authority increases bank
reserves, allowing the banking system to purchase
the new bonds through the creation of new deposits
(i.e., an increase in money supply). The finns'
demand for money has not increased except transiently: they have borrowed the money to spend, not
to hold.
At this point, there is an increase in the supply of
money that is not matched by any increase in the
demand for money. The change in money supply,
therefore, is exogenous in the sense used in this
paper. The finns borrowing the money will spend it.
The recipients of that expenditure will find themselves with excess money balances, which they in
tum will get rid of by spending more. Output and
prices will expand in the process until the rise in the
aggregate demand for money matches the increase
in money supply. Thus, even with interest rate pegging by the monetary authorities, it is possible for
changes in the supply of money to cause changes in
the demand for money, rather than the other way
around.

tirely endogenous. The purpose of the alternative
specifications described in the next section of this
paper is to provide a partial adjustment mechanism
consistent with money supply exogeneity.

The conventional specification of money demand
is inadequate for describing this situation because
its dynamics model a case in which money is en-

II. Alternative Specifications
The alternative formulations of short-run money
demand are summarized in Table I. This table lists,
for each specification, the variable that adjusts to
changes in the exogenous variables, as well as the
exogenous, or shock, variables themselves-i.e.,
the variables whose changes make observedmoney
deviate from the public's long-run demand for
money. The various specifications can be grouped
into two major categories. The first category consists of variants of the conventional specification,

which view the quantity of money as adjusting with
a lag to changes in the demand for money. In contrast, the members of the second group-the exogenous money specifications-view the demand for
money as adjusting with a lag to changes in the
supply of money.

Supply-adjusting equations
The conventional versions begin with the Chow
specification (I.A. I), whose properties we explored extensively in the preceding section. Its use

of money divided by prices as the dependent variable implies that the quantity of money adjusts fully
within a quarter to changes in the price level. But
the equation also assumes that there is only partial
adjustment to changes in interest rates and real
income. This first feature seems implausible, and
has led others to propose I.A.2, which makes the
quantity of nominal money adjust with a lag to
changes in interest rates, income and prices. 12 A
third variant, proposed by William H. White,
specifies that money adjusts without any lag to
changes in money demand that are caused by
changes in interest rates (i.e., interest rates are not a
shock variable), but retains the lag in response to
changes in real income and prices (I. A. 3).
Table I lists the Judd-Scadding formulation of
money demand as the last of the conventional specifications (I.A.4). Its inclusion in this category is
somewhat problematic. Like the conventional specifications, it views the quantity of money as adjusting with a lag to changes in money demand. In this
regard, it looks very similar to the Goldfeld formulation (1.A.2). However, the Judd-Scadding equation also recognizes that changes in the observed
quantity of money can result from exogenous
changes in the supply of money.
The equation is part of a monthly money market
model, which incorporates the Brunner-Meltzer
point that changes in the demand for bank loans
cause exogenous shifts in the supply function of
money. As was outlined in Section I, costs of adjusting portfolios cause the public to hold these
exogenous changes in money in the short run, rather
than to try to get rid of them. The Judd-Scadding
specification recognizes this point by adding to the
public's observed holdings of money balances the
exogenous changes in money caused by the growth
of bank loans. Thus, observed money adjusts with a
lag both to changes in demand factors (income,
interest rates and prices) and a supply factor
(changes in bank loans). The authors have previously found that these bank loan effects are statistically and economically significant in monthly data
from 1976 through mid-1982. 13

money adjusts with a lag to changes in the quantity
of money. With one exception, all of these variants
have one of the arguments of money demandeither the interest rate, income, or prices-as the
adjusting variable. The adjustment of money demand then is implicitly specified in terms of the
adjustment of this variable. For example, in the
Artis-Lewis formulation (1. B.2), interest rates are
assumed to adjust to clear the market for money.
Thus the specification is in terms of the partial
adjustment of interest rates to, among other things,
the quantity of money. However, since money demand is a function of the interest rate, this specification can be rewritten in terms of the adjustment of
money demand to the quantity of money.
In the same way, the Coats, Jonson and CarrDarby formulations assume that prices adjust to
clear the market for money. Again implicit in these
formulations is the idea that the demand for money
is adjusting since the (nominal) demand for money
depends, among other things, on prices. The one
exception to having only one variable clear the
market is Starleaf's formulation, in which the adjustment is specified explicitly in terms of money
demand, with no assumption made whether it is
interest rates, income or some combination of the
two that adjusts to clear the market for money.
The three price-adjusting variants differ from
each other in whether or not they distinguish between actual and expected inflation, and between
actual and anticipated money growth. The Jonson
formulation is the simplest, with actual prices adjusting with a lag to changes in actual money. The
Coats formulation, on the other hand, distinguishes
between actual and expected prices. Prices adjust
fully on a contemporaneous basis to expected
changes in prices (LlP)e. However, growth in money
that is inconsistent with the expected change in
prices creates a deviation between money and the
long-run demand for it that is ultimately removed by
the adjustment of actual inflation to the rate of
growth of money. Thus in the Coats formulation
prices adjust with a lag not to the actual change in
money but only to the excess of money growth over
the expected rate of inflation.
Similarly, the Carr-Darby formulation assumes
that prices adjust completely without any lag to
anticipated changes in money. Partial adjustment

Demand-adjusting equations
The second class of short-run money functionsvariants I.B.I through I.B.5-consists of partial
adjustment specifications in which the demand for

justified by arguing that the costs of adjusting portfolios to anticipated changes are much smaller because they can be planned for in advance.

occurs only with respect to unanticipated changes in
money. This distinction is consistent with a rational
expectations viewpoint, and presumably can be

III. The Canonical Form
Since Ais the speed with which actual money adjusts
to the demand for it, (1- A) oflast period's deviation
remains after taking into account yesterday 's adjustment. The second contribution consists of the exogenous disturbances to money demand in the current
period, caused by changes in its arguments-.-interest rates and income. Again, since a contemporaneous adjustment of Ais made to these disturbances,
the residual deviation that remains is (1- A) of these
disturbances.
Letting mt = m t m?be money disequilibrium,
(3) can be written as,

Although the different formulations vary in their
assumptions about which variable adjusts to clear
the market for money, they can all be expressed
according to a general rule: i.e., they have the same
canonical form. All of the formulations are descriptions of how long-run equilibrium in the market for
money is disturbed by changes in certain variables
in the short run, and how long-run equilibrium is
ultimately restored. To illustrate, consider the
Chow specification (equation l.A.I, Table 1). It
has the quantity of real money balances adjusting
with a lag to changes in the (long-run) demand for
money. This formulation can be rewritten as
m t - m?

(4)

= (I-A)(mt-I - m?-I)

- (1- A)Limf(Lii,Liy).

which describes the dynamic process by which longrun equilbrium is restored, and identifies the source
of disequilibrium, in this case, changes in money
demand.
All the other formulations shown in Table 1 can
be put in the same canonical form. The Jonson
formulation, for example, in which prices rather

(3)

This equation shows that the extent to which money
deviates today from the long-run demand for it is a
function of two things. First is the amount of last
period's deviation that is carried over to today.

All of the equations were estimated with real
money balances as the dependent variable. Longrun demand, md , was expressed in terms of its basic
arguments-interest rates and income-and these
arguments were used as explanatory variables. Two
interest rates were used: a short-term market rate, in
this case the four- to six-month commercial paper
rate~ and the rate on passbook savings accounts.
Real GNP was used as the income variable in all
equations except the Carr-Datby specification,
which uses permanent income. The expected inflation rate series used to estimate the Coats equation
was an updated series on the permanent or underlying inflation rate reported by Scadding (1979). The
unanticipated money series used in the Carr-Darby
equation consisted of the regression residuals from
fitting a time series model to changes in money. 14
The definition of money used throughout was MI,
and the estimation period is 1959/Q 1-1974/Q 2.
The Cochrane-Orcutt procedure was used for the
equations that could be estimated using ordinary
least squares. Some of the equations, however, had

than money do the adjusting, can be written as

(5)
Thus, the Jonson fonnulation adds changes in nominal money to the list of exogenous variables that
disturb long-run equilibrium. In the conventional
fonnulation, on the other hand, it does not appear
because it is one of the variables assumed to adjust
to remove disequilibrium. Table 2 lists the canonical version for all of the variants described in
Table I.

Estimation
This canonical fonn is also used to organize the
estimation results shown in Table 3, where the estimated adjustment parameter (A) is reported along
with the impact elasticities for the exogenous disturbance variables. These impact elasticities are
(1- A) times the respective long-run elasticities. For
changes in money and prices, the long-run elasticities are constrained to be unity. The othersincome and interest rate elasticities-are left free to
be estimated by the data.

to be estimated by nonlinear least squares (adjusted
for first-order serial correlation) because of nonlinear constraints on the parameters. Estimates did not
converge when an attempt was made to allow for
serial correlation in the White variant (3.A.3). For
this equation, the estimates without any adjustment
for serial correlation are reported.
Estimation results
The estimation results are presented in Table 3. A
comparison of the standard errors of the estimates of
the equations provides a clear ordering of success.
Two of the worst performances are turned in by
equations 3. B. I and 3. B.2, in which income and/or
interest rates adjust to restore equilibrium. These
equations produce standard errors of .0062 and
.0056-over double the standard errors of the best
in the other groups. These errors translate into annualized errors of 2.5 and 2.2 percentage points, respectively. Furthermore, equation 3.B.2 yields a
negative estimate of the adjustment parameter that
is greater than I, implying that the dynamic process
is unstable.
The conventional specifications, equations
3.A.I-3.AA, have significantly smaller standard
errors than those of the preceding group, with the
exception of the White formulation. The JuddScadding and Goldfeld equations 3.A.4 and 3.A.2
show annualized standard errors of 1.6 percentage
points, while Chow (3.A.1) shows 1.8 percentage
points. All three equations yield quite similar
parameter estimates. For example, they indicate
that 20 to 25 percent of last quarter's disequilibrium
is restored each quarter. In addition, they all indicate that the interest elasticity of money demand is
relatively small, ranging from 0.19 to 0.32 in the
long run. The White formulation, on the other hand,

gives a mediocre performance. Its standard error is
the worst of any equation by a wide margin, and it
shows implausibly high income and interest rate
elasticities that also have the wrong sign.
The best performance as a class is turned in by the
price adjusting equations. The Coats, Carr-Darby
and Jonson specifications have standard errors that
are 35 to 45 percent lower than the conventional
group. A further advantage of these specifications is
that no significant autocorrelation appears in the
residuals, whereas the conventional specifications
all have statistically significant autocorrelation.
Since evidence of autocorrelated residuals may
indicate misspecification, and since it is argued by
some that the dynamics of the conventional form
are misspecified, this is a potentially damaging
result for the conventional specification.
The major problem with both the Jonson and
Carr-Darby equations is that real income enters with
statistically insignificant coefficients, although the
sign on this variable conforms to theory. In the
Coats equation, the implied long-run income elasticity is significant, and its value of 0.51 is comparable to the estimates in the conventional models.
These results suggest that the Coats specification, in
which unanticipated prices adjust to changes in
money, interest and income, yields the best performance of any equation tested over the sample
period.
Only 7 to 8 percent of disequilibrium is eliminated each quarter in the Jonson and Coats equations, while the Carr-Darby equation has even
slower adjustment of 3 percent. This compares to
adjustment of about 20 percent in the Goldfeld
equation. However, this difference can be explained by which variable does the adjusting. In the

error of 22 percentage points, with a mean error
(ME) of -19 percentage points (actual minus predicted). The standard Goldfeld equation has a
RMSE of 38 percentage points and a ME of - 35
percentage points.
The large negative mean errors of all the formulations reflect the well-known shift in the demand for
money in 1975-76. Clearly, all equations tested
show such a shift. However, the shift evidenced by
the price adjusting formulations is smaller than for
the conventional ones. In I977/Q I, the quarter in
which the large cumulative shifts in all four
equations end, the" Coats, Carr~Darby and Jonson
equations are off track by from 3.6 to 6.0 percent
while the conventional equations are off by about 10
percent. Finally, the simulation of the Coats formulation uniformly outperforms all other equations.

Goldfeld specification, money adjusts (relatively
quickly) to prices and other variables, whereas in
the Jonson, Coats and Carr-Darby equations, prices
adjust relatively slowly to money and other variables.
Simulation Results
Table 4 contains the results of dynamic simulations over 1974/Q3-1980/Q3 of the equations in
Table 3 that yielded reasonable estimation results.
The White, Artis-Lewis, and Starleaf equations
were excluded because they did not meet this criterion.
The simulation results suggest an ordering of
performance similar to that of the estimation results:
the price-adjusting models outperform the conventional specifications. Specifically, the root-meansquared-error (RMSE) over 1974/Q3-1980/Q3
from Coats' equation translates into an annualized

IV. Conclusions
The empirical results in this paper suggest several
conclusions. First, money demand equations in
which prices adjust to exogenous changes in
money, interest and income outperform equations
in which money is the adjusting variable. Equations
in which money is the adjusting variable, in turn,
outperform equations where interest rates and
income are the adjusting variables. Second, the
Goldfeld specification, which has been used almost
exclusively in the literature, in which money is the
adjusting variable, was not found to be the equation
most consistent with the quarterly data during the
period 1959-80. The uniformly superior specification was that of Coats, in which unanticipated
prices adjust to exogenous changes in money,
interest rates and income. Third, no specification
tested was free of the cumulative shift in the demand
for money in 1974/Q3-1976/Q4. However,
equations in which prices are specified as the adjusting variable significantly reduced the size of overpredictions of Ml produced by dynamic simulations. The Coats specification was especially successful in this regard, producing a simulation error
which by 1977/Q I was 66 percent smaller than the
error from the Goldfeld equation.
Two more points are of interest. The first concerns interest rate volatility and monetary policy.

Our results indicate that it is inappropriate to use a
conventional Goldfeld equation, which assumes a
dynamic process fitting a world with an endogenous
money supply, to draw inferences about the interest
rate volatility that would result from close short-run
monetary control. Put somewhat differently, it is
inappropriate to solve a Goldfeld equation for the
rate of interest, and then forecast the interest rate on
the basis of changes in an exogenous money supply.
This procedure, which is commonly followed in
large econometric models, often suggests that a
small change in money growth rates would produce
wild interest rate swings in the short-run. This conclusion is not reliable because it is based on a
misspecified process of dynamic adjustment in the
money demand function. A specification of that
process depends critically on which variables are
made exogenous and which endogenous. Thus, if
the assignment of exogenous and endogenous variables were changed (say, for a hypothetical policy
simulation), the specification of dynamic adjustment would also need to be changed for the results
of the simulation to be reliable.
Second, the finding that the best performance
was turned in by money demand equations with
prices adjusting to exogenous changes in money
and interest rates seems consistent with the point

can be independent of money demand, applies pressure on interest rates. In order to peg the interest
rates, the Fed would increase bank reserves and the
money supply. Thus the supply of money and the
rate of interest can both be exogenous to the demand
for money.

made by Brunner and Meltzer discussed earlier.
Their point is that changes in money supply can
occur independently of changes in money demand
even if the Fed pegs interest rates. This can occur,
for example, when the demand for credit rises as
corporations finance spending on new plant and
equipment. The increased credit demand, which

FOOTNOTES
1. See Judd and Scadding (1982a).

7. See Tucker (1966).

2. Laidler (1980) has compared the empirical properties of
some, but not all of these formulations. Also see Laidler
(1980) and White (1981) for a discussion of theoretical
issues raised by alternative dynamic specifications.

8. This view seems entirely consistent with inventorytheoretic money demand functions of Baumol (1952) and
Miller and Orr (1966 and 1968).

3. See Chow (1966).

10. See Judd and Scadding (1979).

9. See Modigliani, Rasche and Cooper (1972).

4. See Goldfeld (1973).

11. See Brunner and Meltzer (1976).

5. See, for example, Tucker (1966), Starleaf (1970) and
Darby (1972).

12. See Goldfeld (1976) and White (1978).
13. See Judd and Scadding (1981 and 1982b).

6. It is possible to give equation (2) an interpretation in
which changes in (nominal) money are exogenous. This is
done by noting that the left-hand variable is the change in
real balances, and that this change is simply the difference
between nominal money growth and the rate of inflation.
Hence it can be argued that it is the rate of inflation that is
adjusting to money market disequilibrium, caused, among
other things, by changes in money growth. Rearranging (2)
to reflect this interpretation yields

14. The following equation was used
IllnM\ =2.20+ .481lInM1/-1 + .111lInM1 t _ 2 - .08U t _ 1
(3.41) (4.37)
(0.96)
(0.71)
FF=.21

DW=1.92

SEE=2.88

.iPt = .iMt A(m1_1-m/-1) - Mm1(lli,IlY),
in which the growth in money appears as one of the righthand exogenous variables. The difficulty with this interpretation, as several writers have noted, is that it implies full
contemporaneous adjustment of inflation to changes in
money growth.

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Full text of Economic Review (Federal Reserve Bank of San Francisco) : Fall 1982 : Money: Demand and Control

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