CHAPTER 18
THE MONEY SUPPLY AND MONETARY POLICY
Chapter Outline
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How is the Money Supply Determined?
Open Market Operations
The Money Supply and the Monetary Base
Bank Lending and the Money Supply
The Money Multiplier
The Value of the Multiplier
Short Run Control of the Money Supply
Policy Implementation With Minimum Required Reserve Ratios
The Zero Reserve Requirement
Government Deposits and Settlement Balances
The Overnight Rate and the Transmission of Monetary Policy
Targets and the Implementation of Monetary Policy
The Current Implementation of Monetary Policy
Working With Data
Changes from the Previous Edition
Section 18-1 has been rewritten to give a minor history of the evolution of money in Canada. The
section on the deposit expansion process has been eliminated, and Section 18-2 has been incorporated
with Section 18-1. Section 18-2 is now the old Section 18-3. All the material from Section 18-3 onwards
has been rewritten, with a more consistent explanation of the conduct of monetary policy. Boxes 18-1 to
18-3 are new. Box 18-4 is the previous material on the term structure of interest rates. The material on
the random walk of stock prices has been eliminated.
Learning Objectives
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Students should be able to derive the money multiplier and calculate changes in money supply
resulting from changes in the monetary base.
Students should be able to explain how the monetary base is affected by open market operations.
Students should be able to identify factors that can affect the size of the money multiplier.
Students should know how the Bank of Canada can control the settlement balances available to the
banks through its management of government deposit accounts.
Students should know how the Bank of Canada can control the money supply in the short run by
controlling the overnight rate
Students should understand the Monetary Conditions Index, and what it means for the stance of
monetary policy.
Students should be able to identify the immediate and intermediate targets and the ultimate goals for
monetary policy and be able to discuss their relative merits.
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Accomplishing the Objectives
The first section of this chapter deals with the question of how the money supply is determined.
Students will likely be very interested in the brief history of money in Canada at the beginning of this
section.
For interested students, more can be found on the Bank of Canada webpage at
www.bankofcanada.ca/en/currency.html. We then proceed with a traditional analysis of the money
creation process, using balance sheets of the banking system, the non-financial private sector and the
Bank of Canada. The money supply is related to the Monetary Base and the money multiplier. To
simplify the examples, the discussion ignores the distinction between demand deposits and time deposits
(and thus the distinction between M1 and M2) and simply defines money as the sum of currency (CU)
and bank deposits (D):
M = CU + D
The Monetary Base is defined as the sum of currency (CU) and bank reserves (R):
B = CU + R
The money multiplier is defined as money supply divided by the monetary base. Thus the formula
for the money multiplier is derived as
M/B = (CU + D)/(CU + R) = [(CU/D) + (D/D)]/[(CU/D) + (R/D)] = (cu + 1)/(cu + re)
with
cu = CU/D = currency-deposit ratio, and
re = R/D = reserve-deposit ratio.
The money multiplier (mm) is always greater than 1, which implies that any change in the
monetary base will lead to a larger change in total money supply, that is,
M = [(1 + cu)/(re + cu)](B) = mm(B).
The Bank of Canada can change the monetary base through open market purchases or sales. In
the case of an open market purchase, the Bank of Canada buys government securities from banks and the
general public, increasing the reserves of the banking system. When calculating the change in money
supply resulting from such a change in the monetary base, the money multiplier is generally assumed to
be constant. However, the money multiplier can change as banks and consumers respond to different
market conditions, affecting the reserve-deposit and currency-deposit ratios. (It is fairly obvious that the
money multiplier increases as the reserve-deposit ratio or the currency-deposit ratio decreases.)
The central bank controls money supply only indirectly through its control of the monetary base,
since the behaviour of the public (through changes in currency holdings) and banks (through changes in
reserve holdings) affect money supply as well. The payment habits of the public and the convenience and
cost of obtaining cash determine how much currency is held relative to bank deposits. Similarly, the
reserve-deposit ratio is influenced by regulations and by the trade-off between profitability and safety that
banks face.
The money multiplier analysis is useful in terms of establishing linkages between the monetary
base and the potential size of the money supply. It illustrates that changes in the monetary base have
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direct effects on bank lending and ultimately on the size of the money supply. This was important to the
earlier monetary policy operations of the 1970’s, which were based on money supply growth rate targets,
but it is not the current focus of the Bank of Canada’s monetary policy operations.
Monetary policy in Canada is now based on a target inflation rate, and is implemented through
control of the settlement balances held by banks in the Bank of Canada, and the Bank’s setting of targets
for short term interest rates. Under the zero reserve requirements chartered banks and other direct
clearers must hold settlement balances in their accounts at the Bank of Canada that are not less than zero.
The Bank of Canada controls the supply of these settlement balances to the system through its
management of Government of Canada deposit balances. The supply of settlement balances available to
the system has an important impact on the shortest-term interest rates. Individual banks that find
themselves short of balances at the end of the day must borrow, either from other banks who hold excess
balances, or from the Bank of Canada. Conversely, individual banks with excess balances want to lend
the excess at interest to enhance their profitability. The result is a market for overnight loans of
settlement balances in which the interest rate is sensitive to changes in the supply of such balances.
The Bank of Canada implements monetary policy by setting a target range for the interest rate on
overnight loans, and managing the supply of clearing balances as required to achieve the target interest
rate. Daily changes in clearing balances are made by the Bank through its management of government
deposits held both in the Bank of Canada and on deposit in the banks. A transfer of balances from
government accounts with the Bank of Canada to government accounts in the banks, a redeposit,
increases settlement balances in the system and puts downward pressure on short rates. Conversely, a
drawdown transfers deposits from the banks to the Bank of Canada, reducing settlement balances and
putting upward pressure on short rates. The Bank of Canada announces the target range for interest rates
on overnight loans, set its Bank Rate at the top of that target range and then manages the supply of
settlement balances in the system to achieve its interest rate targets. As a result monetary policy is
conducted through interest rate control consistent with a target for the rate of inflation.
Although the Bank of Canada places less public emphasis on the Monetary Conditions index
(MCI) it is a useful tool for students to understand the current monetary policy stance. Students can
compare the MCI to the ever popular “Taylor Rule” which is discussed in Box 18-3.
Suggestions and Pitfalls
Probably the best way to introduce the Bank of Canada’s monetary policy options is to ask
students to define the overnight rate and the bank rate, and to identify their current levels. A discussion of
current economic conditions and of anticipated actions by the Bank should follow. This will make it clear
that the Bank's conduct of monetary policy is not simply of theoretical interest but that it has very real
consequences that will affect students' daily lives.
Although the ultimate goal of the Bank of Canada is still to control inflation, the short run
implementation of Bank of Canada policy is still evolving. Instructors can motivate a discussion of policy
by having students go the Bank of Canada web page at http://www.bankofcanada.ca/ . It is helpful for
students to relate the conduct of monetary policy to the IS/LM model discussed earlier. Essentially, the
Bank of Canada conducts monetary policy via an interest rate rule which is changed periodically, based
on fixed announcement dates. This would be an excellent place to use the tools on money supply rule
versus interest rate rule that were introduced in Chapter 12.
It should be stressed that the IS-LM framework only depicts the very short run when prices are
fixed. But if prices are allowed to vary, interest rate targets may not work well, since the real balance
effect (the price adjustment) will shift the LM-curve back again. It is important that students be aware of
both the short-run and the long-run effects of monetary policy, since they are quite different in nature.
The initial (short-run) effect of an increase in money supply is to lower interest rates. This will stimulate
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the economy, leading to increased credit demand which will then put renewed upwards pressure on
interest rates. Since expansionary monetary policy can easily lead to inflation, (nominal) interest rates are
likely to go above their original level in the long run.
The recessions of the early 1980s and early 1990s were largely attributed to the Bank of Canada's
restrictive monetary policy. Since then the Bank of Canada's approach to monetary policy appears to have
become more eclectic. The Bank of Canada now monitors a variety of macroeconomic data and responds
to changes in the inflation rate, the unemployment rate, the trade deficit, and even commodity prices.
Currently, the Bank of Canada has many different targets to choose from (M1, M2, M3, interest rates, the
monetary base, nominal income), which gives it considerable flexibility in setting monetary policy. Some
attention is also given to credit, since consumers and firms often decide how much to spend based on how
much credit is available rather than how much money is on hand.
Solutions to the Problems in the Textbook:
Discussion Questions:
1.
Open market operations are the main tool used by the Bank of Canada to change the size of the
monetary base with the objective of changing the money supply. If the Bank wants to increase the
money supply, the Bank can buy government bonds from the public (mostly banks), thereby
creating new monetary base and bank reserves. These increased reserves will induce banks in
their pursuit of profit to extend their loans and their deposits thereby creating more money and a
larger money supply. If the Bank wanted to reduce the money supply, an open market sale of
some of its holdings of government bonds, paid for by the public drawing down their bank
deposit balances, would result in the destruction of some of the existing monetary base. Banks
would find they are short of reserves and would reduce their lending and deposits accordingly.
The money supply would contract.
2.
The clearing system is the set of institutional arrangements established to effect settlement of
cheques drawn on one bank in the system but deposited in another bank. For example, a person
who banks with the Bank of Nova Scotia might make a rent payment by cheque to a landlord who
banks with the Royal Bank. The Royal Bank, having credited the landlord’s account on deposit
of the rent cheque, requires payment for the cheque from the Bank of Nova Scotia, which will
debit the tenant’s bank account accordingly. Each day thousands of such transactions take place
and, rather than settle each one, the clearing system establishes a daily net balance of transactions
between each pair of banks and deposit institutions in the system. That net balance is then settled
by a transfer of settlement balances in the Bank of Canada between the accounts of members of
the payments association.
3.
The currency-deposit ratio is the ratio of currency outstanding to bank deposits. The Bank of
Canada cannot directly influence this ratio, since it is determined by the behaviour of the public
and influenced by the convenience of obtaining cash or seasonal patterns (increased Christmas
shopping, for example). However, by changing bank regulations or interest rates, the Bank of
Canada may indirectly affect how much currency the public is willing to hold.
4.
Credit cards and ATMs should reduce the desired currency-deposit ratio, thereby increasing the
money multiplier.
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5.
A bank run results in a rise in the currency-deposit ratio and thereby reduces the deposit
multiplier and the money supply.
6.
First, deposit insurance reduces fears of bank failures, which would result in deposit losses. This
enables banks to hold lower reserves and lowers the desired currency-deposit ratio of the public.
Both actions increase the multiplier. Furthermore, if deposit insurance prevents panic shifts to
currency it makes the deposit multiplier more stable.
7. a.
If most disturbances come from the money sector (a shift in money demand), then interest rate
targets work better than money targets. In the IS-LM diagram below we can see that if money
demand increased, the LM-curve would shift to the left and the interest rate would increase. By
targeting the interest rate at i*, and increasing money supply in response to the increase in
demand, the LM-curve stays in its initial position, and the Bank has held the economy in the
original equilibrium.
7.b.
If most of the disturbances come from the expenditure sector, then the Bank of Canada is better
off targeting money supply. If spending increases, the IS-curve shifts to the right and the interest
rate increases. The Bank will make the disturbance worse if it gets the interest rate back to its
original level by increasing money supply. Instead, the Bank should keep money supply (and thus
the LM-curve) stable, to keep the disturbance at a minimum.
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8.
The Bank of Canada has much more control over intermediate targets (money supply or interest
rates) than it does over the ultimate targets (GDP, unemployment or inflation). In addition,
changes in these intermediate targets do not have an immediate effect on the ultimate targets.
Therefore, the Bank gets earlier feedback on the effects of changing its policy instruments.
However, concentrating solely on intermediate targets rather than ultimate targets does not
guarantee that the ultimate targets will be reached.
9.
The concept of arbitrage implies that, in equilibrium, prices will make financial investors equally
willing to buy or sell an asset. If investors are not equally willing to buy and sell an asset, then
there is no opportunity for arbitrage. People buy or sell assets to take advantage of the resulting
profit opportunity. But in doing so, they cause prices to adjust up to the point where no further
arbitrage opportunity exists. Therefore, if people always take advantage of such profit
opportunities, financial markets will always adjust to an equilibrium.
10.
If stock prices follow a random walk, they cannot be predicted from existing information. In
other words, stock price changes only occur if (by surprise) new information becomes available.
This implies that even the best informed financial investors cannot make a killing in the stock
market. In other words, either no riskless profit opportunities exist, or all such opportunities have
already been taken advantage of. If stock prices did not follow a random walk, financial investors
could find ways to reap great benefits by taking advantage of existing profit opportunities that
have not been realized by others.
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Application Questions
1. Nonbank Public
a) Deposits Loans
$1000 $1000
Bank A
Bank B
Deposits Loans
$1000
$1000
b)
Reserves Deposits
-1000
-1000
Reserves Deposits
Deposits
1000
1000 Bank A: -1000
Bank B: +1000
T-bills
Reserves Deposits
Deposits
-1000 Bank A: 1000
Bank B: -1000
c) T-bills
1000
Deposits
-1000
d) T-bills Loans
1000 1000
-1000
-1000
Reserves
1000
Bank of Canada
Loans
1000
T-bills
-1000
2.
The open market purchase has raised bank cash reserves and deposit liabilities by 0.95. With a
reserve ratio of 0.10 the banks have:
(1-0.10)(0.95) = 0.855
in excess reserves. Bank lending would increase by 0.855 in the next round. The total expansion
of the money supply arising from the money multiplier would be
M = (0.0526 +1)/(0.526 + 0.10)B
= 6.89
3. a)
b)
c)
Some variation in the money multiplier comes from variation in the reserve-deposit ratio. Under
100 percent banking, this would be eliminated.
The balance sheets for the bank would differ on the asset side. All assets would be held as
reserves.
Banks would have to use service charges to generate revenue to cover their operating costs.
4. A redeposit of government balances :
Assets
Direct clearers
Bank of Canada
5.
Settlement balances +1
Liabilities
Government Deposits +1
Government Deposits –1
Settlement balances +1
The zero reserve requirement means banks are required to maintain a zero or positive balance
each day in their accounts at the Bank of Canada. In addition, they have a monthly requirement
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that the sum of all positive daily settlement balances less the sum of all daily overdraft loans
taken to avoid negative daily positions, must not be less than zero. If a bank has a negative
cumulative monthly settlement balance it must take an advance at the Bank Rate equal to its
deficiency, or pay a fee equal to the Bank Rate (expressed as a daily rate) times its deficiency.
6.a)
According to the expectations theory of the term structure, the interest of a ten-year bond is
simply the average of all one-year bonds covering these ten years. In other words
n
i = (1/10) it
t=1
b)
If there were no uncertainty, then the interest rate of the ten-year bond should be exactly the
average of all the one-year bonds covering these ten years, in this case, 10 percent. The fact that
the rate is 12 percent, reflects that there is uncertainty and that the ten-year bond offers a risk
premium of 2 percent.
Additional Problems:
1.
How does an increase in the currency-deposit ratio affect the money multiplier? What
about an increase in the reserve-deposit ratio?
The money multiplier is defined as mm = (1 + cu)/(cu + re), where
cu = CU/D = currency-deposit ratio, and
re = R/D = reserve-deposit ratio
An increase in the currency-deposit ratio means that people hold more currency and banks have fewer
funds to create deposits. Therefore the money multiplier decreases. An increase in the reserve-deposit
ratio means that banks now hold more reserves and thus fewer deposits can be created. Again, the money
multiplier decreases.
2.
Assume that an increasing number of department and grocery stores accept credit and
debit cards and more consumers use these cards to do their shopping. How will the money
multiplier and money supply be affected?
If more consumers make purchases using credit or debit cards rather than cash, then less currency is held
and the currency-deposit ratio will be lower. This implies a larger money multiplier and, given a fixed
stock of high-powered money, a larger money supply.
3.
Assume money supply (M) is $1,200 billion, total bank deposits (D) are $800 billion and the
required reserve-deposit ratio is 10%. If the Bank of Canada purchases $3 million worth of
Treasury bills, what is the greatest amount by which total money supply could change?
Why would the actual change in money supply probably be somewhat lower?
We know that M = CU + D ==> CU = M - D = 1,200 - 800 = 400.
If we assume that banks do not hold excess reserves, then
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R = (0.1)D = (0.1)800 = 80 and
B = CU + R = 400 + 80 = 480.
Thus the money multiplier is M/B = mm = 1,200/480 = 2.5.
If the Bank of Canada buys $3 million worth of Treasury bills, then the maximum increase in money
supply is $7.5 million, since
M = mm(B) = 2.5*3 = 7.5,
assuming that banks do not hold excess reserves. However, since banks actually do hold excess reserves,
we can assume that the money multiplier will actually be somewhat smaller than 2.5 and that the effect on
money supply will therefore be less than $7.5 million.
4.
Assume the currency-deposit ratio is 30%, the required reserve-deposit ratio is 8% and the
excess reserve-deposit ratio is 2%. How much would money supply change if the Bank Of
Canada made open market sales valued at $20 million?
The money multiplier is defined as: M/B = mm = (1 + cu)/(cu + re).
For this example the size of the money multiplier is equal to
mm = (1 + 0.3)/(0.3 + 0.08 + 0.02) = (1.3)/(0.4) = 3.25.
An open market sale valued at $20 million would decrease the monetary base (B) by $20 million.
Therefore, money supply (M) would decrease by $65 million, since
M = mm(B) = (3.25)(-20) = - 65.
5.
Assume bank deposits are $3,200 billion, the required reserve-deposit ratio is 10%, and
currency outstanding is $400 billion. What should the Bank of Canada do to decrease
money supply by $100 million?
Ms = Cu + D = 400 + 3,200 = 3,600
and
B = Cu + R = Cu + (.1)D = 400 + 320 = 720
==> money multiplier = Ms/B = mm = 3,600/720 = 5
==> Ms = mm(B)
==> - 100 = 5(B)
==> B = - 20
If the Bank of Canada wants to decrease money supply by $100 million, bank reserves have to be
decreased by $20 million through the open market sale of government securities. (Note: The assumption
was that excess reserves are zero (XR = 0), which may not be true.)
6.
True or false? Why?
"An open market sale raises the monetary base and therefore money supply."
False. An open market sale occurs when the Bank of Canada sells government bonds to the private sector
in return for currency (mostly to banks, so their reserves held in the form of deposits at the Bank will
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decrease). Therefore the monetary base will decrease and money supply will do the same, since banks
cannot loan out as much as previously.
7.
True or false? Why?
"Reserve requirements act as an unfair tax on banks."
True. Banks are forced to hold their reserves either as vault cash or as deposits at the Bank of Canada and
neither earns any interest. Since other financial institutions have no such requirement, it could be argued
that the reserve requirement unfairly taxes banks. On the other hand, reserves guarantee a certain amount
of liquidity for the banking system, which may be necessary should there be a run on banks. The reserves
held as deposits at the Bank also serve to facilitate the check clearing process. For these reasons, the tax
can be viewed as necessary and therefore less "unfair."
8.
Comment on the following statement:
"The elimination of required reserves on bank deposits would decrease the Bank Of
Canada's control over money supply. But if money supply increases uncontrollably, then
high rates of inflation will result."
The Bank of Canada has a number of policy instruments at its disposal to control the level of bank
reserves (and thus money supply), and the required-reserve ratio is only one such instrument. The Bank
can always influence bank reserves through the use of open market operations. Even if reserve
requirements are abolished, the money multiplier will always have a finite value, since banks will always
hold some (excess) reserves to meet their daily cash needs or emergency needs. But if the reserve
requirement were eliminated, then the money multiplier would become larger, since banks would not
choose to voluntarily hold as many reserves as the Bank required. However, large scale open market
operations would still enable the Bank of Canada to exercise great influence over money supply.
9.
Explain why bond prices vary inversely with interest rates.
The present value (price) of a bond is the sum of the discounted yearly interest payments received plus the
present discounted face value of the bond. In the formula for the present value of a bond, the market
interest rate is in the denominator, so an increase in the interest rate will decrease the present value (price)
of the bond. Clearly, the longer the time of maturity, the greater the change in value that comes from an
interest rate change.
10.
List some of the factors that determine the yield (interest rate) on different securities.
The yield (interest) that is paid on securities depends on some of the following factors:
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the lower the liquidity of a security, the higher the yield that has to be paid in order to attract
financial investors;
the higher the default risk of a corporation, the higher the yield it has to pay to compensate for
this increased risk;
the longer the maturity, the higher the interest rate risk, and therefore, the higher the yield
required to compensate for this higher risk;
higher administration costs or different tax treatment also may affect the yield;
foreign securities often have to pay higher yields to compensate for higher risk due to uncertain
political circumstances or possible currency fluctuations.
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11.
If a previously upward-sloping yield curve starts to flatten out and eventually becomes
downward-sloping, how would you interpret this change?
Financial investors have expectations about whether interest rates will increase or decrease and they react
accordingly. If they expect the economy to enter a recession, they expect that interest rates will fall. As
they try to lock in high yields for the long term, the demand for long-term securities increases, leading to
an increase in long-term security prices and thus a decrease in long-term yields. The yield curve will
flatten out and eventually become downward-sloping. Naturally such behaviour is not always guaranteed
and a downward-sloping yield curve can also be the result of decreasing inflationary expectations in
absence of a recession. However, in many cases, the yield curve can be a fairly reliable forecasting
device.
12.
If the yield curve becomes increasingly steeper over time, what kind of economic conditions
would you forecast and why? In your answer explain why the so-called expectations theory
is self-fulfilling.
Financial investors respond to changing expectations about market interest rates. If the yield curve begins
to get steeper, it is a sign that investors expect interest rates to go up in the future. If financial investors
expect interest rates to rise, they fear a capital loss from holding long-term securities, so they try to sell
them, driving their prices down and their yields up. They use these funds to buy short-term securities,
leading to higher short-term security prices and lower short-term yields. The expectations have fulfilled
themselves, as we will get an upward-sloping yield curve. Therefore the yield curve can serve as a
forecasting tool. Since interest rates tend to rise in booms or periods of high expected inflation, we will
see the yield curve getting steeper before such periods.
13.
Explain the relationship between short-term and long-term interest rates according to the
following theories: (i) the expectations theory, (ii) the liquidity preference theory, and (iii)
the market segmentation theory.
The liquidity preference theory suggests that long-term securities have to offer a risk premium because
of their higher interest rate risk, so the yield curve can be expected to slope upward.
According to the expectations theory long-term interest rates are an average of current and future
expected short-term rates. If people expect interest rates to decrease they try to lock in high yields by
buying long-term securities. Therefore the demand for long-term securities goes up and long-term bond
prices increase, that is, long-term yields decline. As people shift out of short-term securities, short-term
security prices decrease and short-term yields go up. We get a downward-sloping yield curve if interest
rates are expected to go down. (An analogous argument can be made for an upward-sloping yield curve.)
Another explanation is provided by the market segmentation theory, which argues that different
financial investors have different preferences in terms of the maturity of the securities they like to hold.
Banks prefer to hold short-term maturity securities while pension plans prefer to hold long-term
securities. The prices (and therefore the yields) of various securities are determined by the relative
demand for and supply of these securities in the money or capital markets. Since these markets are
sufficiently segmented, the shape of the yield curve is determined to some degree by who is in the market
for specific securities at any given time.
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14.
How much would you be willing to pay for a one-year maturity bond with a 15% coupon
rate and a face value of $4,400 if the market interest rate is 10% ? Would you rather buy a
consol that pays you $440 each year for that same price? Why or why not?
The present value of the one-year maturity bond is:
PV = 660/(1 + .1) + 4,400/(1 + .1) = 600 = 4,000 = 4,600.
The present value of the consol is determined as follows:
PV = 440/(.1) = 4,400
Thus, it would be a bad idea to buy the consol for $4,600.
15.
Assume you bought a one-year maturity bond with a coupon rate of 8.1% and a face value
of $10,000 for a price of $9,000. Calculate the current yield and the yield to maturity of this
bond.
The current yield is the interest you receive on the funds you have invested, that is,
i = 810/9,000 = 0.09 = 9.0%
The yield to maturity includes the interest you receive on the funds invested plus the capital gain that
you receive from buying the security at less than face value. Thus
9,000 = [810 + 10,000]/(1+i) ==> 1+i = 10,810/9,000 = 1.201 ==> i = 20.1%
16.
Assume you had a winning ticket from the lottery, paying you $50,000 per year for the rest
of your life. If the market interest rate is 5% and you could sell this ticket to anyone who
wants it, about how much could you get for it?
The present value of this lottery ticket can be calculated by the sum of all yearly future payments,
discounted using an appropriate discount rate. For simplicity, we can treat this as a perpetuity that pays
you a fixed amount R = 50,000 every year forever. The present value of the ticket is therefore
PV = R/i = $50,000/.05 = $1,000,000
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