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Review ___________
Vol. 69, No. 7

August/September 1987

5 Solving the 1980s’ Velocity Puzzle:
A Progress Report
24 A Revision in the M onetary Base

The Review is published 10 times p e r year by the Research and Public Inform ation Department o f the
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Federal R eserve Bank o f St. Louis
Review
August/Septem ber 1987

In This Issue . . .

For more than a third o f a century, the velocity o f money — the ratio o f GNP to
M l — grew at a relatively stable rate o f slightly more than 3 percent per year. This
stable relationship contributed to the rise o f monetarism and the adoption of
m onetaiy aggregate targets by the Federal Reserve. Since 1982, however, there has
been a dramatic change in the behavior o f velocity: it has grown more variably
and, on average, has declined by more than 2 percent per year.
This dramatic and unanticipated turnaround has produced a myriad o f wouldbe explanations. In the first article in this Review, “ Solving the 1980s’ Velocity
Puzzle: A Progress Report,” Courtenay C. Stone and Daniel L. Thornton evaluate
the validity o f the major theories about velocity’s puzzling behavior in recent
years. After grouping the various theories into three categories — misspecification, structural shifts and cyclical factors — the authors show that, with the
possible exception of one variant o f the financial innovations explanation, no
single theory successfully solves the velocity puzzle. Moreover, w hile certain
explanations in tandem appear to offer some insight into velocity’s behavior, they,
too, prove insufficient to solve the complete puzzle.

The adjusted m onetaiy base, a series published by the Federal Reserve Rank of
St. Louis, is a measure o f the Federal Reserve’s influence on the money stock. In
the second article in this issue, “A Revision in the M onetaiy Rase,” R. Alton Gilbert
describes how this series was recently revised to incorporate the final phase-in of
the reserve requirement structure specified in the Monetary Control Act o f 1980.
The new structure o f reserve requirements is used in deriving the adjusted
m onetaiy base from Novem ber 1980, when the phase-in began, to the present.
Data for the prior series, which are used for periods before November 1980, are
linked to the post-November 1980 data to create a continuous adjusted m onetaiy
base series.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

Solving the 1980s’ Velocity Puzzle:
A Progress Report
Courtenay C. Stone and Daniel L. Thornton

M . HE velocity o f m oney measures the relationship
between nominal incom e and the m oney stock. In its
simplest form, the quantity theory o f money states
that nominal incom e is equal to the money stock
m ultiplied by its velocity. If velocity is reasonably
stable, changes in the m oney stock have predictable
consequences on nominal income; if the money stock
is controllable as well, the quantity theoiy has useful
implications for econom ic policy.' The relationship
between m oney growth and inflation can be derived
from the quantity th eoiy framework by “breaking u p ”
nominal incom e into its two components — the price
level and real output. Thus, the stability of the monevprice link, holding real output constant, is also related
closely to the stability o f velocity.
For over a third o f a century — from 1946 to 1981 —
the growth o f the velocity o f money, measured as the
ratio o f gross national product (GNP) to the narrow
money stock (M l), was stable. Its stability contributed

Courtenay C. Stone is a senior econom ist and Daniel L. Thornton is a
research officer at the Federal Resen/e Bank o f St. Louis. Rosemarie V.
M ueller provided research assistance. The authors w ould also like to
thank M ichael Darby for helpful suggestions on an earlier draft.
’The money stock need not be perfectly controllable; neither, for that
matter, must velocity be constant. M ovem ents in velocity (or its
growth), however, must be explainable by the behavior of the
variables that influence it. This idea, fundam ental to macroeconom ic
policy, was developed by Friedman (1956). See Thornton (1983) for
a discussion of the role of velocity for policy purposes.

to the rise o f monetarism and the adoption o f m one
tary aggregate targets by the Federal Reserve and other
central banks around the world. Its stability also re
sulted in two em pirically based rules o f thumb that
came to be used fairly successfully as guides to m oney
grow th’s effects on incom e and inflation. Now, how
ever, analysts believe that these rules have failed to
explain the course o f incom e and inflation during the
1980s, due to a relatively sudden and unanticipated
drop in velocity.
Given the important role that velocity plays in eco
nomic and policy analysis, it is not surprising that
considerable effort has been devoted to solving this
velocity puzzle. Unfortunately, these efforts have pro
duced a w elter o f com peting and occasionally confus
ing explanations. To bring some order to this disarray,
this article highlights the problems that have resulted
from the puzzling behavior o f velocity in recent years
and examines the more prominent explanations o f the
velocity puzzle.
Because the concept o f velocity stems directly from
the theoiy o f the dem and for money, anything that
affects velocity can be related to some aspect o f the
demand for money. (See shaded insert on the follow
ing page.) Because the demand-for-money approach
is likely to be less intuitive to the general reader,
however, w e w ill discuss the various explanations o f
the velocity puzzle in terms o f velocity itself.

AUGUST/SEPTEMBER 1987

FEDERAL RESERVE BANK OF ST. LOUIS

Velocity and the Demand for Money
The demand for money is usually expressed as de
pending on GNP and various other factors, denoted bv Z.
That is, the demand for money can he written as:
(1) M l = ftGNP, Z).

Under certain technical conditions it is possible to re
write (1) as:
(2) Ml = GNP f(Z), or
(31 Ml/GNP = f(Z).
Since velocity is simply the reciprocal of equation 3, it
can be written as:
(4) Velocity = GNP/M1 = —1— = giZ).
fIZl

it is possible to characterize all "explanations" of the
velocity puzzle in terms of equation 4, which is a slightly
rewritten version of the demand for money. For example,
suppose that equation 1 is not the correct specification
of the demand for money, that instead, money demand
depends on some broad transactions measure, T, rather
than GNP. The true measure of velocity would not be
equation 4: instead it would be:
15) T/Ml = k(Z).
If velocity as defined in equation 4 were stable for a
number of years it would imply that GNP was roughly
proportional to T, or GNP = aT, where a is a constant.
Consequently, the usual measure of velocity is just a
times the "tme" measure, that is, IGNP/M1) = ql(T/M1I.
While the level of the usual measure of velocity would be
wrong, its movements would mimic movements in the
true velocity measure. If this characterization were cor
rect, the crucial question is not "Why did velocity de
cline?” ; instead, it is "What caused the break in the
relationship between T and GNP?"
Alternatively, GNP may be proportional to T in the long
run but there may be short-run, cyclical variations in
GNP relative to T. This characterizes the argument that
GDFD is a better measure of transactions than GNP when
there are sizable changes in net exports and inventories.
The tax-cut explanation of the decline in velocity is
analogous, except that a reduction in marginal lax rates

can increase the demand for money, permanently re
ducing velocity. It argues that the demand for money
depends on after-tax income, not on GNP. A cut in the
marginal tax rates increases after-tax income and, hence,
the demand for money relative to GNP. The usual mea
sure of velocity falls, though the "correct measure,"
based on after-tax income, does not.
The arguments based upon the incorrect measure of
money are analogous to those that contend the use of
GNP is inappropriate. For example, let M* denote the
theoretically correct measure of money. If GNP is- the
correct scale variable, the correct measure of velocity
would be:
(61 GNP/M* = w(Z).
The extent to which equation 4 is a good proxy for
equation 6 depends on the relationship between M* and
M. Again, the interesting questions are “Why was equa
tion 4 stable for so long?” and "What caused the recent
shift in the relationship between M l and M*?”
Structur al shift arguments imply that there has been a
change in the functional relationship determining veloc
ity, that is, a change in g(-). Such a change could be due to
a number of factors. The key point is that the former
relationship no longer explains velocity. The important
issues are to identify the factor(s) that produced this shift
and to identify the new relationship. In some sense,
specification problems can be thought of as structural
shifts because they are presumed to result from some
shift in the underlying relationships, for example, be
tween GNP and T or between Ml and M*.
The cyclical explanation can be characterized by unu
sual movements in the factors that determine the de
mand for money, Z. Unusual movements in these vari
ables can produce the appearance of unusual behavior
in velocity. For example, one element of Z is the nominal
interest rate. Because the demand for money is inversely
related to the nominal rate of interest, a decrease in the
interest rate could increase the demand for money rela
tive to GNP, causing measured velocity to decline. For
this explanation to be valid, however, there should have
been a similar rise in velocity when the interest rate was
rising.

AUGUST/SEPTEMBER 1987

FEDERAL RESERVE BANK OF ST. LOUIS

WHAT WENT WRONG AND WHEN?
Tw o fundamental relationships between M l and
specific econom ic measures have been supported em
pirically for decades. One relationship is the link be
tween m oney and GNP, a measure o f total incom e in
the economy. The second relationship is the link be
tween money and prices. Charts 1 and 2 show the
dramatic changes in these relationships that occurred
during the 1980s.
Chart 1 depicts the behavior o f the incom e velocity
(GNP divided by M l ) for the past 40 years; as the chart
suggests, something unusual occurred to velocity
around 1982. From 1946 through 1981, it rose fairly
steadily at about 3.6 percent per year; since then, it has
declined at an annual rate o f about 2.4 percent.
Chart 2 shows the relationship since 1948 between
annual inflation (as measured by the growth o f the
GNP deflator! and the average growth in M l over a
three-year period; use o f M l ’s trend growth is de
signed to capture the long-run impact o f m oney on
prices. W hile the rate o f inflation deviated from the
trend growth o f M l, sometimes substantially, from
1948 to 1981, the deviations generally w ere temporary.
More importantly, the larger deviations w ere attribut
able to non-monetary events (for example, govern
ment mandated wage-price controls, OPEC oil price
actions and the like). Since 1982, however, inflation has
been substantially and persistently below the trend
growth in M l. These deviations are not easily attribut
able to a specific non-monetary event.
Numerous attempts have been made to explain the
recent changes in velocity. In this paper, these expla
nations are grouped loosely into three categories: misspecification, a portmanteau category w e call "struc
tural shifts” and cyclical factors.2

MISSPECIFICATION
The most w idely used velocity measure, the income
velocity o f M l, is calculated bv dividing nominal GNP
bv the nominal stock o f M l. Both GNP and M l are
empirical counterparts to theoretical concepts that
appear in various theories o f the demand for money.
One explanation for the shift in velocity is that GNP or

2A number of these are considered in studies by Rasche (1986),
Darby et. al. (1987), Hetzel (1987), Trehan and Walsh (1987) and
Kretzmer and Porter (1987). The categories considered here are
somewhat more general than those considered by Trehan and
Walsh.

M l or both have becom e less reliable proxies for their
corresponding theoretical concepts. This problem is
called a specification problem.3

GNP Vs. Transactions Measures
One specification problem could arise if m oney is
held primarily to make daily transactions.4 If these
include intermediate and financial transactions, the
usual velocity measure could vary with changes in the
proportion of such transactions relative to transac
tions on final goods and services. Because GNP mea
sures only final output, it w ill differ w idely from the
level o f expenditures on all transactions. In this case,
GNP is a useful proxy for total transactions only if the
proportion o f GNP to total transactions remains rela
tively constant.
This problem can manifest itself in several wavs. For
example, suppose consumers purchase more goods
and, as a result, increase their m oney holdings in
proportion to their increased desire to spend. If these
newlv purchased goods are imported or drawn from
domestic inventories o f previously produced goods,
GNP w ill remain unchanged w hile the demand for
m oney rises. Consequently, the usual measure o f ve
locity w ould decline, w hile an alternative measure
based on total transactions w ould remain unchanged.
Thus, using GNP as the transactions measure to calcu
late velocity may produce sizable swings in velocity
w henever there are large swings in inventories or net
exports. Some analysts have argued that gross domes
tic final dem and (GDFD), which equals GNP minus
inventory adjustments and net exports, is preferable
to GNP as the transactions proxy.5 Unfortunately, the
substitution o f GDFD for GNP does not explain the
velocity pu zzle o f the 1980s. As chart 3 indicates, this
velocity measure performs essentially the same as the
usual measure both before and after 1981. Conse
quently, simply replacing GNP with GDFD does not
explain the protracted velocity decline during the
1980s.K

3See the appendix to Thornton (1983) for an illustration of the
specification problem involved in finding the appropriate m easure of
“ incom e.'’
“There are two distinct, though not mutually exclusive theories of the
demand for money: the transactions approach and the asset ap
proach. The asset approach em phasizes the role of m oney as an
asset and, hence, as an alternative way of holding wealth. The
transactions approach em phasizes the role of money as a medium
of exchange. For a useful discussion of this distinction in relation to
the velocity issue, see Spindt (1985).
5Radecki and W enninger (1985).
6Rasche (1986) also rejects this explanation for much the same
reason.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

C h a rt 1

Velocity

2 \r I 1 1__
1946

C h a rt 2

Inflation and Ml-Trend Growth

J— L J __ 2

1 1__ I__ __ I__ I__ I__ L J __ I__ I__ __ I__I__ I__ __ I__ I__ L -L.J— I— I__ __ I__ 1
— I— — I— I— 1
66

1986

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

C h a rt 3

Velocities of GNP and GDFD
Ratio
7.5

Ratio
7.5

Q u a r t e r ly D a t a

7.0

\ J

6.5

\\
\\
\\
U -

j r
6.0

5 .0

6.0

_ /

5.5

6 .5

5 .5

5 .0

6DF D/ M1
GNP / M1
4.5

4.5

y *

4.0

3 .5

3.5

1 1 1

3 .0
1961

1 1 1
67

1
73

Recently, McGibany and Nourzad (1985) have of
fered another variant o f the specification problem.
They too argue that the dem and for m oney is based on
expenditures instead o f current incom e or GNP. In
their view, the 1980 tax cut initially increased disposa
ble personal and business incom e relative to GNP and,
hence, raised desired expenditures relative to GNP;
consequently, the tax cut increased the demand for
money, resulting in a fall in velocity.7
One way to evaluate this explanation is to look at fhe
ratio o f disposable personal incom e to GNP. If their
explanation is valid, this ratio should increase when
velocity is falling and decrease when velocity is rising.
As chart 4 indicates, however, this has not generally
happened during the 1980s. While there was an initial
expansion in disposable incom e following the tax cut,
the ratio o f disposable incom e to GNP has generally
declined since 1982."

7Recently, M cGibany and Nourzad (1986) have provided estimates
indicating that the demand for m oney is inversely related to the
average tax rate.
8Rasche (forthcoming) rejects the tax cut hypothesis by arguing that,
for it to explain the velocity decline, marginal tax rates would have had
to have fallen continuously over the 1980s.

i
75

i
77

i
79

1
81

1
83

i
85

3.0

1 987

Others have argued that the recent velocity decline
is related to a sharp rise in financial transactions
relative to total output. According to this view, the rise
in financial transactions caused an increase in the
demand for m oney relative to GNP. One way to assess
this claim is to compare velocity measures using
broad measures o f financial and non-financial trans
actions in place o f GNP.’ These alternatives are pre
sented in chart 5. The non-financial transactions ve
locity measure shows the same pattern as the GNP
velocity measure. Consequently, explanations o f the
velocity puzzle that rely on the recent slowing o f GNP
growth relative to the growth o f more general nonfinancial transactions measures are implausible.
The financial transactions velocity measure does
not show the downturn in the 1980s that characterizes
the non-financial and GNP-based velocity measures.
Nor, however, does it show substantial increases dur
ing the 1980s which w ould be required if the rise in
financial transactions is to account for the decline in
M l velocity. In fact, the annual growth rate o f the
financial transactions velocity measure has averaged
9These data were obtained from the Board of G overnors of the
Federal Reserve System.

AUGUST/SEPTEMBER 1987

FEDERAL RESERVE BANK OF ST. LOUIS

C h a rt 4

Ratios of G N P /M 1 and Disposable Incom e/G NP
Ratio
7.5

Rat io
.7 4

Q u a r t e r ly D a ta

ry\ .

7.0

.73

1.5

.72

6.0

/Vs

t \

5 .0

f \

; ( }

5.5

/ \

i \ a

' V

.70

1 1i
V

4.5

.71

fi
1
1

I M\ / h >
w v
1

\>j

.69

i Disposable income/GNP
^

SCA LE

.68

.67

4 .0

GNP/M1
^ S C A IE

.66

3.5

3 .0

_ L - 1 ..... 1 - .
1961

i
67

i
69

i
71

i
75

i
77

.65

1 987

C h a rt 5

Velocities of Financial and N onfin ancial Transaction Debits
Ratio
280

Ratio
23.0

Q u a r te r ly D a ta

Nonfim ncial transactio n debts/M I
s c a le |

250

21.5

220

______ ^

19 0

20.0

18.5

\
\

160

/
/\

130

1 7. 0

\
\

15.5

/
r

100

/
14.0

12.5

Rn ancial transactio n debts/MI
fsc UE
1

40
1970

10FRASER
Digitized for

1
77

1 1

11.0
1 987

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

C h a rt 6

Ratios of GNP/M 1 and NYSE/GNP

about 10 percent since 1981, somewhat below its 12
percent annual growth rate from 1970 to 1981. If this
measure accurately represents total financial transac
tions, its velocity movement does not support the view
that the velocity problem resulted from a shift from
non-financial transactions to financial transactions.
A somewhat different way to assess w hether a rise in
financial transactions produced the fall in velocity is
shown in chart 6; it compares the movement of veloc
ity with that o f the annual ratio o f the value o f shares
sold on the N ew York Stock Exchange (NYSE) to GNP
since 1926.'" While the ratio o f NYSE sales to GNP has
risen somewhat during the 1980s, there has been no
consistent relationship between this ratio and velocity
over the past 60 years.

GNP Vs. Wealth
Another potential specification problem arises from
the use o f GNP to calculate velocity instead o f using a

,0lt has been argued that the recent decline in velocity can be
explained by the rise in stock m arket transactions, see Morgan
Guarantee (1986).

measure o f “permanent incom e” or wealth. The per
manent incom e theory o f consumer dem and suggests
that individuals primarily base their consumption de
cisions on their permanent incom e or wealth, rather
than on current income. Analogously, the demand for
m oney may be more closely related to permanent
incom e or wealth." Panel A in figure 1 illustrates the
theoretical relationship between permanent incom e
and measured incom e during cyclical fluctuations. If
the demand for m oney depends upon permanent
income, it will fluctuate less than w ill current income
over the business cycle. Thus, measured velocity will
rise (fall) as measured incom e increases (decreases)
relative to permanent incom e because the amount of
m oney held w ill change less than measured income.
Chart 7 displays both the usual velocity measure
and one based on permanent incom e estimates.12
Once again, it does not appear that the velocity d e
cline in the 1980s is explained by movements in cur

s o r example, see Friedman and Schwartz (1982, p. 38).
,2The m easure of perm anent incom e used here was suggested by
Darby (1972).

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

F ig u r e 1

Cyclical M o vem en t in A ctu al GNP and M easu red Velocity
and the Effect of a O ne-Tim e Increase in Perm anent Income

(B)

(A)

C h a rt 7

Velocities of G N P /M 1 and Permanent In c o m e /M l
Ratio

Ratio

Q u a r t e r ly D a ta

7 .5

7 .0

6 .5

/ V

i
/

6.0

i* '

6.0

Permanent in c o m e /M I

5 .5

___ '■

5 .0

?^GM P/M 1
4 .5

4 .5

4 .0

3 .5

3 .0

3 .5

/
.

I ... I
1961

Digitized for
12FRASER

I
63

I
65

1
67

1
71

1
75

1
77

___L
79

1
81

J___
83

1
85

!
1987

3 .0

FEDERAL RESERVE BANK OF ST. LOUIS

rent relative to permanent income. Although the
downturns in the permanent incom e velocity m ea
sure are less pronounced than those in the current
incom e velocity measure, the general downward shift
in velocity during the 1980s shows up clearly in the
permanent incom e velocity measure.
There is an explanation consistent with the perma
nent income or wealth approach to the demand for
m oney and the observed decline in the incom e veloc
ity o f m oney in recent years. Suppose that a rise in
permanent incom e or wealth relative to current in
come produced a sharp rise in the dem and for
money.13In this event, depicted in panel B in figure 1,
there w ould be an associated drop in current income
velocity.
Because wealth is the present value o f the expected
future net income, it w ill increase either if expected
incom e increases or the expected real interest rate
used to discount future incom e declines. If there was a
rise in expected incom e without a corresponding in
crease in measured incom e during the 1980s, velocity
w ould have fallen as the demand for money increased
relative to GNP. Eventually, measured incom e w ill rise
or expected incom e will decline as individuals realize
that their expectations w ill be unfulfilled.14 Conse
quently, after sufficient time has elapsed, velocity will
return to its former path.
If the rise in wealth is due solely to a sharp fall in
society’s preference for current relative to future con
sumption, however, the path o f measured income
w ould be unaffected and the level o f velocity w ould be
permanently below its form er path. This possibility
seems unlikely, because it implies a permanent fall in
the real interest rate.13

,3Rasche (1986), Santoni (1987) and Kopcke (1986) also consider
the wealth explanation. Though their approaches are different, both
Rasche and Santoni reject the wealth explanation for the velocity
puzzle. Kopcke, on the other hand, finds evidence to support it. His
wealth measure, however, includes financial assets that have off
setting liabilities; consequently, at best, it represents a proxy for
financial transactions.
14Since wealth is the discounted present value of the stream of
expected future income, an exogenous increase in wealth relative to
current income can result only from a fall in the “ real” interest rate or
an increase in the expected future income stream. If these latter
expectations are correct, m easured incom e will eventually increase,
and velocity will eventually return to its long-run level as either the
nominal m oney stock expands or the price level falls. If the expecta
tions prove to be wrong, this too will be discovered and velocity will
rise subsequently.
15The perm anent fall in the real interest rate necessary to explain the
fall in velocity is inconsistent with recent estim ates of the ex ante real
interest rates during the 1980s. See Holland (1984).

AUGUST/SEPTEMBER 1987

Potential Problems with Using M l
Some have suggested that using M l as the m oney
stock measure w hen calculating velocity causes sig
nificant problems. They argue that the relevant m one
tary measure cannot be obtained simply by adding
together the stocks o f various “m onetary” assets (cur
rency, checkable deposits, and so on), because each
component may provide different quantities o f m one
tary services per unit. Consequently, critics have sug
gested that an index o f the monetary “ services” pro
vided by the stock o f all relevant financial assets is
preferable to the use o f M l for evaluating the relation
ship between m oney and spending or prices.16If this
criticism is valid, changes in “ simple-sum” monetary
aggregates like M l and M2 may deviate markedly from
changes in their underlying monetary services w hen
ever substantial shifts among various m onetaiy assets
occur. In such cases, the usual measure o f velocity
may show sizable variations, w hile those based on the
underlying m onetary services measures should be
relatively stable.17
Various monetary services indices (MSI) and the MQ
measure have been developed; they are currently
com piled and maintained by the Federal Reserve
Board on an experimental basis.18The MSI1 measure is
an index o f the monetary services associated with
components o f the M l m oney stock. The M Q measure
is an index o f all financial assets that can be directly
used in transactions; it incorporates the components
of M l plus telephone transfers, m oney market mutual
fund balances and m oney market deposit accounts.
Chart 8 shows velocity measures based on the MSI1
and MQ.19 These velocity measures show the same
general pattern for recent years as the usual M l veloc
ity measure. Similar results hold for broader m onetaiy
services indices. Consequently, despite their theoreti
cal appeal, substituting monetary service flows for M l
in measures o f velocity does not explain the recent
behavior of velocity.20

16See Batten and Thornton (1985) for a discussion of these issues.
,7This need not be the case, however. See Milbourne (1986).
18The m onetary services indices originally were called Divisia m one
tary aggregates; they were developed by W illiam Barnett (1980).
The MQ m easure was developed by Paul Spindt (1985). The current
monetary services indices differ from the original Divisia m easures
in several respects; see Farr and Johnson (1985).
19These alternative m oney measures are only available since 1/1970.
“ This interpretation is invariant to alternative measures of income
(perm anent income or GDFD).

AUGUST/SEPTEMBER 1987

FEDERAL RESERVE BANK OF ST. LOUIS

C h a rt 8

Velocities of M onetary Indexes M Q , MSI 1 and M l

1 97 0

1987

N O T E : D a ta n o r m a liz e d f ir s t q u a r t e r 1 9 7 0= 1.

STRUCTURAL SH IFTS AND THE
VELOCITY PUZZLE
Some analysts have suggested that there have been
one or more structural shifts in the money/income
relationship. Unlike the specification problems previ
ously discussed, this explanation presumes that the
fundamental relationship between m oney and in
com e has changed even if the demand for m oney is
correctly specified in terms o f M l and GNP.’ ’ (For a

2'One structural shift argum ent not considered explicitly in the text
was presented recently by Roley (1985). He suggested that the
velocity puzzle of the 1980s was actually caused by the welldocumented, albeit still unexplained, structural shift in the demand
for m oney that took place in 1974. He argues that the downward
shift in velocity in the 19 8 2-8 3 period is consistent with the behavior
of M1 velocity from 1974 through 1981; it is inconsistent, however,
with M1 velocity before 1974. Roley’s observation does not solve
the velocity puzzle — although about 13 years have passed, we still
don't know w hy m oney demand shifted in the m id-1970s.
Furthermore, if his suggestion were valid, the mid-1970s' velocity
increase should have been as dram atic as its drop in the 1980s. A
glance at chart 1 shows that this is not the case. Moreover, Roley’s
M1 series was derived from the flow of funds accounts. When
conventional money stock and m oney demand equations are used
instead, his results are not confirmed.

Digitized for
14FRASER

different structural shift argument, see shaded insert
on the opposite page.

Financial Innovation and Deregulation
Several analysts have suggested that the introduc
tion o f NOWs, Super NOWs and m oney market deposit
accounts (MMDAs) and the removal o f regulation Q
interest rate ceilings in recent years have produced a
shift in the relationships between M l and both spend
ing and inflation. In particular, the redefinition o f M l
to include interest-bearing checkable deposits (NOWs
and Super NOWs) as w ell as non-interest-bearing de
mand deposits and currency is alleged to have altered
significantly its “moneyness;” n ow M l is presumed to
include a significant amount o f savings balances.22
Consequently, changes in M l resulting from changes
in these savings balances are likely to have a smaller

22jh e reader should note the sim ilarity between this and the specifica

tion problem. The argum ent here is that savings balances are now
effectively hidden among transactions balances so that a given level
of interest-bearing checking account balances effectively can repre
sent different am ounts of “ transactions m oney.” This is a specifica
tion problem, and results from a fundam ental change in the institu
tional structure.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

A Time Series Explanation of the Velocity Puzzle
Some analysts have argued that the decline in velocity
can be explained by analyzing the statistical properties
of economic time-series data. To understand this expla
nation for the seemingly abrupt change in velocity in
recent years requires a brief discussion of the time series
properties of economic variables.
The time series properties of a variable describe how it
behaves over time. A variable that tends to return to its
mean (average) level through time is said to be “station
ary." Many economic time series are not stationary in
this sense; instead, they show positive or negative
growth over time. Time series that display such growth
patterns are often said to be “trend stationary” and many
economic series, including GNP, prices, the money stock
and velocity, have long been viewed as trend stationary,
orTS processes.
In addition to the TS process, there is an alternative
stationary time series process that describes variables
whose first- or higher-order differences are stationary;
these are called "difference stationary (DS) processes.”
The simplest DS process is the well-known random walk.
Unlike TS variables, a variable whose behavior fits the
random walk has no trend to which it returns as it moves
over time.1
Recently, Nelson and Plosser (1982) and Haraf (1986)
have concluded that velocity is better represented by the
DS than the TS model. According to this view, the recent
change in velocity could have been produced bv a large

impact on output and prices than previously.-3Specifi
cally, there may be extended periods when significant
increases in M l produce little or no associated growth
in spending or inflation; on these occasions, velocity
w ould decline substantially.24Moreover, if the savings
portion o f M l is related to GNP differently than its

23From another perspective, the growth rate of old M2 velocity had a
trend growth rate of zero; see O tt (1982). Some have argued that
new M1 is close to old M2 — old M1 plus tim e and savings deposits,
so perhaps the trend growth rate of its velocity, too, will be about
zero. W hile the period since 1981 is too short to establish a trend,
the growth rate of the new M1 velocity over this period has been
about - 2 . 4 percent.
24W hile the experim ental m onetary aggregates should reduce or
elim inate such problems, this does not seem to be the case. See
Batten and Thornton (1985, pp. 3 2 -3 3 ) for a discussion of this point.

shock that caused velocity to wander off in a new direc
tion; the probability it will wander back is very small.
As Rasche (1986), McCallum (1986) and others have
pointed out, however, it is extremely difficult to deter
mine whether velocity is a TS or DS process; the test used
to discriminate between the competing representations
is not powerful when used on time series data like
velocity. Consequently, there can be reasonable dis
agreement about which representation is more accurate.
Unfortunately, knowing whether velocity is better
characterized by a TS or DS process does not tell us what
we would like to know. Suppose velocity has a DS time
series. While this might indicate that an unusually large
shock caused velocity to wander off in a new direction in
recent years, it leaves a more interesting and more im
portant longer-run velocity puzzle: Why was velocity’s
growth rate stable for the past 30 years? Is it plausible
that, for such a long period, there were no shocks large
enough to make velocity walk away from its apparent
trend before 1982? Moreover, and more importantly,
what economic factors determine velocity’s DS process
and what was the nature of the shock that caused veloc
ity to walk off in a new direction? Even if economists
could be completely certain about the time series pro
cess that generates velocity, these fundamental eco
nomic questions would remain.
'A random walk may be said to drift; however, this drift param eter
is not related to tim e as it would be in a trend stationary process.

transaction components, the relationship between
the growth rates o f M l and GNP may be permanently
altered.
These savings balances appear only in the “other
checkable deposits” (OCD) component o f M l. Thus,
the validity o f this explanation can be examined by
comparing the behavior o f velocity measures using
M IA (which consists o f currency and non-interestbearing checkable deposits) or currency alone with
that o f the M l velocity measure during the 1980s. By
increasing the cost o f holding currency and demand
deposits, the introduction o f interest-bearing checka
ble deposits (NOWs and Super NOWs) should have
induced a relative shift from demand deposits and
currency into these new accounts; this, in turn,
should produce a significant rise in currency and M IA
velocity measures. Once individuals’ portfolios are

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

C h a rt 9

Velocities of G N P /M 1 and G N P /M 1 A

realigned, however, the prior currency and M IA veloc
ity relationships should be restored.

interest rate w ill cause the dem and for m oney to rise
relative to GNP and, hence, velocity w ill decline.

Charts 9 and 10 show the M IA - and currencyvelocity measures. The M lA-velocity measure and, to a
lesser extent, the currency-velocity measure rose
sharply in the first quarter o f 1981 when NOWs were
introduced nationwide. Contrary to this structural
shift explanation, however, both measures subse
quently declined.25

The theoretical basis for this argument stems from
basic consumer dem and theory, which argues that
the responsiveness o f the demand for a com m odity to
changes in its price increases with the number and
closeness o f substitute goods. The financial innova
tions of the 1980s produced new and close substitutes
for traditional dem and deposit and currency com p o
nents o f M l. While the interest rate is not the price of
money, it represents a significant opportunity cost for
holding it. Consequently, the financial innovations o f
the 1980s should have increased the responsiveness o f
some o f the components o f M l to changes in the
interest rate. The “other-checkable-deposit” com p o
nent o f M l bears interest, and the interest rate paid on
these deposits is n ow free to change with market
rates.26Consequently, this com ponent o f M l should be

Another explanation for the change in M l velocity is
an increased responsiveness o f various M l com p o
nents to changes in the interest rate. According to this
explanation, the financial innovations o f the 1980s did
not necessarily cause a downward shift in velocity due
to a shift o f savings balances into transactions ac
counts; instead, they altered the sensitivity o f M l bal
ances to interest rates. Since the demand for m oney is
inversely related to the interest rate, a decline in the

25This is the basis for R asche’s (1986) rejection of this explanation.
The introduction of these new accounts, however, m ay have
increased the interest elasticity of the demand for the M1A
components.

Digitized 16
for FRASER

“ Businesses cannot hold interest-bearing checking accounts. See
G ilbert and Holland (1984) for a sum m ary of the major innovations
and deregulations of the 1980s. Also, the currency com ponent of M1
generally is m ore closely tied to real income than to interest rate
movements.

AUGUST/SEPTEMBER 1987

FEDERAL RESERVE BANK OF ST. LOUIS

C h a r t 10

Velocities of G N P /M 1 and GNP/Currency
Ratio

Q u a r t e r ly D a ta

Ratio

P/currency
SC ALE^

relatively unresponsive to interest rate movements.
This could be mitigated by the fact that rates on these
deposits appear to have been slow to adjust to
changes in other market interest rates.
This view suggests that the relationship between
velocity and interest rates should have strengthened
since the financial innovations o f the 1980s. Indeed,
this pattern is reflected in Chart 11, which shows 1VI1
velocity and the three-month Treasury bill rate. Prior
to 1981, velocity appears to be unrelated to m ove
ments in the T-bill rate. Since 1981, however, the two
have similar patterns. This is consistent with a num
ber o f studies which report an increased interest sen
sitivity o f M l balances during the 1980s.27 (Additional
analysis is provided in the appendix.) It remains to be
seen whether the apparent change in M l ’s interest
sensitivity alone can account for the aberrant behavior
o f M l velocity.
27For example, Hetzel (1987), Trehan and Walsh (1987) and Rasche
(1986). Rasche reports mixed results and concludes that this argu
ment needs further study and analysis.

CYCLICAL EXPLANATIONS OF THE
VELOCITY PUZZLE
Until now, w e have assumed im plicitly that the
supply o f m oney passively expands to m eet society’s
demand. Another interpretation argues that substan
tial exogenous changes in the supply o f M l can induce
cyclical swings in measured velocity because o f their
lagged effect on the economy. For example, an acceler
ation in the growth rate o f M l initially may produce a
less than proportionate rise in the level o f nominal
GNP, and, thus, an initial decline in velocity. Eventu
ally, however, when the m onetary change has w orked
its w ay throughout the econom y fully, the longer-run
relationship between M l growth and the rate o f
spending is reestablished, and velocity returns to its
long-run path.
This analysis can explain a continuous fall in veloc
ity relative to its underlying trend only if M l growth is
continuously accelerating. The “ever-and-ever-faster
M l grow th” explanation for the velocity decline in the

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

C h a r t 11

Velocity of G N P /M 1 and the Three-Month Treasury Bill Rate

1980s is examined in chart 12. Although m oney growth
has been rapid since 1982, it does not appear to have
been accelerating fast enough relative to previous
years to produce the recent sharp decline in velocity.28

Expected Inflation and Velocity
Another explanation is that velocity’s recent behav
ior results from changes in the public’s expectations of
inflation. According to this view, the demand for
m oney is inversely related to the expected rate of

“ There is a 4 percentage point spread between peak trend-M1
growth in the 1980s and the late 1970s. Hence, even if there were no
nominal output response to the more rapid M1 growth over the entire
period, the acceleration in M1 growth, at most, could account for a 4
percentage point decline in trend velocity growth; that is, from about
3 percent to about - 1 percent. In addition, this explanation im plies a
significant lengthening in the estimated lag on m oney growth in the
St. Louis equation during the 1980s, which has not been confirmed.
Another cyclical explanation not considered explicitly in the text
has been suggested by Friedman (1983), M ascaro and M eltzer
(1983) and Tatom (1983a, 1983b); in their view, an im portant
influence on the demand for m oney is m onetary uncertainty. Sup
pose that people increase their m oney holdings relative to their
current income when they become more uncertain about their future
incomes. If m onetary uncertainty increased sufficiently in recent
years, this could explain the velocity puzzle.

Digitized 18
for FRASER

inflation. Thus, when inflation (and presumably in
flationary expectations as well) is declining, the d e
mand for m oney should rise, and the velocity of
m oney should fall. Since the nominal interest rate can
be thought o f as com posed o f the real rate plus a
premium for the expected rate o f inflation, this expla
nation is closely aligned to the interest sensitivity
argument. The principal difference between them is
that proponents o f the expected-inflation explanation
do not argue that the relationship has undergone a
structural change.29Judd 11983), Tatom (1983a, 1983b)
and Friedman (1983) have argued that the decline in
velocity in the 1981-83 period can be attributed pri
marily to disinflation and the associated decline in
market interest rates that substantially low ered the
opportunity costs o f holding m oney relative to GNP.
In one sense, this explanation is specious or, at the
very least, suspicious if extended to velocity m ove
ments in more recent years. If inflationary expecta-

“ The expected rate of inflation also could have an independent effect
on the dem and for m oney, e.g., m d = f (i, ir e), where ir° is the
expected rate of inflation. This issue has not been resolved.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

C h a r t 12

Short-Run and Trend G row th of M l

tions have fallen over the past five years, they must
have done so for non-monetary reasons; as chart 2
shows, trend M l growth has risen rapidly since 1983.
These non-m onetaiy factors must have been suf
ficiently powerful to have swamped the usual in
fluence that rapid trend m oney growth has on in
flation and inflationary expectations.

the rise in the real exchange value o f the dollar during
the early 1980s made holding dollars relatively more
attractive, increasing the dem and for m oney relative to
incom e and reducing velocity.30 Since the real ex
change value o f the dollar has generally m oved with
changes in the U.S. inflation rate, this argument is
closely related to the inflation argument.

Furthermore, if disinflation and declining nominal
interest rates caused velocity to decline, then, by the
same argument, velocity should have risen sharply
when inflation accelerated and nominal interest rates
rose during the 1970s. Unfortunately, this is not the
case. Chart 13 shows M l-velocity and the e?c post
inflation rate. While velocity moves with the inflation
rate after 1981, it does not appear to be affected sub
stantially by the inflation rate over the pre-financialinnovations period. Velocity growth during the 1970s
is not rapid enough to support this explanation.

This explanation is examined in chart 14, which
shows the movements in velocity and the nominal
trade-weighted exchange rate since 1973. The nominal
rather than the real exchange rate is used for two
reasons. First, movements in the nominal exchange
rate are more appropriate in assessing the relative
returns on two different monies. Second, movements
in the nominal and real trade-weighted exchange
rates have been highly correlated since 1973. Thus, the

Hetzel and Mehra (1985) suggest that the demand
for m oney balances varies positively with the real
value o f the dollar in foreign exchange markets. Their
explanation is based on the currency-substitution hy
pothesis, which states that different currencies are
close substitutes for each other. In this explanation,

“ This argum ent does not seem firm ly based in either the transactions
or asset approaches to the dem and for m oney. Except for some
border situations, there is very limited substitutability between two
currencies for transactions purposes. On the other hand, money
balances, even interest-bearing checking accounts, are dominated
on a risk-adjusted return criterion by other non-m oney assets.
Consequently, it is unlikely that foreign m oney is held as an asset in
portfolios.

FEDERAL RESERVE BANK OF ST. LOUIS

C h a r t 13

Velocity of G N P /M 1 and Inflation

C h a r t 14

Velocity of G N P /M 1 and Trade-W eighted Exchange Rate

Digitized 20
for FRASER

AUGUST/SEPTEMBER 1987

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

C h a r t 15

Velocities of G N P /M 1 A and Permanent In co m e /M IA

general pattern o f exchange rate movements is the
same whether the nominal or real exchange rate is
used.
Chart 14 shows that the exchange rate explanation
does not provide a satisfactory answer to the velocity
puzzle. From 1973 to 1981, exchange rate movements
appear to have no influence on velocity. W hile velocity
did decline from 1981 to 1983, w hen the exchange rate
was rising, it also fell sharply in 1985 and 1986 when
the exchange rate was plummeting.

TWO EXPLANATIONS MAY BE BETTER
THAN ONE
Darby, Mascaro and M arlow (1987) have recently
suggested that the velocity puzzle o f the 1980s is a
product o f financial innovation and cyclical effects in
measured velocity. Incorporating both effects, chart 15
compares the usual velocity measure with a measure
derived by dividing permanent incom e by M IA. There
is a sharp rise in the permanent income/MlA velocity
measure beginning with the nationwide introduction
o f NOW accounts. The movement in this measure

following that event is consistent with a gradual ad
justment to the initial and subsequent innovations
that increased the cost o f holding M IA, such as the
introduction o f Super NOWs in January 1984 and the
reduction o f the minimum balance requirements on
these accounts in January 1985.
The permanent income/MlA velocity measure, un
like virtually all velocity measures shown in the pre
vious charts, does not decline during the bulk o f the
1980s. This measure does not decline until the last
three quarters o f 1986; however, it turns up again
during the first half o f 1987. Darby, Mascaro and
M arlow suggest that the 1986 decline can be explained
by the extremely rapid M IA growth during the last
three quarters o f the year. Consequently, a combina
tion o f the effects o f financial innovations, cyclical
movements in GNP and sharp acceleration in M IA
growth could account for much o f the velocity puzzle
o f the 1980s.

SUMMARY AND CONCLUSIONS
This article reviews a number o f suggested explana
tions o f the puzzling downturn in M l velocity during

FEDERAL RESERVE BANK OF ST. LOUIS

the 1980s and attempts to assess the credibility of
each. Alone, none o f these explanations can account
for the behavior o f M l velocity. Perhaps, instead, sev
eral influences have com bined to produce the
anomalous velocity behavior that has pu zzled many
researchers.
If there are several influences at work, financial
innovations and cyclical variations in measured in
come seem to be among the best candidates. This
combination works w ell in explaining the velocity
puzzle through the first quarter o f 1986. W hen com
bined with cyclical variation in velocity induced by
rapid m oney growth, it may explain the behavior of
velocity through last year. Another explanation that
deserves further scrutiny is the possible increased
interest sensitivity of M l balances as a result o f m one
tary innovations during the 1980s.

AUGUST/SEPTEMBER 1987
Judd, John P. “ The Recent Decline in Velocity: Instability in the
Demand for M oney or Inflation?” Federal Reserve Bank of San
Francisco Economic Review (Sum m er 1983), pp. 12-19.
Kopcke, Richard W. “ How Erratic is Money G row th?” Federal Re
serve Bank of Boston New England Economic Review (May/June
1986), pp. 3 -2 0 .
Kretzmer, Peter E., and Richard D. Porter. “ Total Transaction M ea
sures and M1 G row th,” Contemporary Policy Issues (January
1987), pp. 6 4 -7 5 .
Mascaro, Angelo, and Allan H. Meltzer. “ Long- and Short-Term
Interest Rates in a Risky W orld,” Journal o f Monetary Economics
(Novem ber 1983), pp. 4 8 5-518.
McCallum, Bennett T. “ On ‘Real’ and ‘Sticky-Price’ Theories of the
Business C ycle,” Journal o f Money, Credit and Banking (Novem ber
1986), pp. 3 9 7-414.
McGibany, Jam es M., and Farrokh Nourzad. “ Interest Rate Volatil
ity and the Demand for M oney,” The Quarterly Review o f Eco
nomics a nd Business (Autumn 1986), pp. 7 3 -8 3 .
_________ _ “ Income Taxes and the Income Velocity of M oney: An
Empirical Analysis,” Journal o f M acroeconom ics (Fall 1985), pp.
5 23-35.

REFERENCES

Milbourne, Ross. “ Financial Innovations and the Demand for Liquid
Assets,” Journal o f Money, Credit, and Banking (Novem ber 1986),
pp. 506-11.

Barnett, W illiam A. “ Econom ic M onetary Aggregation: An Applica
tion of Index Num ber and Aggregation Theory,” Journal o f Econo
metrics (Septem ber 1980), pp. 11-48.

Morgan Guarantee. “ Demystifying M oney’s Explosive G row th,”
M organ Economic Quarterly (March 1986), pp. 10-13.

Batten, Dallas S., and Daniel L. Thornton. “ Are W eighted Monetary
Aggregates Better Than Sim ple-Sum M1 ?” this Review (June/July
1985), pp. 2 9-40.

Nelson, Charles, and Charles Plosser. “ Trends and Random W alks
in M acroeconom ic Tim e Series: Some Evidence and Im plica
tions,” Journal o f M onetary Economics (Septem ber 1982), pp.
139-62.

Darby, Michael R. “ The Allocation of Transitory Income Among
C onsum ers' Assets,” American Economic Review (Decem ber
1972), pp. 9 28-41.

Ott, Mack. “ Money, Credit and Velocity,” this Review (May 1982),
pp. 2 1 -3 4 .

Darby, Michael R., Angelo R. Mascaro, and Michael L. Marlow.
“ The Empirical Reliability of M onetary Aggregates as Indicators:
19 8 3-1 9 8 6 ,” U.S. Departm ent of Treasury Research Paper No.
8701 (1987).
Darby, Michael R., W illiam Poole, David E. Lindsey, Milton Friedman,
and Michael J. Bazdarich. “ Recent Behavior of the Velocity of
M oney,” Contemporary Policy Issues (January 1987), pp. 1-33.
Farr, Helen T., and Deborah Johnson. “ Revisions in the Monetary
Services (Divisia) Indexes of M onetary Aggregates,” mimeo,
Board of Governors of the Federal Reserve System (1985).
Friedman, Milton. “ W hy a Surge in Inflation is Likely Next Year,”
Wall Street Journal (Septem ber 1,1983).
--------------- - “ The Quantity Theory of M oney — A Restatem ent,” in
Studies in the Quantity Theory o f M oney (The University of Chicago
Press, 1956), pp. 3 -2 1 .
Friedman, Milton, and Anna J. Schwartz. M onetary Trends in the
United States and the United Kingdom, 1 867-1975 (University of
Chicago Press, 1982).
G ilbert, R. Alton, and A. Steven Holland. “ Has the Deregulation of
Deposit Interest Rates Raised M ortgage Rates?” this Review
(May 1984), pp. 5 -1 5 .
Haraf, W illiam S. “ The Recent Behavior of Velocity: Implications for
Alternative Policy Rules,” m anuscript (1986).
Hetzel, Robert L. “ W ill Recent High Growth Rates of M oney Revive
Inflation?” Contemporary Policy Issues (January 1987), pp. 4 1 -5 3 .
Hetzel, Robert L., and Yash Mehra. “ U.S. Inflation and the Real
Exchange R ate,” manuscript, July 1985.
Holland, A. Steven. “ Real Interest Rates: W hat Accounts for Their
Recent R ise?” this Review (Decem ber 1984), pp. 18-29.

Digitized 22
for FRASER

Radecki, Lawrence J., and John W enninger. “ Recent Instability in
M 1’s Velocity,” Federal Reserve Bank of New York Quarterly
Review (Autumn 1985), pp. 16-22.
Rasche, Robert H. “ M1 -Velocity and M oney Demand Functions: Do
Stable Relationships Exist?” , Journal o f Monetary Economics
(forthcoming).
_________ _ “ Velocity and the Choice of Policy Regim es,” The Cato
Journal (Fall 1986), pp. 6 6 3-66.
Roley, Vance V. “ The Demand for M1 by Households: An Evalua
tion of Its Stability,” Federal Reserve Bank of Kansas City Eco
nomic Review (April 1985), pp. 17-27.
Santoni, G. J. “ Changes in W ealth and the Velocity of M oney,” this
Review (March 1987), pp. 16-26.
Spindt, Paul A. “ M oney is W hat M oney Does: M onetary Aggrega
tion and the Equation of Exchange,” Journal o f Political Economy
(February 1985), pp. 175-204.
Tatom, John A. “ W as the 1982 Velocity Decline Unusual?” this
Review (August/Septem ber 1983a), pp. 5 -1 5 .
__________ “ Alternative Explanations of the 1982-83 Decline in
V elocity,” in M onetary Targeting and Velocity, C onference Pro
ceedings, Federal Reserve Bank of San Francisco, 1983b, pp. 2 2 56.
Thornton, Daniel L. “ W hy Does Velocity M atter?” this Review (De
cem ber 1983), pp. 5 -1 3 .
Thornton, Daniel L., and Dallas S. Batten. “ Lag Length Selection
and Tests of G ranger Causality Between M oney and Incom e,”
Journal o f Money, Credit and Banking (M ay 1985), pp. 164-78.
Trehan, Bharat, and Carl E. Walsh. “ Portfolio Substitution and
Recent M1 Behavior,” Contemporary Policy Issues (January
1987), pp. 5 4-63.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

Appendix
To examine whether velocity has become more interest
sensitive in the 1980s, the growth rate of M l velocity was
regressed on distributed lags of its own past growth rate
and changes in the three-month Treasury bill rate for three
alternative periods from 1/1960 to II/1987. The results are
presented in table 1. The lag length was determined sepa
rately for each period using the final prediction error crite
rion; see Thornton and Batten (1985). The maximum lag
length considered was 12 for the two longer periods and
four for the shorter one. The pre-1980 results indicate that
neither its own past growth nor that of short-term interest
rates significantly influenced M l velocity growth. The lag
lengths selected were zero for velocity growth and the
contemporaneous and first lag for the change in the Trea
sury bill rate. However, even though the lag coefficient on
the change in the T-bill rate is both positive as expected and
statistically significant at the 5 percent level, the hypothesis
that the contemporaneous and lag coefficients are jointly
insignificant cannot be rejected at the 5 percent level.
A considerably different result emerges when the regres

sion is extended to include the 1980s. The lag-length selec
tion procedure now chose a sixth-order lag for velocity
growth and a fourth-order lag for the change in the T-bill
rate. Moreover, the hypothesis that these coefficients are
jointly insignificant is rejected at the 5 percent level; con
temporaneous and past changes in the Treasuiy bill rate
exert a significant influence on current M l velocity growth.
When the equation is estimated only for the period of the
1980s, there is again evidence of a statistically significant
effect of interest rates on M l velocity. Indeed, the sum of the
distributed lag coefficients on the Treasury-bill rate is posi
tive and significant, indicating a longer-run positive rela
tionship between M l velocity and interest rates that does
not appear to have existed in the prior period. Hence, these
results are consistent with the hypothesis that the interest
sensitivity of M l balances changed significantly following
the monetary deregulation and financial innovations of the
1980s. It will take more research, however, to determine
how much of the velocity puzzle can be attributed to this
factor.

Table 1
Estimates of a Velocity Growth Rate Equation1
I/1960-IV/1979
Intercept

1/1960-11/1987

3.138* (7.36)

0.378

(0.71)

0.262* (2.70)

VDOT-1
VDOT-2

- 0 .0 1 9

(0.20)

VDOT-3

0.132

(1.32)

VDOT-4

0.214* (2.34)

VDOT-5

- 0 .0 9 5

VDOT-6
ATBR-0
ATBR-1

1/1980-11/1987
- 0 .2 1 7

(1.06)

0.202* (2.31)
- 0 .0 2 5

(0.04)

0.740

1.579* (2.07)

ATBR-2

0.889

(1.73)

3.066* (5.88)

- 1 .3 5 4 * (2.28)

- 1 .7 7 5 * (2.35)

0.774

ATBR-4

(1.58)

2.999’ (6.16)

ATBR-3

(1.35)

0.806

(1.65)

- 1 .1 1 7 * (2.01)

ZATBR

1.554

0.033

SEE

(1.80)

2.041

(1.83)

2.987* (2.25)

0.418

0.711

3.759

4.014

3.747

—

4.204*

9.437*

F-TBR

2.359

11.315*

15.710*

1.998

2.029

2.096

F-VDOT

(0.31)

0.512* (3.07)

' 111 statistics in parentheses.
•Indicates statistical significance at the 5 percent level.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

A Revision in the Monetary Base
li. Alton Gilbert

J L HE Monetary Control Act o f 1980 mandated a
substantial change in the structure o f reserve require
ments faced by depository institutions. The reserve
requirement structure was phased in over a sevenyear period from Novem ber 1980 to September 1987.
The adjusted monetary base, a measure o f the Fed
eral Reserve’s influence on the m oney stock, has been
revised to reflect this new structure. This article ex
plains w hy the base series was revised and describes
the difference between the previous and revised
series.

THE A DJUSTED MONETARY BASE:
PURPO SE AND COMPOSITION
The adjusted monetary base (AMB) is designed to be
a single measure o f all Federal Reserve actions that
influence the m oney stock, including changes in re
serve requirements. It is equal to the source base plus
the reserve adjustment magnitude (RAM).
The source base consists o f total currency outstand
ing (held by the public and in the vaults o f depository
institutions) plus the reserve balances o f depository
institutions at Federal Reserve Banks.1The level o f the
m oney stock (currency in the hands o f the public plus
checkable deposits) that can be supported with a
given level o f the source base depends on reserve
requirements. I f required reserve ratios are reduced,

R. Alton Gilbert is an assistant vice president o f the Federal Reserve
Bank o f St. Louis. Nancy D. Juen provided research assistance.
'R eserve balances of depository institutions included in the source
base are net of required clearing balances and balances held to
com pensate for float.

24FRASER
Digitized for

fo r example, a given level o f the source base can
support a higher level o f the m oney stock.
RAM is specified in term s o f the reserve requ ire
ments in effect in a base period. It equals the reserves
that w ould be required (given current deposit liabili
ties) if the reserve requirem ents o f a base period w ere
in effect minus the reserves that are actually required.
RAM rises (falls) i f reserve requirem ents are low ered
(raised). Including RAM in the AMB rem oves the e f
fects o f reserve requirem ent changes fro m the rela
tionship between the m oney stock and the AMB, even
though such changes affect the relationship between
the m oney stock and the source base.

THE IMPLICATIONS OF RESERVE
ACCOUNTING FOR AN APPROPRIATE
MEASURE OF RAM
The m oney stock is the product o f the monetary
base m ultiplier and the AMB. The issues involved in
developing an appropriate measure o f RAM can be
analyzed in terms of the determinants of the monetary
base multiplier. This section discusses the relation
ships between the structure o f reserve requirements,
the eauations for measuring RAM. and the determ i
nants o f the AMB multiplier. The appendix presents
the specific equations used for measuring RAM and
derives the determinants o f the AMB m ultiplier associ
ated with each specification.
The AMB measures all three policy actions that
influence m oney growth: open market operations, dis
count w in dow lending and changes in reserve re
quirements. The monetary base multiplier reflects the
effects that choices o f both depository institutions and
the public have on the m oney stock. The determinants

FEDERAL RESERVE BANK OF ST. LOUIS

o f the m ultiplier include the ratio o f currency in the
hands of the public to checkable deposits, the com po
sition o f deposits and the excess reserves held by
depository institutions.
These determinants depend on h ow RAM is mea
sured. The appropriate specification o f RAM, in turn,
depends on the structure o f reserve accounting in
effect. This principle can be illustrated for two features
o f reserve accounting: the reserve requirements of
members and nonmembers and those on time and
savings deposits.
Prior to 1980, only banks that w ere members o f the
Federal Reserve w ere subject to the Fed’s reserve re
quirements; nonmem ber institutions w ere exempt
from these requirements.2Thus, shifts o f deposits be
tween members and nonmembers affected the level o f
deposits that could be supported by a given level of
bank reserves. Also, since there were reserve require
ments on the time and savings deposits o f member
banks, shifts o f deposits between demand deposits
and time and savings deposits at member banks af
fected the amount o f checkable deposits that could be
supported by a given level o f bank reserves. Because
these deposit shifts represented the public’s rather
than the Federal Reserve’s actions, the AMB series was
constructed so that the deposit shifts affected the
AMB multiplier; the effects o f these shifts are dem on
strated algebraically in the appendix. This AMB series
was appropriate for periods before 1980.3
The M onetaiy Control Act o f 1980, however, im
posed identical reserve requirements on both member
and nonmem ber institutions. With the new structure
o f reserve requirements fully phased in, as o f Septem
ber 1987, a deposit shift between members and non

2Before 1980, state-chartered nonm em ber banks were subject to the
reserve requirements of the state in which they were chartered. For
information on the levels of the state reserve requirem ents and their
effects, see G ilbert and Lovati (1978) and Gilbert (1978).
3Given the nature of the prior m easure of RAM, some actions of the
public, such as shifts of deposits among banks, did not affect the
m ultiplier. The structure of reserve requirements on m em ber bank
deposits in effect prior to Novem ber 1972 was based on the location
of m em ber banks. Shifts of deposits among m em ber banks in cities
of different size changed the average reserve requirement on m em
ber bank deposits, but did not affect the AM B m ultiplier.
Under the structure of reserve requirem ents adopted in Novem
ber 1972, there was a graduated structure of reserve requirements
on demand deposits at m em ber banks. Shifts of demand deposits
between large and small m em ber banks changed the average
reserve requirem ent on m em ber bank dem and deposits. Changes
in the average reserve requirement on m em ber bank demand
deposits did not affect the multiplier.

AUGUST/SEPTEMBER 1987

members no longer affects the amount o f checkable
deposits that can be supported with a given amount of
reserves.4 Maintaining the old RAM measure w ould
continue to make the m oney m ultiplier a function o f
the distribution o f deposits between m em ber and
nonmem ber institutions; this distinction, however,
has no relevance under the current system o f reserve
accounting. Thus, the current measure o f RAM must
be changed to make the AMB m ultiplier invariant to
these deposit shifts.
Under the new structure, the only categories o f time
and savings deposits subject to positive reserve re
quirements are Eurodollar liabilities and nonpersonal
time and savings deposits with initial maturities o f 18
months or less."’ With these exceptions, shifts o f d e
posits between checkable deposits and time and sav
ings deposits do not affect the amount o f checkable
deposits that can be supported with a given amount of
reserves. In the new equation for RAM, the base period
reserve requirement on all time and savings deposits
is zero. This feature removes the ratio o f time and
savings deposits to checkable deposits as a determi
nant o f the m oney multiplier.
There is a problem, however, with the use o f this
new equation for RAM in measuring the AMB before
1980. The new equation eliminates as determinants o f
the AMB m ultiplier the distribution o f deposits be
tween members and nonmembers and the distribu
tion o f deposits at m em ber banks between demand
deposits and time and savings deposits. This pro
duces an undesirable revision in the time series rela
tionship between the m oney stock and the AMB prior
to 1980.

THE SOLUTION: LINK TWO
DIFFERENT AMB SERIES TOGETHER
The major challenge in revising the AMB series is
creating a continuous series w hile maintaining the
determinants o f the AMB multiplier that are appropri
ate for periods both before and after Novem ber 1980.
The solution is to link together, at the week ending
November 19,1980, two series based on different equa
tions for RAM. (November 19,1980, was the first reserve

4One exception involves nonm em ber institutions in Hawaii that were
in operation on or before August 1 ,1978; their reserve requirements
will be phased in through January 1993.
5Also subject to reserve requirements are nonpersonal ineligible
acceptances and obligations of affiliates with initial m aturity greater
than seven days.

FEDERAL RESERVE BANK OF ST. LOUIS

settlement week under the reserve requirements spe
cified in the Monetary Control Act.) Using seasonally
unadjusted observations for that week, the value o f the
AMB derived from the new equation for RAM is di
vided bv the value based on the prior equation for
RAM; that ratio equals 0.9704. The AMB for each period
through Novem ber 12, 1980, based on the prior equa
tion for RAM, is then m ultiplied by that ratio.6 This
adjustment leaves unchanged the growth rates o f the
AMB series between any two points in time prior to
November 1980; it also adjusts the level o f the AMB
series prior to Novem ber 1980 to avoid a break in the
series on that date due to the change in the equation
for RAM.
The new measure o f RAM alters the seasonal pat
terns in the AMB. The revised series is not seasonally
adjusted as one continuous series. Instead, the data
through October 1980 are seasonally adjusted without
incorporating data with the new measure of RAM, and
the data since November 1980 are seasonally adjusted
with observations based entirely on the new measure
o f RAM.

THE DATA
Table 1 presents quarterly growth rates o f these
series from 1981. As the table shows, the growth rates
of these series generally rise and fall together. On
average, the new series grew slightly faster than the
old series over this period. Data are not presented for
periods prior to Novem ber 1980, since the construc
tion of the revised series keeps the growth rates
unchanged.

AUGUST/SEPTEMBER 1987

Table 1
Quarterly Growth Rates of the Adjusted
Monetary Base (compounded annual
rates of change, seasonally adjusted)
Q uarter

Old
series

New
series

1981 1
2
3
4

2.9%
6.5
4.7
3.9

2.4%
7.9
3.8
3.2

1982 1
2
3
4

8.6
8.5
6.8
8.8

8.4
6.7
5.8
9.6

1983 1
2
3
4

11.7
11.3
7.3
7.9

12.0
12.2
8.3
8.5

1984 1
2
3
4

9.0
8.1
6.8
5.4

9.8
7.1
5.6
4.6

1985 1
2
3
4

8.0
7.3
9.0
7.3

7.7
7.5
10.4
8.9

1986 1
2
3
4
1987 1

7.3
8.2
8.8
9.7
10.5

7.0
9.7
10.6
11.2
11.3

CONCLUSIONS
The revision o f the adjusted monetary base AM B)
involves a new equation for the reserve adjustment
magnitude (RAM), the component of the AMB that
reflects the effects o f changes in reserve requirements.
The new measure o f RAM reflects the structure of
reserve requirements specified in the Monetary Con
trol Act o f 1980, which w ere phased in between N o
vember 1980 and September 1987.
6For a discussion of this method of linking together distinct m easures
of the AMB, see Tatom (1980).

Digitized 26
for FRASER

Data prior to Novem ber 1980 are calculated using
the prior measure o f RAM. In this revision o f the AMB,
therefore, the series through October 1980 is distinct
from the series from Novem ber 1980 to the present.
The two distinct series are linked together in N ovem
ber in a w ay that makes the revised AMB one continu
ous series. The prior measure o f RAM is used for
periods prior to Novem ber 1980 to retain the determ i
nants o f the monetary base m ultiplier (M l -f- AMB)
that are appropriate for the reserve requirement struc
ture then in effect.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

REFERENCES
Gilbert, R. Alton. “ New Seasonal Factors for the Adjusted Monetary
Base," this Review (Decem ber 1985), pp. 29-3 3 .
-----------------“ Calculating the Adjusted Monetary Base under Con
temporaneous Reserve Requirem ents,” this Review (February
1984), pp. 27-32.
_________ _ “ Revision of the St. Louis Federal R eserve’s Adjusted
Monetary Base,” this Review (Decem ber 1980), pp. 3 -1 0 .
_________ _ “ Effectiveness of State Reserve Requirem ents,” this
Review (Septem ber 1978), pp. 16-28.

_________ , and Jean M. Lovati, “ Bank Reserve Requirem ents and
Their Enforcement: A Com parison Across States,” this Review
(March 1978), pp. 2 2 -3 2 .
_________ , and Michael E. Trebing. “ The New System of C ontem
poraneous Reserve Requirem ents,” this Review (Decem ber
1982), pp. 3 -7 .
Tatom , John A. “ Issues in M easuring An Adjusted M onetary Base,”
this Review (Decem ber 1980), pp. 11-29.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1987

Appendix
Two Equations for the AMB and the Corresponding
Monetary Base Multipliers
This appendix presents the equation for the AMB
adopted in 1980 and the n ew equation that is n o w used to
measure the AMB for the period from N ovem ber 1980 to the
present. The determinants o f the AMB m ultiplier are d e
rived for each measure o f the AMB. See table A1 for defini
tions o f the terms used in specifying the AMB and its m oney
multiplier.

Table A1
Terms Used in Specifying the Adjusted
Monetary Base and the Monetary Base
Multiplier
Description

Term

OLD MEASURE OF THE AMB
In a revision o f the m onetary base in 1980, the AMB was
m easured as follows:
(A l) AMB, = SB, + 0.12664 (TDM!,.,,

AMB

Adjusted m onetary base

Source base

RAM

Reserve adjustm ent magnitude

CDM

Checkable deposits of m em ber banks

Demand deposits of m em ber banks due to foreign
banks and official institutions

Demand deposits of m em ber banks due to the U.S.
Treasury

TDM

Transaction deposits of m em ber banks

TSM

Tim e and savings deposits of m em ber banks

Required reserves

Currency in the hands of the public

E xcess reserves, in cluding the va u lt cash of
nonm em ber banks

Share of total checkable deposits at nonmem ber
banks

Total checkable deposits — those at m em bers and
nonmem bers

+ 0.031964 (TSM),_14 - HR,
The deposit data, w h ich are for m em ber banks only, are
lagged 14 days to reflect the fact that the required reserves
for each w eek w ere based on deposits o f tw o weeks earlier.
The weights on the transaction deposits o f m em ber banks
(0.12664) and the time and savings deposits o f m em ber
banks (0.031964) are the average reserve requirem ents on
these categories o f deposits in the period from January 1976
through August 1980.'
In deriving the m ultiplier associated w ith the AMB series
specified in equation A l, the tim e lags on the deposit data
are ignored to sim plify the equation. The first step in deriv
ing the m ultiplier involves expressing the source base as the
sum o f its com ponents.
(A2)

SB = CP + RR + E
AMB = SB + RAM
= CP + RR + E + 0.12664 (TDM) +
0.031964 (TSM) - RR

(A3)

= CP + E + 0.12664 (CDM + FM + GM)

= CDM + FM + GM

CP + CD

E - CD

FM 4- CD

GM -s- CD

TSM -r CD

Demand deposits of all depository institutions due to
foreign banks and official institutions

Demand deposits of all depository institutions due to
the U.S. Treasury

Transaction deposits at all depository institutions

F ^ CD

G - CD

+ 0.031964 (TSM)
Total checkable deposits, the deposit com ponent o f M l,
equals the checkable deposits o f m embers plus those o f
nonm em bers. Using low er case “ n ” as the fraction o f check
able deposits at nonmembers, the com ponents o f the AMB
in equation A3 can be respecified as follows:

1See Gilbert (1980) for a description of this measure of the AMB.
Digitized 28
for FRASER

= CD + F + G

AUGUST/SEPTEMBER 1987

FEDERAL RESERVE BANK OF ST. LOUIS
(A4) AMB = CD (k + e + 0.12664 (1 —n + fm + gm)
+ 0.031964(tm) )
The AMB m ultiplier can be specified as follows:
Ml
1+ k
(A 5 )------ = ----------------------------------------------AMB
k + e + 0.12664(l-n + fm + gm)
+ 0.031964(tm)
Thus, given the equation for the AMB adopted in 1980, the
AMB m ultiplier is a function of:
1. the ratio o f currency in the hands o f the public to checka
ble deposits (k),
2. the ratio o f excess reserves to checkable deposits (e),
3. the fraction o f checkable deposits at nonm em ber institu
tions (nl,
4. the ratio o f the dem and deposits o f m em ber banks due to
foreign banks and official institutions divided by total
checkable deposits (fm),
5. the ratio o f the dem and deposits o f m em ber banks due to
the U.S. Treasury divided by total checkable deposits
(gm), and
6. the ratio o f time and savings deposits at m em ber banks to
checkable deposits (tm).
The revised measure o f the AMB prior to N ovem ber 1980
is obtained by m ultiplying the measure described above by
a specific ratio; this ratio is the level o f the n ew measure o f
the AMB divided by the level o f the prior measure for the
w eek ending Novem ber 19, 1980. M ultiplying the AMB spe
cified above by this fixed ratio alters the level o f the AMB
m ultiplier for periods prior to Novem ber 1980; however, this
procedure leaves both its determinants and its grow th rate
unchanged.

(A6) AMB, = SB, + (0.12) TD ,_„ - RR,
The base period reserve requirem ent on transaction d e
posits, 12 percent, is the marginal reserve requirem ent on
most o f the transaction deposits o f depository institutions
under the n ew structure o f reserve requirements.
Contem poraneous reserve requirem ents becam e effec
tive the w eek ending February 8, 1984. The m ethod forcalculating the AMB in this period is presented in equation
A7.3
(A7I AMB, = SB, + 10.12) TD,_, - RR,

Seasonal Adjustment
Contem poraneous reserve requirements altered the sea
sonal patterns o f the AMB. In a previous revision o f the AMB,
Gilbert (1985) described a m ethod for deriving seasonal
factors for the period after February 1984. That m ethod is
applied to this new series on the AMB. It involves develop
ing a counter-factual series for weeks prior to February 1984
that reflects estimates o f the seasonal patterns in the AMB if
contem poraneous reserve requirements had been in effect.
T he counter-factual series is calculated for the period Janu
ary 1975 through January 1984. Observations for that series
are com bined with actual values o f the AMB for the period
since February 1984 to derive seasonal factors that are used
for seasonally adjusting the AMB data for the period since
February 1984.

The New AMR Multiplier
Using steps similar to those in equations A2 and A3, the
new measure o f the AMB can be specified as follows:
IA8I AMB = CP + E + 0.12 IC D + F + Gl

THE NEW MEASURE OF THE AMB
Reserve Accounting
The tim ing o f data in the n ew equation for calculating the
AMB is different for the periods under lagged and contem
poraneous reserve requirements. For the periods under
lagged reserve requirements, that is, for the w eekly reserve
maintenance periods through the w eek ending February 1,
1984, the AMB is calculated as indicated in equation A6.3

2The deposit component of equation A6 is transaction deposits of all deposi
tory institutions for the week ending on a Wednesday, 14 days before the end
of the current maintenance period. Historical data are no longer available on
transaction deposits for weeks ending on Wednesdays. When the Federal
Reserve adopted contemporaneous reserve requirements in February 1984,
the weekly data series on deposits, currency and vault cash of depository
institutions were converted from averages for weeks ending on Wednesdays
to averages for weeks ending on Mondays. It is possible to derive a series for
deposits in weeks ending on Wednesdays (TD,_14) from the data on transac
tion deposits for weeks ending on the surrounding Mondays (TDt_16 and
TD,_9), as indicated in the following equation:
TD,_)4 = (5/7) TD,_16 + (2/7) TD,_9.
Data on transaction deposits derived in this manner are used in the calcula
tion of the AMB through February 1, 1984.

The AMB multiplier- can be expressed as follows:
Ml
1 + k
(A 9 )------ = ----------------------------AMB
k + e + 0.12 (1 + f+ g )
The AMB multiplier, based on the n ew equation for the AMB
(equations A6 and A7), is a function of:
1. the ratio o f currency in the hands o f the public to checka
ble deposits (kl,
2. the ratio o f excess reserves to checkable deposits (e),
3. the ratio o f dem and deposits o f depository institutions
due to foreign com m ercial banks and official institutions
to checkable deposits (f), and
4. the ratio o f U.S. Treasury deposits at depository institu
tions to checkable deposits (g).

3For a description of contemporaneous reserve requirements, see Gilbert and
Trebing (1982). For an earlier discussion of the implications of contempora
neous reserve requirements for the measurement of RAM, see Gilbert
(1984).