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BASE DRIFT AND THE LONGER RUN GROWTH
OF. M1: EXPERIENCE FROM A DECADE OF
MONETARY TARGETING
Alfred Broaddus and Marvin Goodfriend*

I.
INTRODUCTION: THE NATURE OF BASE DRIFT

This article discusses a technical aspect of the
Federal Reserve’s monetary targeting procedure that
has come to be known as “base drift.” The Fed has
been announcing target ranges for the growth of M1
and other monetary aggregates since 1975.1 These
ranges have been expressed in terms of rates of
growth from a base quarter to the quarter four
quarters later. 2 The term “base drift”, refers to the
Fed’s practice of using the actual dollar level of an
*The authors are both Vice President and Economist,
Federal Reserve Bank of Richmond. Marvin Goodfriend
is temporarily on leave from the Bank as a Senior Staff
Economist with the President’s Council of Economic
Advisers. The authors wish to thank Sandra D. Baker,
Associate Economist, for valuable research assistance.
1

M1 is the narrowly defined money supply. It currently
includes (1) currency outside the Treasury, Federal Reserve Banks, and the vaults of commercial banks; (2)
travelers checks of nonbank issuers; (3) demand deposits
at all commercial banks other than those due to domestic
banks, the U. S. government, and foreign banks and
official institutions less cash items in the process of
collection and Federal Reserve float; and (4) other
checkable deposits (OCD) consisting of negotiable order
of withdrawal (NOW) and automatic transfer service
(ATS) accounts at depository institutions, credit union
share draft accounts, and demand deposits at thrift institutions. The currency and demand deposit components
exclude the estimated amount of vault cash and demand
deposits respectively held. by thrift institutions to service
their OCD liabilities.
2

The Fed began announcing target ranges following the
passage of House Concurrent Resolution 133 in March
1975. The first targets for each aggregate were expressed
in terms of growth rates from March 1975 to March 1976.
Subsequent targets were expressed as growth rates from
a particular quarter to the quarter four quarters later.
From 1975 through the end of 1978, a new four-quarter
target was established in each successive quarter Since
then, under the terms of the Humphrey-Hawkins Act
of 1978, targets have generally been set only once a
year. These targets extend from the fourth quarter of
the base year to the fourth quarter of the current year.
The one exception to this procedure since 1978 occurred
in mid-1983 when a new target was set for the second
half of the year. With this exception only the nonoverlapping fourth quarter-to-fourth quarter targets are considered in this article.

aggregate in the base quarter as the base level for the
target range, rather than the midpoint of the targeted
range set in the preceding targeting period.
Figure 1 provides a hypothetical illustration. The
figure assumes that the 6 percent midline of the 4 to
8 percent target range set for the growth rate of M1
at the beginning, of year 1 implies an M1 level of
$500 billion in the fourth quarter of the year. The
actual growth of M1 in year 1, however, exceeds the
target range, so that the actual level in the fourth
quarter is $520 billion. In this situation, the base
level for the target range in year 2 is $520 billion, and
the amount of base drift is $20 billion.
A long-standing objective of Fed monetary policy
has been to reduce the longer run growth of M1 and
the other monetary aggregates over time to noninflationary rates in order to restore price stability. 3 T o
date, however, relatively little progress has been made
toward reducing the longer run growth of M1. Most
3

The importance of this objective has been emphasized
by all Federal Reserve Chairmen in recent years. For
example, Chairman Burns made the following statement
in testimony before the Banking and Currency Committee
of the, House of Representatives on July 30, 1974:
A return to price stability will require a national
commitment to fight inflation this year and in the
years to come. Monetary policy must play a key
role in this endeavor, and we, in the Federal Reserve,
recognize that fact. We are determined to reduce,
over time, the rate of monetary and credit expansion
to a pace consistent with price stability.
See Burns (1974), p. 258.
More recently, Chairman Volcker made the following
statement before the Senate Committee on Banking,
Housing, and Urban Affairs on February 25, 1981:
These technical considerations should not obscure the
basic thrust of our policy posture. Our intent is not
to accommodate inflationary forces; rather, we mean
to exert continuing, restraint on growth in money
and credit to squeeze out inflationary pressures. That
posture should be reflected in further deceleration in
the monetary aggregates in the years ahead and is
an essential ingredient in any effective policy to
restore price stability.
See Volcker (1981), p. 240.

FEDERAL RESERVE BANK OF RICHMOND

Figure 1

HYPOTHETICAL ILLUSTRATION OF BASE DRIFT

economists believe that the Fed should give greater
emphasis to M1 than the other monetary aggregates,
because M1 has had the most predictable relationship
with nominal GNP over the longer run, and it is
more amenable to Fed control than the other aggregates. Perhaps for these reasons, M1 is the monetary
aggregate that receives the greatest attention from the
general public. The trend growth rate of M1 was
6.7 percent over the nine-year period from the beginning of 1976, which was the first full year for which
monetary targets were announced, until the end of
the fourth quarter of 1984, compared to 5.6 percent
in the preceding ten years. 4,5 Further, there has
been little change in the trend rate within the period.6
4

These rates were calculated on a least squares basis.
The calculation for the 1976-1984 period was made using
the effective M1 data in Table I.

5

Making similar comparisons for M2 and M3 would be
more problematic than in the case of M1 because of the
sharper break in the data when the definitions of the
aggregates were changed at the beginning of 1980.

4

ECONOMIC

REVIEW,

In terms of the mechanics of the Fed’s targeting
procedure, one can allocate the discrepancy between
the objective and actual M1 growth to two factors
that at least in principle are separable: (1) insufficient reductions in the targeted rates of growth and
(2) net upward base drift over the period. The next
two sections of this article develop an estimate of the
contribution of base drift to the discrepancy in the
case of M1. Section II explains the construction of
an “effective” M1 time series and a corresponding
set of target ranges for effective M1 that are used in
developing the estimate, and Section III reports the
estimate. The remainder of the article is organized
as follows. Section IV explains why base drift
matters. Section V assesses the potential benefit of
base drift in the case of permanent monetary distur6

The 6.7 percent trend rate includes the period of exceptionally rapid growth in M1 in 1982 and 1983, which in
hindsight appears to have been appropriate in that as of
early 1985, inflation has remained low. See the discussion
in Sections V and VII of this article.
NOVEMBER/DECEMBER

1984

bances. An alternative targeting procedure that would
eliminate base drift is outlined in Section VI. The
effective M1 data constructed in Section II provide
evidence on the role of monetary targeting in the
recent reduction of inflation. This evidence is discussed in a postscript in Section VII. Section VIII
briefly summarizes the main points made in the
a r t i c l e .7
II.
CONSTRUCTING A TIME SERIES FOR
EFFECTIVE M1 AND CORRESPONDING
TARGET RANGES FOR EFFECTIVE M1

In order to measure base drift accurately over time,
it is necessary to construct data series for both M1
itself and the M1 target ranges that are conceptually
consistent both over time and with one another.
Doing so is complicated by two events that occurred
during the period. First, M1 was redefined at the
beginning of 1980. Second, as explained below, the
reported growth of M1 was distorted by the legalization and rapid growth of negotiable order, of withdrawal (NOW) accounts and other interest-bearing
transactions accounts in several years during the
period. This section describes. how each of these
problems is handled. The mechanics involved are
somewhat tedious but are essential to a full understanding of the results presented below.
Tables I and II contain the constructed data. Table
I shows “effective” M1, i.e., M1 adjusted for the
shifting of funds between various categories of deposit accounts occasioned by deregulation. These
adjustments were made on an ex post basis using the
latest estimates of the actual shifting that occurred.
The details of the adjustments are described below.
Table II shows the target ranges for the growth of
effective M1. In the majority of the years covered,
these ranges are the same as the ranges announced by
the Fed. In one year where the growth rate of effective M1 diverged from the growth rate of reported
M1 due to deregulation, however, it is necessary to
infer the target for the growth of effective M1 from
the publicly announced targets for the growth of
reported M1. The guiding principle is to develop a
series for the target ranges that indicates the growth
rate of effective M1 that the Fed sought for each
7

It should be noted that the potential problems with base
drift were recognized by several economists shortly after
the Fed began announcing targets.
See, in particular,
Poole (1976) and Kane (1975).

year, whether the rate was expressed or implied. The
nature of each adjustment is described below.8
Change in the Definition of M1
M1 as it was defined before 1980, which is referred
to as “old M1” in this article, included mainly ‘currency in the hands of the public and demand deposits
at commercial banks. In 1980, a “new M1” series was
defined that includes the major components of old
M1 and, in addition, what are now designated “other
checkable deposits” (OCD). OCDs include NOW
accounts and automatic transfer service (ATS) accounts at commercial banks and thrift institutions,
credit union share draft accounts, and demand deposits at mutual savings banks.9
Prior to 1980 the Fed established M1 targets in
terms of old M1. Since 1980, the M1 targets have
been set in terms of new M1. In measuring base drift
it is necessary to calculate the deviation of the particular measure of M1 that was actually targeted in a
given year from the midpoint of the target range for
that year. Therefore, the most straightforward way
to proceed is to calculate money growth and base
drift prior to 1980 using old M1 and subsequently to
make the calculation in terms of new M1. This is
what was done. Fortunately, the difference between
the respective dollar levels using the two definitions
is small in the quarter when the definition was
changed. 10 Specifically, new M1 exceeded old M1
8

It is important to note that while the adjustments made
in constructing the effective M1 series (Table I) were
made on an ex post basis, the adjustments to the target,
ranges (Table II) were made on an ex ante basis. That
is, estimates of the actual shifting of funds caused by
deregulation were used in constructing the effective M1
series. In contrast, the adjustments to the target ranges.
where they occur, reflect the deposit shifts that the Fed
anticipated would occur during a year as seen at the
beginning of the year.
9

See footnote 1 in this article for the precise current
definition of M1, which, in addition to the changes made
in 1980, incorporates some additional minor changes made
in 1981. It should be noted that the Fed published data
for two M1 series, known as M-1A and M-1B, in 1980
and 1981. The M-1A measure, which was close to the
pre-1980 M1, was dropped at the beginning of 1982, and
All references in this
M-1B was designated as. M1.
article to M1 in 1980 and 1981 are to what was then
designated M-1B.
10

This small difference in dollar levels results from the
netting out of two discrepancies. As noted above, M1 as
currently defined includes OCDs, while old M1 excludes
them, which tends to raise the level of M1 as currently
defined relative to the level under the old definition. In
addition however, old M1 included demand deposits of
foreign commercial banks and foreign official institutions,
which are excluded under the current definition. This
second discrepancy raises the level of old M1 relative to
the level under the current definition.

FEDERAL RESERVE BANK OF RICHMOND

5

Table I

EFFECTIVE M1
(Quarterly Average Data)
($ billions)
Quarter

M1

Quarter

1975:4

295.1

1980:1

394.3

1976:1

298.5

2

390.0

2

303.3

3

404.5

3

306.4

4

414.1

4

312.1

1981:1

413.2

1977:1

317.9

2

417.9

2

323.8

3

420.5

3

330.8

4

424.1

4

336.9

1982:1

435.4

1978:1

342.5

2

437.9

2

350.4

3

444.8

357.3

4

462.3

361.1

1983:1

477.5

3
4

M1

1979:1

364.4

2

491.8

2

371.8

3

503.8

380.8

4

510.0

1984:1

519.4

2

527.6

3

533.7

4

536.3

3
4

385.6/387.4

Notes for Table I
1. Data for 4Q75 through 4Q79 are based on the old definition
of M1 to maintain comparability with the target ranges. These
data were derived from the final data released by the Board
of Governors using the old definition. (The data through 1978
are contained in “Historical Money Stock Revisions,” February
1979. The data for 1979 are contained in the Board’s H.6
release dated January 10, 1980.) Subsequent data are based
on the new definition, which was referred to as M-1B in 1980
and 1981. These data were derived from published data as of
January 1985.
For 4Q79, the first figure is for the old
definition and the second figure is for the new definition.
The difference between the two figures is $0.9 billion.

by less than $2 billion or by roughly 0.5 percent on
an effective basis as described directly below in the
fourth quarter of 1979, just prior to the change in
definition. For this reason, simply switching from
the old M1 measure to the new measure in the first
quarter of 1980 introduces only a small error in the
cumulative base drift calculation.
Adjustments for Shifts into and out of NOW
Accounts and Similar Accounts Due to
Deregulation 11
As pointed out above, the reported growth of M1
was distorted by the ongoing deregulation of transactions accounts on several occasions during the
period covered by this analysis. Both the distortions
themselves and the manner in which the Fed dealt
with them differed from one year to the next. The
following paragraphs describe the situation on each
occasion and indicate the nature of the adjustments
made in each case in constructing the data in Tables
I and II.
1979. In late 1978 all commercial banks were
permitted to offer ATS accounts, which are interestbearing transactions accounts functionally equivalent
to NOW accounts. Funds switched from demand
deposits to ATS accounts presumably retained the
characteristics of transactions accounts. Therefore,
shifts from demand deposits, which were in old M1,
to ATS accounts, which were not, caused the reported growth of old M1 to understate the effective
growth of M1 in 1979. Consequently, an estimate
of the volume of funds shifted from demand deposits
to ATS accounts was added to old M1 in 1979 in
constructing the effective M1 series in Table I. This
adjustment raised the M1 growth rate in 1979 by
1¼ percentage points.
At the beginning of 1979, the Fed announced a
target range for reported M1 of 1½ to 4½ percent.
11

All of the adjustments described in this article are
based on estimates published by the Board of Governors
of the Federal Reserve System.

2. Data for 1Q79-4Q79 are adjusted to correct for the shift of
funds from demand deposits to ATS accounts following the
authorization of ATS accounts in late 1978.
ATS accounts
were not included in M1 under the old definition, and the
adjustment in 1979 added these funds back into M1. This
adjustment raised the growth rate of M1 from 4Q78 to 4Q79
by 1.25 percentage points. This adjustment and all adjustments
in subsequent notes to this table are based on estimates
published by the Board of Governors.

4. Data for 1981 are adjusted to correct for the shift of funds
from assets not included in the new definition of M1 into NOW
accounts as a result of the legalization of NOW accounts
nationwide.
This adjustment reduced the growth rate of M1
from 4QB0 to 4QB1 by 2.7 percentage points.

3. Data for the second half of 1980 are adjusted to correct for
shifts of funds from assets not included in the new definition
of M1 into ATS accounts in anticipation of the legalization of
NOW accounts nationwide scheduled for December 31, 1980.
This adjustment reduced the growth rate of M1 from 4Q79 to
4QB0 by 0.5 percentage point.

5. Shifts of funds associated with the legalization of NOW
accounts nationwide are believed to have been substantially
completed by the end of 1981. In order to maintain a continuous series, however, the cumulative downward adjustment
of $13.4 billion applied to the 4QB1 figure was applied to all
subsequent figures.

6

ECONOMIC

REVIEW,

NOVEMBER/DECEMBER

1984

At the time, the Fed estimated that shifts of funds
from demand deposits to ATS accounts would reduce old M1 growth by 3 percentage points over the
year. The 1½ to 4½ percent target range explicitly
allowed for this anticipated reduction in the reported
growth rate. 12 The implication is that the Fed was
willing to accept effective M1 growth in a range of
4½ to 7½ percent as shown in Table II.
1980. The Monetary Control Act of 1980, which
was signed into law in March of that year, authorized
NOW accounts nationwide effective December 31,
1980. Consequently, many banks in states where
NOW accounts were not yet permitted marketed
ATS accounts aggressively in the second half of 1980
to position themselves competitively for the anticipated legalization of NOWs the following year. In
1980, however, in contrast to 1979, the Fed set
targets in terms of new M1, which included ATS
accounts. For this reason, a different kind of adjustment for shifts into ATS accounts, was needed in
constructing the effective M1 series for 1980, Specifically, since ATS accounts are included in new M1,
the shifting of funds from demand deposits to ATS
accounts did not affect new M1 and therefore required no adjustment. Some funds, however, were
shifted into ATS accounts from savings accounts and
other instruments not included in new M1. These
shifts increased reported new M1. It was assumed
that these latter funds largely retained their nontransactions character after they were shifted into ATS
accounts and hence into new M1. This implies that
reported new M1 growth overstated the effective
growth of transactions balances in 1980. Therefore,
an estimate of the portion of the growth of ATS and
similar accounts due to transfers of funds from savings and other non-M1 instruments was subtracted
from reported new M1 in the second half of 1980 in
constructing effective M1 in Table I. This adjustment reduced the growth rate one-half of a percentage
point in 1980.
In announcing its targets for 1980, the Fed recognized, that if NOW accounts were legalized during
12

See “Monetary Policy Report to Congress” (March
1979), p. 196. It should be noted that the target range
for reported growth was raised from 1½ - 4½ to 3 - 6
percent in the middle of 1979. (See “Monetary Policy
Report to Congress” (March 1980), p. 187.) This increase
reflected new estimates which indicated that the growth
of ATS accounts would reduce the reported growth rate
by only 1½ percentage points, over the year rather than
by the 3 percentage points estimated at the beginning of
the year. However, the implied target for effective growth
was not changed, i.e., both the estimated impact of the
shifting of funds and the target range for reported growth
were revised by the same amount.

Table II

EXPRESSED OR IMPLIED ANNUAL TARGET RANGES
FOR EFFECTIVE M1 AND CORRESPONDING
ACTUAL EFFECTIVE M1 GROWTH, 1975-1985

1. The ranges in this table are the same as, or were derived from,
the target ranges that were announced by the Federal Reserve
at the beginning of the year to which the target applied. For
1979 and subsequent target years announcements have been
contained in the Federal Reserve’s annual Monetary Policy
Report to Congress, which is usually published in the March
For 1976, 1977, and
issue of the Federal Reserve Bulletin.
1978, the announcements are contained in Burns (1976), Burns
(1977), and Miller (1978), respectively.
2. The target ranges for 1979 and 1981 are adjusted for anticipated shifts into or out of NOW accounts or similar, accounts
The ranges for the periods 4Q79as explained in the text.
4Q80 and 4Q80-4Q81 are the ranges that were set for what
war then referred to as M-18.
P

preliminary

the year, the legalization would cause shifts of funds.
Because it was not clear at the beginning of the year
if legalization would occur or when, no allowance
was made for it in setting the range. Therefore, the
4 to 6½ percent announced range was the target
range for effective M1 growth.13
1981. NOW accounts were authorized nationwide
at the beginning of 1981, and this change produced
substantial shifts of funds from non-M1 instruments,.
such as savings deposits, to NOW accounts during
the year. Presuming again that these funds retained
13

See “Monetary Policy Report to Congress” (March
1980), p. 178.

FEDERAL RESERVE BANK OF RICHMOND

7

their nontransactions character, it follows that the
reported growth of M1 overstated effective growth.
At the beginning of the year, the Fed estimated that
the shifting of funds would reduce effective M1
growth relative to reported growth by 2.5 percentage
points. The 3½ to 6 percent range announced at the
beginning of 1981 and shown in Table II reflects
these anticipated shifts.14
The effective M1 data for 1981 in Table I reflect
the most recent estimate of the actual NOW account effect, which indicates that in fact the shifts
reduced the growth rate for the year by 2.7 percentage points. It should be noted that the effective
M1 levels reported in Table I for 1981 incorporate
both the 1981 adjustments and the adjustment for the
final quarter of 1980, since any adjustment must be
carried permanently in a continuously adjusted series
such as this one. The two adjustments together put
effective M1 $13.4 billion below reported M1 in the
fourth quarter of 1981.
1982, 1983 and 1984. In order to maintain a consistent series, all of the data in Table I for 1982, 1983
and 1984 incorporate the $13.4 billion adjustment
made in the final quarter of 1981. No further adjustments, however, are made in these years. This
absence of further adjustments may seem curious in
view of the authorization of money market deposit
accounts (MMDAs) in late 1982 and Super NOW
accounts in early 1983. Since the MMDA accounts
were not included in M1, any transfers of funds from
accounts included in M1 to the MMDAs would cause
the reported M1 data to understate effective growth
of M1 if it is assumed that the funds retained
their transactions character after the shift. On the
other hand, since the Super NOW accounts were
included in M1, any transfers of funds from nontransactions accounts not included in M1 to the
Super NOWs would cause the reported M1 data to
overstate the effective growth of M1 to the extent
that the funds retained their nontransactions character after the shift. As it turned out, the Fed’s estimates of these two shifts are roughly equal and
therefore offsetting. 15 For this reason, no further
adjustments are made.

III.
THE ESTIMATE OF CUMULATIVE BASE DRIFT

With the “effective” M1 data and the corresponding target ranges in hand, the computation of cumulative base drift is straightforward. The heavy solid
line in Figure 2 plots the effective M1 series from
Table I. The target ranges attached to this line are
the adjusted fourth quarter-to-fourth quarter target
ranges for effective M1 given in Table II. (To avoid
cluttering the chart, the numerical ranges are shown
along the horizontal axis.) As the chart shows, M1
finished the year near the midpoint of its range on
two occasions : in 1976 and in the second half of 1983.
It ended 1981 slightly below the lower bound of the
range, and it ended 1984 in the lower half of the
range. In every other year, it ended the year either
in the upper third of the range (1979) or above it
(1977, 1978, 1980, 1982, and the first half of 1983).
This tendency to exceed the range more frequently
than not has led to substantial net upward base drift
over the period as a whole. One way to estimate the
cumulative drift is to compare the actual level of
M1 at a point near the end of the period with the
level that M1 would have attained if the Fed had
(1) hit the midpoint of its target range at the end of
every year and (2) set the same ranges for growth
rates that it actually set. The midlines of the target
ranges drawn with dashed lines in Figure 2 indicate
the path M1 would have followed if the midpoints
had been hit. On this path, effective M1 would have
been $477.2 billion in the fourth quarter of 1954,
compared with the actual level of $534.5 billion net of
the definitional discrepancy in 1980. The $57.3 billion
difference between these levels is a measure of the
net upward base drift that occurred under the Fed’s
targeting procedure from the fourth quarter of 1975
through the end of 1984. In other words, about 25
percent of the increase in effective M1 during this
nine-year period can be attributed to base drift.16
The estimate given above is a rough approximation
of cumulative base drift because the Fed might have
set somewhat different targets from those actually set
if it had hit the midpoint of the range each year. For
this reason, the estimate is unavoidably hypothetical.
16

14

In 1981, in contrast to other years in which such
shifting occurred, the Fed released and focused on “shiftadjusted” (i.e., what this article has called “effective”)
M1 data, and it also announced its target range in terms
of effective growth.
15

See “Monetary Policy Report to the Congress” (February 1984), p. 80.

8

ECONOMIC

REVIEW,

It should be noted that while base drift is measured
here as any deviation from the midpoint of the target
range, the Fed itself has avoided setting the midpoint of
its range as a point target. In some years, it has explicitly
indicated that growth at a rate different from the rate
implied by the midpoint would be acceptable. Nevertheless, since the base for each target range is a point, it
seems reasonable to quantify base drift in terms of deviations from the midpoints of the ranges.
NOVEMBER/DECEMBER

1984

Figure 2

ACTUAL LEVELS AND TARGET RANGES FOR EFFECTIVE M11/

In particular, if changes in the midline target growth
rates were negatively correlated with the base drift
at the end of the preceding target year, the estimate
would be biased upward. This is the case because
with negative correlation, if there had been no base
drift as in the hypothetical, situation shown by the
dashed lines in Figure 2, the growth targets would
have been higher on average than those that were
actually set. Figure 3 shows the observed relationship
between actual base drift and subsequent change in
the target. There is no evidence of negative correlation. Indeed, Figure 3 suggests a positive correlation, which would imply that the above estimate is
biased downward.
IV.
WHY BASE DRIFT MATTERS

The preceding section showed that cumulative base
drift has been quantitatively significant during the
years that the Fed has used the present targeting
procedure. Moreover, because there has been both
upward and downward base drift over the period, the

cumulative measure understates the quantitative significance of base drift on a year-to-year basis.17 Beyond its quantitative impact, however, allowing base
drift would seem to rob the Fed’s targeting strategy
of some of its most important benefits.
Erosion of Public Confidence in the
Effectiveness of the Targeting Procedure
The effectiveness of monetary targeting in controlling inflation depends largely on the public’s
confidence in the Fed’s commitment to long-run
control of the money stock. More specifically, the
public must believe that the Fed will hit its announced
targets on average over time. The contribution of
the present targeting procedure to this confidence is
almost certainly diminished by the frequent discrepancies between the targets and actual money growth
in particular years and the incorporation of each miss
in the base set for the next annual target.
17

Annual base drift measured as a percentage of midline
target levels at the end of each target year can be seen in
Figure 3.

FEDERAL RESERVE BANK OF RICHMOND

9

Figure 3

THE RELATIONSHIP BETWEEN
BASE DRIFT AND SUBSEQUENT
CHANGE IN MIDLINE TARGET GROWTH

deviation might be at the end of the year, the money
stock is back on target when the new range is set.
This feature of the present targeting procedure substantially reduces the disciplinary benefits of monetary targeting.
Propagation of Transitory Disturbances

Diminished Incentive for the Fed
to Hit Its Target
A closely related point is that the allowance of base
drift reduces the incentive for the Fed to hit its target
in any particular year. At least as far as the procedure is concerned, any target miss that occurs in a
given year is forgiven when the target for the next
year is set, and the miss is therefore only temporarily
in the public eye.18 The Fed’s incentive to correct a
deviation from the target that arises during a year is
therefore reduced because no matter how large the
18

In principle, base drift could be offset by moving subsequent targeted growth in the opposite direction. However,
as seen in Figure 3, in practice change in targeted growth
seems to be positively correlated with prior base drift.
In any case, it would not seem desirable to use a targeting procedure where announced growth rates are
routinely adjusted in response to prior money supply
disturbances. The alternative procedure outlined in Section VI would not require such routine adjustment.

10

ECONOMIC

REVIEW,

The secular inflation rate tends to follow the trend
rate of M1 growth over time. With unbiased monetary targeting, where target misses are truly random,
the Fed could control inflation on average with the
current targeting procedure as long as persistently
noninflationary target paths were set. Even in these
circumstances, however, allowing base drift would
be an inferior targeting strategy.
Figure 4, which is similar to Figure 1, illustrates
this point with another hypothetical example. In the
first of the two years shown, actual M1 grows at a
rate close to the midline of the target range through
the first three quarters of the year. It then declines
in the final quarter of the year to point B, which is
only slightly above the 4 percent lower bound of the
range. The growth rate targeted in the second year
is shown to be the same as in the first year. Because
of the downward base drift, however, the level of the
target path given by the midline of the range has
declined by the difference between points C and B.
That is, the target path in the second year is $9 billion
below what it would have been if the base had not
been allowed to drift. This hypothetical example has
its counterparts in actual experience. As shown in
Figure 2, above-target growth in 1978 significantly
raised the level of the target path for 1979, and belowtarget growth in 1981 lowered the path for 1982.
To the extent that short-run target misses are due
to transitory shifts in credit or money demand,19 base
drift needlessly allows temporary disturbances to
affect the money stock and the price level permanently. Consequently, uncertainty about the future
price level tends to be greater with base drift than
without it. The contribution that monetary targeting
makes to economic efficiency by reducing uncertainty
surrounding the future price level is therefore smaller
when base drift is built into the targeting procedure.20
In short, because M1 growth is prone to significant
quarterly disturbances that would otherwise be transitory, it would not appear to be desirable for the Fed’s
targeting procedure to build these disturbances into
the following year’s target path.
19

See Goodfriend (1982).

20

For more
(1984).

NOVEMBER/DECEMBER

discussion

1984

of

this

point

see

Goodfriend

Figure 4

EFFECT OF A SHORT-RUN DISTURBANCE ON THE LONGER RUN TARGET

V.
BASE DRIFT AND “PERMANENT”
MONETARY DISTURBANCES

Figure 2 shows that a sizable portion of the cumulative upward base drift to date arose at the end of
the 1982 targeting year and during the 1983 targeting
year. As is well known, the velocity of M1 declined
unusually sharply in the late stages of the recession
that ended in the fourth quarter of 1982 and expanded
unusually slowly during the first year of the recovery.
In this situation, the Fed deliberately allowed M1
growth to exceed its target range substantially in the
second half of 1982 in order to prevent the economy
from weakening further. 21 Since it thought that the
decline in velocity might be permanent, the Fed apparently felt comfortable basing its 1983 range at the
high actual level of M1 in the fourth quarter of
1982. 22
21

See “Monetary Policy Report to Congress” (March
1983), p. 134.

On the basis of this episode, it might be argued that
base drift is a desirable feature of the Fed’s targeting
strategy, since it allows the Fed to accommodate
permanent disturbances in the relationship between
income and the public’s demand for money. Even if
it were. possible to identify such permanent disturbances at the time they occur, however, it does not
follow that allowing base drift as a routine feature of
the targeting procedure would be either necessary or
desirable. Faced with such a disturbance, it might be
necessary for the Fed to raise its targeted growth rate
temporarily or to raise, the level of the target path.
Discretionary adjustments of the targets in reaction
to conclusive evidence of permanent monetary disturbances, however, would be very different from rou22

Similar reasoning led the Fed to set a new base for
the period between the second quarter of 1983 and the
fourth quarter of 1983 after M1 growth had exceeded its
original 1983 range during the first half of the year. It
should be noted that the Fed de-emphasized M1 between
October 1982 and July 1984. The 1983 M1 range was
referred to officially as a “monitoring” range.

FEDERAL RESERVE BANK OF RICHMOND

tinely permitting any base drift to affect the target
path.
VI.
AN ALTERNATIVE TARGETING STRATEGY

Two relatively simple changes in the Fed’s targeting procedure would eliminate base drift and the
problems associated with it.23 First, whatever money
growth rate the Fed chooses to target in a given
year, the base level for the target path should be
the midpoint of the target range for the preceding
year. In terms of Figure 1, the base level for the
midline of the second year range should be the end
point of the first year midline, or $500 billion. This
change would be sufficient to eliminate base drift. 24
A second helpful modification, although strictly
speaking not needed to eliminate base drift, would be
to set the upper and lower bounds of the target range
in terms of a band rather than the present wedge.
The band would give the Fed the same room to
maneuver throughout the targeting year. In particular, the Fed would have more room to maneuver
early in a targeting year, when it might be desirable
to deal gradually with money supply disturbances
inherited from the previous targeting year.
Figure 5 shows how this procedure would work
using the hypothetical data from Figure 4. As drawn,
the chart indicates that the 6 percent target for money
growth in the first year is retained in the second
year. If the targeted growth rate were. lowered to,
say, 5 percent in year 2, the slope of the path would
be lowered in the second year, but the base would
still be the $500 billion level given by the midline of
the year 1 target range in the fourth quarter of the
first year. The width of the band could be 2 or 3
percentage points of the targeted level. Obviously, a
narrower band would encourage greater monetary
control in the short run and vice versa.
In the example in Figure 5, actual M1 ends year 1
near the lower bound of the target band. The example can be used to illustrate the advantages of both
of the modifications suggested above. Regarding the
first modification, since point A would be the year 2
target, the modified procedure would require the Fed
to aim to offset the first year shortfall in year 2 rather
than forgiving the miss as under the present pro23

These modifications were originally suggested by Poole
(1976), pp. 255-57.

24

If there were conclusive evidence of a permanent monetary disturbance, the base could be adjusted to take account of it, but such adjustments would only be made
under exceptional circumstances.

12

ECONOMIC

REVIEW,

cedure. The Fed would also have a stronger incentive to prevent a target miss from occurring in year 1.
This additional discipline would almost certainly increase the public’s confidence in the Fed’s ability to
achieve its longer run objective of fostering steady,
noninflationary growth in the money supply.
Regarding the second modification, it would be
much easier for the Fed to use the year 1 target as
the base for year 2 with a target band than with a
wedge. As should be evident from Figure 5, if the
Fed were to eliminate base drift but retain the wedgeshaped range from the old procedure, the money
supply would be more likely to begin each new targeting year outside the range. This situation would
be difficult for the Fed and confusing to the public.
Using a band would allow the Fed to move the
money supply gradually back to the target midline
while remaining inside the target range.
VII.
A POSTSCRIPT ON THE ROLE OF
MONETARY TARGETING IN THE
RECENT REDUCTION IN INFLATION

The United States has experienced a sharp reduction in inflation since 1980. For example, annual
inflation as measured by the GNP deflator declined
from 10.2 percent in 1980 to 4.3 percent in 1982 and
has remained below 4 percent since then. The Fed
must be given credit for pursuing the restrictive
monetary policy that made this reduction in inflation
possible. What role did monetary targeting per se
play in achieving the reduction.? The effective M1
data in Table I provide some evidence on this
question.
Inflation actually increased sharply during the first
five years of monetary targeting. Annual inflation
as measured by the GNP deflator rose from 4.7
percent in 1976 to 8.2 percent in 1979 and 10.2
percent in 1980. As shown in Table II, effective M1
overshot the upper bound of the Fed’s target ranges
in 1977 and 1978, and it came in within the upper
third of the implied range in 1979. This performance created doubts about the Fed’s commitment to
its money supply targets and tended to encourage
the increase in inflation in the late 1970s.
After renewing its commitment to disinflationary
policy in October 1979, the Fed again let effective
M1 overshoot its target in 1980, and the inflation
rate remained high throughout that year. Then, in
sharp contrast to the preceding four years, effective
M1 actually undershot its range in 1981. As the data
in Table I show, effective M1 grew 4.6 percentage
NOVEMBER/DECEMBER

1984

Figure 5

A TARGET BAND TO ELIMINATE BASE DRIFT

points slower in 1981 than its average annual growth
over the preceding five years.25 Further, the 2 percent
downward base drift in 1981 (see Figure 3) was
built into the 1982 target path. This slower M1
growth was not the gradual deceleration built into
the Fed’s announced targets. Rather, it was a sharp
deceleration that brought about an ‘unexpectedly rapid
decline in inflation-and may have worsened the 19811982 recession. 26 In short, the discipline of mone25

The effective M1 data in Table I may understate the
deceleration somewhat, since, as noted in Section II, the
data in the Table I series for the years prior to 1980 are
based on the old definition, which excluded OCDs. Since
OCDs began to grow significantly more rapidly in the
late 1970s, an effective M1 series that uses the current
definition throughout shows more rapid growth in the
five years preceding 1981 and hence a sharper deceleration in 1981. Specifically, average annual effective growth
in the five years preceding 1981 under the current definition is 7.4 percent, and the 1981 deceleration is therefore
5.0 percentage points.

26

It should be noted that during the course of 1981, the
Fed felt that the weakness in M1 growth might be due in
part to a lasting decrease in velocity resulting from imIts limited
provement in cash management practices.
reaction to the weakness in M1 was also affected by relatively strong growth in M2 and M3. See “Monetary
Policy Report to the Congress” (March 1982), p. 129.

tary targeting per se does not appear to have contributed significantly to the reduction in inflation.
Instead, it appears that the reduction was due to the
shock of an unanticipated undershooting, of the M1
target range following a four-year period during
which growth either exceeded the range or came in
well in the upper portion of the range.
By the summer of 1982, the unusual decline in M1
velocity together with the recession and developing
strains in financial markets led the Fed to deemphasize its M1 target. M1 grew over the next
four quarters at a very high 12.3 percent rate. In
retrospect, the 1982 decision to accommodate the
increased demand for M1 appears to have been
appropriate in the sense that inflation has remained
low.
An argument can be made, however, that the unusual decline in velocity in 1982 and some of the
strain in financial markets that accompanied it have
been due to the substantial deceleration in the
growth of effective M1 in 1981 and the sharp reduction in actual inflation that followed. It was reasonable to expect that velocity would decline as falling

FEDERAL RESERVE BANK OF RICHMOND

13

inflation reduced nominal interest rates and lowered
the cost of holding money. But it was extremely
difficult to predict either how much or how quickly
the public would revise its inflationary anticipations
downward in the face of the pronounced monetary
shock ; hence, it was particularly difficult to forecast
the size and timing of the decline in velocity. As
mentioned above, in retrospect rapid money growth
in 1982-1983 has proven to be appropriate. Nevertheless, making monetary policy choices during a
rapid disinflation is particularly difficult. If M1 had
followed the gradual announced deceleration built
into the targets, inflation would more likely have
come down gradually, the recession and financial
strains might have been less severe, and velocity
might have fallen more gradually and predictably.
VIII.
SUMMARY

This article has described the nature of base drift.
estimated its cumulative impact on the effective

growth of M1 since 1975, and indicated several ways
in which it undermines the Fed’s present monetary
targeting strategy. As noted in Section III, net base
drift was substantially upward over the 1975-1984
period, although in retrospect some part of the drift
that occurred in 1982 and 1983 may have been fortuitous in the sense that inflation has remained low
through 1984. In any event, since there has been
both upward and downward base drift during the
period, the cumulative drift tends to understate the
quantitative significance of base drift on a year-toyear basis. As pointed out in Section IV, the allowance of base drift greatly reduces the disciplinary
features of monetary targeting and therefore probably
reduces its effectiveness and credibility. The modifications of the present procedure noted in Section VI
would eliminate base drift, give the Fed an incentive
to control the growth of the money supply more
closely in the short run, and in all likelihood increase
the public’s confidence in the Fed’s commitment to
restore and maintain price stability.

References
Axilrod, Stephen H. “U. S. Monetary Policy in Recent
Years: An Overview.” Federal Reserve Bulletin
71 (January 1985), pp. 14-24.
Burns, Arthur F. Statement before the Committee on
Banking and Currency. U. S. House of Representatives, July 30, 1974, in Federal Reserve Policy and
Inflation and High Interest Rates. Hearings before
the Committee on Banking and Currency, House of
Representatives, 93rd Congress, 2nd session, 1974,
pp. 251-59.
. Statement before the Committee on Banking, Currency, and Housing. U. S. House of Representatives, February 3, 1976, in Federal Reserve
Bulletin 62 (February 1976), pp. 119-25.
Statement before the Committee on Banking, Finance, and Urban Affairs. U. S. House of
Representatives, February 3, 1977, in Federal Reserve Bulletin 63 (February 1977), pp. 119-24.
Goodfriend, Marvin. “A Model of Money Stock Determination with Loan Demand and a Banking System
Balance Sheet Constraint.” Economic Review,
Federal Reserve Bank of Richmond 68 (January/
February 1982), pp. 3-16.

14

ECONOMIC

REVIEW,

“Rational Expectations, Interest Rate
Smoothing, and the ‘Optimality’ of a Non-TrendStationary Money Supply Rule.” Federal Reserve
Bank of Richmond, February 1984.
Kane, Edward J. “New Congressional Restraints and
Federal Reserve Independence.” Challenge, November-December 1975, pp. 43-44.
Miller, G. William. Statement before the Committee on
Banking, Finance, and Urban Affairs. U. S. House
of Representatives, March 9, 1978, in Federal Reserve Bulletin 64 (March 1978), pp. 185-89.
“Monetary Policy Report to the Congress.” Reports
submitted to the Congress pursuant to the Full
Employment and Balanced Growth Act of 1978.
Federal Reserve Bulletin, March issues since 1979.
“Interpreting the Fed’s Monetary
Poole, William.
Targets.” Brookings Papers on Economic Activity,
No. 1, 1976; pp. 247-59.

NOVEMBER/DECEMBER

1984

A MONETARIST MONEY DEMAND:
FUNCTION
Robert L. Hetzel

Introduction
In the first part of this article, inflation as a monetary phenomenon is discussed. The discussion is
from the perspective of the modern formulation of
the quantity theory. (See, in particular, Chapter 2
in Friedman and Schwartz, Monetary Trends in the
United States and the United Kingdom [2]). In
the second part of the article, empirical estimation
of the relationship between money growth and inflation is discussed. The article that accompanies this
one; “The Behavior of the M1 Demand Function in
the Early 1980s” contains the results of estimating
this relationship for the post-Korean War period in
the United States.
The Quantity Theory Framework
The modern formulation of the quantity theory
places the determination of the price level within the
analytical framework of supply and demand. The
price level, or more appropriately its inverse, is the
goods price of money. The price level is determined
“by the interaction of the supply and demand for
money.
A discussion of the determination of the price level
must begin with the distinction between real and
nominal variables.
Nominal variables are either
measured directly in current dollars or in a way that
depends upon the use of dollars as a measure of value:
Examples of nominal variables are the number of
dollars in circulation and the dollar expenditure of
the public on final goods and services. Because market, rates of interest, at least in principle, vary directly
in response to changes in the future price level anticipated by the public, they are also examples of nominal
variables. Real variables, in contrast, are measured
in ways that do not make use of current dollars as
the unit of account. Examples of real variables are
the exchange rate between two commodities and final
physical output. The quantity of money expressed in
terms of its purchasing power over goods and services
is a real variable.

The public cares about the real quantity of money
it holds, while the actions of the central bank determine the nominal quantity of money available for the
public to hold. The price level translates the real
quantity of’ money demanded, by the, public into the
corresponding nominal quantity demanded. The price
level varies in order to equate this nominal quantity
demanded to the given nominal quantity supplied.
The quantity equation serves as a useful summary
of the supply and demand relationship that determines the price level. In expression (1), the nominal
money stock, M, equals the product of a factor k
and nominal expenditure, where nominal expenditure
is expressed as the product of the price level, P; and
real expenditure, Y. By definition, k is the fraction
of nominal expenditure held as nominal money
balances.
(1) M=k[P*Y]
The definitional relationship shown in (1) can be
transformed into a substantive economic hypothesis
by interpreting it within the framework of a supply
and demand relationship.

For this purpose, (1) is rewritten as (2). Now, M
is interpreted as the nominal quantity of, money
supplied. The product in brackets, k * Y, is interpreted as the real quantity of money demanded.
Finally, the price level, P, adjusts to equate money
demanded to money supplied. Below, expression (2)
is given substance as a theory of the determination of
the price level through specific hypotheses about the
behavior of its components and their interaction.
Interpretation of (2) within the framework of supply
and demand, however, already entails the substantive
economic hypothesis that the determinants of the
supply of money can generally be considered as con
ceptually distinct from the determinants of the demand for money.

FEDERAL RESERVE BANK OF RICHMOND

15

The Money Supply

Adjustment of the Price Level to Money

From the perspective of the quantity theory, the
nominal quantity of money is assumed to be determined largely independently of the public’s demand
for money. The public adjusts to the nominal money
stock by varying the rate of its nominal expenditure.
Conversely, the nominal money stock does not adjust
to the rate of expenditure of the public: Each individual economic entity can proportion its money
holdings to its expenditure by varying its money
holdings, but collectively this behavior is not possible.
Collectively, the public proportions its money holdings to its expenditures through a change in expenditures. From the quantity theory perspective, major
changes in the nominal expenditure of the public
reflect the public’s adjustment to changes in the
money stock.

The price level is the rate of exchange between real
output and dollars. It translates the real quantity of
money desired by the public into a corresponding
desired nominal quantity. As discussed below, the
quantity theory assumes that ultimately the price
level adjusts when, at the pre-existing price level,
changes in the nominal quantity of money supplied
produce excess supply or demand for money.

Money Demand
Holders of money care about the real quantity of
money they hold, that is, what they can purchase in
terms of goods and services with their money holdings. The real quantity of money demanded is expressed in (2) by the terms k * Y. Y is considered
here to be real annual expenditure on final output.
The demand for real money holdings is, then, expressed as a fraction k of the annual real expenditure
of the public. The term k * Y expresses the fraction
of a year’s real expenditures that the desired real
money stock would finance. The inverse of k is the
expenditure velocity of money, that is, the number
of times that a dollar on average is used in a year to
effect transactions involving the sale of final goods
and services. The term k is considered to be a predictable function of a small number of variables, for
example, the nominal rate of interest and real income
or wealth.
The statement that inflation is a monetary phenomenon is true in a trivial sense in that the price
level is determined by the interaction of the demand
for and the supply of money. This statement, however, refers to the empirical generalization that
changes in the demand for money proceed in a fairly
predictable, moderate fashion, while changes in the
supply of money frequently occur that are large relative to changes in the demand for money.
16

Changes in nominal money are not offset, except
over short periods, by changes in k, the factor expressing the way in which the public’s demand for
real money balances depends upon variables such as
real income and the market rate of interest. On the
contrary, changes in k may reinforce the effect of
prior changes in money growth. For example, an
increase in the rate of growth of the money supply
will at some point result in a higher anticipated inflation rate, which will increase market rates of interest.
As money becomes more expensive to hold, the public
will reduce its real money holdings. This reduction, a
reduction in k, will drive the price level up beyond
what was implied by the increased money growth.
Historically, changes in money growth have affected
real expenditure before affecting the inflation rate.
The effect of money on real expenditure and output
is referred to as the nonneutrality of money and is
not well understood theoretically. According to the
quantity theory tradition, however, this effect causes
movements in the money supply to be the major
source of the business cycle. As explained below, the
quantity theory assumes that the ultimate impact of
changes in money is on changes in the price level,
not on real economic activity.
Nothing about the number of dollars in circulation
affects in any fundamental way the real resource
endowments of an economy, the technological capacity of an economy to transform endowments into
output, or the preferences of individuals with respect
to consumption of this output. For these reasons, a
change in the nominal quantity of money cannot
exert a permanent effect on real economic activity.
The hypotheses of this section can be summarized
by reference to expression (2). A change in M will
not be absorbed by an offsetting change in k, nor will
a change in M affect Y in a lasting way. A change in
M must ultimately affect P. The sections that follow
constitute a discussion of one way of quantifying the

ECONOMIC REVIEW, NOVEMBER/DECEMBER 1984

empirical relationship existing between money and
price level.
Empirical Association of Money Growth
and Inflation
A functional form is suggested in this section for
examining the empirical evidence on the ability of
the, growth rate of the money supply to predict inflation. (See Hetzel [3].) The following section displays the associated algebra.
Initially, a functional form is posited to explain the
public’s demand for real money holdings. This form
is assumed to depend upon time, a nominal interest
rate, and real expenditure. In order to estimate this
functional form, dependent and independent variables
must be chosen and a lag structure imposed on the
latter. This task is effected through choice of an
“adjustment equation” in the spirit of (2) in which
the public adjusts its real money holdings through
variation in the price level. The price level varies
so as to translate the real money holdings desired by
the public into a desired nominal quantity equal to
the nominal quantity supplied by the central bank.
Combining the basic functional form expressing the
public’s demand for real money holdings with this
adjustment equation yields an expression relating the
price level to contemporaneous and lagged values’ of
the nominal interest rate, real expenditure, and the
nominal money stock. This expression can be estimated as a regression equation.
Algebra
A standard money demand function is as follows:

Real money holdings, the ratio of nominal money
holdings to the price level, M/P, are denoted by m.
Real money holdings demanded by the public; m*,
depend upon time (t), a nominal interest rate (R),
and real expenditure (Y). Also, k is a constant; a
is the trend rate of growth in the demand for money;
and b and c are the elasticity of the demand for real
money balances with respect to the nominal rate of
interest and real expenditure, respectively. The
symbol e denotes the base of the system of natural
logarithms.
An adjustment equation in the quantity theory

spirit is (4), where ln is the natural logarithm. (A
difference in the logarithms of variables, multiplied
by 100, can be interpreted as the percentage difference in the variables.)

The percentage change in the price level is assumed
ancy between the nominal money stock determined
by the central bank and the nominal money stock
desired by the public at the inherited price level.
(The desired nominal money stock is the product of
the desired real money stock and the price level.)
Combining (3) and (4) yields

I, is a shift operator, L k X t = X t-k , that is, it shifts
the date of a variable into the past. Also,

The immediately preceding term indicates that the
variables it multiplies, ln f (X t) and ln Mt in (5),
enter as a sum of contemporaneous and past values
with weights that decline geometrically, that is, by
the variables that comprise ln f (Xt) are allowed to
enter with a simple distributed lag pattern, rather
than with a geometrically declining lag pattern, that
is, the coefficients on the affected variables are not
constrained to follow a particular pattern. (The geometrically declining lag pattern was assumed only for
expositional purposes.)
Below, in (6) ln f(Xt) is written out as follows :

(The use of first differences, indicated by the A,
causes the k and the t in the at term to drop out.)
Estimation
The functional form (5) is shown below in first
difference form as regression equation

FEDERAL RESERVE BANK OF RICHMOND

17

The 8 notation indicates the use of simple distributed
lags. The trend rate of growth of the demand for
money is a, while the respective sums of the bi and ci
coefficients are the. elasticity, of the demand for real
money balances with respect to the nominal rate of
interest and real income, respectively. The error
term is u. N is population. Dividing real expenditures and nominal money by population means that a
change in population that leaves per capita real expenditure and per capita nominal money holdings
unchanged will not affect the price level.
Regression equation (6) is in principle amenable
to estimation as a money demand function. The
price level, rather than the real money holdings of the
public, is the dependent variable. The derivation of
(6), however, was performed under the quantity
theory assumption that nominal money holdings are
given to the public. The behavior of the price level,
therefore, determines the behavior of real money
holdings.
The estimation of (6) as a money demand function
presents a number of difficulties. The specification
of the adjustment equation (4) should in principle
determine the specification of the functional forms
(5) and (6). The theory needed to specify (4) in a
satisfactory way is, however, largely lacking. What
is needed is a theory explaining the way in which a
change in nominal money produces changes over time
in the price level. The way in which a change in
nominal money breaks down in the short run into
changes in real expenditure and in the price level is,
however, one of the major unresolved issues in economics. Satisfactory estimation of money demand
functions requires a better understanding of the dynamics of the process whereby the public eliminates
discrepancies between actual and desired real money
holdings.
Failure to account satisfactorily for these dynamics
could cause the behavior of the central bank to affect
the apparent structural stability of the estimated
money demand regression. Estimation of (6) could
be affected by supply side, rather than solely demand
side, behavior. For example, if the central bank were
18

to cause the behavior of nominal money to become
more predictable, some theories would predict a
reduction in the time required for a change in money
to change the price level. The mean lag associated
with the estimated distributed lag coefficients on
money in (6) would fall.
The above comments need to be qualified, however,
by noting that estimation of (6) can still offer evidence on shifts in the public’s money demand function. Over a period of time long enough for the price
level to adjust fully, the quantity theory implies that
real money holdings are demand determined by the
public. A persistent underprediction of the price
level, say, with (6), and thus overprediction of the
level of real money holdings, must be explained by
the behavior of the demand for money, not the supply
of money. This hypothetical underprediction of the
price level would reflect a leftward shift in the public’s money demand function.
A problem related to those discussed above is that
over periods of time short enough for money to affect
real economic activity, the price level, the dependent
variable in (6), and the rate of interest and the rate
of real expenditure, independent variables in (6), are
simultaneously determined. A single equation estimation procedure applied to (6) will not capture this
mutual interaction and, consequently, will yield biased
estimates of the true parameters of the public’s money
demand function.
Finally, the true functional form of the money
demand function might not be (3), but might be an
alternative functional form such as the Cagan [1]
money demand function. With this latter form, real
money holdings depend upon the inflation rate expected by the public. The price level, consequently,
depends upon the money supply expected to obtain in
the future. Estimation of the parameters of the
money demand function requires knowledge of the
process generating the money supply. (See Sargent
[4].) Ordinarily, estimation of (6) would be expected to produce a sum of coefficients on the contemporaneous and lagged money terms close to one
so that a one percentage point change in money
growth would lead to a one percentage point change
in the inflation rate. If the Cagan money demand
function were the appropriate function, however, the
sum of estimated coefficients on money might differ
from one in that the money terms are serving as a
proxy for expected money growth.
Despite, the problems discussed above, estimation
of (6) remains a useful way of organizing an overview of the data relevant for assessing the stability of

ECONOMIC REVIEW, NOVEMBER/DECEMBER 1984

the public’s money demand function. Problems of
specification and simultaneous equations bias do not
alter the fact that (6) depends upon the public’s
money demand function in an essential way. Stability over time of an estimated regression equation
like (6) constitutes empirical evidence in favor of a
stable money demand function. Estimation of (6)
permits, in particular, an assessment of the degree to
which the empirically regular association between
money growth and inflation, predicted by the quantity
theory, exists. This estimation is performed in the
following article within a context of a discussion of
whether the recent deregulation of the financial systern has altered the character of M1.

References
1. Cagan, Phillip. “The Monetary Dynamics of Hyperinflation,” in Milton Friedman, ed., Studies in the
Quantity Theory of Money. Chicago: The University of Chicago Press, 1956.
2. Friedman, Milton, and Anna J. Schwartz. Monetary
Trends in the United States and the United Kingdom: Their Relation to Income, Prices, and Interest
Rates, 1867-1975. Chicago: The University of Chicago Press, 1982.
3. Hetzel, Robert L. “Estimating Money Demand
Functions.” Journal of Money, Credit, and Banking
16 (May 1984), 185-193.
4. Sargent, Thomas J. “The Demand for Money during
Hyperinflations under Rational Expectations.” International Economic Review 18 (February 1977),
59-82.

FEDERAL RESERVE BANK OF RICHMOND

19

THE BEHAVIOR OF THE M1 DEMAND
FUNCTION IN THE EARLY 1980s
Robert L. Hetzel

Introduction
Since the last half of 1982, the rate of inflation
has been below the rate that would have been predicted on the basis of the historical relationship
between the rate of growth of M1 and the rate of
inflation. This fact indicates that a rightward shift
in the public’s M1 demand function has occurred.
Two alternative explanations of the nature of this
shift are exposited in the first part of this article.
Both explanations assume that the shift is associated
with the deregulation of the financial system in the
early 1980s. One explanation assumes that there
was a onetime permanent change in the character of
the public’s M1 demand function. The other assumes
that shifts will occur in the public’s M1 demand function while the public adjusts to the deregulation of
the financial system; however, after this adjustment
is completed, the M1 demand function will reassume
its pre-1980s characteristics.
The breakdown of the prohibition of the payment
of interest on the checkable deposits of consumers
has been associated with the introduction of various
kinds of interest-bearing transactions accounts,
known as other checkable deposits (OCDs). The
first explanation offered for the recent behavior of
the public’s M1 demand turns on the fact that M1
now includes instruments suitable for saving, as well
as for effecting transactions. In the spirit of this
first explanation, it is conjectured that the public’s
M1 demand function has come to resemble permanently its demand function for M2 as formerly defined, which included savings, as well as transactions,
balances. (This explanation is suggested by Friedman and Schwartz (1983/1984) and is referred to
below as the Friedman/Schwartz hypothesis.) The
second explanation offered turns on the fact that the
new interest-bearing checkable deposits require minimum balances. In the spirit of the second explanation, it is conjectured that consumers, in the process
of establishing new OCD accounts, make onetime
transfers of funds from savings accounts in order to
satisfy these minimum balance requirements. (This
20

explanation is suggested by Cook and Rowe (1984)
and is referred to below as the initial balance hypothesis.)
Both of these hypotheses predict a rightward shift
in the public’s M1 demand function in the early
1980s. It is, therefore, not possible currently to use
the behavior of the public’s real M1 balances in order
to discriminate between them. With the passage of
time and the subsidence of new deregulation affecting
transactions balances, their implications for the behavior of the public’s real M1 balances diverge. This
latter fact is exploited below in order to make two
sets of predictions of inflation for 1985, given an
assumption about the rate of growth of M1 and given
the assumption that the rate at which new OCDs are
being introduced falls to a low level sustainable in the
long run. Given the validity of this latter assumption,
these contrasting predictions of inflation should offer
evidence during 1985 useful in discriminating between the two hypotheses discussed here and, therefore, useful in assessing the contemporaneous character of the public’s M1 demand function.
Two Alternative M1 Demand Functions
Especially after the nationwide introduction of
interest-bearing NOW accounts in January 1981, M1
has comprised deposits suitable for saving as well as
for effecting transactions. In this respect, M1 is now
similar to M2 as defined prior to January 1980.1 The
choice of an M1 demand function that takes account
of the current presence in M1 of interest-bearing
1

In 1980, M1 was redefined to include the various new
kinds of interest-bearing checkable deposits offered to
consumers, NOW and ATS accounts and credit union
share drafts. In January 1983, Super NOW accounts
were authorized and added to the definition of M1. Also
in 1980, the monetary aggregate M2 was redefined.
Before 1980, M2, in addition to currency and demand
deposits, comprised savings and small time deposits of
banks plus time certificates of deposits other than the
large negotiable certificates of deposit of large banks.
After 1980, small time and savings deposits at depository
institutions other than banks, money market mutual fund
shares, and overnight Eurodollar deposits and overnight
repurchase agreements were added to the definition of
M2.

ECONOMIC REVIEW, NOVEMBER/DECEMBER 1984

checkable deposits is motivated by a suggestion of
Milton Friedman and Anna Schwartz (1983/1984).
Friedman and Schwartz have contended that the
construction of a money series with consistent economic properties is better achieved by splicing the
recent M1 time series, which includes interest-bearing
checkable deposits, with the historical time series for
old M2, rather than with the historical time series for
M1, which excludes interest-bearing deposits.
The relationship of a particular definition of money
to macroeconomic variables like the expenditure of
the public and the level of market rates of interest is
summarized by a money demand function. The introduction into M1 of instruments suitable for saving
can reasonably be conjectured to have altered the
parameters that characterize the M1 demand function
in a way that moves them toward the values of the
parameters that characterize the old M2 demand
function. In particular, it is plausible that the current
demand function for M1 would exhibit, relative to its
pre-1981 behavior, a lower trend rate of decline in
the demand for M1 and higher interest rate and income elasticities of demand for M1. If this conjecture
is correct, the characteristics of the public’s current
M1 demand function probably lie in between those of
the pre-1981 M1 demand function and those of the
former old M2 demand function.2 With the passage
of time, economists will be able to estimate the characteristics of the current M1 demand function with
data that start in January 1981. At present, not
enough time has elapsed in order to make this estimation feasible. Consequently, in order to give the
Friedman/Schwartz hypothesis content, the somewhat arbitrary decision is made that the introduction
of interest-bearing checkable deposits into the definition of M1 has caused the public’s current M1
demand function to become identical to its former old
M2 demand function.
In the above spirit, the following simple empirical
evaluation is performed in this article. A money
demand regression equation is estimated that highlights the relationship between the rate of growth of
the money supply and inflation. When this regression is estimated through the 1970s with M1 and
2

Current M1 does not include the time and savings
deposits at commercial banks that were in old M2 (although it does include some deposits at thrift institutions
that were not included in old M2). Also, the introduction
of MMDAs decreases the attractiveness of OCDs as
savings vehicles. On a priori grounds, it appears that old
M2 served as a vehicle for saving to a greater extent than
M1 does now. This line of reasoning suggests that the
characteristics of the contemporaneous M1 demand function lie in between the former M1 and former old M2
demand functions.

simulated for the early 1980s with M1, inflation is
overpredicted. When this regression is estimated
through the 1970s with old M2, however, and then
simulated for the early 1980s with M1, inflation is
reasonably well predicted. These results provide
empirical support for the Friedman/Schwartz hypothesis.
These same results, however, are also consistent
with the initial balance hypothesis about the rightward shift in M1 demand. This hypothesis emphasizes the transfer of funds from savings accounts to
meet minimum balance requirements assumed to accompany the opening of new OCD accounts. As
long as the transitional period persists during which
the public is opening new OCD accounts in response
to deregulation, the public’s demand for real M1
balances will be unusually strong. After this transitional period, however, the public’s M1 demand
should return to normal. The relationship that
existed prior to the 1980s between the rate of growth
of M1 and the rate of inflation should again serve as
a basis for predicting the rate of inflation.
Consequently, as pointed out in the introduction,
after this transitional period, predictions of inflation
will differ depending upon the validity of the Friedman/Schwartz or initial balance hypotheses. Again,
these hypotheses are that the public’s M1 demand
function has come to resemble permanently its former
old M2 demand function or, alternatively, that the
public’s M1 demand function will reassume its previous characteristics once consumers have had time to
adjust to the removal of interest-rate ceilings. On
the basis of these different hypotheses, two divergent
sets of predictions for inflation are made for 1985.
The actual behavior of inflation in 1985 should, therefore, aid in discriminating between these hypotheses.
Before these predictions are presented, the form of
the money demand regression equations used to predict inflation is discussed. The ability of these regression equations to predict, recent inflation is also
described.
Estimating Money Demand Functions
Money demand regression equations usually employ the ratio of nominal money to the price level as
the dependent variable. Entering these two variables
as a ratio, however, constrains the functional form
very considerably. A less constraining functional
form is employed here that makes the price level the
dependent variable, while a distributed lag on present
and past money becomes an independent variable,
along with the real expenditure of the public and an

FEDERAL RESERVE BANK OF RICHMOND

21

interest rate. A similiar functional form was originally used by Harberger (1963) and more recently
has been advanced by Laidler (1982, chap. 2), Fama
(1982), and Coats (1982). A discussion of this
form of money demand regression equation is presented in the preceding article in this Review, “A
Monetarist Money Demand Function,” and in Hetzel
(1984).
The regression equation is shown below in firstdifferenced form. P is the price level; R the nominal
rate of interest; Y real expenditure of the public; M
nominal money; and N population. Also, A is the
first difference operator; ln the natural logarithm;
and u an error term. The trend rate of growth of the
demand for money is a, while the respective sums of
the bi and ci are the elasticity of the demand for real
money balances with respect to the nominal rate of
interest and real income, respectively. Regression
equation (1) is estimated under the assumption that
nominal money, M, is given. The behavior of the
price level, P, therefore, determines the behavior of
real money balances.

the interval from 1952Q1 to 1979Q4.4 The estimation results using M1 are displayed in Table I in a
form that shows the sum of the estimated distributedlag coefficients.5
The estimated constant term indicates a trend rate
of decrease in the demand for M1 of about 2 percent
per year. The sum of the estimated coefficients on
the interest rate terms indicates a small, but statistically-significant, interest elasticity of the demand
for M1. The sum of the estimated coefficients on the
real expenditure terms indicates a real expenditure or
income elasticity of the demand for M1 of about .5.
4

The end date was chosen in order to employ an interval
of estimation identical to the interval used in estimation
with old M2. The old M2 series is available only through
1979Q4.
The estimation employs M1 as redefined in
checkable deposits grew from close to zero in 1975 to
4.3 percent of redefined M1 in 1979Q4. (This percentage
grew rapidly after the nationwide introduction of NOW
accounts in 1981Q1. In 1981Q4, it was 17 percent.) By
ending the estimation in 1979Q4, similar estimation
results are produced using M1 defined to include and
exclude other checkable deposits.
5

The regression employs simple distributed lags with lag
lengths chosen in order to maximize the corrected Rsquared statistic. Examination of the autocorrelation and
partial autocorrelation function of the residuals indicated
that the errors are generated by a first-order autoregressive process. The estimation, therefore, was performed
with a Cochrane-Orcutt procedure.

Table I

REGRESSION OF INFLATION ON M1 GROWTH

The estimation employs first differences of the
natural logarithms of quarterly average observations,
multiplied by 400. Equation (1) then represents a
regression of the annualized quarterly inflation rate
on a constant and on contemporaneous and lagged
annualized quarterly percentage changes in the nominal rate of interest, in real expenditure per capita,
and in nominal money balances per capita. The
interest rate is the 4-6 month commercial paper rate.
Real expenditure is gross domestic purchases in 1972
dollars. 3 Estimation is by ordinary least squares over
a Gross domestic purchases (GDP) equals gross national
product (GNP) less exports plus imports.
GDP is a
better measure of expenditure by U. S. residents than
GNP. Recently, the rise in the U. S. current account
deficit has caused GDP to grow faster than GNP. The
price level employed is the implicit GDP deflator. This
index is more representative of the prices paid by U. S.
residents than the GNP implicit price deflator because it
excludes export prices and includes import prices. Recently, the GNP deflator has risen more rapidly than the
GDP deflator because of the rise in the foreign-exchange
value of the dollar and the fall in the price of imported oil.

22

ECONOMIC

REVIEW,

Notes: M1 is M1; R the 4-6 month commercial paper rate; Y
gross domestic purchases in 1972 dollars; P the implicit gross
M and Y ore divided by the
domestic purchases deflator.
total population of the United States including armed forces
overseas.
NOB is the number of observations; NOV the
logarithm.
number of variables estimated; RSQ the corrected R-squared;
SER the standard error of the regression equation; D-W the
variables
statistic.
First-differenced
are
Durbin-Watson
Estimation uses simple distributed lags.
multiplied by 400.
The sum of the estimated coefficients is shown, with the
standard error of the sum in parentheses.
R comprises 6 contemporaneous and lagged values; Y, 7 such
values; and M1, 10 such values. Estimation performed with
First-order autoregressive paraCochrane-Orcutt
procedure.
meter estimated as .41 with standard error of .08.

NOVEMBER/DECEMBER

1984

The negative coefficient on real expenditures indicates that a one percent increase in real expenditure
or income would, for a given level of M1, produce a
decline in the price level (an increase in real M1
balances) of about .5 percent. As indicated by
the fact that the estimated coefficient on M1 is insignificantly different from one, a one percentage point
change in the rate of growth of M1 produces a one
percentage point change in the rate of inflation.
The results of estimating the money demand regression equation (1) with M2 as defined formerly
(old M2) are displayed in Table II. The endpoint of
the interval of estimation, 1952Q1 to 1979Q4, coincides with the discontinuance of publication of the
old M2 series. The major differences in results from
estimation with old M2, rather than with M1, are a
smaller estimated trend rate of decline in money
demand (a smaller constant term) and an increased
income elasticity of money demand (a sum of coefficients larger in magnitude on the real expenditure
terms). These differences result from the inclusion
in old M2 of instruments used by consumers as
saving vehicles, that is, small time and savings deposits at commercial banks.
Within-sample errors in predicting calendar year
inflation rates are shown in Table III. The errors
are generally smaller for predictions made with old
M2 than with M1. With old M2, only two calendar
year errors exceed 1.5 percentage points (1963,
1964), while with M1 five calendar year errors exceed 1.5 percentage points (1952, 1953, 1964, 1974,
1976) and two exceed two percentage points (1952,
1974). For M1, the root mean square of the calendar

year errors from 1952 through 1979 is 1.1, while the
mean absolute error is .87. For M2, the root mean
square of the calendar year errors from 1952 through
1979 is .89, while the mean absolute error is .74.
The Recent Behavior of M1 Demand
Regression equation (1), estimated with M1 as
shown in Table I, was simulated with M1 over the
out-of-sample period 1980Q1 through 1984Q3. The
percentage error in predicting the price level is reported in the first column of Table IV. 6 The pre6

Because the regression is estimated in percentage
change form, in order to recover predictions in level
form, it is necessary to cumulate percentage changes
from a base level for 1979Q4. The base level used was
the actual price level for 1979Q4. In the simulation, the
sum of the coefficients on the per capita money growth
variable was constrained to equal one. Imposition of this
constraint affected the regression equation reported in
Table I only very slightly. The predictions were made
without use of the information contained in the autocorrelation of the error term.

Table III

ERRORS IN PREDICTING CALENDAR YEAR
INFLATION RATES

1967

1954

1968

1955

1969

1956

1970
1971
1972

1959

1973

1960

1974

1961

1975

1962

1976

1963

1977

1964

1978

1965

Notes: M2 is old M2, that is, as defined before, Jan. 1980. R
comprises 6 contemporaneous and lagged values; Y, 11 such
values; and M2, 10 such values.
Estimation performed with
Cochrane-Orcutt procedure. First-order autoregressive parameter estimated as .41 with standard error of .09. Otherwise,
see first paragraph of notes to Table I.

1953

1958

REGRESSION OF INFLATION ON OLD M2 GROWTH

1966

1957
Table II

1952

1979

Errors ore actual minus predicted values of calendar year
Notes:
inflation rates of the gross domestic purchases implicit price
Calendar year inflation rates are calculated using
deflator.
Predictions used in calcusuccessive fourth quarter levels.
lating the errors in columns labeled M1 est. and M2 est. ore
made with regression equations estimated with M1 (Table I)
No use was made of the
and M2 (Table II), respectively,
information contained in the positively correlated regression
errors in predicting the price level.

FEDERAL RESERVE BANK OF RICHMOND

23

POST-SAMPLE SIMULATION RESULTS:
PERCENTAGE ERROR IN PREDICTING
THE PRICE LEVEL

the actual price level by about 10 percent. As measured by the money demand regression equation (1),
this overprediction of the price level indicates a rightward shift in the public’s M1 demand function.

Notes:
Errors are calculated as the difference between the actual
and predicted level, divided by the predicted level, of the
implicit price deflator for gross domestic, purchases. The predicted values used in calculating the errors in column 1 were
generated using the regression equation estimated with M1
and summarized in Table I.
This regression was simulated
out of sample with the M1 series. The predicted values used in
calculating the errors in column 2 were generated using the
regression equation estimated with old M2 and summarized
in Table II. This regression was also simulated out of sample
with the M1 series. No use was made of the positively
autocorrelated regression errors, so the simulations are cornpletely dynamic in character.

If the Friedman/Schwartz hypothesis is correct
that the phasing out of the prohibition of payment of
interest on consumer demand deposits has caused M1
to come to resemble M2 as formerly defined, then the
demand for M1 in the early 1980s can be understood
as behaving like the demand for old M2 prior to the
1980s. In this spirit, regression equation (l), estimated with old M2 as shown in Table II, was simulated with M1 over the out-of-sample period 1981Q1
to 1984Q3. 8 The percentage error in predicting the
price level is reported in the second column of Table
IV. The predictions appear reasonably accurate.
After about four years, the price level is over predicted by 2.9 percent.
Most of the error in predicting the price level over
this period occurs in 1983. From 1982Q4 to 1983Q4,
the predicted inflation rate exceeded the actual inflation rate by 2.1 percentage points. As revealed by
Table III, the magnitude of the error exceeds the
magnitude of the calendar year error produced from
the within-sample simulations for all years for estimation with old M2, but is smaller for two years for
estimation with M1. The error for 1983 may be
related to the introduction in January 1983 of Super
NOW accounts. The inflation rate, however, begins
to be overpredicted in 1982Q4, rather than in
1983Q1. Alternatively, the historically high rates of
growth of M1 in 1982Q4, 1983Q1, and 1983Q2 in
combination with the severely depressed level of economic activity may have produced a transitory level
of excess real balances, as measured by regression
equation (1). 9 This explanation is consistent with

Table IV

8

dicted price level exceeds the actual price level by an
ever-increasing amount over the post-estimation,
period. 7 By 1984Q3, the predicted price level exceeds
7

This fact casts doubt on an explanation for the rightward shift in the public’s M1 demand function common
in 1982. It was argued that the 1982 recession increased
uncertainty and, consequently, increased the public’s precautionary demand for M1. As measured by the M1
demand function estimated from 1952Q1 to 1979Q4, the
public’s M1 demand function continued to shift rightward after the recovery began in 1982Q4, however. According to the above explanation, the recovery, by reducing economic uncertainty, should have ended, and
even reversed, the rightward shift begun in 1982.

24

The out-of-sample simulation begins in 1981Q1 because
of the assumption that it was the nationwide introduction
of NOW accounts in 1981Q1 that caused the behavior of
the public with respect to M1, to come to resemble its
former behavior with respect to old M2. The estimated
regression equation is modified slightly by constraining
the coefficients to sum to one. No use is made of the
information contained in the autocorrelated errors. In
order to recover predictions in level form, percentage
changes are cumulated from the actual 1980Q4 value of
the price level.
9

What is meant by the expression “excess real balances”
is that some of the adjustment to the unusually high rates
of growth of M1 was accounted for by variables other
than those included in regression equation (1). In particular, individuals and businesses may have drawn down
the level of trade credit that they ordinarily extend among
themselves.

ECONOMIC REVIEW, NOVEMBER/DECEMBER 1984

and $2500 was assumed for NOW accounts and
Super NOWs, respectively. It was also assumed
that all of the minimum balance requirements on
these deposits is met by shifting funds from savings
accounts. Shift-adjusted M1 was then constructed
by subtracting from M1 an estimate of that part of
NOW and Super NOW accounts represented by
minimum balance requirements. Regression equation
(1), estimated with M1 as shown in Table I, was
then simulated from 1980Q1 through 1984Q3 with
this shift-adjusted M1 series. The overprediction of
the price level of about 10 percent shown in column 1
of Table IV was reduced only about three percentage
points. (An attempt to use a cost variable in the
regression that accounted for the increase in the own
rate of return on M1 that occurred due to the explicit
payment of interest on NOWs and Super NOWs
helped only marginally.) The initial balance hypothesis thus requires that consumers, when opening new
OCD accounts, transfer into these accounts an
amount from savings deposits that exceeds the minimum balance requirements. This latter assumption
appears plausible.
The results presented above are summarized in
Charts 1 and 2. Both charts display actual, annualized quarterly inflation rates from 1952Q1 to 1984Q3.
In Chart 1, this series is predicted by the regression
equation fitted with M1 (Table I) and simulated

the reduction in the overprediction of the price level
that appears from Table IV to have started in
1984Q3.
If the Friedman/Schwartz hypothesis is valid, the
recent inflation rate has been low relative to historically high rates of’ growth of M1 in 1982 and 1983
only in part because of the increased demand for M1
due to a decrease in the cost of holding M1 caused
by the fall in market rates and an increase in the own
marginal rate of return on M1. More important
influences in retarding inflation have been the lowering of the trend rate of decline in the demand for M1
and the increased income elasticity of demand for M1.
This latter factor has combined with high rates of
growth of real expenditure since 1982Q1 to keep the
rate of inflation low relative to money growth. Also,
the fact that the recent behavior of inflation is reasonably well predicted under the assumption that the
public’s behavior toward M1 since 1981Q1 resembles
its former behavior toward old M2 suggests that
there was a one-time change in the character of the
M1 demand function in response to financial innovation, with this function approximately stable before
and after the change.
An attempt to implement empirically the initial
balance hypothesis was less successful. A shiftadjusted M1 series was constructed that begins in
1981Q1. A minimum balance requirement of $500

Chart 1

ACTUAL AND PREDICTED INFLATION:
PREDICTED INFLATION FROM REGRESSION FITTED WITH M1

1952

56

60

64

68

72

76

80

84

Notes: Solid line plots the actual, annualized, quarterly percentage growth rates, continuously compounded, of the implicit
gross domestic purchases deflator. The dotted line plots predicted values from a regression equation fitted with M1. From
1952Q1 to 1979Q4, predictions are within sample; from 1980Q1 to 1984Q3, they are out of sample.
FEDERAL RESERVE BANK OF RICHMOND

25

with M1. 10 From 1952Q1 to 1979Q4, these predictions are within sample; and from 1980Q1 to
1984Q3, they are out of sample. The within-sample
predictions appear reasonably accurate.11 Beginning
in 1982, however, inflation is overpredicted to a significant degree. This overprediction indicates a rightward shift in the public’s M1 demand function, at
least as measured by regression equation (1).
In Chart 2, the quarterly inflation rate is predicted

by the regression equation fitted with M2 (Table
I I ) .1 2 From 1952Q1 to 1979Q4, these predictions
are within sample; and from 1981Q1 to 1984Q3, they
are out of sample. Within sample, the regression was
simulated with M2, but out of sample, it was simulated with M1. The within-sample predictions are
reasonably accurate. In the out-of-sample period, the
downward trend in the inflation rate that begins in
1981 is predicted, although inflation is overpredicted
in 1983.

10

The estimated regression equation is modified slightly
by constraining the coefficients on money to sum to one.
Predictions do not make use of the information contained
in the autocorrelated errors.

Predicting Inflation

11

From 1955 through 1960 and from 1974 through 1978,
inflation is somewhat underpredicted. This underprediction indicates a moderate leftward shift in the M1 demand
function. The reduction in M1 demand may have been
caused, in the first instance, by the significant increase in
competition for consumer deposits associated with the
increase in the importance of the thrift industry. The
reduction in M1 demand may have been caused, in the
second instance, by the increase in the importance of cash
management techniques prompted by the high level of
nominal rates on interest in the 1970s. Dummy variables
were incorporated in regression equation (1) in order
to estimate the magnitude of these shifts (but were not
used in any of the results reported in the paper). The
magnitude of these shifts is small relative to changes in
the rate of growth of M1. Although the public’s M1
demand function did exhibit shifts between 1952 and
1979, the moderate magnitude of these shifts relative to
changes in the rate of growth of M1 suggests the usefulness of the view of inflation as a monetary phenomenon.

The Friedman/Schwartz hypothesis implies that
the deregulation of the financial system in the early
1980s has altered permanently the characteristics of
M1. The initial balance hypothesis implies that the
inclusion in M1 of instruments suitable for consumer
saving has caused only a onetime rightward shift in
the M1 demand function; for example, the constant
term in the money demand regression equation (1)
has experienced. a temporary reduction. After the
initial adjustment by the public to financial deregu12

See note 10 above.

Chart 2

ACTUAL AND PREDICTED INFLATION:
PREDICTED INFLATION FROM REGRESSION FITTED WITH OLD M2

1952

56

60

64

68

72

76

80

84

Notes: Solid line plots the actual, annualized, quarterly percentage growth rates, continuously compounded, of the implicit
gross domestic purchases deflator. The dotted line plots predicted values from a regression equation fitted with old M2.
From 1952Q1 to 1979Q4, the simulations are within sample and are performed with old M2. From 1981Q1 to 1984Q3, the
simulations are out of sample and are performed with M1.

26

ECONOMIC

REVIEW,

NOVEMBER/DECEMBER

1984

lation, the M1 demand function will again exhibit its
pre-1981 characteristics. Only with the passage of
time can these two competing hypotheses be tested.
Two sets of predictions of future inflation are made
below in order to aid in discriminating between these
hypotheses in 1985.
First, the inflation rate is predicted for 1984Q4
and for 1985 under the assumption that the public’s
M1 demand function will henceforth reassume its
pre-1981 character. Specifically, inflation is predicted
by simulating with M1 the regression equation estimated with M1 through 1979Q4 (reported in Table
I ) .1 3 Second, the inflation rate is predicted under
the assumption that the characteristics of M1 as currently defined will resemble those of M2 as formerly
defined. Specifically, inflation is predicted by simulating with M1 the regression equation estimated with
old M2 through 1979Q4 (reported in Table II). 14
Predictions of future inflation are conditional upon
the future values assumed for the pertinent explanatory variables. It is assumed that the paper rate will
not change. It is assumed that for 1984Q4 through
1985Q4 per capita real gross domestic expenditure
will grow at an annualized rate of 2 percent. (This
figure is virtually the historical growth rate for this
series between the two business cycle troughs 1949Q4
and 1982Q4.) Also, it is assumed that M1 will grow
at the midpoint of its current four-quarter target
range for 1984Q4, 6 percent, and at the midpoint of
its tentative target range for 1985, 5.5 percent. Over
the decade from 1974 through 1983, the rate of
growth of population was virtually one percent per
year. Under the assumption that population will
continue to grow at this rate, a rate of growth of 5
percent is assumed for per capita M1 for 1984Q4,
and a rate of growth of 4.5 percent for 1985.
The two sets of simulations described above are
reported in Table V. They are, of course, conditional
predictions and will need to be adjusted in light of
the actual behavior of the explanatory variables like
per capita growth in M1. The important point is
that the predictions diverge. By the end of 1985, the
predicted rate of inflation is three percentage points
higher under the assumption that the public’s M1
demand function has reverted to its pre-1981 char13

The coefficients on money are constrained to sum to
one.
l4

See note 13 above.

acter than under the assumption that it has come to
resemble the former old M2 function.15 The behavior
of the actual inflation rate will, therefore, offer evidence on whether the current characteristics of the
M1 demand function have reverted to the pre-1981
characteristics or have changed permanently to reflect
the inclusion in M1 of assets with a savings, as well
as a transactions, property. Assuming that the Federal Reserve System achieves a rate of growth of M1
equal to the midpoint of its target range, and that the
rate at which new OCDs are introduced subsides,. an
inflation rate in 1985 around six percent will favor
the initial balance hypothesis, while an inflation rate
around three percent will favor the Friedman/
Schwartz hypothesis.16
15

The high rates of real expenditure through 1984Q3
depress the predicted inflation rates. Because the coefficients on real expenditure in the regression estimated
with M2 are relatively large in magnitude, this depressing
effect is larger for predictions made with this regression.
Also, the depressing effects last longer for predictions
made with this regression because the distributed lag
relationship between inflation and growth in real expenditure is relatively long.
16

Note that if the initial balance hypothesis is correct,
inflation should actually be somewhat higher than six
percent. In January 1985, the legal minimum balance
requirement on Super NOWs is scheduled to be reduced
from $2,500 to $1,000. According to the logic of this
hypothesis, this reduction should cause a leftward shift
in the public’s M1 demand function as funds previously
used to satisfy minimum balance requirements are moved
back into savings instruments.
For a given rate of
growth of M1, the inflation rate should be temporarily
higher.

Table V

PREDICTIONS OF FUTURE INFLATION RATES

Notes:
Predictions in column 1 are mode with regression equation
(1) estimated with M1 from 1952Q1 to 1979Q4 and simulated
Predictions in column 2 are made with regression
with M1.
equation (1) estimated with old M2 from 1952Q1 to 1979Q4
and simulated with M1.

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27

An Alternative Explanation of M1 Demand
The exposition in this article has concentrated on
two alternative explanations for the recent behavior
of M1 demand because of the author’s belief that the
data on M1 demand that will become available in
1985 will allow one to discriminate between these
explanations. In this section; a third explanation for
M1 demand is discussed. Discrimination between
this last explanation and alternative explanations of
M1 demand will require additional observations for
periods over which interest rates move significantly.
The strength in M1 demand in 1982 and 1983 could
be explained by a rise in the interest elasticity of the
demand for real M1 balances (Brayton 1983) in
combination with the significant drop in the level of
market rates of interest relative to the own rate on
OCDs (Judd 1983 and Judd and Motley 1984). The
rise in the interest elasticity of M1 demand could have
been caused by the appearance of substitutes for M1
like money market mutual funds and money market
deposit accounts (Dotsey 1981/1982). An explanation of the behavior of M1 demand in this spirit
requires that regression equation (1) be modified in
order to take account of the own rate of return on
M1. Construction of this latter variable is discussed
below.
In the case of consumer demand deposits, as opposed to corporate demand deposits, circumvention of
the prohibition of the payment of interest on demand
deposits is a cumbrous procedure. Implicit interest
has been paid on consumer demand deposits by offering check clearing services below cost. This arrangement allows consumer demand deposits to offer a
positive average return. Consumers can increase the
return yielded on their demand deposit balances by
using them more intensively, that is, by writing a
greater number of checks for a given average balance.
They can not, however, increase the return yielded
by- their deposits by holding a larger balance. Specifically, while the implicit average yield on consumer
demand deposits is positive, the implicit marginal
yield is zero (Offenbacher 1982). The introduction
of explicit payment of interest on OCDs has caused
the marginal own yield on these deposits to become
positive. A marginal own rate of return on M1 could
be constructed as a weighted average of the marginal
own rates of return of the various components of M1.
The own rate of return on consumer demand deposits
and on currency would be zero; the own rate of
return on OCDs would be an average of the explicit
rates paid on these deposits; and the own rate of
return on corporate demand deposits would be, a
28

ECONOMIC

REVIEW,

market rate of interest reduced by a factor that accounts for the tax levied by non-interest-bearing required reserves.17
A cost variable that would allow for the maximum
effect on the demand for money in 1982 and 1983 of
the fall in market rates and the increase in the own
rate on M1 is the spread between a short-term
interest rate, for example, the rate of interest on
3-month Treasury bills, and the own rate of return on
M1 (Brayton 1983). This spread measures the
cost of holding M1 balances, that. is; the cost of utilizing the monetary services rendered by M1.18 T h e
hypothesis of this section builds on the fact that the
percentage decline in this spread exceeded the percentage decline in market rates and also on the
conjecture that the magnitude of the coefficient on
such a variable increased in the 1980s. The increased
demand for M1 in 1982 and 1983 is, then, accounted
for by the fall in market rates of interest, both absolutely and relative to the own rate of return on M1.
This fall, in combination with a heightened sensitivity
of M1 demand to spreads between market rates and
own rates on M1, caused an increase in M1 demand.
Evidence useful for evaluating the above hypothesis
will become available when major movements in the
cost of holding M1, as measured by the cost variable
described above, occur. At such a time, a money
demand regression equation of the kind estimated in
Table I, that is, one exhibiting only minimal interestrate elasticity, will produce prediction errors for real
M1 balances that are negatively correlated with the
movement in market rates.
Implications for Policy
The character of the public’s M1 demand function
possesses important implications for monetary policy.
An illustration of this fact concerns the value of the
noninflationary trend rate of growth of M1. If the
Friedman/Schwartz hypothesis is correct, the decrease in the trend rate of decline in the demand for
M1 and the increase in the income elasticity of de17

The division of demand deposits between corporate and
consumer deposits, necessary in order to construct the
own rate of return on M1 as suggested, is only available
beginning in the 1970s in the Board of Governors DeFor this reason, it
mand Deposit Ownership Survey.
was not possible to incorporate an own rate of return
variable into the money demand regression equation (1),
estimation of which carried out for the period beginning
in 1952Q1.
18

In principle, a long-term rate of interest minus the own
rate of return on M1 should enter also. Given the correlation in the movement of long and short rates, entering
both variables would not add significant explanatory
power to the right-hand variables in a regression equation.
NOVEMBER/DECEMBER

1984

mand for M1 will lower the inflation rate associated
with any given rate of growth of M1. The noninflationary trend rate of growth of M1 can be solved for
from regression equation (1) by determining what
rate of growth of money is compatible with zero
inflation, given estimates for the secular behavior of
the interest rate, real expenditure, and population
growth, and given the relevant parameter estimates.19
If the Friedman/Schwartz hypothesis is correct that
M1 now possesses the characteristics of old M2, the
19

It is assumed here that there will be no secular change
in the level of the interest rate. It is assumed that the
secular rate of growth of real per capita gross domestic
expenditure will be two percent, the virtual actual average
between the business cycle troughs in 1949Q4 and
1982Q4. Also, it is assumed that population growth will
be one percent per year. the virtual-actual average over
the decade from-1974 to 1983. With respect to parameter
estimates, it is assumed that the sum of the coefficients
on money is one. The other key parameter estimates are
the secular rate of decline in the demand for M1 and
the elasticity of the demand for M1 with respect to the
real expenditure of the public. These estimates are taken
to be the constant term (.76) and the sum of the estimated coefficients on the real expenditure term (-.94)
that are reported for estimation of (1) in Table II (again
under the assumption that the demand function for M1
now resembles that for old M2).

noninflationary rate of growth of M1 rose after 1981
about two percentage points to a current level slightly
in excess of two percent per year.
Summary
Two competing hypotheses have been exposited in
this article concerning the nature of the public’s M1
demand function in the 1980s. They were chosen
because of the likelihood that observations on the
behavior of the public’s demand for real M1 balances
in 1985 will offer evidence on their validity. The
first hypothesis, labeled the Friedman/Schwartz hypothesis, predicts a lower rate of inflation in 1985
than the second hypothesis, labeled the initial balance
hypothesis. A third hypothesis was also exposited.
Evidence relevant for assessing its validity will become available in 1985 if a major movement in market
rates of interest occurs. Knowledge of the nature of
the public’s M1 demand function is important in
order to assess the impact on the expenditure of the
public of a particular rate of growth in M1. This
knowledge is also important in order to determine the
value of the noninflationary rate of growth of M1.

References
Brayton, Flint; Terry Farr; and Richard Porter. “Alternative Money Demand Specifications and Recent
Growth in M1.” Board of Governors of the Federal
Reserve System (May 23, 1983), mimeographed.
Coats, Warren L., Jr. “Modeling the Short-Run Demand for Money with Exogenous Supply.” Economic Inquiry (April 1982), pp. 222-239.

Hetzel, Robert L. “Estimating Money Demand Functions.” Journal of Money, Credit, and Banking
(May 1984), pp. 185-193.
Judd, John P. “The Recent Decline in Velocity: Instability in Money Demand or Inflation?” E c o n o m i c
R e v i e w , Federal Reserve Bank of San Francisco
(Spring 1983), pp. 12-19.
and Brian Motley. “The ‘Great Velocity
Decline’ of 1982-83: A Comparative Analysis of
M1 and M2.” Economic Review, F e d e r a l R e s e r v e
Bank of San Francisco (Summer 1984), pp. 56-68.
Laidler, David. Monetarist Perspective. C a m b r i d g e :
Harvard University Press, 1982.

Fama, Eugene F.
“Inflation, Output, and Money.”
Journal of Business (April 1982), pp. 201-231.
Harberger, Arnold C. “The Dynamics of Inflation in
Chile” in M e a s u r e m e n t i n E c o n o m i c s . S t a n f o r d ,
CA: Stanford University Press, 1963.

Offenbacher, Edward; Paul Spindt; and Clif Wilson.
“Recent. Behavior of the Divisia Monetary Aggregates.” Board of Governors of the Federal Reserve
System (April 9, 1982), mimeographed.
Schwartz, Anna J. “Monetary Issues.” N B E R R e porter (Winter 1983/4), pp. 14-18.

FEDERAL RESERVE BANK OF RICHMOND

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