Money Growth and Inflation:
How Long is the Long-Run?
Terry J. Fitzgerald
efforts to maintain low inflation, policymakers currently pay
relatively little attention to the growth rate of the money supply.
Yet many studies have found a close relationship between money
growth and inflation, at least in the long run. But how long
must money growth be strong before it should be of concern to
policymakers? That is, what is the shortest period of time over
which money growth seems to be reliably associated with inflation?
Inflation is always and everywhere a monetary
Milton Friedman, Wincott Memorial Lecture,
London, September 16, 1970
"Given continued uncertainty
, the [Federal Reserve Open Market] Committee would have little
confidence that money growth within any particular range selected
for the year would be associated with the economic performance
it expected or desired."
presented February 23, 1999
The growth rate of the money supply currently receives
little attention in the conduct of monetary policy. While guarding
against rising inflation is one of the Federal Reserves
primary objectives, the Fed has found the short-run relationship
between money growth and inflation too unreliable for money growth
to merit much attention.
At the same time, many studies
have found a strong relationship between long-run averages of
money growth and inflation.1
This relationship seems to provide a straightforward strategy
for maintaining low inflationchoose the growth rate of
money that corresponds to the desired long-run rate of inflation.
In fact, some economists have concluded from this evidence that
the problem of controlling inflation has been successfully solved.2
There are two keys to reconciling
findings of a close long-run relationship between money growth
and inflation and policymakers relative lack of interest
in money growth rates. First, most studies that report a close
connection in the long run use data for many countries, and it
is sometimes noted that the finding appears to rely heavily on
the presence of countries with high rates of money growth and
inflation. It is much less clear that a close relationship exists
within countries with relatively small changes in money growth
such as the United States.
The second key is the time period
associated with each observation. Even if a close relationship
between money growth and inflation exists over the long run,
that relationship largely disappears when one considers relatively
short time horizons such as a year or a quarter. Figure 1
illustrates the lack of a relationship in quarterly U.S. data.
In conducting monetary policy, the Federal Reserve monitors and
seeks to influence inflation and other economic variables over
annual and quarterly intervals. A close relationship between
money growth and inflation that exists only over very long time
horizons is of little use to policymakers trying to control inflation
over the next quarter or year.
Because there is the possibility
of a close relationship between money growth and inflation in
the long run, the lack of a clear relationship in the short run
raises an obvious questionHow long is the long run? That
is, over what time horizon, if any, does a direct link between
money growth and inflation emerge? This Economic Commentary
seeks to address that question for the United States.
Knowing the length of the long
run is important for current policymaking. If there is a close
relationship between money growth and inflation in the long run,
then ignoring money growth in short-run policymaking poses a
risk. The long run is, after all, a series of short runs. If
rapid money growth is ignored for too many short runs, or too
long a short run, then the long-run relationship could begin
to take hold. That would force inflation-fighting policymakers
to respond by reducing money growth rates, possibly creating
an economic slowdown or a recession. This scenario is especially
relevant in todays economic environment, where money growth
as measured by some monetary aggregates has been relatively strong
over the past couple of years. The shorter the long run is, the
more troublesome ignoring high money growth over this period
On the other hand, if no close
relationship emerges for the United States even over fairly long
time periods, then that evidence would support ignoring money
growth as an inflationary factor, at least within the ranges
of money growth experienced over the past 40 years. This finding
would not necessarily be inconsistent with studies that have
found a close long-run relationship because many of those studies
include data from countries with high and volatile money growth
rates. It may be the case that while a close relationship is
apparent in the data when large changes in money growth are observed,
no clear relationship emerges when the changes are relatively
modest, such as in the United States. In those cases, other inflationary
factors may dominate the effect of relatively small changes in
To investigate the length of
the long run, an analysis was conducted that compares the relationship
between money growth and inflation over eight-, four-, and two-year
periods in the United States since 1959. The findings depend
greatly on the monetary aggregate used to measure money growth.
Broader definitions of money, namely the M2 and M3 monetary aggregates,
provide results that suggest a relatively close relationship
between money and inflation over a long run as short
as four years. However, results using narrower definitions of
money, namely M1 and the monetary base, show no clear relationship
over any of these time horizons.
Too Many Dollars: A
Simple Theory of Inflation
Before discussing the results of
the analysis, it will be helpful to have in mind a simple textbook
theory that is widely thought to explain the basic relationship
between the money supply and prices. Inflation occurs when the
average level of prices increases. Individual price increases
in and of themselves do not equal inflation, but an overall pattern
of price increases does.
The price level observed in the
economy is that which leads the quantity of money supplied to
equal the quantity of money demanded. The quantity of money supplied
is largely controlled by the Federal Reserve.3 When the supply of money increases
or decreases, the price level must adjust to equate the quantity
of money demanded throughout the economy with the quantity of
money supplied. The quantity of money demanded depends not only
on the price level but also on the level of real income, as measured
by real gross domestic product (GDP), and a variety of other
factors including the level of interest rates and technological
advances such as the invention of automated teller machines.
Money demand is widely thought to increase roughly proportionally
with the price level and with real income. That is, if prices
go up by 10 percent, or if real income increases by 10 percent,
empirical evidence suggests people want to hold 10 percent more
When the money supply grows faster
than the money demand associated with rising real incomes and
other factors, the price level must rise to equate supply and
demand. That is, inflation occurs. This situation is often referred
to as too many dollars chasing too few goods. Note that this
theory does not predict that any money-supply growth will lead
to inflationonly that part of money-supply growth that
exceeds the increase in money demand associated with rising real
GDP (holding the other factors constant). This observation is
used in the following section.
To answer the question of how long
the long run is, the relationship between money growth and inflation
is examined across three time periodstwo, four, and eight
years. The question is whether the relationship between money
growth and inflation is notably close over any of these time
horizons, and, if it is, how clearly that relationship holds
up over shorter time horizons.
The strategy used to analyze
the relationship is graphical. The analysis is conducted through
a series of figures, each of which has the same basic form. The
figures in the first set (2a, 2b, 2c) display
averages of the inflation rate and money growth over time. What
differs across the figures is the period over which the data
are averaged. Each data point shows the average annual growth
rate in inflation or money growth over the previous two, four,
or eight years.
The figures in the second set
(3a, 3b, 3c) are identical in form
except that money growth minus real output growth is plotted
instead of money growth alone. Recall that the simple theory
of inflation held that money growth in excess of real output
growth should be more closely connected with inflation. It is
of interest, then, to see whether adjusting for differences in
real output growth across periods leads to a closer relationship.
The statistic labeled R2
contained in each figure measures the fraction of the variation
in inflation that can be accounted for by variations in money
growth.4 An R2
of 0 means that money growth accounts for none of the variation
in inflation, while an R2 of 1 says that money growth
accounts for all of the variation in inflation.
Data since 1959 are used for
the analysis. While data are available much farther back in time,
the relationship between money growth and inflation was quite
different in earlier years.5
Data from the most recent 40 years are likely to be more relevant
to the current economic environment.
The simple theory of inflation
outlined above provides no guidance as to the definition of money
to be used. The M2 monetary aggregate, a fairly broad definition
of money, is used in the graphical analysis. The results for
other monetary aggregates are briefly discussed later.
2a shows two-year averages
and illustrates again why policymakers are leery of relying on
money growth to control inflation. It shows that even large movements
in money growth have no clear relationship with movements in
the inflation rate over two-year periods.
The relationship becomes somewhat
closer for longer time averages, particularly the eight-year
averages shown in figure
2c. There, the tent-shaped pattern of inflation, rising until
the early 1980s and falling steadily since, is generally matched
by the pattern of money growth. Slightly more than half of the
eight-year movements in inflation are accounted for by changes
in money growth (R2 equals 0.57).
Figures 3a, 3b,
and 3c display a
parallel set of figures but with real output growth subtracted
from money growth. These figures show that adjusting for differences
in real output growth across periods provides a substantial tightening
in the relationship between money growth and inflation. Figure 3c illustrates a strikingly close relationship
between eight-year averages, with money growth accounting for
more than 80 percent of the movements in inflation. Even using
four-year averages, money growth accounts for two-thirds of the
variation in inflation, and almost half using two-year averages.6
These results suggest that there
is a close relationship between money growth and inflation in
the long run. Furthermore, they suggest that the long run may
not be long at all, perhaps as short as four years, once differences
in real output growth across periods are taken into account.
But before getting carried away with this apparently strong finding,
it is important to note some qualifications.
First, to make use of the long-run relationship between inflation
and money growth less real output growth, policymakers need accurate
forecasts of real GDP growth over a relatively long horizon.
Economic forecasters have had very limited success in providing
them. Using the historical average of GDP growth as a forecast
produces the same relationship displayed in figures 2a through 2c, a relationship that is substantially less
Second, the results presented
are based on only 40 years of data. There is a very limited amount
of information one can extract from these data, especially regarding
eight- and four-year averages. One should not be overconfident
that the close relationship observed over these 40 years will
continue into the future. Furthermore, the experience of the
early 1990s illustrates that there can be notable deviations
from the general relationship. For example, figure 3b shows that the four-year average
of money growth minus real output growth slowed substantially
from 1991 through 1995 and has increased rather sharply since.
Despite the finding of a fairly close relationship between money
growth and inflation using four-year averages, inflation fell
steadily over this entire period. However, even taking into account
these first two qualifications, the overall results reported
in the figures are still rather compelling.
Perhaps the most important qualification
is that the finding of a close long-run relationship is not consistent
across various definitions of money. Recall that the monetary
aggregate M2 was used in the previous analysis. When the analysis
is repeated using M3, a broader definition of money, the results
are similar to those reported for M2. However, when narrower
definitions of money are used, namely M1 and the monetary base,
the results are quite different. In particular, there is no clear
relationship between money growth and inflation, even for eight-year
These qualifications demand that
a more tempered view be taken of the findings reported in the
previous section. While some long-run relationship appears to
exist, at least for the broader monetary aggregates, it is difficult
to state with much precision when this relationship begins to
But suppose these qualifications
are ignored for a moment. What would the close relationship between
M2 growth and inflation using four- and eight-year averages tell
us about the current economic situation? At first glance, the
answer appears to be not much. The results simply describe historical
relationships in the data, with economic forecasting playing
no role. However, if the view is taken that the long run is a
series of short runs, some insights might be gained by examining
the recent behavior of money growth, output growth, and inflation.
2a shows that two-year
average growth in M2 has increased substantially in recent years,
up to about 7.5 percent. That represents the fastest two-year
growth in M2 in over 10 years. Adjusting for the strong growth
in real GDP in recent years, however, makes this rate of money
growth appear less threatening. Figure
3a shows that money growth less output growth is only moderately
greater than the current inflation rate and well within the historical
pattern of fluctuations above and below the inflation rate.
However, if the recent growth
rate of M2 were to continue in the next two-year short run, so
that money growth averaged 7.5 percent over a four-year horizon,
the findings reported here suggest that there may be an impending
increase in inflation. Even if real GDP growth is assumed to
continue at 4.0 percent over the next two yearsa very optimistic
assumptionthe resulting increase in money growth less real
GDP growth would average 3.5 percent over a four-year horizon.
3b shows that
money growth less output growth of 3.5 percent over a four-year
horizon has historically corresponded to an average inflation
rate of roughly the same magnitude. A 3.5 percent inflation rate
would represent a substantial increase over the 1.1 percent rate
experienced over the last two years. If real GDP growth were
to slow to less than 4 percent in the next two years, while M2
growth remained steady, the outlook for inflation would be more
dire. Of course, if M2 growth slows over the next two-year short
run, the implications for inflation are less negative, especially
if output growth remains robust.
Little attention is currently paid
to the growth rate of the money supply in formulating monetary
policywith obvious reason. The relationship between money
growth and inflation from quarter to quarter and year to year
is not well understood, and this is the time frame within which
policymakers generally operate. In fact, it was the breakdown
in a perceived short-run relationship during the early 1990s
that led policymakers to largely de-emphasize money growth in
The graphical analysis presented
here suggests that a relatively close relationship between money
growth and inflation may exist over eight-year time horizons,
at least for the broader monetary aggregates. This finding serves
as a reminder that ignoring money growth for too long a period
may be unwise. While money growth may not provide a particularly
useful guide for short-run policymaking, long-run trends in inflation
may still be largely determined by the long-run growth rate of
the money supply.
1. For a recent
example, see George T. McCandless, Jr. and Warren E. Weber, Some
Monetary Facts, Federal Reserve Bank of Minneapolis,
Quarterly Review (Summer 1995), pp. 211, which also
provides a summary of other studies.
2. See, for
example, the article by Robert E. Lucas, Adaptive Behavior
and Economic Theory, Journal of Business, vol. 59,
no. 4 (October 1986), p. 402. Lucas makes it clear that this
assertion applies to long-run averages of money growth and inflation.
3. This statement
abstracts from the difficulty inherent in controlling the money
supply in practice. This is especially true for broader monetary
aggregates such as M2 and M3, large parts of which respond to
aggregate economic conditions.
4. For those
readers familiar with regression analysis, this statistic is
the regression R2 obtained by regressing the inflation rate on
the growth rate of the money supply and a constant. It is simply
the square of the correlation between inflation and money growth.
5. See Lawrence
J. Christiano and Terry J. Fitzgerald, The Band-Pass Filter,
Federal Reserve Bank of Cleveland Working
Paper No. 9906 (1999), for one illustration of the changing
nature of the relationship between money growth and inflation
before and after 1960.
6. The values
of the R2 statistic obtained by regressing the inflation
rate on the growth rate of the money supply minus real output
growth and a constant using eight-year averages of the growth
rates of the monetary base, M1, and M3 are 0.20, 0.16, and 0.80,
Terry J. Fitzgerald
is an economic advisor at the Federal Reserve Bank of Cleveland.
He thanks Jeffrey C. Schwartz and Eduard Pelz for excellent research
The views stated herein are those of the authors and not necessarily
those of the Federal Reserve Bank of Cleveland or of the Board
of Governors of the Federal Reserve System.
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