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“The Quantity Theory of Money is correct if the velocity of money is constant”

The Quantity Theory of Money, developed by the classical economists, states that
movements in price level are caused solely from the changes in the quantity of money and
that price level is directly proportional to money supply. Hence in essence a money supply
expansion only causes price inflation. Thus, for instance if Money supply doubles, the price
level in the economy doubles as well.

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The best way to illustrate the concept is using the equation of exchange:

MV=PY, which is an identity and where

M= Money Supply (stock of money)
P= Price Level
Y= Real Income (taken as a proxy for the number of transactions)
V= Velocity of circulation

Assuming velocity is constant, we can rearrange the equation to:
P= MV/Y= M * (V/Y)

Treating velocity as a constant, the quantity theory of money would be correct only if both
real income “Y” and velocity “V” were constants. In that case there would exist a direct
proportional relationship between money supply and price level, and the equation of
exchange could be rewritten as:

P=kM, where k=V/Y is a constant.

Thus, in the case both velocity and real income were constant and not just velocity, if money
supply is doubled for example, then for the identity to hold, the price level must also double
and the quantity theory of money would hold true. Of course, all of this is assuming that all
other factors which could potentially affect price level (such as positive supply shocks ; for
example a in sharp drop oil prices pushing down the costs of production and hence the price
level in the economy) are held constant which is another major assumption.

The above result can also be illustrated by taking a total differential of the equation of
exchange with respect to time t:

dM/M + dV/V = dP/P + dY/Y

Rearranging the above equation gives:

dP/P = dM/M + dV/V – dY/Y

Thus, in the case velocity and real income were constant, dV/V and dY/Y would be both zero
and:

dP/P = dM/M,

that is there would exist a one for one, linear relationship between the growth rates of money
supply and price level. In fact, the conclusion of the quantity theory of money would still
hold true even if both velocity and real income grew at some uniform rate over time. In that
case dV/V and dY/Y would be constants and the total differential equation could be written
as:

dP/P = dM/M + v – r, where v and r represent constant rate of change of velocity and real
income over time.

Thus, even in the scenario where there are no upward or downward fluctuations in velocity
and real income, there would exist a direct proportional relationship between money supply
and price level.

Since classical economists such as Irving Fischer, saw wages and prices as completely
flexible and not rigid or sticky1, they believed that real income (or aggregate output) Y,
would always be at the full employment level, and thus could also be treated as constant. This
led to the classical economists concluding that since both velocity and aggregate output were
constants, any expansion in money supply would have to be matched by a proportionate
increase in the price level.

The above result can also be explained using ISLM analysis.

Figure 1

Interest
Rates, i

LM1

LM2

IS1
IS1

DRPeal Output, Y

YF Y1

Real G

1 Mishkin, Frederic.S. “The Economics Of Money, Banking and Financial Markets,” (2010)

Figure 2

Price Level, P

LRASS

In the figure above, IS curve (representing equilibrium in the goods market) and the LM
curve (representing equilibrium in the market for money) intersect at YF, that is the economy
is at full employment or natural rate level of output as indicated by YF, the level of output at
which price has no tendency to change. Assuming flexible prices, a rise in the money supply
would cause the LM1 curve to shift to the right to LM2, causing the output to rise above the
natural rate to Y1. As a result, prices in the economy would start to rise, causing a fall in real
money balances M/P, which is equivalent to a fall in money supply holding price fixed. This
resulting fall in real money balances would cause the LM2 to shift to the left and would keep
on shifting until it reaches back to its initial position, that is until the increase in money
supply has been completely offset by an equivalent proportional increase in price bringing
back the real money balances M/P to their original level and the output level back to its full
employment level. Thus, the increase in money supply has left output unchanged
(assuming velocity is constant) and has simply caused a proportionate rise in the price level
and thus backs the conclusion of the quantity theory of money.

However, whether prices and wages are flexible is a matter of considerable debate and where
the classical economists propose complete flexibility, the Keynesians propose that prices and
wages are rigid or sticky at least in the short run and hence a rise in money supply could
initially increase aggregate output to a higher level, (as also illustrated using the ISLM
framework) a concept best illustrated using the AD-AS framework.

SRAS2

SRAS1

PL
PS

Initial Price

YF Y1

Real Ou

A rise in money supply would cause an excess supply of money, and people not wanting to

t p R u e t , a Yl O u t p u t , Y

and hence interest rates to decrease. This fall in interest rates would reduce the cost of
borrowing causing a rise in investment and would also cause a depreciation in the currency
as there would be an outflow of financial investment funds, thereby causing a rise in net
exports (assuming Marshall-Lerner Condition) is satisfied. As a result, the Aggregate demand
in the economy would increase causing the AD1 curve to shift to the right to AD2. Since
prices and wages are sticky in the short run, a rise in AD caused by an increase in money
supply causes a rise in both price level P (to PS) and real output Y ( to Y1, above YF) but not
an equivalent proportional increase in price level. In the long run however, since output has
risen above the natural rate or the full employment level, and prices and wages are flexible,
an output above the natural rate would cause tightness in the labor market, putting upward
pressure on wages, thereby increasing the cost of production for firms and shifting the short
run aggregate supply curve (SRAS1) to the left to SRAS2, where it would intersect AD2, at
the full employment level and a higher price level of PL , illustrating the self correcting
mechanism of the economy. Thus, as illustrated above, only in the long run when prices and
wages are flexible, would a rise in money supply translate into a direct equivalent
proportionate rise in price level P. Thus, based on the AD-AS framework, the quantity theory
of money holds true perhaps only in the long run but not in the short run when prices and
wages are sticky.

Furthermore, it is also reasonably possible that the economy is not at the full employment
level and instead there is a great degree of slack in the economy in terms of unemployment of
resources, such as in the aftermath of the Financial crisis of 2008. During this time, some
commentators were skeptical of the rapid increase in money supply and feared that US and
other economies might suffer from periods of rapid increase in price levels, which turned out
not to be the case. This phenomenon can be best illustrated using the diagram below:

Figure 3

AS

Price Level, P

Y2 Rea

Y1

Real Output, Y
l Output,

As illustrated above, in a scenario, where the there is a great degree of unemployment of
resources and slack in the labor market due to high labor unemployment, the aggregate
supply in the economy could be initially viewed as highly elastic. In such a case a rise in
money supply would cause a rise in Aggregate Demand through the same transmission
mechanism as discussed before but since there is a great degree of slack in the economy and
the labor market, and the level of real output is well below its natural rate, a rise in aggregate
demand caused by a rise in money supply would merely translate into higher aggregate
output, and there would be no resulting shifts in the aggregate supply in the economy, due to
the great degree of slack in labor market, with labor potentially willing to work on low wages
and hence little upward pressure on wages. Thus, only when output is at or has reached its
natural rate or full employment level YF (which won’t always be the case and is again a long
run phenomenon), would a further increase in money supply, cause a rise in aggregate
demand that would be met by a direct proportionate increase in price level.

Moreover, since velocity is assumed to be constant, we can also rewrite the equation of
exchange as:

M/P = Md =kY, where k=1/V is a constant

Seen this way, the quantity theory of money can also be looked at as a theory of money
demand (Md). Since money demand equals money supply in equilibrium, assuming velocity
is constant, the quantity theory of money suggests that demand for real money balances is
determined solely by real income, meaning that money is demanded solely for transactionary
purposes and no other factors such as interest rates have an effect on the demand for money.
However, it can be argued as was done by economists such as Keynes and Tobin that money
is held not only for transactionary motives but also for precautionary and speculative
motives, and that money demand is also a function of interest rates in the economy where
interest rates are seen as an opportunity cost of holding money and that the higher the interest
rate is, (holding other factors constant), the higher the opportunity cost of holding money and
hence the lower the money demand. Hence, it can be argued that not only income but also
interest rates effect the demand for money and that interest rates are inversely related to
money demand 1.

Therefore, in conclusion, it can be said that even if the velocity of money is constant, the
quantity theory of money would hold true only if certain other qualification are made, mainly
that output is at its full employment level and hence can reasonably be assumed to not
fluctuate, that prices and wages are flexible and that the economy is not a dynamic but a
static system, qualifications that could only be considered true in the long run but not in the
short run.

“Unconventional monetary policy, such as quantitative easing, is in conflict with the
Taylor – rule approach to conducting monetary policy”.

Most central banks, like the Federal Reserve Bank in the US, conduct monetary policy by
targeting short term rates and in 1993, John Taylor of Stanford University came up with the
“Taylor Rule”, a rule that indicates what the federal funds rate (overnight interbank lending
rate in the US) should be in response to deviations from the Federal Reserve’s inflation and
output targets, namely:

Federal funds rate = inflation rate + equilibrium federal funds rate (=2%) + 1?2 (inflation
gap) + 1?2(output gap)

where the inflation gap is the deviation of current inflation from the target rate of 2%
inflation and output gap is the percentage deviation of real GDP from potential (full
employment) GDP2.

The Taylor rule was a step in favour of what is called ” rule based monetary policy”, where
central banks are tied to some rule based policy variable or nominal anchor and not allowed
to adjust policy variables based solely on discretion. And up until the financial crisis of 2007-
2008 the Taylor Rule acted as a significant guide to the federal funds rate target rate as
illustrated in Figure 1( Data in Appendix 1):

10.00
8.00
6.00
4.00
2.00
0.00
-2.00
-4.00

Federal Funds Rate and Taylor Rule

Federal Funds Rate

Taylor Rule

2

Taylor, John B. “Discretion versus policy rules in practice.” Carnegie-Rochester conference series on public policy. Vol. 39. North-

Holland, 1993.

1989-10-01
1990-08-01
1991-06-01
1992-04-01
1993-02-01
1993-12-01
1994-10-01
1995-08-01
1996-06-01
1997-04-01
1998-02-01
1998-12-01
1999-10-01
2000-08-01
2001-06-01
2002-04-01
2003-02-01
2003-12-01
2004-10-01
2005-08-01
2006-06-01
2007-04-01
2008-02-01
2008-12-01
2009-10-01
2010-08-01
2011-06-01
2012-04-01
2013-02-01
2013-12-01
2014-10-01
2015-08-01
2016-06-01

In response to the financial crisis, the Federal Reserve Bank (and other major central banks,
such as Bank of England and the European Central Bank) lowered their short term rates to
near 0% (as also suggested by the Taylor Rule) taking the rates to their effective lower
bound. However, once the short term rates had reached near or at 0%, there was little or no
room to lower short term rates further and with the US and other major economies still
suffering from the effects of the worst financial crisis since the Great Depression, the central
banks in these economies were running out of ammunition (even if rates could be made
negative, they can only go slightly negative as holding cash, a zero interest paying asset
becomes a more profitable option for banks rather than lending to one another and getting
back less money in return). In this time of financial crisis, The Taylor rule suggested that the
correct federal funds rate be quite negative, going as low as nearly -2% at one point. Since
this was not a viable option, the Federal Reserve Bank (Fed) along with other major central
banks kept their short term rates close to 0% and searched for other more unconventional
policy tools that would ease the credit crunch and also help stimulate the level of aggregate
expenditure in the economy, to help it come back out of its recessionary state and avoid
deflation, fears of which had started to grow13.

Thus, the central banks of major economies such as the Fed adopted unconventional
monetary policy tools such as that of quantitative easing which involved purchasing of large
quantities of medium to long term assets including government bonds and private sector
obligations such as corporate bonds which would drive up their prices and hence lower the
returns on these assets thereby helping to bring down medium to long-term interest rates,
which are the more relevant interest rates for economic agents. The policy tool was also
aimed at easing the credit crunch at the time of the financial crisis by providing banks and
other major financial institutions with the much required liquidity needed to prevent defaults
and encourage depository institutions to engage in lending activities, which would allow the
transfer of savings to productive investment opportunities and help bring the economy out of
its recessionary state1. Moreover, in line with a rule based approach that is aimed at
increasing the predictability of central banks actions, Quantitative Easing could be seen as
imperative in signalling to economic agents central banks actions and future stance of
monetary policy, more specifically the objective of keeping short term rates low for a
considerable period. By buying large quantities of medium to long assets, central banks such
as the Fed, aimed at sending a credible signal to economic agents of keeping rates low
because if the central banks were to renege and start raising rates, they would suffer huge
capital losses on the securities they purchased.

Thus contrary to the view that unconventional monetary policy such as Quantitative Easing
(QE) is in conflict with the Taylor rule approach to monetary policy, it could be argued that
QE had to be adopted in essence due to the failure/limitations of the Taylor Rule (in general a
rule based approach) to suggest a viable policy option during large negative shocks to the
economy, such as at the time of the Financial crisis of 2007-2008 and to credibly signal to
economic agents the stance of monetary policy and central banks future course of action, both
of which is what a rule based monetary policy, such as the Taylor Rule approach, aims to
achieve. Hence, it could be argued that such unconventional methods were adopted not in
conflict but as complements to the Taylor Rule approach to monetary policy, which
suggested quite negative interest rates in the aftermath of the financial crisis. Negative
interest rates as suggested by the Taylor Rule, though not a realistic option, can be taken as
an indication that further easing of monetary policy is required and that is exactly what the

3Bernanke, Ben.S. , “The Taylor Rule: A benchmark for Monetary Policy?,” (2015), https://www.brookings.edu/blog/ben-
bernanke/2015/04/28/the-taylor-rule-a-benchmark-for-monetary-policy/

Fed and other central banks did, by creating more money and purchasing securities of longer
maturities, lowering medium to long termrates to make up for their inability to lower short
term rates further and thus adopted a more accommodating, loose monetary policy.

However, in a broader context it could be argued that unconventional monetary policy tools
such as QE, is in conflict with the Taylor rule approach to monetary policy as it gives rise to
more discretion in monetary policy decision making as opposed to a rule based monetary
policy. The primary idea behind a rule based approach, an illustration of which is the Taylor
Rule, is to avoid the time-inconsistency problem, where monetary policy is eased to avoid
recessions and hence loses sight of long term goals such as that of price stability in order to
achieve short term gains. Thus for example, private agents may deliberately create shocks to
force up wages and firms costs, anticipating that the central banks would ease monetary
policy rather than risking a recession or rise in unemployment. Quantitative Easing and other
unconventional monetary policy acts (such as the Fed buying hundreds of billions of dollars’
worth of debt and mortgage backed securities issued by government sponsored agencies in
the US) can be potentially viewed as also examples of central banks moving away from a rule
based approach and sticking to the existing tools at their disposal to adopting a very flexible
and accommodative monetary policy stance policy where the central banks are willing to
intervene to any extent to the aid of financial institutions. It was discretionary policies like
the QE (such as unconventional loans to banks), which led to the Philladelphia Fed president
Charles Plosser to argue in April 2008 (before QE was even adopted) that:

“Discretion in lending practices runs the risk of exacerbating moral hazard and encouraging
financial institutions to take excessive amounts of risk.”

And former Chairman of the Federal Reserve Paul Volker to claim that the Fed has gone ” to
the very edge of its lawful and implied powers”. 4

By adopting accommodative discretionary monetary policy such as QE, central banks
potentially give rise to risk taking behaviour among financial institutions and investors.
Financial institutions would be encouraged to invest in risky projects and issue risky loans
knowing that the in the case of defaults and shortage of liquidity, the central bank will be
willing to go to any extent in its lender of the last resort role just like when the The Fed did in
partially financing the takeover of ailing investment bank Bear Sterns in 2008. Moreover, by
buying large quantities of long term assets and lowering both short term and long term yields,
central banks could also potentially incentivise risk taking behaviour amongst investors who
in pursuit of ” better returns” may allot a greater share of their portfolios to risky assets such
as stocks and corporate junk bonds5. Thus by adopting such unconventional monetary
policies such as QE which are discretionary in nature, the central banks give rise to risk
taking behaviour and encourage economic agents to cause negative shocks to the economy,
knowing that central banks would come to their rescue; unlike under a rule based monetary
policy approach, such as the Taylor Rule approach, where there is less flexibility and more

4 Fox, Justin. ” Second Guessing the Fed,” June 2008,

5

Yu, Edison. “Did quantitative easing work?.” Economic Insights 1.1 (2016): 5-13.

accountability and transparency with respect to central banks actions.

Thus in conclusion, it could be argued that even though the QE programme adopted by
central banks was essentially to supplement the already very low short term rates (the
negative rates suggested by the Taylor Rule could be taken as a signal of further easing of
monetary policy as very negative rates are not possible ), they are in essence contradictory to
the rule based monetary policy approach as illustrated in the Taylor Rule.