August 1, 1999

Federal Reserve Bank of Cleveland

Money Growth and : How Long is the Long-Run?

by Terry J. Fitzgerald

“Inflation is always and everywhere a monetary phenomenon.” There are two keys to reconciling find- ings of a close long-run relationship — , Wincott Memorial In their efforts to maintain low in- between growth and inflation and Lecture, London, September 16, 1970 policymakers’ relative lack of in flation, policymakers currently pay relatively little attention to the "Given continued uncertainty … , the money growth rates. First, most studies growth rate of the . [Federal Reserve Open ] Com- that report a close connection in the long Yet many studies have found a close mittee would have little confidence that run use data for many countries, and it is money growth within any particular sometimes noted that the finding appears relationship between money growth range selected for the year would be to rely heavily on the presence of coun- and inflation, at least in the long run. associated with the economic perfor- tries with high rates of money growth But how long must money growth be mance it expected or desired." and inflation. It is much less clear that a strong before it should be of concern close relationship exists within countries —Humphrey–Hawkins Report to policymakers? That is, what is the with relatively small changes in money presented February 23, 1999 shortest period of time over which growth such as the United States. money growth seems to be reliably The second key is the time period associ- associated with inflation? The growth rate of the money supply ated with each observation. Even if a currently receives little attention in close relationship between money the conduct of . While growth and inflation exists over the long guarding against rising inflation is one run, that relationship largely disappears of the Federal Reserve’s primary objec- when one considers relatively short time tives, the Fed has found the short-run horizons such as a year or a quarter. relationship between money growth Figure 1 illustrates the lack of a relation- and inflation too unreliable for money ship in quarterly U.S. data. In conducting growth to merit much attention. monetary policy, the Federal Reserve monitors and seeks to influence inflation At the same time, many studies have and other economic variables over found a strong relationship between annual and quarterly intervals. A close long-run averages of money growth and relationship between money growth and 1 inflation. This relationship seems to inflation that exists only over very long provide a straightforward strategy for time horizons is of little use to policy- maintaining low inflation—choose the makers trying to control inflation over growth rate of money that corresponds to the next quarter or year. the desired long-run rate of inflation. In fact, some have concluded Because there is the possibility of a from this evidence that the problem of close relationship between money controlling inflation has been success- growth and inflation in the long run, the 2 fully solved. lack of a clear relationship in the short run raises an obvious question—How long is the long run? That is, over what time horizon, if any, does a direct link between money growth and inflation ISSN 0428-1276 emerge? This Economic Commentary FIGURE 1 MONEY GROWTH VS. INFLATION, seeks to address that question for the QUARTERLY U.S. DATA 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 . This scenario is especially relevant in today’s economic environ- ment, where money growth as measured SOURCES: U.S. Department of Labor, Bureau of Labor Statistics; Board of Governors of the Federal Reserve System; and DRI/McGraw–Hill. by some monetary aggregates has been relatively strong over the past couple of years. The shorter the long run is, the money and inflation over a “long run” as demand is widely thought to increase more troublesome ignoring high money short as four years. However, results roughly proportionally with the growth over this period becomes. using narrower definitions of money, level and with real income. That is, if On the other hand, if no close relation- namely M1 and the monetary base, show go up by 10 percent, or if real ship emerges for the United States even no clear relationship over any of these income increases by 10 percent, empiri- over fairly long time periods, then that time horizons. cal evidence suggests people want to hold evidence would support ignoring money 10 percent more money. ■ Too Many Dollars: growth as an inflationary factor, at least A Simple Theory of Inflation When the money supply grows faster within the ranges of money growth ex- Before discussing the results of the than the money demand associated with perienced over the past 40 years. This analysis, it will be helpful to have in rising real incomes and other factors, finding would not necessarily be incon- mind a simple textbook theory that is the must rise to equate supply sistent with studies that have found a widely thought to explain the basic rela- and demand. That is, inflation occurs. close long-run relationship because tionship between the money supply and This situation is often referred to as too many of those studies include data from prices. Inflation occurs when the average many dollars chasing too few . countries with high and volatile money level of prices increases. Individual price Note that this theory does not predict growth rates. It may be the case that increases in and of themselves do not that any money-supply growth will lead while a close relationship is apparent in equal inflation, but an overall pattern of to inflation—only that part of money- the data when large changes in money price increases does. supply growth that exceeds the increase growth are observed, no clear relation- in money demand associated with rising ship emerges when the changes are rela- The price level observed in the economy real GDP (holding the other factors con- tively modest, such as in the United is that which leads the quantity of money stant). This observation is used in the States. In those cases, other inflationary supplied to equal the quantity of money following section. factors may dominate the effect of rela- demanded. The quantity of money sup- tively small changes in money growth. plied is largely controlled by the Federal ■ Evidence on the Long Run Reserve.3 When the supply of money To answer the question of how long the To investigate the length of the long run, increases or decreases, the price level long run is, the relationship between an analysis was conducted that compares must adjust to equate the quantity of money growth and inflation is exam- the relationship between money growth money demanded throughout the econ- ined across three time periods—two, and inflation over eight-, four-, and two- omy with the quantity of money supplied. four, and eight years. The question is year periods in the United States since The quantity of money demanded de- whether the relationship between 1959. The findings depend greatly on the pends not only on the price level but also money growth and inflation is notably monetary aggregate used to measure on the level of real income, as measured close over any of these time horizons, money growth. Broader definitions of by real (GDP), and, if it is, how clearly that relation- money, namely the M2 and M3 monetary and a variety of other factors including ship holds up over shorter time hori- aggregates, provide results that suggest a the level of interest rates and technologi- zons. relatively close relationship between cal advances such as the invention of automated teller machines. Money MONEY GROWTH AND INFLATION FIGURE 2a 2-YEAR AVERAGES FIGURE 2b 4-YEAR AVERAGES FIGURE 2c 8-YEAR AVERAGES

ADJUSTED MONEY GROWTH AND INFLATION

FIGURE 3a 2-YEAR AVERAGES FIGURE 3b 4-YEAR AVERAGES FIGURE 3c 8-YEAR AVERAGES

NOTE: Money is defined as M2. Inflation is defined using the implicit GDP price deflator (chained). Adjusted money growth is defined as money growth minus real GDP growth. SOURCES: U.S. Department of Labor, Bureau of Labor Statistics; Board of Governors of the Federal Reserve System; and DRI/McGraw–Hill.

The strategy used to analyze the relation- Recall that the simple theory of inflation Data since 1959 are used for the analy- ship is graphical. The analysis is con- held that money growth in excess of real sis. While data are available much far- ducted through a series of figures, each output growth should be more closely ther back in time, the relationship be- of which has the same basic form. The connected with inflation. It is of interest, tween money growth and inflation was figures in the first set (2a, 2b, 2c) display then, to see whether adjusting for differ- quite different in earlier years.5 Data averages of the inflation rate and money ences in real output growth across peri- from the most recent 40 years are likely growth over time. What differs across the ods leads to a closer relationship. to be more relevant to the current eco- figures is the period over which the data nomic environment. are averaged. Each data point shows the The statistic labeled R2 contained in average annual growth rate in inflation or each figure measures the fraction of the The simple theory of inflation outlined money growth over the previous two, variation in inflation that can be ac- above provides no guidance as to the four, or eight years. counted for by variations in money definition of money to be used. The M2 growth.4 An R2 of 0 means that money monetary aggregate, a fairly broad defin- The figures in the second set (3a, 3b, 3c) growth accounts for none of the varia- ition of money, is used in the graphical are identical in form except that money tion in inflation, while an R2 of 1 says analysis. The results for other monetary growth minus real output growth is plot- that money growth accounts for all of aggregates are briefly discussed later. ted instead of money growth alone. the variation in inflation. Figure 2a shows two-year averages and Second, the results presented are based ■ The Current Situation illustrates again why policymakers are on only 40 years of data. There is a very But suppose these qualifications are leery of relying on money growth to limited amount of information one can ignored for a moment. What would the control inflation. It shows that even large extract from these data, especially re- close relationship between M2 growth movements in money growth have no garding eight- and four-year averages. and inflation using four- and eight-year clear relationship with movements in the One should not be overconfident that averages tell us about the current eco- inflation rate over two-year periods. the close relationship observed over nomic situation? At first glance, the these 40 years will continue into the answer appears to be not much. The The relationship becomes somewhat future. Furthermore, the experience of results simply describe historical rela- closer for longer time averages, partic- the early 1990s illustrates that there can tionships in the data, with economic ularly the eight-year averages shown be notable deviations from the general forecasting playing no role. However, if in figure 2c. There, the tent-shaped pat- relationship. For example, figure 3b the view is taken that the long run is a tern of inflation, rising until the early shows that the four-year average of series of short runs, some insights might 1980s and falling steadily since, is gen- money growth minus real output growth be gained by examining the recent erally matched by the pattern of money slowed substantially from 1991 through behavior of money growth, output growth. Slightly more than half of the 1995 and has increased rather sharply growth, and inflation. eight-year movements in inflation are since. Despite the finding of a fairly accounted for by changes in money close relationship between money Figure 2a shows that two-year average growth (R2 equals 0.57). growth and inflation using four-year growth in M2 has increased substantially averages, inflation fell steadily over in recent years, up to about 7.5 percent. Figures 3a, 3b, and 3c display a parallel this entire period. However, even taking That represents the fastest two-year set of figures but with real output into account these first two qualifica- growth in M2 in over 10 years. Adjust- growth subtracted from money growth. tions, the overall results reported in the ing for the strong growth in real GDP in These figures show that adjusting for figures are still rather compelling. recent years, however, makes this rate of differences in real output growth across money growth appear less threatening. periods provides a substantial tightening Perhaps the most important qualification Figure 3a shows that money growth less in the relationship between money is that the finding of a close long-run output growth is only moderately greater growth and inflation. Figure 3c illus- relationship is not consistent across vari- than the current inflation rate and well trates a strikingly close relationship ous definitions of money. Recall that the within the historical pattern of fluctua- between eight-year averages, with monetary aggregate M2 was used in the tions above and below the inflation rate. money growth accounting for more than previous analysis. When the analysis is 80 percent of the movements in infla- repeated using M3, a broader definition However, if the recent growth rate of tion. Even using four-year averages, of money, the results are similar to those M2 were to continue in the next two- money growth accounts for two-thirds reported for M2. However, when nar- year short run, so that money growth of the variation in inflation, and almost rower definitions of money are used, averaged 7.5 percent over a four-year half using two-year averages.6 namely M1 and the monetary base, the horizon, the findings reported here sug- results are quite different. In particular, gest that there may be an impending ■ A Few Words of Caution there is no clear relationship between increase in inflation. Even if real GDP These results suggest that there is a close money growth and inflation, even for growth is assumed to continue at 4.0 relationship between money growth and eight-year averages.6 percent over the next two years—a very inflation in the long run. Furthermore, optimistic assumption—the resulting they suggest that the long run may not These qualifications demand that a increase in money growth less real GDP be long at all, perhaps as short as four more tempered view be taken of the growth would average 3.5 percent over years, once differences in real output findings reported in the previous sec- a four-year horizon. growth across periods are taken into tion. While some long-run relationship account. But before getting carried away appears to exist, at least for the broader Figure 3b shows that money growth less with this apparently strong finding, it is monetary aggregates, it is difficult to output growth of 3.5 percent over a four- important to note some qualifications. state with much precision when this year horizon has historically corre- relationship begins to take hold. sponded to an average inflation rate of First, to make use of the long-run rela- roughly the same magnitude. A 3.5 per- tionship between inflation and money cent inflation rate would represent a sub- growth less real output growth, policy- stantial increase over the 1.1 percent rate makers need accurate forecasts of real experienced over the last two years. If GDP growth over a relatively long hori- real GDP growth were to slow to less zon. Economic forecasters have had than 4 percent in the next two years, very limited success in providing them. while M2 growth remained steady, the Using the historical average of GDP outlook for inflation would be more dire. growth as a forecast produces the same Of course, if M2 growth slows over the relationship displayed in figures 2a next two-year short run, the implications through 2c, a relationship that is sub- for inflation are less negative, especially stantially less clear. if output growth remains robust. ■ Conclusion ■ Footnotes Little attention is currently paid to the 1. For a recent example, see George T. growth rate of the money supply in for- McCandless, Jr. and Warren E. Weber, Terry J. Fitzgerald is an economic advisor at mulating monetary policy—with obvi- “Some Monetary Facts,” Federal Reserve the Federal Reserve Bank of Cleveland. He Bank of Minneapolis, Quarterly Review thanks Jeffrey C. Schwartz and Eduard Pelz ous reason. The relationship between (Summer 1995), pp. 2–11, which also pro- money growth and inflation from quar- vides a summary of other studies. for excellent research assistance. ter to quarter and year to year is not well The views stated herein are those of the understood, and this is the time frame 2. See, for example, the article by Robert E. author and not necessarily those of the Fed- within which policymakers generally Lucas, “Adaptive Behavior and Economic eral Reserve Bank of Cleveland or of the operate. In fact, it was the breakdown in Theory,” Journal of Business, vol. 59, no. 4 Board of Governors of the Federal Reserve (October 1986), p. 402. Lucas makes it clear a perceived short-run relationship during System. that this assertion applies to long-run aver- the early 1990s that led policymakers to ages of money growth and inflation. largely de-emphasize money growth in Economic Commentary is published by the formulating policy. 3. This statement abstracts from the diffi- Research Department of the Federal Reserve culty inherent in controlling the money sup- Bank of Cleveland. To receive copies or to be The graphical analysis presented here ply in practice. This is especially true for placed on the mailing list, e-mail your request suggests that a relatively close relation- broader monetary aggregates such as M2 and to [email protected] or fax it to M3, large parts of which respond to aggre- ship between money growth and infla- 216-579-3050. Economic Commentary is gate economic conditions. tion may exist over eight-year time hori- also available at the Cleveland Fed’s site on zons, at least for the broader monetary 4. For those readers familiar with regression the World Wide Web: http://www.clev.frb.org. aggregates. This finding serves as a analysis, this statistic is the regression R2 reminder that ignoring money growth for obtained by regressing the inflation rate on We invite comments, questions, and sugges- too long a period may be unwise. While the growth rate of the money supply and a tions. E-mail us at [email protected]. money growth may not provide a partic- constant. It is simply the square of the corre- lation between inflation and money growth. ularly useful guide for short-run policy- Now on our Web Site! See a glossary of making, long-run trends in inflation may 5. See Lawrence J. Christiano and Terry terms used in this Economic Commentary still be largely determined by the long- J. Fitzgerald, “The Band-Pass Filter,” Fed- when you visit us online. run growth rate of the money supply. eral 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 mone- tary base, M1, and M3 are 0.20, 0.16, and 0.80, respectively.