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Velocity 5 tion owner could pay it out to a house painter in October; and the painter might spend it
Money stock
on a Christmas present in December. In this way, the same dollar is used five times during
the year. If it were used only four times during the year, its velocity would be 4, and so on.
No one has data on every transaction in the economy. To make velocity an operational
concept, economists need a workable measure of the dollar volume of all transactions. As
mentioned in the previous chapter, the most popular choice is nominal gross domestic prod-
uct (GDP), even though it ignores many transactions that use money, such as the huge vol-
ume of activity in financial markets. If we accept nominal GDP as our measure of the money
value of transactions, we are led to a concrete definition of velocity as the ratio of nominal
GDP to the number of dollars in the money stock. Because nominal GDP is the product of
real GDP (Y) times the price level (P), we can write this definition in symbols as follows:
Value of transactions Nominal GDP P 3 Y
Velocity 5 5 5
Money stock M M
The equation of exchange By multiplying both sides of the equation by M, we arrive at an identity called the
states that the money value equation of exchange, which relates the money supply and nominal GDP:
of GDP transactions must be
Money supply 3 Velocity 5 Nominal GDP
equal to the product of the
average stock of money
Alternatively, stated in symbols, we have
times velocity. That is:
M3V5P3Y
M3V5P3Y


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Chapter 14 279
The Debate over Monetary and Fiscal Policy



The equation of exchange provides an obvious link between the stock of money, M, and
the nominal value of the nation™s output, P 3 Y. This connection is merely a matter of
arithmetic, however”not of economics. For example, it does not imply that the Fed can
raise nominal GDP by increasing M. Why not? Because V might simultaneously fall
enough to prevent the product M 3 V from rising. In other words, if more dollar bills
circulated than before, but each bill changed hands more slowly, total spending might not
rise. Thus, we need an auxiliary assumption to change the arithmetic identity into an eco-
nomic theory.
The quantity theory of money transforms the equation of exchange from an arithmetic The quantity theory of
money assumes that veloc-
identity into an economic model by assuming that changes in velocity are so minor that
ity is (approximately) con-
velocity can be taken to be virtually constant.
stant. In that case, nominal
You can see that if V never changed, the equation of exchange would be a marvelously GDP is proportional to the
simple model of the determination of nominal GDP”far simpler than the Keynesian money stock.
model that took us several chapters to develop. To see this, it is convenient to rewrite the
equation of exchange in terms of growth rates:
%DM 1 %DV 5 %DP 1 %DY
If V was constant, making its percentage change zero, this equation would say, for exam-
ple, that if the Federal Reserve wanted to make nominal GDP grow by 4.7 percent per
year, it need merely raise the money supply by 4.7 percent per year. In such a simple
world, economists could use the equation of exchange to predict nominal GDP growth by
predicting the growth rate of money. And policy makers could control nominal GDP
growth by controlling growth of the money supply.
In the real world, things are not so simple because velocity is not a fixed number. But
variable velocity does not necessarily destroy the usefulness of the quantity theory. As we
explained in Chapter 1, all economic models make assumptions that are at least mildly
unrealistic. Without such assumptions, they would not be models at all, just tedious
descriptions of reality. The question is really whether the assumption of constant velocity
is a useful abstraction from annoying detail or a gross distortion of the facts.
Figure 1 sheds some light on this question by showing the behavior of velocity since
1929. Note that the figure includes two different measures of velocity, labeled V1 and V2.
Why? Recall from Chapter 12 that we can measure money in several ways, the most pop-
ular of which are M1 and M2. Because velocity (V) is simply nominal GDP divided by the
money stock (M), we get a different measure of V for each measure of M. Figure 1 shows
F I GU R E 1
the velocities of both M1 and M2.
Velocity of Circulation,
1929“2007
SOURCE: Constructed by the authors; data from Bureau of Economic Analysis, Federal Reserve




10.5
10.0
9.5
9.0 3.0
V1
8.5
8.0
7.5 2.5
7.0
6.5 V2
6.0 2.0
Velocity (V1)




Velocity (V2)




5.5
5.0
4.5 1.5
4.0
3.5
3.0 1.0
2.5
2.0
1.5 0.5
Board, and Robert Rasche.




1.0
0.5
0.0
1930 1940 1950 1960 1970 1980 1990 2000 2010 1930 1940 1950 1960 1970 1980 1990 2000 2010
Year Year
(a) (b)




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Part 3
280 Fiscal and Monetary Policy



You will undoubtedly notice the stark difference in the behavior of V1 versus V2. V1 is
nowhere near constant; it displays a clear downward trend from 1929 until 1946, a pro-
nounced upward trend until about 1981, and quite erratic behavior since then. V2 is much
closer to constant, but it has risen noticeably since the 1980s. Furthermore, closer exami-
nation of monthly or quarterly data reveals rather substantial fluctuations in velocity, by
either measure. Because velocity is not constant in the short run, predictions of nominal
GDP growth based on assuming constant velocity have not fared well, regardless of how
M is measured. In a word, the strict quantity theory of money is not an adequate model of
aggregate demand.


Some Determinants of Velocity
Because it is abundantly clear that velocity is a variable, not a constant, the equation of ex-
change is useful as a model of GDP determination only if we can explain movements in
velocity. What factors decide whether a dollar will be used to buy goods and services four
or five or six times per year? While numerous factors are relevant, two are important
enough to merit discussion here.

Efficiency of the Payments System Money is convenient for conducting transac-
tions, which is why people hold it. But money has one important disadvantage: Cash
pays no interest, and ordinary checking accounts pay very little. Thus, if it were possible
to convert interest-bearing assets into money on short notice and at low cost, rational in-
dividuals might prefer to use, say, credit cards for most purchases, making periodic
transfers to their checking accounts as necessary. That way, the same volume of trans-
actions could be accomplished with lower money balances. By definition, velocity
would rise.
The incentive to limit cash holdings thus depends on the ease and speed with
which it is possible to exchange money for other assets”which is what we mean by the
“efficiency of the payments system.” As computerization has speeded up banks™ book-
keeping procedures, as financial innovations have made it possible to transfer funds
rapidly between checking accounts and other assets, and as credit cards have come to
be used instead of cash, the need to hold money balances has declined and velocity
has risen.
In practice, improvements in the payments system pose severe practical problems for
analysts interested in predicting velocity. A host of financial innovations, beginning in the
1970s and continuing right up to the present day (some of which were mentioned in
Chapter 12™s discussion of the definitions of money), have transformed forecasting veloc-
ity into a hazardous occupation. In fact, many economists believe the task is impossible
and should not even be attempted.

Interest Rates A second key determinant of velocity is the rate of interest. The reason
is implicit in what we have already said: The higher the rate of interest, the greater the
opportunity cost of holding money. Therefore, as interest rates rise, people want to hold
smaller cash balances”which means that the existing stock of money circulates faster, and
velocity rises.
It is this factor that most directly undercuts the usefulness of the quantity theory of
money as a guide for monetary policy. In the previous chapter, we learned that expan-
sionary monetary policy, which increases bank reserves and the money supply, also de-
creases the interest rate. But if interest rates fall, other things being equal, velocity (V)
also falls. Thus, when the Fed raises the money supply (M), the product M 3 V should
increase by a smaller percentage than does M itself.

Thus, we conclude that
Velocity is not a strict constant but depends on such things as the efficiency of the fi-
nancial system and the rate of interest. Only by studying these determinants of velocity



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Chapter 14 281
The Debate over Monetary and Fiscal Policy



can we hope to predict the growth rate of nominal GDP from knowledge of the growth
rate of the money supply.


Monetarism: The Quantity Theory Modernized
Adherents to a school of thought called monetarism try to do precisely that. Monetarists Monetarism is a mode of
analysis that uses the equa-
realize that velocity changes, but they claim that such changes are fairly predictable”certainly
tion of exchange to organize
in the long run and perhaps even in the short run. As a result, they conclude that the
and analyze macroeco-
best way to study economic activity is to start with the equation of exchange in growth-
nomic data.
rate form:
%DM 1 %DV 5 %DP 1 %DY
From here, careful study of the determinants of money growth (which we provided in
the previous two chapters) and of changes in velocity (which we just sketched) can be
used to predict the growth rate of nominal GDP. Similarly, given an understanding of
movements in V, controlling M can give the Fed excellent control over nominal GDP.
These ideas are the central tenets of monetarism.
The monetarist and Keynesian approaches can be thought of as two competing theo-
ries of aggregate demand. Keynesians divide economic knowledge into four neat com-
partments marked C, I, G, and (X 2 IM) and then add them all up to obtain aggregate
demand. In Keynesian analysis, as we have learned, money affects the economy by first
affecting interest rates. Monetarists, by contrast, organize their knowledge into two alter-
native boxes labeled M and V and then multiply the two to obtain aggregate demand. In
the monetarist model, the role of money is not necessarily limited to working through
interest rates.
The bit of arithmetic that multiplies M and V to get P 3 Y is neither more nor less
profound than the one that adds up C, I, G and (X 3 IM) to get Y, and certainly both are
correct. The real question is which framework is more useful in practice. That is, which
approach works better as a model of aggregate demand?
Although there is no generally correct answer for all economies in all periods of time, a
glance back at Figure 1 (page 279) will show you why most economists had abandoned
monetarism by the early 1990s. During the 1960s and 1970s, velocity (at least V2) was
fairly stable, which helped monetarism win many converts”in the United States and
around the world. Since then, however, velocity has behaved so erratically here and in
many other countries that there are few monetarists left.
Nonetheless, as we will see later in this chapter, some faint echoes of the debate
between Keynesians and monetarists can still be heard. Furthermore, few economists
doubt that there is a strong long-run relationship between M and P. They just question
whether this relationship is useful in the short run. (See the box “Does Money Growth
Always Cause Inflation?” on the next page.)



FISCAL POLICY, INTEREST RATES, AND VELOCITY
As we learned in the previous chapter, Keynesian economics provides a powerful and
important role for monetary policy: An increase in bank reserves and the money supply
reduces interest rates, which, in turn, stimulates the demand for investment. But fiscal pol-
icy also exerts a powerful influence on interest rates.
To see how, think about what happens to real output and the price level following, say,
a rise in government spending. We have learned that both real GDP (Y) and the price level
(P) rise, so nominal GDP certainly rises. But the previous chapter™s analysis of the market
for bank reserves taught us that rising prices and/or rising output”by increasing the
money volume of transactions”push the demand curve for bank reserves outward to the
right. If there is no change in the supply of reserves, the rate of interest must rise. So
expansionary fiscal policy raises interest rates.



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Licensed to:
Part 3
282 Fiscal and Monetary Policy




P O L I C Y D E B AT E
Does Money Growth Always Cause Inflation?
Monetarists have long claimed that, in the famous words of the late The answer appears to be “yes.” The accompanying charts use re-

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