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Federal Reserve Bank of St. Louis
Review
August/September 1983

In This Issue . . .




This issue of Review contains four articles relating to monetary policy and
banking.
In the first article, “Was the 1982 Velocity Decline Unusual?” John A. Tatom
analyzes recent movements in velocity. Velocity, the ratio of the nation’s GNP to
its money stock, fell sharply in 1982. Since velocity is an indicator of the public’s
demand for money, many analysts have interpreted the decline as an unantici­
pated shift in the public’s desired holdings of transaction balances. According to
this view, the shift worsened economic performance and raised serious doubts
about the future prospects of controlling both inflation and spending by controlling
the monetary aggregates.
Tatom explains that velocity normally displays a cyclical pattern, rising faster
than average during expansions and falling in recessions. He points to three
reasons why velocity declines in recessions. First, money stock growth often
accelerates after the economy enters a recession. Spending in the economy
responds proportionately, but with a lag. As a result, velocity growth is tempo­
rarily depressed, then temporarily raised. The initial change, depressing velocity
growth, tends to occur immediately; it is observed during the recession and
reinforces the velocity decline associated with the slowing in money growth that
preceded the recession.
Second, real income falls during a recession. Because the public’s preference for
money does not fall proportionately with its reduced demand for goods and
services, M l tends to rise relative to GNP.
Finally, during recessions, businesses often develop excess inventory. The
temporary production adjustments to eliminate this excess initially push produc­
tion down sharply relative to sales. During such a period of inventory adjustment,
measured velocity falls sharply.
To assess whether recent velocity movements were unusually large, Tatom uses
a model that describes velocity movements from 1948 to mid-1981 to compare
velocity movements from mid-1981 through 1982 with actual developments.
Tatom shows that the 1982 velocity decline was not unusual when compared with
the estimates based on past velocity movements.
In the second article, “Changes in the Monetary Growth Rate and the Time
Pattern of Interest Rates, ” W. W. Brown and G. J. Santoni re-examine the widely
held view that permanent increases in the monetary growth rate cause market
interest rates initially to decline, then ultimately to rise above their original
levels. The path that interest rates follow when adjusting to a change in the
monetary growth rate is important for two reasons. First, if changes in money
growth change the ex ante real interest rate, even temporarily, the result will be
sizable disturbances in general economic activity. Second, the timing of the
adjustment in market interest rates reveals information about the lag in the
response of economic activity to changes in monetary policy.
Brown and Santoni examine monthly data on interest rates and monetary
growth over the period July 1914-February 1983 to determine whether changes

3

In This Issue . .


4


in monetary growth induce changes in interest rates and, if so, what the direc­
tion, magnitude and timing of the effect are. When the data period is partitioned to
control for the effects of the different monetary institutions (for example, the gold
standard), they find that interest rates have responded to monetary impulses in the
commonly believed manner only since 1971. Even in this case, however, the
initial decline in short-term interest rates associated with an increase in the
monetary growth rate is quite small; the subsequent rise is proportionate to the
increase in money growth. Further, interest rates appear to adjust fully to a change
in monetary growth within one year.
In “The Effect of State Banking Laws on Holding Company Banks, ” Donald M.
Brown investigates the effect of state banking laws on the financial and market
characteristics of banks owned by bank holding companies.
Brown applies a statistical approach known as probit analysis to a sample of
banks from six unit-banking states. In those states that permit multi-bank holding
companies, he finds that the financial and market characteristics of one-bank and
multi-bank holding company subsidiaries differ significantly from one another, as
well as from independent banks. Such characteristics associated with one-bank
holding company subsidiaries also differ from those of independent banks in states
that prohibit multi-bank holding companies. Furtherm ore, one-bank holding
companies in this group of states share financial characteristics of both the onebank and multi-bank holding company subsidiaries in the other group of states.
This suggests that, if it were legal in those states to form multi-bank holding
companies, some of the holding companies would choose to own several banks.
Finally, Brown finds that banks are more likely to be owned by bank holding
companies in states that permit multi-bank holding companies than in those that
do not.
Brown concludes that studies which attempt to examine the effects of holding
company ownership on bank financial ratios and market characteristics should
control both for differences among state banking laws and for differences between
one-bank and multi-bank holding companies.
In the last article in this issue, “Inflation: Assessing Its Recent Behavior and
Future Prospects,” R. W . Hafer examines the effect of monetary and nonmonetary
factors in explaining the recent decline in inflation. Hafer finds that the decline in
the average rate of money growth during the past few years accounts for the
downward trend in inflation. Moreover, he finds that the drop in the inflation rate
below that implied by the rate of money growth is explained, to a large degree, by
the downward movement in the relative price of energy.
When the influence of the declining relative price of energy abates, however,
Hafer argues that “inflation will tend to move back in line with the average growth
of money. ” Using estimates obtained from the I/1960-I/1983 sample period, and
assuming that the average rate of money growth continues to grow at 7 .5 percent
(the trend growth in 1/1983), the author simulates the inflation rate for the period
1983-85 for different assumptions about energy price changes. If relative energy
prices remain unchanged, inflation was simulated to be about 6 .5 percent in 1983
and above 7 percent in 1984 and 1985. If relative energy prices decline throughout
1983 then stop declining, inflation was simulated to be about 6 percent in 1983 and
about 7 percent for 1984 and 1985. Hafer concludes that the popular notion that
inflation finally has been tamed is likely to be invalid unless the average growth of
money is significantly reduced.

Was the 1982 Velocity Decline Unusual?
JOHN A. TATOM

A H E nation’s GNP growth in 1982 was so weak
relative to the pace of monetary expansion that the
velocity of money — the ratio of GNP to M l — fell
significantly. This decline contrasts sharply with the
steadily rising trend in velocity over the past 35 years.
The Council of Economic Advisers (CEA) refers to
1982 velocity behavior as “historically atypical” and
“not fully understood. ” In explaining the large velocity
“shift,” the C EA attributes a major role to changes in
asset demands of individuals and businesses, arising
from new financial opportunities or changes in asset
preferences. The C EA phrases the importance of un­
usual shifts in velocity growth succinctly:
The p resum ption, on th e basis o f past exp erien ce, is
th at m ost velocity changes are tem p orary . Thus, in­
creasin g th e rate o f m onetary grow th in response to
tem p orary declines in velocity runs th e risk o f providing
excessive liquidity and in creasin g inflation, w hile a fail­
u re to recognize a continuing shift in liquidity p refer­
e n ce o r velocity runs th e risk o f providing inadequate
liquidity and red u cin g real G N P.

Had velocity growth not shifted last year, nominal
GNP growth would have been substantially higher,
and the recession presumably would have not been as
lengthy or as severe.
Some observers, interpreting this development as
the breakdown of monetarist theory, have suggested
that “If velocity has become impossible to predict, it
could be 20 years before monetarism becomes the
linchpin of policy again. ”2 Before concluding that the

1Economic Report o f the President (Government Printing Office,
1983), pp. 21-22.
2See “The Failure of Monetarism,” Business Week, April 4, 1983,
pp. 64-67. In the same article, Robert J. Gordon remarks that
“monetarism has been decimated by the collapse of velocity in
1982.”




link between monetary growth and spending has been
broken or addressing the implications of such a break­
down for monetary policy, it is useful to place last
year’s velocity developments in historical perspective
and to examine the extent of any deviation in the
historical relationship between velocity and the factors
that influence it.

THE RECENT BEHAVIOR OF
VELOCITY IN HISTORICAL
PERSPECTIVE
On an annual basis, the velocity of M l grew steadily
from 1959 to 1981, averaging a 3 .2 percent rate of
increase. In 1982, M l velocity fell at a 2 .3 percent rate.
Since the standard deviation for velocity growth from
1959-81 was only 1.20 percent, the recent decline, as
the C EA has indicated, appears substantial. Indeed,
any decline would appear unusual based on the record
of systematic increases in velocity since 1959.
Declines in velocity are not unprecedented, how­
ever. For example, on an annual basis, M l velocity fell
at a 1.5 percent rate from 1953 to 1954.3 Moreover,
there have been years in the postwar period when
velocity growth was virtually nil, such as 1952 (0.2
percent) and 1958 (0.1 percent).4

■^The current measure of M l begins in 1959. The old measure used
before 1980 is used here for the period 1947 to 1959. In 1959, the
two measures were nearly identical so that an historical series is
obtained by splicing the two series.
4L.

R. Klein and R. F. Kosobud, “Some Econometrics of Growth:
Great Ratios in Economics,” The Quarterly Journal o f Economics
(May 1961), pp. 173-98, argue that, adjusted for its trend rate of
growth, velocity is one of the “great” ratios that might be viewed as
a fundamental parameter for economic theory. They reach this
conclusion, notwithstanding their evidence indicating periodic
sharp velocity declines relative to trend.

5

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

C h a rt 1

Velocity (G N P /M 1 )

1947 48

49

SO

51

52

S h a d e d a re a s r e p r e s e n t p e r io d s

77

78

79

80

81

82 1983

i re c e s s io n s .

The Quarterly Record

to look back to 1945 or earlier recessions to find more
rapid decreases in velocity.

Additional insight into the 1982 velocity decline can
be obtained using quarterly data. Velocity fell at an
11.2 percent annual rate in the first quarter of 1982,
rose at a 3 .3 percent rate in the second quarter, fell at a
3 .4 percent rate in the third quarter, then fell at a 9.9
percent rate in the last quarter of 1982. Chart 1 shows
quarterly levels of velocity since 1947; periods of reces­
sion are shaded. Note that there are numerous quar­
ters in which velocity fell, especially during recessions.

Table 1 shows velocity’s growth rate from peak to
trough in eight postwar recessions. While a decline in
velocity in such periods is not unusual, the size of the
peak-to-trough decline in the recent recession is the
largest recorded. The velocity decline was fairly small
in the four previous recessions. Indeed, in the 1970
recession, velocity was flat, and in the 1973-75 reces­
sion it rose. Yet, except for the 1973-75 recession,
when the unemployment rate rose 3 .5 percentage
points from peak to trough, the four previous reces­
sions were not as severe as the recent experience when
unemployment rose 3 .3 percentage points from peak
to trough.5 The recent experience compares more

From the first quarter of 1947 to the third quarter of
1981, velocity declined in 32 of the 138 quarters, or
about one-fourth of the time. Moreover, velocity typi­
cally fell in periods of economic decline. There are 25
quarters that span the peak-to-trough periods; velocity
declined in 64 percent of them. Nonetheless, the mag­
nitude of the velocity declines in the first and fourth
quarters of 1982 far exceed the largest one-quarter
decreases in velocity of about 6 percent observed in
1/1948, 11/1948, IV/1953 and 1/1958. One would have
Digitized for 6FRASER


T h e data in table 1 suggest that velocity movements in the 1973-75
recession, when velocity actually increased, were more anomalous
than recent velocity movements. The 1973-75 change is consistent
with a one-time downshift in the demand for money occurring
during that recession. See R. W. Hafer and Scott E . Hein, “The
Shift in Money Demand: What Really Happened?” this Review
(February 1982), pp. 11-16.

AUGUST/SEPTEMBER 1983

FEDERAL RESERVE BANK OF ST. LOUIS

closely to that in the first three postwar recessions,
when the unemployment rate rose about 3 .2 percent­
age points from peak to trough.6

EXPLANATIONS OF RECENT
VELOCITY MOVEMENTS
The recent behavior of velocity is broadly consistent
with the velocity declines that occurred in most pre­
vious recessions. Nonetheless, analysts have advanced
a variety of hypotheses to account for the 1982 velocity
experience. Two of these explanations are convention­
al: they are that (1) declining inflation, or (2) declining
interest rates, have reduced the cost of holding money
and, consequently, the demand for money relative to
goods and services has increased.7
A second group of hypotheses includes those that
usually are not incorporated in conventional analyses.
Principal among these is that recent financial innova­
tions have lowered the cost of holding money, thereby
increasing its demand and reducing velocity. Another
hypothesis in this vein is that international asset pref­
erences have changed so that foreigners’ demand for
the U.S. money stock is greater. According to this

6Declining velocity in recessions is not a postwar phenomenon.
Using Robert Gordon’s estimates of quarterly GNP and Milton
Friedman and Anna Schwartz’ data on M l, a measure of M l
velocity can be constructed since mid-1914. In the seven reces­
sions from 1919-45, velocity fell in all and, with one exception, at a
faster pace than in the 1981-82 recession. The periods are (growth
rates in parentheses): III/1918—1/1919 ( —28.8 percent), 1/1920—
111/1921 ( - 6 . 6 percent), II/1923-III/1924 ( - 6 . 7 percent), III/
1926-IV/1927 ( - 2 . 2 percent), II/1929-I/1933 ( - 1 2 . 8 percent),
II/193T—11/1938 ( - 5 . 8 percent), and I/1945-IV /1945 ( - 2 2 . 5 per­
cent). See Robert J. Gordon, “Price Inertia and Policy Ineffective­
ness in the United States, 1890-1980, ’’ Journal o f Political Econ­
omy (December 1982), pp. 1087—117; and Milton Friedman and
Anna Jacobson Schwartz, A Monetary History o f the United States,
1867-1960 (Princeton University Press, 1963).
7See Bluford H. Putnam, “This Money Bulge Isn’t Inflationary,’’
Wall Street Journal, April 27, 1983, for a discussion of these
explanations and others. Also, see John P. Judd, “The Recent
Decline in Velocity: Instability in Money Demand or Inflation?”
Federal Reserve Bank of San Francisco Economic Review (Spring
1983, forthcoming). Judd claims that declining interest rates ex­
plain the pattern of money growth since the end of 1981 and that
the demand for money contained in the San Francisco money
market model was stable. Velocity fell because of this predictable
strength in money demand. Judd does not argue that the sensitivity
of money demand to changes in interest rates and inflation has
changed. An example of the latter argument is contained in Flint
Brayton, Terry Farr and Richard Porter, “Alternative Money
Demand Specifications and Recent Growth in M l” (Board of
Governors of the Federal Reserve System, May 23, 1983; pro­
cessed).




Table 1
Growth Rates of Velocity in the Last
Eight Recessions
Peak-Trough
IV/1948 - IV/1949
11/1953 —11/1954
111/1957 — 11/1958
11/1960 — 1/1961
IV/1969- IV/1970
IV/1973 - 1/1975
1/1980 —111/1980
111/1981 - IV/1982

Velocity
growth
rate1
-2.8%
-2 .7
-3 .2
-1 .4

Increase in the
unemployment
rate2
3.2%
3.2
3.2

0.0
1.5
-0 .8

1.6
2.2
3.5
1.4

-4 .3

3.3

'Compounded annual rate of change in GNP/M1, where the old
(pre-1980) measure of M1 is used prior to 1959.
2Percentage-point change in the quarterly average of unemploy­
ment as a percent of the civilian labor force.

view, the international strength of the dollar accounts
for the decline in velocity.8 All four explanations suffer
from a lack of historical perspective that blunts their
intuitive appeal.

Declining Inflation
Inflation has declined steadily since the first quarter
of 1981, but velocity declines did not become a source
of concern until a year later. As measured by the rate of
increase in the GNP deflator, inflation peaked at 10.4
percent in the year ending in the first quarter of 1981.
This rate declined to 7.1 percent over the following
year, then to 4 .7 percent in the year ending in the first
quarter of 1983. The decline in velocity is concentrated
heavily in only two quarters of 1982, long after the
decline in inflation began. Moreover, in the first three
quarters of 1981, when the inflation was slowing sharp­
ly, velocity rose at a 7.1 percent rate. Of course, it is
conceivable that changes in expected inflation lagged
far behind actual inflation developments, but lacking
evidence of such a delayed and discontinuous adjust­
ment process, such a notion can be disregarded.

8Putnam,

“This Money Bulge, ” provides this explanation along with
the declining inflation and financial innovation explanation. Also,
see Vincent Salvo, “Is U.S. Money Growth A Foreign Affair?”
International Finance, (Chase Manhattan Bank, April 25, 1983),
pp. 1, 7, 8 .

7

FEDERAL RESERVE BANK OF ST. LOUIS

Declining Interest Rates
Explanations that focus on declining interest rates
also do not match up well with the recent pattern of
velocity declines. In the first quarter of 1982, corporate
Aaa bond yields averaged 15.01 percent and had risen
from 14.62 percent one quarter earlier or 14.92 per­
cent two quarters earlier. During the remaining quar­
ters of 1982, the bond yield declined to 14.51 percent,
13.75 percent and 11.88 percent.9 The pattern in the
second half of 1982 is consistent with a decline in
velocity. W hat remains unexplained, however, is the
largest decline in velocity, which occurred in the first
quarter.

Financial Innovations
Financial innovations are a widely discussed ex­
planation of velocity shifts. This argument is by far the
most puzzling, because there were no major innova­
tions over the period in which velocity behavior ap­
peared aberrant to most observers. Analysts generally
refer to the introduction of super-NOW accounts or
money market deposit accounts in connection with this
hypothesis. U nfortunately, the form er w ere not
allowed until January 1983 and the latter were autho­
rized in m id-December 1982, three weeks before the
en d of the period of declining velocity discussed
above.10

Foreign Demand fo r the Dollar
The international currency preferences explanation
also does not match the recent velocity pattern. The

T h e use of short-term rates does not alter the disparate pattern. In
the first quarter of 1982, 3-month Treasury bill yields averaged
12.81 percent, higher than the 11.75 percent yield a quarter ear­
lier, although somewhat below the 15.05 percent average yield two
quarters earlier. This rate also declined over the subsequent three
quarters.
10The only example of a major financial innovation in recent years
that fits the hypothesis is the introduction of nationwide NOW
accounts in January 1981. There was a sharp surge in the share of
total checkable deposits held as NOW balances or other checkable
deposits from January to April. Earlier analyses have failed to
reveal any unusual velocity developments in 1981 due to this shift.
See John A. Tatom, “Recent Financial Innovations: Have They
Distorted the Meaning of M l? ” this Review (April 1982), pp.
2 3-35; Scott E . Hein, “Short-Run Money Growth Volatility: Evi­
dence of Misbehaving Money Demand?” this Review (June/July
1982), pp. 27-36; Bryon Higgins and John Faust, “NOWs and
Super-NOWs: Implications for Defining and Measuring Money,”
Federal Reserve Bank of Kansas City Economic Review (January
1983), pp. 3-18. On the absence of effects from the late 1982 and
early 1983 innovations, see John A. Tatom, “Money Market De­
posit Accounts, Super-NOWs and Monetary Policy,” this Review
(March 1983), pp. 5-16.

Digitized for 8FRASER


AUGUST/SEPTEMBER 1983

effective exchange rate has been rising steadily since
the third quarter of 1980, except for a decline in the
fourth quarter of 1981. The rates of increase in the
exchange value of the dollar from III/1980 to III/1981
and from IV/1981 to IV/1982 are 28 .8 percent and 16
percent, respectively. In the first period, velocity rose
5 .6 percent despite the strong appreciation of the dol­
lar. Only in the latter period, when the rate of appre­
ciation slowed, did velocity growth slow.
An earlier example further illustrates the difficulty
with this explanation. In the second quarter of 1981,
just before the recent recession, the exchange value of
the dollar was virtually the same as in the third quarter
of 1977. Over the four-year period, the exchange rate
first fell rapidly (12 percent rate from III/1977 to
IV/1978), then declined more slowly (1.6 percent rate
from IV/1978 to III/1980), and finally surged upward
(28.5 percent rate from III/1980 to 11/1981). Over the
same periods, velocity grew at 4.5 , 1.6, and 5 .6 per­
cent rates, respectively. Thus, velocity growth was
strongest during the period of rapid appreciation.
Moreover, it was only slightly slower— and well above
trend growth — during the period of rapid decline in
the value of the dollar.
The conceptual difficulty with this explanation is
that the movements in the exchange value of the dollar
reflect inflation and monetary growth developments.
At least for the United States, the major provider of the
world money supply, these factors are included in
conventional analyses of GNP growth and velocity. It is
not likely that the exchange rate could exert a major
impact of its own.11

WHY DOES VELOCITY FALL IN
RECESSIONS?
Declining Real Income
The principal reason that velocity declines in a re­
cession is because of a temporary decline in real in­
come. Velocity can be viewed as real income (x) per

“ The currency preferences argument also appears to confuse
money and other financial assets. While the foreign demand for
U. S. financial assets has risen dramatically, especially in 1980 and
1981, foreign ownership of money has not. Estimates based on
individual, partnership and corporate deposits show essentially no
change in the less than 2.5 percent of gross demand deposits due
to foreign holders for December data from 1978 through 1982.
Similarly, bank demand liabilities to foreigners, including all for­
eign banks or excluding foreign financial institutions, have shown
no tendency to increase since 1979. Federal Reserve Bulletin (May
1983), p. A25 and p. A59.

AUGUST/SEPTEMBER 1983

FEDERAL RESERVE BANK OF ST. LOUIS

unit of real money balances (m). An income elasticity of
demand for money less than one will yield procyclical
velocity; for example, a 1 percent decline in real in­
come will induce a smaller reduction in the demand for
real money balances. As a result, velocity, x/m, will fall
during a recession, other things held constant.12

Lagged Adjustment o f GNP to
Monetary Growth
Velocity also typically falls in recessions due to the
link between nominal GNP growth and money growth.
The growth rate of nominal GNP is determined pri­
marily by the growth rate of the money supply. There
are lags, however, in the response of nominal GNP to
changes in money growth. When money growth slows,
GNP growth initially slows by less; thus, velocity
growth rises. Within a few quarters, however, the
effect of the slowing in money growth is reflected in
further reductions in GNP growth so that, while GNP
growth continues to slow and money growth does not,
velocity growth falls.
Furtherm ore, the monetary theory of the business
cycle indicates that, after some time (about two quar­
ters), a substantial decline in the money growth will
cause a recession. The periods of falling velocity
growth associated with a slowing in money growth
coincide with the period of recession induced by a
slowing in m oney.13
The pattern of money growth over the last two years
bears out this type of movement. Table 2 shows the
12Milton Friedman, “The Quantity Theory of Money — A Restate­
ment,” in Milton Friedman, ed., Studies in the Quantity Theory
o f Money (University of Chicago Press, 1956), pp. 18-19, explains
that the demand for money, in principle, depends on “expected
income” or “permanent income.” In recessions, measured income
or GNP declines relative to permanent income. As a result,
money holdings rise relative to measured income or GNP, but not
relative to permanent income. Such a movement in money hold­
ings relative to spending also is expected based on a “precaution­
ary motive” for holding money. As “The Failure of Monetarism”
notes, “In a weak economy, fear of losing one’s job is a strong
incentive for keeping a larger amount of money in a checking
account in order to get at it quickly” (p. 64).
13The theory that velocity declines relative to trend during a reces­
sion because of the same slowing in money growth that causes the
recession was developed and subjected to one of its first tests by
Clark Warburton, “The Theory of Turning Points in Business
Fluctuations,” Quarterly Journal o f Economics (November 1950),
pp. 5 2 9 - 4 9 . See also M ilton F ried m an , “ A T h eoretical
Framework for Monetary Analysis,” in Robert J. Gordon, ed.,
Milton Friedm ans Monetary Framework (University of Chicago
Press, 1974), pp. 1-62. Friedman provides a theory of nominal
income in which velocity is procyclical due to deviations of mone­
tary growth from the expected growth of nominal income (see
especially pp. 38-48). He also indicates that this result is rein­
forced by deviations in money supply growth from growth in the
demand for money (pp. 51-53).




Table 2
Recent Growth Rates of the Money
Stock (M1) and Its Velocity_______
Quarter

Money

Velocity

1980/111
IV

16.9%
9.8

1981/1
II
III
IV

5.0
9.2
3.1
3.3

14.8
-2 .5
9.8
0.4

1982/1
II
III
IV

11.0

-1 1 .2
3.3
-3 .4

3.3
6.3
13.7

-6.2%
5.2

-9 .9

growth rates of M l and velocity for the period from
III/1980 to IV/1982. During quarters in which money
growth accelerated, such as III/1980, 11/1981, 1/1982
and IV/1982, velocity growth was negative. Moreover,
these periods followed unusually slow money growth,
such as in the second half of 1981 and in 11/1982.
In periods when velocity growth slowed, including
III/1 9 8 0 , 11/1981, IV /1981, 1/1982, III/1 9 8 2 and
IV/1982, the slowing was due in part to the contempo­
raneous acceleration in money growth and in part to
the adverse reactions of GNP growth to past slowings
in money growth.

The Course o f Inventory Adjustment
When sales growth slows in the late stage of a cyclical
expansion or the early stage of a recession, firms may
either fail to anticipate the decline, anticipate that the
decline is more temporary than is the case, or simply
choose to adjust production growth more slowly. In
each event, firms would fail to reduce production as
much as sales fell, thus accumulating undesired inven­
tories. Since inventory investment, whether desired
or not, is included in spending on final goods and
services, GNP can be temporarily strong compared
with desired spending, or GNP velocity can be raised
relative to final sales (GNP less inventory investment)
velocity.
Similarly, when sales expand in the late stages of a
recession or early stages of recovery, firms may not
anticipate the expansion, anticipate that it is only tem­

9

AUGUST/SEPTEMBER 1983

FEDERAL RESERVE BANK OF ST. LOUIS

C h a rt 2

G row th Rates of GNP Velocity and Final Sales Velocity 11

L i G N P v e lo c ity is G N P / M 1 . F in a l sales velo city is fin a l s a le s /M l. T h e g ro w th ra te s a r e a n n u a liz e d tw o -q u a rte r c h a n g e s in th e lo g a rith m .
S h a d e d a r e a s re p re s e n t p erio d s o f business recessio n s.

porary, or simply engage in production smoothing;
thus, they initially will m eet the sales increase out of
inventory rather than stepped-up production. In this
case, GNP will not keep pace with final sales, so that
velocity measured relative to GNP will fall compared
with velocity measured relative to final sales.
Chart 2 shows the growth rates of GNP velocity and
final sales velocity since 1948. Two-quarter periods are
used to smooth the data somewhat. The average
growth rates of the two series from 1/1948 to 11/1983
are nearly identical (3.17 percent for GNP and 3.18
percent for final sales). The two measures of velocity
growth are fairly similar except around the end of
the shaded recession periods and the beginning of
the recoveries. At these times, much wider swings
occu rred in G N P velocity due to inventory ad­
justm ents.14
14For a discussion of the importance of inventory movements be­
fore, during and after recessions, see John A. Tatom, “Inventory
Investment in the Recent Recession and Recovery,” this Review
(April 1977), pp. 2-9 . Also, Frank DeLeeuw, “Inventory Invest-

Digitized for 10
FRASER


Table 3
Recent Developments in Real Inventory
Investment, Output and Sales
Quarter
1981/IV

Real
inventory
investment
$

6.0

Real GNP
growth rate

Real
final sales
growth rate

-4.9%

-2.3%

1982/1
II

-1 0 .2
-3 .4

-5 .5
0.9

-1 .3
-0 .9

III

-1 .3
-2 2 .7

-1 .0

-1 .5

-1 .3

4.5

IV

ment and Economic Instability,” Survey o f C urrent Business
(December 1982), pp. 23-31, provides evidence of this greater
volatility of production and demonstrates that the source of this
“instability” is producers’ lagged responses to changes in demand,
especially in the adjustment of goods in process and material
inventories.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

Contribution of In ven to ry Investm ent Fluctuations to G N P G ro w th

S h a d e d a r e a s r e p re s e n t p e r io d s o f b u s in e s s r e c e s s io n s .

The recent divergence in the two measures of veloc­
ity growth is large, because of the sharp swings in
inventory investment in the first and fourth quarters of
1982. Table 3 shows real inventory investment from
the preceding peak to the end of 1982, as well as real
final sales and real G N P growth. The pace of inventory

reductions in both the first and fourth quarters of 1982
( —$10.2 billion and —$22.7 billion (1972 prices), re­
spectively) are among the largest on record, with the
latter exceeding the previous record of —$14.3 billion
in early 1975. In both of these quarters, real final sales
growth accelerated. Each of these sales accelerations
was associated with a sharp acceleration to double-digit
money growth (see table 2). In each case, the improve­
ment in real sales was met out of inventory, indicating
either that producers failed to anticipate the improve­
ment, or that they were willing to treat it as an oppor­
tunity to eliminate undesired inventory, allowing pro­
duction growth to rise more smoothly.
As noted above, GNP growth is more volatile than
that of real final sales due to relatively large swings in
inventory investm ent. On average, these swings
should cancel out so that GNP growth matches final



sales growth. One way to assess the contribution of
inventory swings to GNP growth is to decompose GNP
into the product of two components: S and (1 + I/S),
where S is final sales and I is the change in business
inventories. The growth rate of nominal production
(400 Ain GNP) can be broken down into a component
that arises from the growth of sales and a second com­
ponent, the production growth which meets changes
in the ratio of inventory investment to final sales [400
Ain (1 + I/S)]. Chart 3 shows this second component
along with total GNP growth from 1947 to the second
quarter of 1983.
On average, the growth rate of production matches
that of final sales; the contribution of inventory swings
[400 Aln(l + I/S)] is essentially zero ( —0.01 percent),
though it ranges widely from about —8 .8 percent to
13.5 percent in some quarters. The most pronounced
effects are in recessions, when large negative effects
are registered, and in the initial stages of recovery,
when some of the large positive contributions of the
end of inventory depletions are evident. Not surpris­
ingly, the negative effects of inventory depletion in the

11

FEDERAL RESERVE BANK OF ST. LOUIS

first and fourth quarters of 1982 are among the largest
negative effects shown in chart 3.

WAS VELOCITY GROWTH IN 1982
REALLY AN ABERRATION?
Weak or negative velocity growth is common during
recessions because of (1) the influence of the transitory
reduction in GNP with its smaller attendant reduction
in the demand for money, (2) the pattern of money
growth that usually gives rise to the recession, and (3)
inventory adjustments that typically depress produc­
tion relative to sales before or during the initial stage of
a recovery.
To assess the cyclical nature of velocity, one must
account for the strong trend in its growth rate, as well
as several transitory or, perhaps, permanent effects
arising from monetary and fiscal policy changes and
other shocks. The direct cyclical component of velocity
is captured by relating the level of velocity to the GNP
gap, the percentage by which the nation’s potential
output exceeds its actual real G N P .15 An increase in
the GNP gap reflects a decline in real income relative
to potential output. Its effect on velocity indicates the
operation of the income elasticity of money demand
and captures, in part, the transitory effect of cyclical
inventory movements on observed GNP.
It is well-known that current GNP growth depends
on past as well as current monetary policy actions.
Because the demand for goods and services responds
with a lag, current GNP or velocity measures are sub­
ject to temporary movements arising from changes in
money growth. Fiscal policy also can influence GNP; a
fiscal measure, specifically the growth rate of highemployment federal expenditures, is included in the
velocity equations below.16
15The GNP gap (G) is measured here by the difference in the
logarithm of each series. This Bank’s potential output series is
used to measure the gap. It is explained in John A. Tatom, “Poten­
tial Output and the Recent Productivity Decline,’’ this Review
(January 1982), pp. 3-16. Changes in the GNP gap are highly
correlated with other cyclical measures such as changes in mea­
sures of the capacity utilization rate or unemployment rate, so that
they can often be used interchangeably. For example, the simple
correlation coefficient between quarterly changes in the unem­
ployment rate and the GNP gap is 0.70 over the period III/1948—
III/1981.
16The inclusion of lagged effects of monetary and fiscal policy is
based on the Andersen-Jordan equation for GNP growth. See
Keith M. Carlson, “A Monetary Analysis of the Administration’s
Budget and Economic Projections,” this Review (May 1982), p.
14; and John A. Tatom, “Energy Prices and Short-Run Economic
Performance,” this Review (January 1981), pp. 3-17. The latter
suggests the inclusion of some other factors that are discussed
below. Lagged adjustment to money supply changes has also been

Digitized for12
FRASER


AUGUST/SEPTEMBER 1983

There are other factors that influence velocity, espe­
cially the opportunity cost of holding money instead of
other assets. An increase in the cost of holding money
reduces the demand for it and raises velocity, other
things being equal. A major component of the cost of
holding transaction balances is the rate of depreciation
of the value of money, or the general rate of increase of
prices. In addition, other assets can be held instead of
money so that the real rate of return on alternative
investments influences the decision to hold money.
Given the expected inflation rate, movements in nom­
inal interest rates reflect movements in real rates of
return.
Velocity, then, is hypothesized to be a function of (1)
current and past levels of the money stock (M) and
high-employment expenditures (E); (2) inflation ex­
pectations, which, if expectations are unbiased, can be
measured by changes in the rate of increase of the GNP
deflator (P); (3) the rate of interest, in this instance,
measured by the Aaa bond yield (r); and (4) slack,
measured by the GNP gap. Two other factors that
affect GNP at least temporarily — strikes that tempo­
rarily affect production and spending (S), measured by
days lost due to strikes relative to the size of the civilian
labor force, and movements in the relative price of
energy (pe), measured by the producer price of fuel
and related products and power deflated by the busi­
ness sector implicit price deflator — are included.

Estimating Velocity Growth
To find the historical relationship of velocity growth
to these factors, differences in logarithms are used to
measure growth rates, in which case the variable is
expressed with a dot above it.17 An estimate for veloc-

emphasized recently by Jack Carr and Michael R. Darby, “The
Role of Money Supply Shocks in the Short-Run Demand for
Money,” Journal o f Monetary Economics (September 1981), pp.
183-99. An earlier formulation and test of this hypothesis may be
found in Leonall C. Andersen, “Observed Income Velocity of
Money: A Misunderstood Issue in Monetary Policy,” this Review
(August 1975), pp. 8-19. The results here have the same prop­
erties and policy implications as the Andersen-Jordan equation.
17Arithmetically,

velocity growth in a quarter is the sum of the rates
of increase of prices and real output, less the growth rate of money
during the quarter. Thus, the strong significance of these factors
on the right-hand-side of equation 4 is not surprising. The use of
accelerations in money and prices reduces biases arising from the
arithmetic relationship. The fact that the coefficients on contem­
poraneous money, gap and inflation are significantly different
from unity reinforces the explanatory power of the equation. The
simple correlation coefficients between AM, AG and AP are (AM,
AG) —0.08, (AM, AP) —0.03, and(AG, AP) —0.06. Biases arising
from the arithmetic relationship do not appear to be a substantial
problem for the interpretation or quality of the regression re­
ported in table 4.

AUGUST/SEPTEMBER 1983

FEDERAL RESERVE BANK OF ST. LOUIS

Table 4
A Model of GNP Velocity Growth:
111/ 1948- 111/1981
V, = 3.825 - 0.801 AM, - 0.555 AM,_, - 0.371 AM,_2
(9.49) (-11.10)
( - 6.44)
( - 3.80)
- 0.248 AM,_3 - 0.188 AM,_„ + 0.032 E,
(-2.79)
(-2 .2 2 )
(2.74)
- 0.005 E,_, - 0.029 E, 2 - 0.004E,_3 - 0.855 AG
(-0.41 )
(-2 .4 6 )
(-3 .8 5 )
(-15.88)
+ 0.015 r, + 0.443 AP, - 0.248 AS, - 0.040 p?
(1.16)
(6.96)
(-4 .1 3 )
(-2 .0 8 )
- 0.030 pf , +
(-1.39 )
Rz = 0.80

0.077 pf_ 2
(3.40)

SE = 1.94

DW = 2.01

and 3 .5 percent, before returning to 3 .8 percent five
quarters later. There is no permanent effect of money
growth on velocity growth, only transitory effects that
disappear after five quarters.
The effect of the GNP gap on velocity is highly
significant: each 1 percent increase in the gap reduces
velocity by almost 0 .9 percent. An increase in highem ploym ent federal expenditures initially raises
velocity, then reduces it. Energy price increases in­
itially reduce velocity, then raise it, other factors re­
maining the same.20 An increase in inflation signifi­
cantly and permanently raises the level of velocity. The
interest rate is not significant at conventional levels,
but is included since it has the expected sign and a
t-statistic that is greater than one.21 Finally, strikes
temporarily reduce velocity.22

p = 0.45
(t = 5.81)

Velocity Growth in the Recent Recession
ity growth from III/1948 to III/1981 is given in table
4 .18 The coefficients on the monetary growth terms
indicate the cumulative sum of the effects of a rise in M
on velocity growth.19 Thus, an acceleration in money
growth in period t by 1 percent initially reduces veloc­
ity growth in period t by 0 .8 percent; subsequently,
velocity growth is depressed by less: 0 .6 percent one
quarter later, 0 .4 percent two quarters later, then 0 .2
percent, 0 .2 percent and, five quarters later, not at all.
If velocity had been growing at 3 .8 percent, assuming
all other influences remain the same, such a sustained
increase in money growth would yield a series of veloc­
ity growth rates that fell and then rose: 3 .0 percent,
initially, then 3 .2 percent, 3 .4 percent, 3 .5 percent,

18Long lag searches (up to 2 0 quarters for money and federal
expenditure growth) were conducted for a sample period 1/1955III/1981, because data limitations are too great for the period
beginning in III/1948. The optimal lag structure, chosen by Ftests of sequential addition of individual lags and groups of lags,
was the same as that used here.
19Suppose that V, = p 0M, + PiM ,_i + ... + pnM,_„; then V, =

0oA M , + (p0+ Pi)A!Vl,_! + . . . + ( 2 £ ( )£ & , _ „ _ ! +
i = 0
11

•

•

•

( X PJ.M,_n.Ifthe permanent effect of a rise in M on V is zero, the
i= 0

last term vanishes. In the equation in table 4, the absence of a
permanent effect can be tested by adding the money growth rate
lagged five quarters to the equation. When this is done, its coef­
ficient ( —0 .1 0 3 ) is n ot significantly different from zero
(t= —0.78). Consequently, this permanent effect is constrained to
zero in table 4 and for the examination of the recent experience.
The coefficients on the AM terms are estimated to lie along a
second-degree polynomial without endpoint constraints. The Fstatistic for the polynomial restriction is F 2,n 6 = 2.47, so that the
polynomial restrictions cannot be rejected.




When velocity growth is simulated for the 1981-82
recession, the equation tracks the actual developments
quite well (see table 5). Despite the sharp reductions in
velocity in the first and fourth quarters of 1982, un­
usual errors do not result. While undue attention to
every wiggle in velocity growth is clearly to be
avoided, it is worth noting that the record movements
in inventories during these two quarters and their

2(lThe sum of the federal expenditure effects on velocity is —0.047
and it is not significantly different from zero (t = 1. 6 8 ). The sum of
the energy price effects, 0.007, is also insignificant (t = 0.24).
High-employment expenditures and energy prices have no
permanent effect on velocity.
21When a short-term interest rate, the 4- to 6 -month commercial
paper rate, is used instead of the Aaa bond yield, its insignificant
(t = 0.78) coefficient is 0.003. Otherwise, the equation estimates
are virtually identical. Allowing the interest elasticity of velocity
to be a positive function of the interest rate, by using Ar rather
than Ain r, resulted in a higher standard error of estimate for both
long- and short-term rates. For both rates, moreover, the coef­
ficient reverses sign and the t-statistic falls below one-half. The
small t-statistic reported for r in table 4 does not result from
collinearity with changes in the inflation rate; the correlation
coefficient of these two variables is virtually zero ( —0.007).
22The model shown in table 4 can also be used successfully for final
sales velocity growth, except that strikes, interest rates, and con­
temporary energy price changes do not affect it significantly. The
model has the same properties; money growth, high-employment
expenditure growth, and changes in the relative price of energy do
not have significant permanent impacts on final sales velocity. The
adjusted R of the final sales velocity growth rate is 0.46 over the
period used in table 4. This equation is stable across the IW1973
and III/1981 breakpoints at a 95 percent confidence level.
The gap coefficient in the final sales equation is much smaller
( —0.44), indicating that the cyclical component of GNP velocity is
capturing some of the inventory adjustment. A decomposition
shows that money growth accounts for most of the sharp negative
swings of GNP velocity growth, however.

13

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

Table 5
Simulating GNP Velocity Growth in the
Recent Recession1
One-quarter
period ending
1981/IV
1982/1
II
III
IV
111/1981-IV/1982

Actual
velocity
growth
0.43%

Simulated
velocity
growth

Table 6
Factors Accounting for Velocity
Growth: 111/1981-IV/19821
Direct Contribution of:

Error

0.88

-0 .4 5

-11.86
3.24
-3 .4 3
-10.43

-9 .5 7
0.79
0.29

-2.29
2.25
-3.71

-7 .8 3

-2.60

-4.41

-3 .0 9

-1 .3 2

Constant
Cycle
Variations in money growth
Inflation changes
Interest rate changes
High-employment federal expenditure growth
Energy price shocks
Strike activity
Unexplained residual
TOTAL

3.9%
-4 .9
-0 .7
-0 .5
-0 .3
-0 .3
-0.1
0.0
-1 .3
-4.3%

Root-mean-squared error 2.53
1Growth rates are expressed as 400 times the change in the
logarithm of velocity.

impact on production and velocity are captured sur­
prisingly well. The mean error for the recession period
(1.32 percent) and the root-mean-squared error (2.53
percent) are not at odds with the quality of the errors
characterizing the prior behavior of velocity growth,
indicated by the equation s standard error of 1.94
oo
percent.
When the equation in table 4 is re-estimated for the
longer period to IV/1982, the F-statistic that is used to
test for a structural change between the earlier period
and the latest five recession quarters is F 5 i2 3 = 1.55,
which is not significant at a 95 percent confidence
level. This F-test and the evidence in table 5 indicate
that the historically weak performance of velocity in
the recent recession is not unusual; that is, it has
resulted from the normal working of factors that tend to
depress GNP velocity in recessions, not from a major
breakdown of past relationships.24
The coefficients in the velocity growth equation can
be used to decompose the simulated growth rates into
the direct contribution of each variable during the

23The equation in table 4 can be used to generate simulations for
velocity growth in earlier recessions (see table 1 ) on a comparable
basis. When this is done, the direction of the velocity movement
in each of the seven previous recessions is accurately simulated;
the mean absolute error for these seven recessions is 1.07 percent.
24The equation in table 4 is stable according to a Chow test. Also,
when the sample period is broken at the fourth quarter of 1973,
the F-statistic is F 15103 = 1.45, which is not significant at a 5
percent significance level.

Digitized for14
FRASER


'Based on table 4 coefficients and actual changes in the factors
influencing velocity. The results are converted to compounded
annual rates. Total does not add due to rounding.

recent recession.25 The results for the recent recession
period appear in table 6. The primary factor accounting
for the decline was the normal cyclical response to the
transitory decline in income associated with the reces­
sion; this effect, measured by the change in the GNP
gap and indicated in the table as the “cycle” influence,
was —4 .9 percent. The second major factor was the
transitory effect arising from variations in money
growth before and during the recession. Since the
primary determinant of the decline in real output or
the size of the GNP gap is the pattern of past monetary
growth, the lion’s share of the recent behavior of veloc­
ity is directly or indirectly attributable to the volatile
path of monetary growth.
Other factors played minor roles. In particular, de­
clining inflation and declining interest rates each con-

25The major controversy addressed here is the velocity decline in
the recent recession, especially in 1982. In the first quarter of 1983,
velocity fell at a 5.75 percent compounded annual rate. The de­
cline, while substantially smaller in size than those in the first and
fourth quarters of 1982, is noteworthy for its size in the absence of
a major swing in the contribution of inventory liquidations. In­
deed, while real inventory investment remained negative,
$ —15.4 billion (1972 prices), the contribution of inventory invest­
ment to GNP growth was positive, + 2 .3 percentage points, since
the pace of liquidation slowed. More important, when the velocity
model is used to make a one-quarter-ahead forecast from IV/1982,
the predicted velocity growth rate is —0.9 percent. Thus, the
error in 1/1983 is significantly larger (2.5 times larger) than the
standard error of the estimating equation. None of the F-test
results or conclusions about the five-quarter simulation experi­
ment in table 5 are altered if the first quarter of the recovery is
included, however.

FEDERAL RESERVE BANK OF ST. LOUIS

tributed 0.5 percentage points or less to the decline.
Nonetheless, these other factors amplified the decline
somewhat.26

CONCLUSION
The velocity of money fell sharply in the recent
recession, suggesting to some observers at least that
the relationship of the money stock to total spending
had broken down. Indeed, many observers went on to
posit new hypotheses concerning the reasons for the
velocity decline such as financial innovations, for­
eigners’ attractions to dollar assets, or unusually strong
reactions to the slowing of the U .S. inflation rate or
interest rates. Upon closer scrutiny, however, the tim­
ing and magnitude of these developments do not
match up well with velocity developments in the re­
cent past.
The velocity decline does appear, superficially, to
represent a major break from past experience and,
therefore, to be a source of concern for policymakers.
After all, in 1982 velocity fell at a 2 .3 percent rate (year
over year) after rising at a 3 .2 percent average rate over
the previous 22 years, suggesting a shortfall of 5.5
percentage points. On a quarter-to-quarter basis, the
decline in velocity during the recent recession was
even larger.
It is not unusual, however, for velocity to decline in a
recession. It is, in fact, quite typical. Short-term move­
ments in velocity reflect diverse reactions of the econ­
omy to monetary policy actions. In a recession, all of
these reactions generally contribute to a temporary
decline in velocity. Given the length and severity of
the recent recession, where the severity is measured
by the unemployment rate or the gap between the
nation’s potential and actual real GNP, it is not surpris­
ing that velocity registered the largest decline in postWorld W ar II recessions.
“ interestingly, compared with the previous seven postwar reces­
sions, the cyclical component was not unusually large in the recent
recession. The cyclical contribution (compounded annual rate
from cycle peak to trough) in the seven recessions from 1948-49
to 1980 is estimated to be —5.4 percent, —5.2 percent, —5.1
percent, —2.9 percent, —3.0 p ercent,—4 .7 percent and —5.0
percent, respectively. Four of the previous seven effects exceed
the recent cyclical effect.




AUGUST/SEPTEMBER 1983

A detailed development of the standard hypotheses
concerning velocity behavior, including the transitory
influences of monetary growth, fiscal policy, and ener­
gy price shocks on observed spending and velocity,
suggests an empirical formulation that accounts well
for velocity behavior in the post-World W ar II era.
More important, simulations of this historical experi­
ence for the recent recession indicate that there were
no significant breakdowns in the relationship of the
factors accounting for velocity behavior.
In a p reviou s study of v e lo city m ovem en ts,
Andersen concluded that “the use of observed changes
in velocity growth, by themselves, in conducting
monetary policy is often misleading and potentially
dangerous.”27 This conclusion is perhaps most impor­
tant surrounding recessions and the early stages of
recovery when velocity movements are so strongly
influenced by the temporary effects of past monetary
actions.
Monetary growth tends to be most variable around a
period of recession, especially when a sizable decline
initially sets off the recession itself. Such a variation in
money growth creates temporary movements in velo­
city; not only is the supply of money in flux, but real
output is as well, as the demand for money adjusts to
the money supply variation. Variations in real output
and velocity are further enlarged temporarily by in­
ventory adjustments.
In the recent recession, these processes were mag­
nified by the degree and extent of monetary stringency
during some periods prior to the recession. As a result,
the normal cyclical movement of money demand was
large, and swings in inventory investment further dis­
torted, temporarily, the movements of velocity. Other
factors, including the temporary decline in inflation
and movements in interest rates, federal expenditures
and energy prices all worked in the same direction,
reducing velocity in the recent recession. Thus, the
extent of the decline in velocity in the recent recession
was not unusual, nor did it represent an atypical shift
with important, but unknown, implications for policy­
making.

27Andersen,

“Observed Income Velocity of Money,” p. 19.

15

Monetary Growth and the Timing of
Interest Rate Movements
W. W. BROWN and G. J. SANTONI

I t IS widely believed that market interest rates fol­
low a particular time path in response to changes in the
rate of monetary growth. This time path is important
because interest rates are thought to be one of the
conduits of monetary policy.
In particular, an unanticipated but permanent in­
crease in the monetary growth rate will presumbly
lower market interest rates, temporarily resulting in a
reshuffling of resources among competing uses. As a
consequence, an economy characterized by slack will
be pushed to a permanently higher le\ el of aggregate
demand, employment, output and, eventually, higher
market interest rates as a result of the monetary
stimulus.
The length of the time path followed by interest
rates reveals information concerning the lag in mone­
tary policy’s effect. Curiosity about this provided
the initial motivation for earlier empirical investiga­
tions.1 This paper discusses the theoretical argument
and examines some evidence regarding the response of
interest rates to changes in monetary growth.
W. W. Brown is an associate professor o f economics at California
State University, Northridge.
W illiam E. Gibson, “Interest Rates and Monetary Policy,"Journal
o f Political Economy (May/June 1970), pp. 431-55; Burton Zwick,
“The Adjustment of the Economy to Monetary Changes,” Journal
o f Political Economy (January/February 1971), pp. 77-96. Phillip
Cagan, Changes in the Cyclical Behavior o f Interest Rates (Nation­
al Bureau of Economic Research, Occasional Paper 100, 1966);
William E. Gibson and George E . Kaufman, “The Sensitivity of
Interest Rates to Changes in Money and Income,” Journal o f
Political Economy (May/June 1968), pp. 472-78; Phillip Cagan and
Arthur Gandolfi, “The Lag in Monetary Policy as Implied by the
Time Pattern of Monetary Effects on Interest Rates,” The Am er­
ican Economic Review, Papers and Proceedings (May 1969), pp.
277-84; Phillip Cagan, The Channels o f Monetary Effects on In­
terest Rates (National Bureau of Economic Research, 1972);
Michael Melvin, “The Vanishing Liquidity Effect of Money on
Interest: Analysis and Implications for Policy,” Economic Inquiry
(April 1983), pp. 188-202.

Digitized for16
FRASER


THE THEORY
Equation 1 breaks the nominal interest rate, i, into
its two components: the ex ante real interest rate, r,
and the expected rate of inflation, Pe.
(1) i = r + Pe

The waxing and waning of the effects of a change in
monetary growth on each of these components gener­
ates the time path followed by the nominal rate. An
unanticipated change in monetary growth initially
affects the ex ante real rate of interest; this is called the
“liquidity effect. ”2 The permanent change in monetary
growth, once it is known, affects the expected rate of
inflation and is called the “Fisher effect.”

The Liquidity Effect
The theoretical argument concerning the liquidity
effect typically runs as follows: an unanticipated in­
crease in the monetary growth rate results initially in
an excess supply in the money market at the existing
nominal rate of interest. Part of this excess shows up as
an increase in the demand for securities. The prices of
securities are bid up, and nominal yields decline until
the market clears.3

traditionally, the term “liquidity effect” was used to describe the
impact of an unanticipated change in the stock of money on interest
rates. More recently, however, the term has been applied to the
initial effect on interest rates of an unanticipated change in the
stock of money induced by an unanticipated change in the mone­
tary growth rate. W e have adopted the more recent usage of the
term in this paper. Milton Friedman, “Factors Affecting the Level
of Interest Rates,” Money Supply, Money Demand, and Macroeco­
nomic Models, J. T. Boorman and T. M. Havrilesky, eds. (Allyn
and Bacon, Inc., 1972), pp. 205-06.
for example, Cagan, The Channels o f Monetary Effects. Note,
particularly, that “the first round effects of money creation are
ignored . . . . ” (p. 85)

3 See,

AUGUST/SEPTEMBER 1983

FEDERAL RESERVE BANK OF ST. LOUIS

Coincident with the downward movement of nomi­
nal yields in the loanable funds market is a reduction in
the ex ante real rate of interest in the goods market.
The result is that investment demand is stimulated and
saving out of current income is reduced. The conten­
tion is that real investment and consumption rise, stim­
ulating economic activity. The excess demand for real
present resources that follows from this decline in the
ex ante real rate is made up by “the flow of funds
supplied out of the discrepancy between actual and
desired money balances. . . , ”4

F ig u re 1

Panel A: Time Path of the Ex Ante Real Rate

After a sufficient time, the excess supply in the
money market is eliminated by an expansion in nomi­
nal income. This expansion raises the demand for
money, reverses the liquidity effect and returns the ex
ante real interest rate to its original level.

The Fisher Effect
A permanent increase in the monetary growth rate
will result in a permanently higher rate of inflation,
ceteris paribus. Since lending contracts typically spec­
ify fixed nominal payment streams, a higher nominal
rate will be required to compensate lenders for the
increased rate of depreciation expected to occur in the
real value of their receipts. If credit market partici­
pants acquire information regarding the permanently
higher rate of inflation with a lag, the convergence of
the nominal rate upon a higher level will occur gradual­
ly with a corresponding lag.

An Illustration o f the Time Path
Figure 1 depicts hypothesized time paths of the ex
ante real rate of interest, r (panel A), the expected rate
of inflation, Pe (panel B), and the nominal rate of in­
terest, i (panel C), that result from an unanticipated and
permanent increase in the monetary growth rate be­
ginning at time t0.
Assuming that the expected rate of inflation and the
price level do not immediately adjust to the change in
monetary growth, the ex ante real rate of interest
moves along a path like abc and remains below its
initial level until time t3. The liquidity effect is illus­
trated by the movement from a to b; the expansion
effect is shown by the movement from b to c.
Panel B of figure 1 illustrates the time path of the
expected rate of inflation. Given the lag in the acquisi­
tion of information concerning the permanently higher
4lbid., p. 87.



i

'0

rate of monetary growth, the expected rate of inflation
is presumed to adjust along a path like kfg. This is the
Fisher effect.
Panel C presents the time path of the nominal in­
terest rate. It is derived by adding the time path of the
expected rate of inflation to the time path of the ex ante
real rate of interest as suggested by equation 1 to obtain
the path lmn. Note that the nominal rate reaches a
minimum in period ti, which is both higher and occurs
earlier than the minimum of the ex ante real rate.
The path of the nominal rate depends on how swiftly
the expected rate of inflation responds.5 It is possible
5W e assume that nominal rates adjust perfectly to changes in ex­
pected inflation as suggested by Fisher’s theory. For further dis­
cussion of this issue, see John A. Carlson, “Short-Term Interest
Rates as Predictors of Inflation: Comment,” American Economic
Review 0une 1977), pp. 469-75; Jan Walter Elliot, “Measuring the
Expected Real Rate of Interest: An Exploration of Macroeconomic
Alternatives,” American Economic Review (June 1977), pp. 4 2 9 44; Eugene F. Fama, “Short-Term Interest Rates as Predictors of
Inflation,” American Economic Review (June 1975), pp. 269-82.

17

FEDERAL RESERVE BANK OF ST. LOUIS

that the nominal rate will fail to decline in response to
an increase in the monetary growth rate even though
the ex ante real rate does. In the extrem e, if expecta­
tions and the price level were to adjust perfectly and
instantaneously to the permanent increase in mone­
tary growth at to, there would be no liquidity effect. An
excess supply of money, which is a precondition for the
operation of a liquidity effect, would not exist. The
expected rate of inflation and the nominal rate would
move along the paths khg and lqn, respectively.

AN ECONOMIC CONSTRAINT ON THE
TIME PATH
Theory provides little guidance in identifying the
actual time paths that are followed by the nominal and
ex ante real interest rates. This can only be resolved
empirically. The time paths that interest rates follow
when adjusting to a change in monetary growth will be
constrained, however, by the wealth-maximizing be­
havior of individuals. The time paths must be such
that they cannot be predicted (ex ante) by market
participants.

Efficient Markets and the Response o f the
Nominal Rate
On an intuitive level, a systematic and predictable
relationship between the nominal interest rate and
changes in the monetary growth rate that are known to
be permanent (like that shown by the path lmn in panel
C of figure 1) may imply that profitable trading oppor­
tunities are left unexploited by financial market par­
ticipants.6 If transaction costs are low relative to the
predicted change in the value of the security traded,
selling, and selling short at to, will result in trading
profits. Naturally, such trading would tend to elimi­
nate the lag in the adjustment of nominal interest rates,
causing the time path to move toward one like lqn.7

'This point was discussed by Fisher in 1896. “If gold appreciates in
such a way or in such a sense that he (the ordinary man) expects a
shrinking margin of profit, he will be cautious about borrowing
unless interest falls; and this very unwillingness to borrow, lessen­
ing the demand in the ‘money market’ will bring interest down.”
Further, “every chance for gain is eagerly watched. An active and
intelligent speculation is constantly going on, which . . . performs
a well-known and provident social function for society. Is it reason­
able to believe that foresight, which is the general rule, has an
exception when applied to falling or rising prices?” Irving Fisher,
“Appreciation and Interest,” Publications o f the American Eco­
nomic Association (August 1906), pp. 36-37.
7Eugene F . Fama, “Efficient Capital Markets: A Review of Theory
and Empirical Work, ” The Journal o f Finance, Papers and Pro-

Digitized for
18FRASER


AUGUST/SEPTEMBER 1983

The acquisition of new information, of course, is
costly and these costs may increase with the rate of
acquisition. Under these circumstances, interest rates
will adjust to changes in monetary growth with a lag.
The length of the lag will depend upon the relative
costs and benefits of acquiring information more
rapidly.

Efficient Markets and the
Path o f the Real Rate
Since the ex ante real rate of interest reflects the
value of present consumption (short-lived, nondurable
goods) relative to future consumption (long-lived, du­
rable goods), the liquidity effect implies a specific time
path of the relative prices of long- in terms of short­
lived goods. In particular, the time path of the ex ante
real rate in panel A of figure 1 suggests that the prices
of more durable goods (long-lived assets) rise relative
to less durable goods (short-lived assets) from to to t2,
then fall to their “normal” levels from t2 to t3.8
Our previous comments regarding the limits to prof­
itable bond trading apply as well to the predictability of
this U-shaped pattern in the prices of long- and short­
lived assets. That is, predictable U-shaped swings in
the relative prices of various assets (as implied by the
time pattern of the real rate shown in panel A of figure
1) may indicate that profitable trading is possible in

ceedings (May 1970), pp. 383-417; and Frederic S. Mishkin, A
Rational Expectations Approach to Macroeconometrics (National
Bureau of Economic Research, 1983).
sAs an example, see Milton Friedman’s discussion. He reasons that
“from a longer-term view, the new balance sheet (of the public) is
out of equilibrium, with cash being temporarily high relative to
other assets. Holders of cash will seek to purchase assets to achieve
a desired structure. This will bid up the price of assets . . . . These
effects can be described as operating on ‘interest rates,’ if a more
cosmopolitan interpretation of ‘interest rates’ is adopted than the
usual one which refers to a small range of marketable securities.
“The key feature of this process is that it tends to raise the prices
of sources of both producer and consumer services relative to the
prices of the services themselves . . . . It therefore encourages the
production of such sources (this is the stimulus t o ‘investment’ . . .)
and, at the same time, the direct acquisition of services rather than
of the source (this is the stimulus to ‘consumption’ relative to
‘savings’). But these reactions in their turn tend to raise the prices
of services relative to the prices of sources, this is, to undo the
initial effects [our emphasis] on interest rates.
“Of course, all these forces operate simultaneously [our empha­
sis] and there are ebbs and flows and not merely movement in one
direction.’’ Milton Friedman, “The Lag in Effect of Monetary
Policy,” in Milton Friedman, ed., The Optimum Quantity o f
Money and Other Essays (Aldine Publishing Co., 1970), pp. 2 5 5 56.

FEDERAL RESERVE BANK OF ST. LOUIS

these markets. As in financial markets, however, such
trading will tend to limit these changes in relative
prices to magnitudes that essentially reflect the cost of
transacting.9 In short, the time paths of both real and
nominal interest rates will be constrained by the exist­
ence of efficient financial and capital markets.10

SEARCHING FOR A VALID TEST
PERIOD
The conditions that must exist to generate a time
path of interest rates like that shown in panel C of
figure 1 are not trivial. Since the time path presumably
is generated by a monetary policy shock, the institu­
tional environment must be one that allows these
shocks to occur. In particular, the operation of a Fisher
effect will be especially sensitive to the implications
the existing monetary institutions have for the ex­
pected duration of changes in the monetary growth
rate and the possibility that these changes can be in­
duced by the fiat of the monetary authority. In short,
the institutions must be such that exogenously deter­
mined changes in the monetary growth rate are possi­
ble. In addition, since the liquidity effect depends
upon monetary changes being unanticipated, it will
operate only during periods in which the monetary
authority can cause unpredictable changes in money
growth.11 A precondition of this is that changes in
money growth are unrelated to prior movements in
other economic variables, particularly, interest rates.

9See Frank H. Knight, “Unemployment: And Mr. Keyne s Revolu­
tion in Economic Theory,” Canadian Journal o f Economics and
Political Science (1937), pp. 112-13; Frank H. Knight, “Capital,
Time and the Interest Rate, ” Economica (August 1934), pp. 257—
8 6 ; Lloyd W. Mints, Monetary Policy f o r a Competitive Society
(McGraw-Hill, 1950), pp. 58-70; Gustav Cassel, “The Rate of
Interest, the Bank Rate, and the Stabilization of Prices, ” in Read­
ings in Monetary Theory (The Blaldston Company, 1951), pp.
319-33; and Frank H. Knight, The Ethics o f Competition (Books for
Libraries Press, 1969), pp. 273-74.

AUGUST/SEPTEMBER 1983

Unfortunately, data concerning anticipated and un­
anticipated money growth are not directly observable,
and we know of no satisfactory method of empirically
separating actual money growth into these two compo­
nents. In addition, it is not generally possible to direct­
ly observe the ex ante real interest rate. For these
reasons, the liquidity effect tends to be confounded by
the Fisher effect in empirical tests. However, since
one of our main purposes is to discover the lag in the
effect of monetary policy as implied by the time path of
nominal interest rates, this is not particularly trouble­
some.
In the following, we examine various historical
periods during which different monetary institutions
prevailed. Our purpose is to discover a period that will
yield a valid test of the hypothesis concerning the time
path.

The Gold Standard Period: 1900-2912
The Gold Standard Act became law in March of 1900
and remained in force until January of 1934 when it was
superseded by the Gold Reserve Act. During this
period, the price of gold was fixed at $20.67 per ounce
and, equally important, gold circulated as a medium of
exchange. Maintenance of this type of gold standard
imposes binding constraints on the monetary author­
ities that prevent them from generating significant and
long-lived changes in money growth (in the absence of
new gold discoveries or improvements in mining tech­
nology). “The stock of money must be whatever is
necessary to balance international p aym en ts.” 13
Hence, any change in the growth rate of money that, if
maintained, would cause the future supply of money to
deviate from that necessary to maintain the balance of
payments and the fixed exchange rate between the
dollar and gold must eventually be offset by a change in
the opposite direction.

10If the changes in relative prices that are described in footnote 8
always follow the same time sequence, it is possible that profitable
trades are left unexploited. On the other hand, if “all these forces
operate simultaneously,” the possibility of wealth increasing ex­
change is eliminated but so is the time path of the ex ante real rate.
As it stands, the argument appears to be ambiguous concerning
the time path followed by the ex ante real interest rate.

During this period, individuals holding monetary
assets, in large part, were insulated from changes in
the real value of their assets. Under the gold standard,
any unanticipated change in the general level of prices
produced by temporary changes in the quantity of
money “was likely to reverse or ‘correct’ itself, i.e.,

''Fred eric S. Mishkin, “Monetary Policy and Long-Term Interest
Rates: An Efficient Markets Approach,” Journal o f Monetary
Economics (January 1981), pp. 29 -5 5 ; Frederic S. Mishkin,
“Monetary Policy and Short-term Interest Rates: An Efficient
Markets-Rational Expectations Approach,” The Journal o f Fi­
nance (March 1982), pp. 63-72; David A. Pierce, “Relationships
— and the Lack Thereof— Between Economic Time Series, with
Special Reference to Money and Interest Rates "Journal o f the
American Statistical Association (March 1977), pp. 11-22.

12To avoid the confounding effects of the depression years, we have
omitted them from our analysis.




13Milton Friedman and Anna Schwartz, A Monetary History o f the
United States 1867-1960 (Princeton University Press, 1963), p.
191.

19

FEDERAL RESERVE BANK OF ST. LOUIS

average out’ over time. ”14 Friedman and Schwartz
note that “. . . the gold standard ruled supreme when
the act (the Federal Reserve Act) was passed, and its
continued supremacy was taken for granted. . . . ”15
Consequently, since changes in monetary growth
were arguably viewed as temporary during this period,
we would not expect to observe the Fisher effect.
While the gold standard prevented significant and
long-lived changes in money growth, it did not prevent
the occurrence of short-term swings in the growth rate.
The coefficient of variation in the annual growth rate of
money is 87 percent during the 1914-29 period. In
contrast, during the 1970-82 period, which has been
characterized as a period of highly volatile money
growth, the coefficient of variation is 2 0 percent.
Since the liquidity effect is a short-term phe­
nomenon predicated on unanticipated changes in the
monetary growth rate (whether permanent or tempo­
rary), this period would seem to be particularly
appropriate in testing for its presence because the
Fisher effect is arguably zero. Temporary changes in
the growth rate of money did not induce confounding
impacts on the nominal rate. Roughly, movements in
nominal rates should mirror movements in real rates
during the gold standard.16 If money is exogenous with

14Benjamin Klein, “Our New Monetary Standard: The Measure­
ment and Effects of Price Uncertainty,” Economic Inquiry (De­
cember 1975), p. 471; see, as well, I. B. Ibrahim and Raburn M.
Williams, “The Fisher Relationship Under Different Monetary
Standards, ”Journal o f Money, Credit and Banking (August 1978),
pp. 363-70. In addition, the major discoveries of gold had oc­
curred prior to 1900 and the cyanide process was successfully
applied to gold mining in the 1890s.
I5Friedman and Schwartz, A Monetary History, p. 191.
16One might question whether changes in the nominal rate tracked
changes in the real rate of interest during this period. To check
this, we regressed annual changes in the yield of high grade
corporate bonds (Standard and Poor’s) on annual changes in the
ratio of the Consumer Price Index divided by an index of stock
prices (Standard and Poor’s) for the period 1907-29. Given Klein’s
evidence, changes in the bond yield during this period should
reflect changes in the real interest rate. The CPI, of course, is
heavily weighted in the favor of present consumption goods and
thus represents the average price of current consumption. The
stock price index is an index of the prices of capital goods .Changes
in the ratio of these two prices will track changes in the real rate of
interest and be reflected by changes in the bond yield during the
gold standard period. The results are given below (t-values in
parentheses):
Ai

.05 + 16.01A(CPI/STDP)
(5.97)
R2 = .59 D W = 1.81
=

The results are consistent with the claim that changes in bond yields
reflected changes in the real rate of interest during this period.
Interestingly, the relationship breaks down completely for the
more recent period, 1954-82. The results for this period are:

Digitized for20
FRASER


AUGUST/SEPTEMBER 1983

respect to interest rates and if not all of the changes in
monetary growth that occurred were anticipated, then
the estimated relationship for this period should depict
a time path of interest rates similar to that shown in
panel A of figure 1.

The E n d o f the Gold Standard Act
Through the Korean War: 1934—53
From mid-1934 through March of 1953, little varia­
tion occurred in short-term interest rates. F o r exam­
ple, table 1 lists the level of the commercial paper rate
and the number of months during which the rate re­
mained constant at a particular level. The table indi­
cates that the recorded commercial paper rate changed
only four times during the period running from June
1934 through June 1938 and that, during this time, it
remained constant at .75 percent for a period of 26
months. In fact, month-to-month changes in the re­
corded commercial paper rate were zero in all but 46 of
the entire 225 months. In contrast, for the period
1954—82, the rate failed to change in only 25 out of 348
months.
Since there was little month-to-month variation in
either the commercial paper rate or other interest rates
during the 1934—53 period, and since there is reason to
believe that money was endogenous to interest rates
during this period, we have treated it separately in the
empirical tests.17

The Korean War to the Present: 1954—82
Since the end of the Korean W ar, month-to-month
variation in nominal interest rates has been consider­
able. The Gold Reserve Act, however, continued to tie
the dollar, albeit loosely, to gold until August 15, 1971.
Consequently, we have split the 1954—82 period at
this point. During the latter period, the behavior of
the monetary authority has been free of the formal
constraints imposed by gold. If a relationship similar to
that shown in panel C of figure 1 exists between money
and interest rates, it should show up during this
period.

Ai = .38 + ,54A(CPI/STDP)
(.98)
R2 = .15
RH O = .33
(1.84)

D W = 1.62

For further evidence, see Robert J. Shiller and Jeremy J. Siegel,
“The Gibson Paradox and Historical Movements in Real Interest
Rates "Journal o f Political Economy (October 1977), p. 905.
17Friedman and Schwartz, A Monetary History, p. 562.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

EMPIRICAL ESTIMATION
Using monthly nominal interest rates and money
supply data, we have run regressions for each of the
subperiods 1914-29, 1934-53, 1954-70 and 1971-82.
In each case, the money supply is defined as M l
balances.18 The interest rate is defined as the com mer­
cial paper rate (4 -6 month maturity prior to November
1979 and 120-day maturity after). In each period, the
monthly change in the interest rate is regressed on
monthly changes in the rate of monetary growth in the
contemporaneous month and 38 past (lagged) monthly
changes.19 This specification initially was identified as
the u n restricted m odel. In o rd er to d eterm in e
whether the estimated coefficients are sensitive to the
lag length and to identify statistically redundant lags,
the structure was shortened to 24, 18, 12, 6, 3, 1 and
zero months. At each stage, an F-test was applied to
determine whether the omitted lags were significant.20

Table 1
The Unusual Behavior of the
Commercial Paper Rate:
June 1934 - February 1953
Period
6/34-1/35
2/35-3/37
4/37-2/38
3/38-6/38
7/38-12/38
1/39-8/39
9/39-11/39
12/39-5/41
6/41
7/41-11/41
12/41-1/42
2/42-5/42

July 1914 - D ecem ber 1929

6/42
7/42-3/44

Table 2 presents the results for the 1914-29 period.
The test for lag length revealed a lag structure of three
months. All of the estimated coefficients are negative,
and three are significantly different from zero. The
sum over the coefficients is significantly negative as
well. These results suggest that a one percentage-point
(100 basis-point) increase in the monetary growth rate
would have produced a decline of about one basis point
in the commercial paper rate during this period.21
Empirically, the estimated effect is surely miniscule
and, as indicated by the F-statistic (2.08), we cannot
reject the hypothesis that the relationship arose ran­
domly. The constant term in the regression is statisti­
cally insignificant, which is consistent with the efficient

4/44

'’’Ml balances were employed since broader monetary aggregates
are more likely to be endogenous with respect to interest rates.
While the United States was on a gold standard prior to 1914,
monthly Ml data are not available before June 1914.
19This lag length was selected as a point of departure and is based
•upon earlier work concerning the time path. See Cagan and
Gandolfi, “The Lag in Monetary Policy.”
“"This test is sensitive to the initial lag length specified in the
unrestricted model. As a consequence, it is possible that the test
will reject some variables that are, in fact, significant if too long a
lag is specified. To control for this, we ran the tests with the lag
length in the unrestricted model initially set at 38. We then
reduced the number of lags in the unrestricted model to 24 and
ran the test again. This was continued until we exhausted all of the
possibilities.
21For further discussion regarding this process, see Cagan and
Gandolfi, “The Lag in Monetary Policy,” p. 280.




Number of Months

Level of Rate

8
26
11
4

.88%
.75
1.00
.88
Variation

6
8
3
18
1
5
2
4
1
21
1

5/44-6/46
7/46
8/46-11/46
12/46-8/47

26
1
4

9/47-1/48
2/48-7/48
8/48-9/48
10/48-7/49
8/49

5
6
2
10
1

9/49-11/49
12/49
1/50-7/50
8/50-4/52
5/52-2/53

3
1
7
21
10

9

.56
.69
.56
.54
.50
Variation
.63
.67
.69
.72
.75
.77
Variation
1.00
Variation
1.38
Variation
1.56
1.43
1.38
1.33
1.31
Variation
2.31

SOURCE: Board of Governors of the Federal Reserve System,
Banking and Monetary Statistics, 1914-41, pp. 449SI and 1941-70, pp. 674-76.

market hypothesis that interest rate changes have no
trend.
Further, the results for this period are consistent
with a long-run Fisher effect of zero. This result was
expected, given the constraints implied by the gold
standard.
Applying a Granger “causality” test, we examined
the data to determine whether changes in the interest
rate are endogenous to changes in monetary growth,

21

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

Table 2
The Relationship Between Changes in
Money Growth and Changes in Interest
Rates: July 1914 - December 1929
Estimated Equation

Table 3
Causality Tests
Lags

F-statistic
Ai = f(AM)

F-statistic
AM = <j>(Ai)

7/1914-12/1929

3
6
9
12
18

0.93
1.46
1.69
1.50
1.41

1.21
0.83
2.09*
2.43*
1.62

1/1934-12/1953

3
6
9
12
18

0.26
0.44
0.48
0.00
0.40

0.00
0.59
0.58
0.57
0.47

1/1954-12/1970

3
6
9
12
18
24
38

0.71
1.21
1.58
1.62
1.37
1.25
1.24

3.28*
5.01*
3.34*
2.99*
2.50*
2.44*
1.63*

1/1971-2/1983

3
6
9
12
18

14.97*
14.32*
9.74*
8.84*
6.15*

19.50*
9.73*
5.22*
4.31*
2.79*

Period

3
Ai, = Constant + 1 akAMt_ k
___________________________ k = 0___________________
Coefficient
Constant
3o
ai
a2
a3

2a,
Rho
R2 = .19

Estimate1

t-ratio

-.840
-.1 0 2

0.29

-.269
-.169
-.9

1.93*
2.59*
1.72*
2.17*

0.43

5.43*

-.3 7 9

DW = 1.92

1.24

F = 2.08

'Adjusted for first-order autocorrelation.
‘ Significantly different from zero at the 95 percent confidence
level.
Note: Units of the coefficients are in basis points per 1 percentagepoint change in the monthly annualized rate of change in
the money stock.

'Significantly different from zero at the 95 percent confidence
level.

while changes in monetary growth are exogenous to
changes in the interest rate. Lag lengths of 3, 6, 9, 12
and 18 months were used in the test. Our results,
presented in table 3, reject the hypothesis that changes
in the monetary growth rate caused changes in the
interest rate during this period.
On the whole, the results from the gold standard
period are disappointing. W e had hoped that they
would provide some insight regarding the timing and
magnitude of the liquidity effect. The table 2 results,
however, are far from statistically impressive. They
indicate a negligible, at best, liquidity effect. This, of
course, is consistent with our expectations, given
efficient markets, but the interest rate does not return
to its original level as predicted and the causality tests
suggest that the changes in monetary growth that oc­
curred during the period did not “cause” changes in
the interest rate.

January 1934 - D ecem ber 1953
Table 4 presents our results for the commercial
paper rate during the 1934-53 period. As expected,
Digitized for
22FRASER


due to the lack of variation in market rates, no rela­
tionship appears to exist between changes in the mone­
tary growth rate and interest rates. None of the lags
were significant in the F-tests. As a consequence, table
4 only reports the regression for the change in mone­
tary growth contemporaneous to the change in the
interest rate. Even in this case, we cannot reject the
hypothesis that the constant and the coefficient of the
change in monetary growth are zero.
The results of the Granger tests indicate that the
money and interest rate series were independent dur­
ing the period. This held for each lag length used in the
test (see table 3).

January 1954

-

D ecem ber 1970

Our results for the January 1954 - D ecem ber 1970
period are presented in table 5. The lag structure
indicated by the F-test contains 24 months and, as in
earlier periods, the constant is insignificant. These
results generally are not consistent with the appear-

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

Table 4
The Relationship Between Changes in
Money Growth and Changes in Interest
Rates: January 1934 - December 1953
Estimated Equation
Ai, = Constant + a,AM,
Coefficient

Estimate1

Constant

.38

3o
Rho

.000015
.42

t-ratio
.70
.0014
7.17*

Table 5
The Relationship Between Changes in
Money Growth and Changes in Interest
Rates: January 1954 - December 1970
Estimated Equation

24
Ai, = Constant + 2 akA M ,_k
___________________________ k = 0___________________
Coefficient

R2 = .18

DW = 2.00

F = 0.00

’ Adjusted for first-order autocorrelation.
'Significantly different from zero at the 95 percent confidence
level.
Note: Units of the coefficients are in basis points per 1 percentagepoint change in the monthly annualized rate of change in
the money stock.

ance of either a contemporaneous or lagged liquidity
effect in nominal interest rates. While the first four
coefficients are negative, they are statistically indistin­
guishable from zero.
With the exception of lag 24, the remaining coef­
ficients are all positive and 15 are significant. Their
sum (36.00 basis points) differs significantly from zero,
which is consistent with the Fisher effect. The upward
adjustment of the interest rate, however, is less than
that implied by the Fisher effect.22
The results of the Granger test suggest that changes
in the interest rate are exogenous to changes in the
monetary growth rate, while changes in the monetary
growth rate are endogenous to changes in the interest
rate (see table 3). This result held up for each of the lag
lengths employed. It appears that the causality rela­
tionship is one-way, running from interest rates to
money. The theoretical arguments that underpin the
hypothesis regarding the time path, however, are
based on the assumption that money causes interest
rates.

Constant
3o
at
a2
a3
34
a5
3e
37
3e
a9
310
3n
3,2
3,3
3,4
al5
a16
a,7
3,8
3,9
a20
a21
322
323
324
^3 r
Rho
R2 = .31

Estimate1

t-ratio

1.43

0.67
0.84
1.26
1.10
0.55
0.15

-0 .3 0
-0 .7 2
-0 .8 0
-0 .4 3
0.13
0.39
1.92
3.02
2.99
2.67
2.93
2.98
2.10
1.99
1.89
2.14
2.39
2.10
2.20
2.20
1.54
1.28
0.78
0.85
-0 .2 4
36.00
0.45
DW = 1.92

0.45
2.19*
3.39*
3.28*
2.86*
3.05*
3.03*
2.13*
2.05*
1.98’
2.31*
2.62*
2.35*
2.50*
2.52’
1.81*
1.59
1.05
1.41
0.61
2.52*
7.20*
F = 1.87

'Corrected for first-order autocorrelation.
’ Significantly different from zero at the 95 percent confidence
level.
22W e have little faith in the results obtained during this period.
Unlike the other periods we consider, the F-test for lag length is
particularly sensitive to the initial lag specification. Beginning
with a lag length of one month and adding lags, the test reveals a
lag of three months. On the other hand, beginning with 38 months
and dropping lags, the test reveals a length of 24 months. This
ambiguity did not surface in any of the other periods we examined.




Note: Units of the coefficients are in basis points per 1 percentagepoint change in the monthly annualized rate of change in
the money stock.

23

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

Table 6
The Relationship Between Changes in
Money Growth and Changes in Interest
Rates: January 1971 - February 1983
Estimated Equation

12
Ai, = Constant + 2 akAMt_ k
___________________________ k = 0___________________
Coefficient

Estimate1

Constant

-0 .6 6
-2 .6 4
7.58
9.87
11.07

So
ai
a2
a3
a4

11.58
11.00
13.40
9.33
7.60

a5
a7
a8
a9
aio
ai1
ai2
2a*
Rho

6.43
4.66
5.15
3.30
98.33
0.37

R2 = .50

DW = 1.95

0.07
2.48*
5.21*
5.34*

The remaining coefficients are all positive and sig­
nificant. The sum over the coefficients (98.33 basis
points) is significantly different from zero and statisti­
cally indistinguishable from 100 (t = .08) as predicted
by the Fisher effect. Further, the bulk of the adjust­
ment in the interest rate (61.86 basis points) takes place
within six months.

5.15*
4.74*
4.18*
4.96*
3.46*
2.97*

Chart 1 illustrates the time path of the interest rate
that is implied by these results. A comparison ofchart 1
with figure 1 (panel C) indicates the results obtained
for the more recent period conform roughly to those
implied by rapidly changing inflation expectations.24

t-ratio

2.85*
2.39*
3.38*
3.10*
4.63*
4.81*
F = 10.!

’ Adjusted for first-order autocorrelation.
'Significantly different from zero at the 95 percent confidence
level.
Note: Units of the coefficients are in basis points per 1 percentagepoint change in the monthly annualized rate of change in
the money stock.

These results, with respect to both the incomplete
adjustment of the nominal rate and the endogeny of
money with respect to interest rates, can be explained
by the operation of the Gold Reserve Act. Other ex­
planations are no doubt possible. In any case, they
reveal little about the lag in the effect of an exogenously
determined monetary policy. In this sense, the results
obtained for this period, as for the earlier periods, are
disappointing.

January 1971

-

February 1983

Our results for the most recent period in which the
dollar has been legally free from gold are summarized
Digitized for
24FRASER


in table 6. The F-test indicated a lag structure of 12
months. As before, the constant term is not significant­
ly different from zero. More important, the results
are consistent with the existence of a contemporaneous
liquidity effect. The coefficient of the contem po­
raneous change in the monetary growth rate is nega­
tive and significant. As expected, the liquidity effect is
quite small numerically (2.65 basis points) and short­
lived.23

The G ranger test for this period indicates bi­
directional causality. On the whole, the results of the
Granger test suggest that the January 1971-February
1983 period is the only one of those considered that is a
candidate for a valid test of the hypothesis regarding
the time path. It is only during this period that we
cannot reject the hypothesis that changes in the mone­
tary growth rate caused changes in the interest rate.2’

In an effort to highlight the liquidity effect that apparently occurs
in the month contemporaneous to the change in monetary growth,
we regressed Wednesday-to-Wednesdav changes in the 3-month
Treasury bill rate on the weekly change in the growth rate of the
finally revised seasonally adjusted stock of M l. The contempora­
neous and three lags of the monetary variable were included as
independent variables. The data periods were 12/28/77-9/26/79
and 10/3/79—10/6/82. The period was split in this fashion to control
for the Fed’s announced policy shift in October 1979 and its
subsequent reversal in October 1982. The results were dis­
appointing in that a significant relationship failed to emerge in
either subperiod.
24Earlier work on this question concluded that the lag was consider­
ably longer than 12 months. See, for example, Cagan and Gandolfi, “The Lag in Monetary Policy,” pp. 277-84.
20All of the tests were run again with the corporate Aaa bond rate
identified as the dependent variable. Three important differences
between these results and those for the commercial paper rate
were noted. First, during the gold standard period, the lag was 38
months. A statistically significant but very small liquidity effect
(.76 basis points) emerged. The Fisher effect again was zero. The
results of the Granger test indicate one-way causality running
from money to Aaa bond rates. Second, during the January 1954 December 1970 period, the lag was zero months. Neither liquid-

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

C h a rt 1

Time Path of the Interest Rate 1
SAi
l a s i s poi nts

SAi
B a s is points

M o n t h s s u b s e q u e n t to the percent c h a n g e
in the g r o w t h rate of m o n e y at to
|_1_ G iv e n a 100 b a s is - p o in t in cre a se in the m o n e ta ry g ro w th ra te in p e r io d ze ro .

SUMMARY AND CONCLUSION
A widely held view is that changes in the monetary
growth rate operate on the nominal interest rate
through systematically lagged liquidity and Fisher
effects. In particular, increases in monetary growth are
thought to produce initial declines and subsequent
increases in the nominal and real rates of interest.
Our results suggest that only the data from the
period since 1971 represent a fruitful basis for testing
this hypothesis. Before then, the money and interest

ity or Fisher effects were apparent in the data. The Granger test
indicates that money and Aaa bond rates were independent series.
Third, during the January 1971 - February 1983 period, the lag is
1 2 months (consistent with that of the commercial paper rate).
However, the data reject the appearance of a liquidity effect in
nominal interest rates. None of the estimated coefficients are
negative. Eleven coefficients are significantly positive but they
Jsu m to less than 100 basis points. The Granger test indicates
bidirectional causality.




rate data were either independent series or money was
endogenous with respect to interest rates. When these
subperiods are excluded from the sample, the short­
term nominal interest rate is observed to adjust com­
pletely to a change in the monetary growth rate with a
lag of 12 months.
The monthly data for the most recent period reveal a
statistically significant but economically anemic liquid­
ity effect that dissipates rapidly. This was to be ex­
pected, given efficient financial and capital markets.
On the other hand, the results concerning the Fisher
effect are fairly strong. They suggest that an increase
(decrease) in the monetary growth rate that persists for
more than one month will result in an increase (de­
crease) in interest rates, other things constant. As a
change in the monetary growth rate comes to be re­
garded as permanent, short-term rates will fully adjust
within 12 months. The direction and magnitude of the
change in short-term rates will mirror the change in
monetary growth.

25

The Effect of State Banking Laws on
Holding Company Banks
DONALD M. BROWN

J E ^ ANK holding companies are subject to a variety of
state banking laws that govern the extent of branch
banking and the number of banks that can be owned.
In response to different legal environments, significant
differences may result between the reported operating
results of independent banks and holding company
banks; as one consequence, bank financial ratios may
be affected significantly by state banking laws.1 These
financial ratios include measures of bank profitability,
efficiency and portfolio composition. Variables repre­
senting the characteristics of a bank’s market also may
be affected by state banking laws. These market vari­
ables include measures of market structure, size and
growth.
This article has two purposes. The first is to deter­
mine whether bank financial ratios and market vari­
ables are related to bank holding company ownership
or state laws limiting the number of banks owned by
any one holding company. The second is to determine
whether there are significant economic incentives
favoring the formation of multi-bank holding com­
panies over one-bank holding companies.

WHY DO BANK HOLDING
COMPANIES EXIST?
Bank holding companies have specific advantages
over independent banks. They generally avoid being

'Bank financial ratios have been examined extensively by econ­
omists. A lengthy bibliography of this literature, including citations
through part of 1978, may be found in Ronald L. SchillerefF,
Multibank Holding Company Performance (UMI Research Press,
1982).
As used herein, “state banking laws” refer specifically to state
laws governing branch banking and bank holding companies.

Digitized for
26FRASER


taxed on internal dividend payments, they can engage
in a wider range of non-banking activities, they are less
hampered by geographical restrictions, and they can
raise funds by selling the commercial paper of the
parent corporation; they also can circumvent state
branching restrictions. These advantages are more im­
portant to some bank holding companies than to
others; likewise, they are more fully realized by own­
ing some banks rather than others. The economic value
of these advantages is reflected in the prices that hold­
ing companies offer for different banks.
If the costs associated with holding company own­
ership were low relative to the potential gains, all
banks would be owned by holding companies. This, of
course, is not the case. Bank holding companies incur a
variety of costs: regulatory, administrative, even the
one-time cost of getting permission to acquire banks. A
bank will remain independent until the discounted
present value of the advantages of holding company
ownership outweigh the discounted present value of
the costs.
Regardless of the number of banks they own, all
holding companies are subject to the same federal
regulations. Consequently, any gain realized by multi­
bank holding companies must be associated with own­
ership of the banks themselves; it is not related to the
profits associated with the permissible range of non­
bank activities.

THE EFFEC T OF REGULATION ON
BANK HOLDING COMPANIES
Federal Regulatory Constraints
Federal regulatory policy may prevent multi-bank
holding companies from owning certain banks. The

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

Table 1
The Distribution of States Among Categories
of State Banking Laws1
OBHC States
(holding companies
may own only
a single bank)

MBHC States
(holding companies
may own more
than one bank)

Unit Banking
(banks may have only a single
full-service office)

3

7

Limited Branching
(banks may branch within a defined
area — usually a county)

5

11

Statewide Branching
(banks may branch throughout
the state)

0

24

’ State banking laws effective April 1, 1983.
SOURCE: Board of Governors of the Federal Reserve System.

Board of Governors of the Federal Reserve System is
likely to prevent an acquisition by a multi-bank holding
company if that company already has a large market
share or if the acquisition would substantially increase
concentration in a banking market. The Board also may
prevent acquisitions or holding company formations
for reasons other than competition. F or example, it
may rule unfavorably if the holding company is thought
to be financially weak. Consequently, some banks may
be either independent or owned by one-bank holding
companies solely because of actual or anticipated reg­
ulatory denials.

The Adaptation o f Bank Holding
Companies to State Banking Laws

companies represent one way to circumvent the state
branching restrictions described in table 1.
In unit-banking and limited-branching states that
permit multi-bank holding companies, bank holding
companies are not constrained to own only one bank;
each one-bank holding company does so by choice.
Because both one-bank and multi-bank holding com­
panies exist simultaneously in these states, their own­
ers must face different incentives. Consequently, they
may own different types of banks or manage their
banks in ways that produce different operating results
and portfolio compositions.
Any prohibition of branching is more effective if
multi-bank holding companies also are prohibited.3
Even though some holding companies in states pro­
hibiting both types of organizations might wish to own
only one bank, others would choose to own more banks
in the absence of the constraint. The constrained and
unconstrained one-bank holding companies in these
states may have different financial and market charac­
teristics.

State banking laws also may affect bank ownership.
Table 1 categorizes states according to their restric­
tions on branching and bank holding companies and
shows the distribution of the 50 states among these
categories. If the legal constraints imposed by state
laws are binding, banks and bank holding companies
will attempt to circumvent them .2 Multi-bank holding

In states that allow statewide branching, both
branch banks and multi-bank holding companies

2W e cannot know the effect of a constraint with certainty until it is
removed; however, the existence of unit banks and one-bank hold­
ing companies in states that allow both statewide branching and
multi-bank holding companies is strong circumstantial evidence
that state banking laws are not binding on all organizations.

3Table 1 offers some circumstantial evidence. None of the 24 states
that allow statewide branching prohibit multi-bank holding com­
panies. Apparently, once banks are allowed to branch throughout a
state, preventing holding companies from owning more than a
single bank is not an effective constraint.




27

FEDERAL RESERVE BANK OF ST. LOUIS

potentially can achieve the same geographic scope.4
Consequently, multi-bank holding companies and
one-bank holding companies that own branch banks
may not display significant differences in terms of their
financial and market characteristics. On the other
hand, there may be significant differences between a
one-bank holding company that owns a branch bank
and another in the same state that owns a unit bank.

Distortions o f Reported Financial Results
Differences in reported financial characteristics do
not necessarily reflect actual operating differences.
Comparisons of the financial ratios of unit and branch
banks, whether located in the same or different states,
are distorted by financial reporting conventions. Be­
cause the financial results of a bank’s branches are
aggregated for reporting purposes, differences be­
tween the reported financial characteristics of branch
and unit banks may be due partly to lumping different­
sized branches in different locations into a single re­
porting entity. The problem exists if the state allows
limited or statewide branching. It is compounded in
branching states that allow multi-bank holding com­
panies because a multi-bank holding company (subject
to regulatory approval) may choose either to charter a
subsidiary bank separately or make it the branch of
another subsidiary bank. Thus, the reported financial
characteristics will depend upon the permissible legal
forms.

Is There an Economic Incentive fo r
Multi-Bank Holding Companies?
Although it might be argued that the existence of
multi-bank holding companies is prima facie evidence
that some companies have an economic incentive to
own more than one bank, multi-bank holding com­
panies could arise by chance. Assume, for example,

4Federal law effectively prevents interstate branching and inter­
state banking expansion by holding companies. States can extend a
statutory invitation to out-of-state bank holding companies, but
only a handful actually have done so. Alaska allows out-of-state
companies to buy Alaskan banks that have operated for at least
three years. Maine, Massachusetts and New York permit holding
companies from states that reciprocate; the Massachusetts law
limits reciprocity to only New England states. Washington allows
out-of-state holding companies to purchase banks in the state that
are in financial difficulty. Finally, Delaware and South Dakota
allow out-of-state holding companies to own special-purpose
banks, which are operated under rules that prevent them from
actively soliciting deposits from the public. (Information on these
state laws was provided by the staff of the Board of Governors of the
Federal Reserve System.)

Digitized for28
FRASER


AUGUST/SEPTEMBER 1983

that owning two or more banks conferred no net gain to
a bank holding company. It should then make no differ­
ence whether a bank is owned by a one-bank or multi­
bank holding company. Even if banks with certain
observable characteristics typically are owned by bank
holding companies, any specific holding company
could hold either one or several of these banks. In this
example, whether a bank is owned by a holding com­
pany depends upon the bank’s own observed financial
and market characteristics alone.
Assume, now, that some bank holding companies
derive some net advantage from owning several banks.
These advantages may arise from the nature of either
the bank or the bank holding company; they are dis­
tinct, however, from the advantages realized by onebank holding companies. Under this assumption, multi-bank holding companies would own some banks that
would not be owned by one-bank holding companies.
Therefore, a bank’s chance of being owned by a holding
company would depend on state laws regarding multi­
bank holding companies, as well as its individual finan­
cial and market characteristics.
W e cannot say a priori that there are economic in­
centives for some bank holding companies to own
several banks. The issue must be decided on the basis
of empirical evidence. Although a variety of empirical
tests could be chosen, the tests used in this article focus
on the relationship between bank holding company
ownership and a bank’s financial and market character­
istics in unit-banking states.5

EMPIRICAL TESTS OF THREE
PROPOSITIONS AROUT HOLDING
COMPANY RANKS IN UNIT-RANKING
STATES
Three testable propositions regarding certain bank
characteristics in unit-banking states can be derived

5Since this study is confined to a sample of banks from unit-banking
states, it does not provide direct evidence on whether multi-bank
holding companies circumvent state branching restrictions. A
worthwhile direction for future research would be to expand the
sample to include banks from states that allow limited and
statewide branch banking. Empirical tests on the expanded sample
could determine whether the incentives of multi-bank holding
companies are reduced or eliminated in states having less stringent
restrictions on branching.
This study also does not explore the nature of the economic
incentive to own several banks. The evidence presented in the next
section indicates that, whether the incentive arises from cost
advantages, control overprice or some other source, it is apparent­
ly quite strong. Another worthwhile direction for future research
would be to investigate its source.

FEDERAL RESERVE BANK OF ST. LOUIS

from the preceding discussion:
1. The financial and market characteristics of banks
owned by multi-bank holding companies will differ
from those of other banks.
2. The financial and market characteristics of banks
owned by one-bank holding companies will differ
from those of other banks; they will depend on state
laws regarding multi-bank holding companies.
3. A bank is more likely to be owned by a holding
company if the state permits multi-bank holding
companies.

Methodology and Sample Characteristics
These propositions are tested by probit analysis to
estimate the effect of certain independent variables on
the likelihood that a bank is owned by a bank holding
company.6 The following are the dependent variables
in three probit regression models, each of which repre­
sents a choice between alternative forms of ownership:
= 1, if a bank is owned by a multi-bank holding
company,
= 0, otherwise;
Y2 = 1, if a bank is owned by a one-bank holding
company,
= 0, otherwise;
Y3 = 1, if a bank is owned by either a one-bank or
multi-bank holding company,
= 0, otherwise.

The sample on which the probit models are esti­
mated consists of all insured commercial banks in six
western and midwestern unit-banking states. The sam­
ple is divided into two subsamples of three states.
States in one subsample permit multi-bank holding
companies; states in the other prohibit them .7 Any
holding company that owns two or more banks in any
state is defined as a multi-bank holding company; the
others are one-bank holding companies.
Four probit regression equations are estimated for
each of the years 1978 and 1981. The Yj model is

AUGUST/SEPTEMBER 1983

estimated on the subsample permitting multi-bank
holding companies; the Y2 model is estimated sepa­
rately on each subsample; and the Y3 model is esti­
mated on the full sample.

Independent Variables
Table 2 defines the independent variables used in
the probit models and reports their summary statistics
for both 1978 and 1981.8 The same financial variables
have been used in many empirical studies that have
investigated differences between independent and
holding company banks. These variables were con­
structed from financial data in annual bank call reports
and income statements for the years ending December
31, 1978, and D ecem ber 31, 1981. The variables
measuring market characteristics were computed by
aggregating bank financial data across banking mar­
kets, which were defined as either Standard Metro­
politan Statistical Areas (SMSAs) or counties (in the
case of counties not part of SMSAs).
A comparison of the variables’ means in 1978 and
1981 shows that the ratios of operating expense and net
federal funds sold to total assets (ROE and RN FFS)
were markedly higher in 1981, and the ratio of total
loans to total assets (RTL) was lower in 1981. These
differences may be explained by the economic condi­
tions prevailing in 1981, when interest rates reached
historically high levels and loan demand (partly reflec­
tive of interest rates) was low. Increases in the means of
dummy variables SMSA and MBHC between 1978
and 1981 indicate increases in the proportion of sample
banks located in SMSAs and states that allow multi­
bank holding companies.

8Some independent variables were considered for inclusion in the
models but were dropped because they were highly correlated
with other independent variables. In each subsample and in the
fall sample, most simple correlations between included indepen­
dent variables were less than 0.20 in absolute value in both 1978
and 1981. The simple correlations exceeding 0.40 are reported
below:
1978
Correlations

6Probit analysis is a non-linear estimation technique frequently
used when a model’s dependent variable represents the choice
between two alternatives. For explanations of the probit model,
see Robert S. Pindyck and Daniel L. Rubinfeld, Econometric
Models and Economic Forecasts, 2nd ed. (McGraw-Hill Book
Company, 1981), pp. 280-87; and George G. Judge and others,
The Theory and Practice o f Econometrics (John Wiley and Sons,
1980), pp. 591-92.
7In the six states used in this study, Colorado, Missouri and Wyo­
ming permit multi-bank holding companies; Kansas, Nebraska and
Oklahoma prohibit them.




R O E , RNI
CR, SMSA
CR, D C R M BH C
M BH C, D C R M BH C
1981
Correlations
R O E , RNI
C R , SMSA
C R, D CRM BH C
M BH C, D C R M BH C
R EQ , R N FFS

O BH C
Subsample
0.41
-0 .4 2
—

M BH C
Subsample
- 0 .4 1
- 0 .6 1
—

—
O BH C
Subsample
-0 .4 8
- 0 .4 3
—

—

- 0 .5 0
0.41
0.55

M BH C
Subsample
—

-0 .6 3
-

—

—

Full Sample

0.42

Full Sample
—

-0 .5 1
0.41
0.56
—

29

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

Table 2
Definitions and Summary Statistics of Independent Variables
1978
Variable
RNI
ROE
REQ
RTL
RNFFS
TA
SMSA
MBHC

CR1
MKGR
DCR2
DCRTA
DCRSMSA
DCRMBHC

Definition
net after tax income/total assets
operating expense/total assets
equity capital plus reserves/total
assets
total loans, gross/total assets
federal funds sold less federal funds
purchased/total assets
total assets/1,000,000
= 1, if bank is located in an SMSA
= 0, otherwise
= 1, if state where bank is located
allows MBHCs
= 0, otherwise
market Herfindahl index
five-year growth of total market assets
= 1, if CR > .25
= 0, otherwise
DCR x TA
DCR x SMSA
DCR x MBHC

1981

Mean

Standard
deviation

Mean

Standard
deviation

0.010
0.063

0.007
0.022

0.013
0.100

0.009
0.021

0.092
0.551

0.037
0.116

0.092
0.518

0.038
0.122

0.293

0.065
0.111
0.455

0.061
0.043
0.303

0.082
0.158
0.460

0.416

0.493

0.427

0.495

0.257
0.656

0.155
0.203

0.254
0.778

0.150
0.254

0.009
0.013
0.178

0.022
0.113
0.383

0.011
0.013
0.187

0.029
0.114

0.038
0.032

0.390

'The index is calculated on the basis ot shares of total assets:
n
n
CR = 2 (TA/2 TA),
i= 1
where TA, is the total assets of the ith banking organization in the market. Note that 0<CR=s1.
^The variable DCR was not included in the probit models because it is highly correlated with CR. It does enter in the three interaction
variables.

A positive (negative) sign on an independent vari­
able’s coefficient indicates that higher values of the
variable increase (decrease) the likelihood that a bank
is owned by the specified type of bank holding com­
pany. The coefficient of TA is expected to be positive in
the Yj model. This expectation is based not on theory,
but on previous empirical study.9 It assumes that as a
bank’s size increases, ceteris paribus, the likelihood
that the bank is owned by a multi-bank holding com­
pany also increases.
No predictions can be made as to the signs of other
coefficients in the Y] and Y2 models. Although many
9 Multi-bank

holding companies tend to own larger banks. Many of
these organizations own lead banks that are among a state’s largest
banks. Subsidiary banks other than lead banks often are larger than
the average bank in their markets and seldom are among the very
small banks.

Digitized for30
FRASER


empirical studies have investigated the relationship
b etw een holding com pany ow nership and bank
financial ratios, they have potentially important weak­
nesses, including a nearly universal failure to control
for the potential effects of diverse state banking laws.
Moreover, they frequently have produced conflicting
results.

The variables M BHC and DCRM BHC are included
in only the Y3 m odel.10 As the following section ex­
plains, the estimated coefficient of M BH C is predicted

10In the subsample on which the Yj and first Y2 models were
estimated, MBHC took on the value of 1 for all observations, while
DCRMBHC took on the value of 1 or zero. In the subsample on
which the second Y 2 model was estimated, both variables took on
the value of zero for all observations.

AUGUST/SEPTEMBER 1983

FEDERAL RESERVE BANK OF ST. LOUIS

to be positive, and th e estim ated coefficient of
DCRM BHC is predicted to be negative.

The Criteria fo r Accepting or Rejecting the
Propositions
The first proposition is “accepted” (in the statistical
sense) if the likelihood ratio of the Y x estimation is
statistically significant in both 1978 and 1981. This
would indicate that, in unit-banking states that permit
multi-bank holding companies, banks owned by multi­
bank holding companies differ from other banks on the
basis of their financial and market characteristics.
For the first proposition to be accepted, neither the
sizes, statistical significance, nor the signs of the esti­
mated coefficients need to be invariant over the two
years. Coefficients may differ between 1978 and 1981
because changing economic conditions affected multi­
bank holding company subsidiaries and other banks
differently; because the modest increase in the total
number of banks and/or the proportionately large in­
crease in multi-bank holding company subsidiaries
occurring in the subsample between 1978 and 1981
(see tables 3a and 3b) altered the compositions of the
two groups of banks; because the financial and market
characteristics of the two groups of banks are following
different long-term trends; or for a combination of
these reasons. None of these possibilities would obvi­
ate the conclusion that banks owned by multi-bank
holding companies differ from other banks.
The second proposition is accepted if, in both 1978
and 1981, the likelihood ratios of the two Y2 estima­
tions are statistically significant and if the signs or
statistical significance of the coefficients differ between
the two estimations. The former would show that onebank holding company banks differ from other banks in
their financial and market characteristics, regardless of
whether multi-bank holding companies are permitted.
The latter would show that the financial and market
characteristics of one-bank holding company banks de­
pend on whether a state allows or prohibits multi-bank
holding companies. Differences in financial and mar­
ket characteristics between one-bank holding com­
pany banks in the two subsamples would be the result
of differences between constrained and unconstrained
holding companies in the states that prohibit multi­
bank holding companies. Like the first proposition, the
second proposition is not refuted by different coef­
ficient estimates in the 1978 and 1981 estimations.
The coefficients in the Yi and Y2 estimations can be
compared in the same manner. If, in states that allow



multi-bank holding companies, the signs or statistical
significance of the coefficients differ between the Yi
and Y2 estimations, then banks owned by the two types
of holding companies have different financial and mar­
ket characteristics.
The third proposition depends on the coefficient of
MBHC in the Y3 estimation. It is accepted if the esti­
mated coefficient is positive and significantly greater
than zero in both 1978 and 1981. A positive sign would
indicate that, given its financial and market character­
istics, a bank is more likely to be owned by a bank
holding company (either a one-bank or multi-bank
holding company) if it is located in the unit-banking
states that permit multi-bank holding companies.
The interaction variable DCRM BHC is included in
the Y3 model to account for the possible effect of feder­
al regulation on the likelihood of holding company
ownership. The Board of Governors is more likely to
prevent acquisitions by multi-bank holding companies
in highly concentrated markets (DCR = 1) than in less
concentrated markets (DCR = 0); therefore, the coef­
ficient of DCRM BHC is predicted to be negative in
both 1978 and 1981.

Empirical Results
Y1 Estimations — The results of the Yi estimations
are reported in column 1 of tables 3a and 3b. Both
likelihood ratios are highly significant, indicating that
banks owned by multi-bank holding companies differ
from other banks in terms of the independent variables
included in the Y x model. Moreover, most estimated
coefficients also are statistically significant, which indi­
cates that the corresponding independent variables are
different for multi-bank holding company subsidiaries
than for other banks.
Several coefficients had the same sign and were
statistically significant in both years. The estimated
coefficients of TA are positive and statistically signifi­
cant, as predicted. The results also show that, even
after controlling for the influence of bank size (TA),
banks owned by multi-bank holding companies are
located more often in metropolitan areas and less con­
centrated banking markets. The positive coefficients
on the interaction variable DCRTA imply that, ceteris
paribus, a larger bank in a highly concentrated market
is more likely to be owned by a multi-bank holding
company than a smaller bank in the same market.
Other coefficients differed between the two years.
In 1978, banks owned by multi-bank holding com-

31

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

Table 3a
Coefficient Estimate Results of Probit Analysis (1978)
(t-statistics in parentheses)
(1)

Independent
Variables

(2)

MBHC Subsample1
Y,

(3)

(4)

OBHC
Subsample2

Full
Sample

y2

y2

30.57**
(4.85)

y3

Financial variables
RNI

-12.39
(-1 .4 5 )

47.75**
(4.11)

ROE

-2 .5 6
(-0 .5 2 )

16.79**
(3.01)

REQ

0.24
(0.23)

-6.06**
(-2 .8 8 )

RTL

2.01**
(4.30)

-0 .4 4
(-0 .8 7 )

RNFFS
TA

-2.05*
(-2 .5 3 )

1.62
(1.94)

7.49"
(4.68)

-0 .9 9
(-1 .0 2 )

0.44**
(3.26)

0.12
(0.85)

9.87*
(2.48)

-3 .3 3
(-1 .5 0 )

-1 .2 2
(-0 .8 2 )

-14.21**
(-7 .2 8 )

-2.41**
(-3 .1 6 )

1.82**
(5.48)

1.92**
(7.63)

-1.43*
(-2 .2 6 )
3.11**
(3.17)

-0.97*
(-2 .0 6 )
6.49**
(6.14)

Market variables
SMSA

-0.26*
(-2 .4 9 )

MBHC
CR

0.09
(1.18)
0.46*’
(6.61)

-1.17**
(-2 .7 2 )

0.98**
(2.93)

0.16
(0.59)
-1.38**
(-5 .6 4 )

0.16
(0.76)
-0.31*
(-2 .4 1 )

MKGR

0.20
(1.17)

0.05
(0.26)

DCRTA

7.18*
(2.22)

-2 .7 7
(-0 .8 6 )

-0 .8 7
(-0 .5 2 )

4.32*
(2.10)

DCRSMSA

0.59
(1.40)

-0 .3 6
(-0 .6 8 )

0.13
(0.42)

0.29
(1.13)

DCRMBHC
Constant
Likelihood
ratio test
N3
Y=14

-0.35**
(-3 .5 5 )
-1.60**
(-3 .5 8 )

-2.09**
(-4 .5 4 )

221.07**

45.77**

0.61
(1.74)

-1.26**
(-5 .7 5 )

187.29**

348.92**

1,101

1,101

1,546

2,647

369

181

529

1,100

'Significant at 5 percent confidence level.
"Significant at 1 percent confidence level.
’ States that permit multi-bank holding companies.
2States that prohibit multi-bank holding companies.
3Number of observations.
4Number of observations on the dependent variables (Y,, Y2 or Y3) at 1. Other observations at zero. The
numbers do not add across because there are 21 subsidiary banks of multi-bank holding companies in
the one-bank holding company subsample.
Digitized for32
FRASER


FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

Table 3b
Coefficient Estimate Results of Probit Analysis (1981)
(t-statistics in parentheses)
(2)

(1)

Independent
Variables

MBHC Subsample1
Y,

(3)

(4)

OBHC
Subsample2

Full
Sample

y2

y2

y3

38.38**
(5.72)

55.24**
(8.71)

21.47**
(6.38)

2.70
(1.48)

6.17
(1.89)

3.08*
(2.31)

Financial variables
RNI

-7 .0 0
(-1 .7 6 )

ROE

0.42
(0.26)

REQ

-2.38*
(-2 .4 0 )

RTL

0.69
(1.83)

RNFFS
TA

-9.30**
(-4 .9 6 )

-24.90**
(-12.08)

-8.26**
(-9 .5 5 )

0.57
(1.42)

1.03**
(3.08)

1.32**
(5.64)

0.84
(156)

-0 .1 3
(-0 .2 2 )

-2.02**
(-3 .8 5 )

8.31**
(5.76)

-4.77**
(-3 .1 1 )

1.34*
(2.00)

-0 .3 9
(-1 .0 8 )
3.78**
(4.62)

Market variables
SMSA

0.42**
(3.57)

0.08
(0.65)

-0.22*
(-2 .1 8 )

MBHC
CR

0.12
(159)
0.40**
(5.58)

-1.20**
(-2 .9 3 )

0.69*
(199)

0.72**
(2.59)
-0.86**
(-6 .4 4 )

0.20
(0.93)

MKGR

0.20
(1.17)

0.17
(0.94)

DCRTA

5.43*
(2.13)

-0 .7 6
(-0 .3 0 )

-1 .1 6
(-0 .9 3 )

4.83**
(2.82)

DCRSMSA

0.25
(0.58)

-0 .2 3
(-0 .4 7 )

-0 .0 5
(-0.16)

0.07
(0.28)

DCRMBHC
Constant
Likelihood
ratio test
N3
Y=14

-0.31**
(-3 .1 1 )

-0.35**
(-3 .6 1 )
-0.85**
(-2 .7 6 )

-1.10**
(-3 .3 2 )

217.52**

91.54"

0.97*
(2.30)

-0.43*
(-2 .0 2 )

328.62**

397.70**

1,174

1,174

1,575

2,749

448

275

811

1,561

'Significant at 5 percent confidence level.
"Significant at 1 percent confidence level.
1States that permit multi-bank holding companies.
2States that prohibit multi-bank holding companies.
3Number of observations.
“Number of observations on the dependent variables (Y,, Y2or Y3) at 1. Other observations at zero. The
numbers do not add across because there are 27 subsidiary banks of multi-bank holding companies in
the one-bank holding company subsample.



33

FEDERAL RESERVE BANK OF ST. LOUIS

panies devoted a larger share of their portfolios to loans
and sold fewer net federal funds as a proportion of total
assets, while their ratios of equity to total assets did not
vary significantly from other banks. On the other hand,
in 1981, these banks had significantly lower ratios of
equity to total assets, while the share of their portfolios
devoted to loans and net federal funds sold did not vary
significantly from other banks.
Y2 Estimatiom — The Y2 estimations are reported in
columns 2 and 3 of tables 3a and 3b. The highly signifi­
cant likelihood ratios indicate that, regardless of state
policy toward multi-bank holding companies, banks
owned by one-bank holding companies differ from
other banks.
In 1978, the estimated coefficients of the financial
variables had uniformly opposite signs and statistical
significance in columns 1 and 2 (see table 3a). The
differences between the columns were fewer in 1981.
Banks owned by one-bank holding companies earned a
higher return on total assets than other banks in 1981,
whereas the return of banks owned by multi-bank
holding companies did not vary significantly from
other banks; furthermore, multi-bank holding com­
pany subsidiaries tended to be larger than other banks,
and one-bank subsidiaries tended to be smaller (see
table 3b). The findings indicate that one-bank and
multi-bank holding companies had different financial
ratios in the states that permit multi-bank holding
companies.
The estimated coefficients of the market variables
are similar in both 1978 and 1981. In column 2 of the
tables, the estimated coefficients of market concentra­
tion (CR) are positive and significant, whereas in col­
umn 1 the coefficients of CR are negative and signifi­
cant. This difference implies that banks owned by onebank holding companies tend to be located in more
concentrated markets, while banks owned by multi­
bank holding companies tend to be located in less
concentrated markets. The estimated coefficients of
the other market variables in column 2 are not statisti­
cally significant.
A comparison of column 3 with columns 1 and 2 in
the tables shows that banks owned by one-bank hold­
ing companies in unit-banking states that prohibit
multi-bank holding companies exhibit similarities to
both types of holding companies in the other subsam­
ple of states. In column 3, the estimated coefficients of
all financial variables, except R O E, are statistically
significant at the 5 percent confidence level or better.
In 1978, they took the sign of the estimated coefficient
from column 1 or 2 that had the t-statistic of larger
Digitized for 34
FRASER


AUGUST/SEPTEMBER 1983

absolute value. In 1981, this was the case for the esti­
mated coefficients of RNI and TA; estimated coef­
ficients of other financial variables were either statisti­
cally insignificant in columns 1 and 2 (ROE, RTL,
RN FFS) or they had the same sign (REQ). Apparently,
some holding company banks in the states that prohibit
multi-bank holding companies have similar financial
characteristics to one-bank holding company sub­
sidiaries in those states that permit multi-bank holding
companies; others have similar financial characteristics
to multi-bank holding company subsidiaries. This
interpretation is consistent with the characterization,
in the preceding section, of one-bank holding com­
panies in this subsample as either constrained or un­
constrained organizations.
The estimated coefficients of the market variables do
not exhibit the same pattern. In column 3, only the
negative estimated coefficients of the dummy variable
representing metropolitan markets (SMSA) and the
market growth variable (MKGR) were statistically sig­
nificant in both 1978 and 1981. The latter was not
significant in either of the other estimations, and the
former was significant but positive in the Y ) estima­
tions. In 1981, the estimated coefficient of CR in col­
umn 3 was statistically significant, taking the positive
sign of the coefficient estimate in column 2.
Y3 Estimations — The Y3 estimations are reported in
column 4 of tables 3a and 3b. The high likelihood ratios
indicate that holding company banks, as a group, can
be distinguished from independent banks on the basis
of the independent variables. The positive and highly
significant estimate of the M BHC coefficient in both
1978 and 1981 strongly supports the third proposition.
The negative and highly significant estimate of the
DCRM BHC coefficient in both 1978 and 1981 con­
firms the prediction that, ceteris paribus, banks in
highly concentrated markets are less likely to be
owned by a holding company if the state permits multi­
bank holding companies.

CONCLUSIONS
One-bank and multi-bank holding company sub­
sidiaries in unit-banking states have different financial
and market characteristics than other banks. More­
over, the characteristics of the one-bank holding com­
pany banks depend on state laws regarding multi-bank
holding companies. In addition, a bank is more likely
to be owned by a holding company in unit-banking
states that permit multi-bank holding companies than
in unit-banking states that prohibit them.

FEDERAL RESERVE BANK OF ST. LOUIS

These results clearly imply that empirical studies
that examine the effects of holding company ownership
on bank financial ratios should control for differences
among state banking laws, as well as for differences
between one-bank and multi-bank holding companies.
Though this may not appear to be a startling conclu­
sion, recent studies have failed to control for one or
both of these differences.11 Future studies will have to
do so if they are to correctly assess the factors that cause
financial and market characteristics to differ among
banks.

uJohnson and Meinster, Jackson, and Mayne fail to control for
differences in state laws, while Fraas fails to account for differ­
ences between one-bank and multi-bank holding companies; Rose
and Scott, and Graddy and Kyle, fail on both counts. Only Mingo
accounted for both, by limiting his sample to nine unit-banking




AUGUST/SEPTEMBER 1983
states that permit multi-bank holding companies and excluding
subsidiary banks that were owned by one-bank holding com­
panies. By limiting his sample in this way, the author also avoided
the aggregation problem with comparing the financial results of
unit and branch banks. See Rodney D. Johnson and David R.
Meinster, “The Performance of Bank Holding Company Acquisi­
tions: A Multivariate Analysis,” Journal o f Business (April 1975),
pp. 204-12; William Jackson, “Multibank Holding Companies
and Bank Behavior” (Working Paper 75-1, Federal Reserve Bank
of Richmond, July 1975); Lucille S. Mayne, “A Comparative
Study of Bank Holding Company Affiliates and Independent
Banks, 1969-1972,” Journal o f Finance (March 1977), pp. 147-58;
Arthur G. Fraas, The Performance o f Individual Bank Holding
Companies, Staff Economic Studies 84 (Board of Governors of the
Federal Reserve System, 1974); Peter S. Rose and William L.
Scott, “The Performance of Banks Acquired by Holding Com­
panies,” Review o f Business and Economic Research (Spring
1979), pp. 18-37; Duane B. Graddy and Reuben Kyle, III, “Affili­
ated Bank Performance and the Simultaneity of Financial Deci­
sion-Making, "Journal o f Finance (September 1980), pp. 951-57;
and John J. Mingo, “Managerial Motives, Market Structures and
the Performance of Holding Company Banks,” Economic Inquiry
(September 1976), pp. 411-24.

35

Inflation: Assessing Its Recent Behavior
and Future Prospects
R. W. HAFER

T

JL H E inflation rate in the United States has gone
through a remarkable decline during the past three
years. In the first quarter of 1980, the inflation rate,
measured by movements in the GNP deflator, stood at
10.01 percent. In the first quarter of 1983, it was down
to 5 .6 4 percent. This dramatic change has been attrib­
uted to a variety of things. Monetary policy typically is
one reason given for the drop in inflation. Improving
productivity and lower wage demands also have re­
ceived some credit. Declines in oil prices precipitated
by concessions among O PEC oil producers is men­
tioned as w ell.1

and nonmonetary factors in explaining the behavior of
inflation during the past few years. Specifically, it
assesses the impact of energy price developments in
conjunction with monetary growth changes on the
measured inflation rate. Second, it provides some
simulation results for inflation through 1985. If the
future resembles the past — that is, i f the empirical
relationship between money growth and inflation re­
mains intact — recent celebrations of the permanent
demise of inflation are premature.

In general, popular discussion of the inflation prob­
lem suggests that inflation finally has been tam ed.2 As
one analyst noted recently, “It now looks as if we can
have our cake and eat it too — get a solid economic
recovery, while inflation continues to decline.”3 The
purpose of this paper is twofold. First, it provides
evidence about the relative importance of monetary

THE MONEY GROWTH-INFLATION
LINK

'See, for example, Bluford Putnam, “This Money Bulge Isn’t In­
flationary,” WaU Street Journal, April 2 7,1983; Peter Grier, “Why
Continued Success is Likely in Effort to Tame Inflation,” Christian
Science Monitor, February 28, 1983; Harry B. Ellis, “Drop in Oil
Prices, Interest Rates, and Inflation Could Mean Stronger Recov­
ery,” Christian Science Monitor, February 28, 1983; and Jonathan
Fuerbringer, “Consumer Prices Up Slight 0.2% ,” New York
Times, February 26, 1983.
2See “Brokerage Says Inflation May be Under Control for Years,”
Christian Science Monitor, May 19,1983; and Linda Stern, “Econ­
omists Optimistic on Inflation Outlook,” New York Journal o f
Commerce, February 28, 1983. For another viewpoint, see Alfred
L. Malabre, Jr., “Though Consensus Sees Mild Inflation Ahead,
Some Signs Suggest a Returning Price Spiral,” Wall Street Journal,
May 3 ,1 9 8 3 ; Caroline Atkinson, “Inflation Still Alive and Influenc­
ing Policy,” Washington Post, February 24, 1983; and “Index
Forewarns Inflation Resumption,” New York Journal o f Com­
merce, May 18, 1983.
3David Jones, chief economist of Aubrey Lanston & C o., quoted in
Grier, “Why Continued Success is Likely in Effort to Tame Infla­
tion.”


36


Economists define inflation as a persistent rise in the
general level of prices for goods and services. Inflation
is primarily a monetary phenomenon; that is, the
primary factors influencing future inflation are the
current and past behavior of the money stock. This
view is based on empirical evidence amassed over a
variety of periods and across diverse economies. As
one example, Friedman and Schwartz conclude, after
examining the link between money growth and infla­
tion in the United States and the United Kingdom from
1867 to 1975, that “except only for the United States
interw ar period, the ultim ate effect of m onetary
change is absorbed by prices.”4
While this monetarist approach to explaining infla­
tion focuses attention primarily on the growth of the
money supply, it does not ignore the effect of non­
monetary factors in the short run. While nonmonetary
4Milton Friedman and Anna J. Schwartz, Monetary Trends in the
United States and the United Kingdom: Their Relation to Income,
Prices, and Interest Rates, 1867-1975 (University of Chicago
Press, 1982), p. 627.

FEDERAL RESERVE BANK OF ST. LOUIS

forces, such as wage and price controls, wage increases
above p rod u ctivity changes or O P E C oil price
changes do not have a lasting influence on the rate of
inflation, they can produce temporary effects on the
measured inflation rate. Consequently, inflation often
deviates temporarily from the rate determined solely
by the growth of money.

AUGUST/SEPTEMBER 1983

F ig u r e

1

The Effect of Nonmonetary Factors on the Measured Rate of Inflation

To see how this can occur, consider the price be­
havior shown in figure 1. The line labeled InP repre­
sents how the log of the price level would behave, over
time, if monetary pressures alone affected prices, and
if the trend rate of money growth were constant. Be­
cause the price level is shown in terms of its logarithm,
the change over time (that is, lnPt — lnPt_j) repre­
sents the growth rate of the price level — the inflation
rate.
Suppose at time t0 an increase in the price of oil
occurs, as it did in late 1973 and again in 1979. One
effect of the oil price increase is to reduce the aggregate
supply of goods through the economic obsolescence of
some existing capital equipment.5 If aggregate de­
mand remains unchanged, the result is an increase in
the level of prices (the jump from InP to InP*) over
and above what would result from trend money
growth alone. The period of adjustment to the new,
higher price level (InP*) is depicted in figure 1 by the
time span to to tj. During this period the rate of change
of prices — that is, the slope of the line InP* relative to
the line InP — is greater than that explained by money
growth alone. This represents the fact that, from to to
tj, the measured rate of inflation is higher than that
attributed solely to monetary factors, represented by
the line InP. Once the adjustment period ends, how­
ever, the rate of inflation returns to the monetary rate,
represented by the common slope of the lines InP* and
InP. Thus, while nonmonetary factors can influence
the measured inflation rate for relatively brief periods,
monetary factors determine the long-term path of
inflation.6
5A discussion of this effect is presented in Denis S. Kamosky, “The
Link Between Money and Prices — 1971-76,” this Review (June
1976), pp. 17-23; and John A. Tatom, “Energy Prices and ShortRun Economic Performance,” this Review (January 1981), pp.
3-17. A broader analysis can be found in Robert H. Rasche and
John A. Tatom, “Energy Price Shocks, Aggregate Supply and
Monetary Policy: The Theory and International Evidence, ” Carnegie-Rochester Conference Series, Vol. 14 (1981).
6Empirical evidence for this argument is presented in Robert J.
Gordon, “World Inflation and Monetary Accommodation in Eight
Countries,” Brookings Papers on Economic Activity (2:1977), pp.
409-68; and James R. Barth and James T. Bennett, “Cost-push
versus Demand-pull Inflation: Some Empirical Evidence,” Jo u r­
nal o f Money, Credit and Banking (August 1975), pp. 391-97. Fo ra
general discussion, see Dallas S. Batten, “Inflation: The Cost-Push
Myth,” this Review (June/July 1981), pp. 20-26.




To illustrate the persistent relationship between
money growth and inflation, chart 1 plots the threeyear average rate of money growth (M1) and the annual
rate of inflation for the past two decades. The threeyear average of M l growth is used because studies
indicate that changes in money growth affect prices
with a lag.7 Although the inflation rate seldom equals
the long-run average rate of money growth exactly, it
moves around the average money growth, as if the
average growth of money sets the norm for the inflation
rate. This observed tendency provides the basis for
monetary policy actions intended to reduce inflation.8
Chart 1 reveals that, while inflation may wander
from the rate dictated by average money growth, such
departures are short-lived. These deviations reflect
the previously discussed transitory influence of non­
monetary factors that impinge on the price level. For
example, the measured rate of inflation was below the

7 See,

for example, Keith M. Carlson, “The Lag From Money to
Prices,” this Review (October 1980), pp. 3-1 0 ; and Albert E.
Burger, “Is Inflation All Due to Money?” this Review (December
1978), pp. 8-12.

“Announcement,” Federal Reserve Bulletin (October 1979),
p. 830. Specifically, “appropriate constraint on the supply of
money and credit is an essential part of any program to achieve the
needed reduction in inflationary momentum and inflationary ex­
pectations.”

8See,

37

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

Chart 1

Trend M o n ey G row th and Inflation

1960 61

62

63

64

65

66

67

68

69

70

71

LI

72

73

74

75

76

77

78

79

80

81

82 1983

[J_ T r e n d m o n e y g r o w t h is m e a s u r e d a s a 1 3 - q u a r t e r m o v i n g a v e r a g e of m o n e y g r o w t h . In fl a ti o n is a 4 - q u a rt e r g r o w t h ra te of
the G N P defl at or .

average money growth rate during the early 1970s,
reflecting the Nixon administration’s imposition of
wage and price controls. The removal of these controls,
along with the dramatic increase in O PEC oil prices in
late 1973, account for the sharp increase in the inflation
rate above average money growth. Oil price shocks
again explain much of the similar behavior of inflation
in the 1978-80 period.9
9See Karnosky, “The Link Between Money and Prices;” Tatom,
“Energy Prices and Short-Run Economic Performance;” and
Rasche and Tatom, “Energy Price Shocks, Aggregate Supply and
Monetary Policy.”


38


Some Evidence
The relationship portrayed in chart 1 suggests that
short-term movements in inflation can be explained by
accounting for the influence of money growth and a few
For a more general discussion of relative price shocks and their
effects on measured rates of inflation, see Alan S. Blinder, “The
Consumer Price Index and the Measurement of Recent Inflation,”
Brookings Papers on Economic Activity (2:1980), pp. 539-65; Stan­
ley Fischer, “Relative Price Shocks, Relative Price Variability, and
Inflation,” Brookings Papers on Economic Activity (2:1981), pp.
3 8 1 ^ 3 1 ; and Lawrence S. Davidson, “Inflation Misinformation
and Monetary Policy,” this Review (June/July 1982), pp. 15-26.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

specific nonmonetary factors that have influenced the
measured rate of inflation. One relationship that has
been used to successfully explain inflation uses a dis­
tributed lag of money growth to capture the “under­
lying” monetary influence on inflation, and changes in
the relative price of energy as one measure of short-run
influences that produce deviations of inflation from its
tren d .10 Estimated for the sample period 1/1960 to
IV/1979, the results are (t-statistics in parentheses):11

influence would give a misleading signal of the effect of
a change in average money growth on the rate of
inflation.14
The results presented in equation 1 conform to the
explanation presented earlier. That is, there is a oneto-one correspondence between money growth and
inflation over the long run, and nonmonetary factors
may account for significant departures from that rate
over shorter time periods.

12
(1) Pt = - 0 .8 3 8 + 1.100 2 Mt_j + 0.008 E'Pt_ !
( - 2 .1 3 ) (12.36) i = 0
(0.51)
+ 0.051 E P t_ 2 - 0 .0 1 1 E P t_ 3 + 0 .0 5 2 E P t_ 4
(2.55)
( - 0 .5 4 )
(3.10)
R2 = 0.815
where P

SE = 1.164

DW = 1.85

= rate of change of prices, measured as the first
difference in the natural logarithm of the GNP
deflator,

M = rate of change in the money stock, measured
as the first difference in the natural logarithm
of M l, and
E P = rate of change in the relative price of energy.12

Summarizing the results, the R2 indicates that the
estimated relationship captures over 80 percent of the
variation in inflation, with slightly over a 1 percent
average prediction error (SE = 1.16). The estimated
coefficient on the money term (1.100) reveals that a 1
percentage-point increase in the long-run average
growth of money will lead to an increase in inflation of
about 1 percentage point.13 Changes in relative energy
prices generally have a significant influence on the
measured inflation rate. Consequently, omitting their

10See Tatom, “Energy Prices and Short-Run Economic Perfor­
mance.” The equation estimated here is slightly modified.
nThe equation is estimated using a contemporaneous and 12 lagged
terms of money growth. An Almon polynominal estimation proce­
dure is employed where the degree of the polynominal is set at
four. No endpoint constraints are used. The estimated equation
also includes two dummy variables to capture the effects of the
wage and price control imposition and removal during the early
1970s. Thus, the dummy variable (D l) has a unity value during the
control period of III/1971—1/1973 and zero otherwise. The second
dummy variable (D2) is used to capture the phasing out of con­
trols, taking on a unity value for the period I/1973-I/1975 and zero
elsewhere. The estimated coefficients (and their t-statistics) are:
D l = - 1 . 8 3 ( - 3 .6 5 ) and D2 = 0.72 (1.24).
12The relative price of energy is defined as the ratio of the fuels and
related products and power component of the producer price
index to the business sector deflator.
13The estimated value of 1.10 is not statistically different from unity
at the 5 percent level of significance (t = 1.12).




EXAMINING THE RECENT DROP IN
INFLATION
Between the first quarter of 1980 and the first quar­
ter of 1983, the rate of inflation has fallen over 4 per­
centage points. How much of this decline is due to the
monetary policies of the past few years? How much
is due to favorable changes in the relative price of
energy?
To answer these questions, equation 1 was used to
produce out-of-sample forecasts of the inflation rate
from 1/1980 to 1/1983. Two forecasting experiments
were conducted using the estimates reported in equa­
tion 1: First, one set of inflation rate forecasts was
generated using the actual pattern of money growth
and relative energy price changes that occurred during
this period. The second set of inflation forecasts was
obtained by assuming that energy prices had remained
unchanged and that changes in money growth alone
were responsible for the reduction in inflation. These
two sets of inflation forecasts are reported in table 1.
The actual rate of inflation during this period also is
presented for purposes of comparison.
The quarter-to-quarter variability in the actual infla­
tion rate is evident in table 1. F o r example, the average
inflation rate across the 13-quarter period was 7.35
percent with a standard deviation of 2.51 percent. The
resulting coefficient of variation (standard deviation/
mean) is 0 .34 percent. In contrast, the inflation rate
forecasts generated using only money growth show
little variation over the period: their standard devia­
tion is only 0.36 percent and, given an average value of
6.63 percent, their coefficient of variation is only 0.05
percent. What these statistics suggest is that quarterto-quarter inflation forecasts that are based on trend
money alone fail to capture much of the sizable shortrun variation in recent inflation.

14Adding the relative energy price terms significantly increases the
explanatory power of the estimated equation at the 5 percent
level. Using a standard F-test, the calculated F-statistic is 5.80.

39

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

Table 1
Inflation Forecasts: 1/1980-1/1983
(1)
Actual

Period
1/1980

(2)
Money only

10.01%
9.66
9.14
9.97

7.50%
6.46
6.82
6.90

10.34
6.60
8.58
8.40

6.67
6.81
6.52
6.23

1/1982
II
III
IV

4.21
4.49
4.88
3.65

1/1983

5.64

II
III
IV
1/1981
II

III
IV

Money & Energy
10.17%
9.39
10.64
9.26
8.27
7.98
8.31
6.72

3.67
-0.21
2.06
2.18

2.07
-1 .3 8
0.28
1.69

6.46
6.42
6.25
6.26

7.11
6.90
5.39
4.85

-2 .2 5
-1 .9 3
-1 .3 7
-2.61

-2.91
-2.41
-0.51
-1 .2 0

6.87

7.58

-1 .2 2

-1 .9 3

0.72

-0 .5 4

2.21
2.37

1.31
1.56

Mean error
Mean absolute error
RMSE

The summary statistics reported in table 1 provide
additional evidence indicating that the forecast errors
are reduced considerably when energy price changes
are in clu d ed along w ith th e m on etary factors.
Although each model has a relatively small mean error,
the mean absolute error and root-mean-squared error
(RMSE) for the money-plus-energy price model is no­
ticeably lower than that for money alone.15
15The root-mean-squared error is defined as

/

T

( H

~

P f)2

where PA is the actual rate of inflation, PE is the forecasted rate,


40


(1) - (3)
-0 .1 6
0.26
-1 .5 0
0.71

The forecast results using money and energy price
effects (column 3, table 1) do better in modeling recent
short-term movements in inflation. This result is made
more explicit by comparing the forecast errors from the
two experiments in the last two columns of table 1. The
forecast errors derived from the “money only” model
display a number of large mistakes. For example, six of
the errors are two or more standard deviations away
from what equation 1 normally would predict. In con­
trast, only two such errors are found in the moneyplus-energy equation’s forecast.

-l

(1) ~ (2)
2.51
3.19
2.32
3.08

Summary statistics:

R M SE =

Errors

(3)

The forecast results suggest that energy price
developments have contributed significantly to the
recent decline in inflation. The overall conclusion
derived from these empirical results is that, while the
downward path of money growth during the past few
years accounts for the basic downward trend of infla­
tion, declining energy prices are the primary reason
why the actual rate of inflation in 1982 was less than the
rate determined by money growth alone.16

IS INFLATION REALLY DEAD?
The average rate of money growth can be viewed as a
measure of the underlying rate of inflation. Although
recent energy price reductions have caused measured
inflation to fall below average money growth, past

and N is the number of periods being forecast. The RMSE for the
full model is well within two standard errors of the equation, in
contrast with that from the forecasts based only on money growth.
16This is not to say, however, that money growth played a minor role
in forecasting recent inflation. To see this, we omitted money
growth and used only energy price changes to forecast inflation.
The result is a dramatic failure to accurately predict inflation: the
mean forecast error across the 1/1980—1/1983 period using only
changes in the relative energy price is —6.93 percent, and the
RMSE is 7.09 percent. These statistics are dramatically larger
than those reported in table 1 for either model.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1983

Table 2
Inflation Simulation Results: 1983-85
Simulated inflation
Year
19832
1984
1985

Money only

Money and relative
price of energy1

6.59%
7.25
7.17

6.19%
6.76
7.17

1See footnote 19 in the text for assumptions about declines in
relative price of energy during 1983.
Simulated values for last three quarters only.

experience suggests that once these nonmonetary in­
fluences have dissipated, inflation will tend toward
the average growth of money. Thus, if there were no
further relative price shocks in the near future and if
money growth were to remain at its present trend rate,
what would the underlying inflation rate be over the
next few years?
Simulated inflation rates for the 1 9 83-85 period
given the above scenario are presented in the first
column of table 2 .17 These suggest that, if the average
rate of money growth remains at 7 .5 percent, its trend
rate in 1/1983, future inflation rates likely will be high­
er than the current rate. For instance, the simulated

17The simulations were calculated by re-estimating equation 1 for
the period I/ 1 9 6 0 -I/ 1 9 8 3 . The results are (t-statistics in paren­
theses):
12
(1') P, = - 0 .7 0 2 + 1.065 2 M,_i + 0.003 E P ,_ i
(-1 .8 5 ) (13.48) i = 0
(0.23)
+ 0.055 EP,_2 + 0.001 EP,_3 + 0.038 EPt_ 4
(3.59)
(0.09)
(2.79)
- 1.716 D1 + 0.782 D2
(-3 .4 2 )
(1.59)
R2 = 0.827

SE = 1.182

DW = 1.83

Adding the extra observations produces some minor changes in
the estimated coefficients. Even so, the basic outcome reported in
equation 1 is duplicated in equation 1'.




rate of inflation for 1983 is over 6 .5 percent, and rates
for 1984 and 1985 exceed 7 percent.
What if the downward drift in relative energy prices
continues throughout 1983?18 To see what effect these
further reductions in relative energy prices would have
on inflation through 1985, simulations were produced
assuming that relative energy prices will decline
throughout 1983, but remain constant from 1984
onw ard.19 These simulations are reported in the
second column of table 2.
The simulations using both money and relative ener­
gy prices are lower than the “money only” results for
1983 and 1984; by 1985, however, the effects on the
inflation rate of the lower relative energy prices in 1982
and 1983 have fully dissipated. At that time, the rate of
inflation is simulated to return back to the average rate
of money growth.

CONCLUSION
Evidence presented in this article indicates that re­
cent declines in inflation are due both to a drop in the
average rate of money growth and to reductions in the
relative price of energy. Once the favorable effects of
these relative energy price declines abate and assum­
ing no changes in the historical money growth-inflation
link, inflation will tend to move back in line with the
average growth of money. Thus, even if relative energy
prices decline over the rest of 1983, unless the average
rate of M l growth declines, it is premature to conclude
that “runaway inflation is now safely behind us.”20
18For an analysis suggesting that this may occur, see Mack Ott and
John A. Tatom, “Are There Adverse Inflation Effects Associated
with Natural Gas Decontrol?” Contemporary Policy Issues (Octo­
ber 1981), pp. 27-46.
ls>The assumptions used are that the relative price of energy will
decline during 1983 at rates of 22.4 percent, 20.0 percent and 6.0
percent in each of the final two quarters. I would like to thank Jack
Tatom for these figures.
20This statement is from Martin Feldstein, quoted in Stern, "Econ­
omists Optimistic on Inflation Outlook.”

41

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