Download Part VIII. Determinants of the Money Supply

Determinants of the Money Supply
In the previous section, we have looked at a very simple model that helps explain what changes
the money supply in the economy. That simple model assumes that the Fed plays the major role
since the banks automatically loan out any additional money they have and all individuals keep
their money in checkable deposits. However, we know that not all banks want to loan out any
additional money they have, and not all individuals want to keep their money in checkable
deposits. In addition, the Fed does not have full control of the reserves (i.e. the Fed cannot force
a bank to take out a loan). Hence, we need to look at a model that allows us to adjust for banks’
and individuals’ behaviors.
In the simple model, the reserves of the banking system is the key target of the Fed. However, the
Fed is not always successful in changing that. The reserves of the banking system can be
influenced by the behaviors of the banks and the general public. Hence, the Fed needs to look at
a broader target that it can control more successfully. In this case, we will look at the monetary
base (or high-powered money) as a potential target for the Fed.
Monetarybase ( MB)  Reserves+ Currency
 RC
We will show in the following scenarios that the impact of the Fed’s action on the monetary base
is not affected by the behaviors of banks and individuals. As we have discussed earlier, the Fed
can actively affect the “money supply” through its discount window operation and open market
operation.
(i) Discount Window Operation
As we have discussed earlier, the Fed can make or recall a discount loan from a bank through its
discount window operation. In an earlier section, we have looked at an example where the Fed
made a discount loan of $1,000 to LaSalle Talman Bank (LTB).
Federal Reserve
Assets
Liabilities
DL +$1000
Reserves +$1,000
LTB
Assets
Liabilities
Reserves +$1,000
DL +$1,000
Chapter 8-1
In this particular scenario, we can see that the Fed’s action through its discount window
operation has a direct impact on a bank’s reserves (and also on the banking system’s reserves
through the multiple deposit creation process).
(ii) Open Market Operation (OMO)
In our earlier discussion on the impact of the Fed’s open market operation on the reserves of a
bank (and the banking system), we make the Fed the dominant player because we made the
assumptions that banks do not hold excess reserves and the public do not hold currency.
However, this is not the case in the real world: Banks do hold excess reserves and the public do
hold currency. In this section, we will examine how the banks’ and the public’s behaviors
influence the impacts of the Fed’s action on reserves and the monetary base.
Before we proceed, we need to point out that we have relaxed the assumption that the Fed only
deals with the banks in its open market operation. From now on, the Fed can trade government
securities with both the banks and the public. In the following scenarios, we will look at how the
purchase of government securities by the Fed affects the reserves in the banking system, the
currency in circulation, and the monetary base. We can easily apply the same analysis to
situations when the Fed sells government securities.
(a) The Fed buying directly from the bank
This scenario is very similar to the scenario we have discussed earlier. Since the Fed bought
$1,000 worth of security from LaSalle Talman Bank, the Fed’s security portfolio would then go
up by $1,000. To pay for those securities, the Fed simply credits LaSalle’s reserves account by
$1,000. As for LaSalle, since it sold $1,000 worth of securities to the Fed, its security portfolio
has gone down by $1,000, but its reserves account with the Fed has gone up by $1,000.
Federal Reserve
Assets
Liabilities
Securities +$1000
Reserves +$1,000
LTB
Assets
Securities -$1,000
Reserves +$1,000
Chapter 8-2
Liabilities
In this particular scenario, we see that the Fed’s action has a direct impact on the bank’s reserves.
Since there is no change in currency, the change in monetary base is the same as the change in
reserves.
(b) The Fed buying directly from an individual
In this scenario, the Fed is buying the securities directly from an individual rather than from a
bank. We will look at the situation when the Fed buys $1,000 of securities from Bob. In this case,
the Fed can pay Bob for the securities either with a check or with cash. We will look at the
impacts of the two payment options separately.
The Fed paying Bob with a check
We will start with the scenario where the Fed pays Bob with a check of $1,000. Since Bob has an
account with LaSalle Talman Bank, he simply deposits that check with the bank. In this case, the
bank’s deposits and reserves will go up by $1,000. The T-accounts of the Fed, LTB, and Bob that
depict the flow of the transaction are presented below:
Federal Reserve
Assets
Liabilities
Securities +$1000
Reserves +$1,000
LTB
Assets
Reserves +$1,000
Bob
Assets
Securities -$1,000
Liabilities
Deposit +$1,000
Liabilities
Deposit +$1,000
In this particular case, when the Fed pay Bob $1,000 with a check for the securities, the reserves
also goes up by $1,000 (assuming that Bob is not withdrawing any of the deposit).
The Fed paying Bob with cash
On the other hand, suppose the Fed pays Bob with cash. In this case, the Fed will have to take
$1,000 of cash out of its vault (which is previously not in circulation) and use it to pay the
individual. If Bob deposits the $1,000 with LaSalle Talman Bank, the cash will become part of
the bank’s vault cash or reserves. In this case, we will have the exact same scenario as above
when the Fed pays Bob with a check. However, it is also possible that Bob simply decides to
Chapter 8-3
keep that $1,000 of cash. In this case, since LaSalle Talman receives no deposit from Bob, it
means that it is out of the picture and its reserves will not change.
Federal Reserve
Assets
Liabilities
Securities +$1000
Currency +$1,000
Bob
Assets
Securities -$1,000
Liabilities
Cash +$1,000
In this case, the currency in circulation will increase by $1,000 but there is no change in the
reserves if Bob decides to keep the cash. As a result, the Fed’s action of buying $1,000 of
government securities will have no impact on reserves but it does increase the currency in
circulation by $1,000 (if Bob decides to keep the cash). However, since the monetary base is
made up of both currency and reserves, the Fed’s action has resulted in an increase of monetary
base by $1,000.
We can further complicate the scenario with Bob deciding to keep $200 of the money received
from the Fed as cash and deposit the other $800 with LaSalle Talman. The T-accounts of the
Fed, LTB, and Bob that depict the flow of the transaction are presented below:
Federal Reserve
Assets
Liabilities
Securities +$1000
Reserves +$800
LTB
Assets
Liabilities
Reserves +$1,000 Deposit +$1,000
Currency +$200
Bob
Assets
Securities -$1,000
Liabilities
Deposit +$800
Cash +$200
As a result, due to Bob’s action of keeping part of the money as cash and depositing the rest into
his checking account, the Fed’s action of buying $1,000 securities from Bob resulted in an
increase in reserves by $800 and an increase in currency by $200. In other words, the Fed’s
action has led to an increase in the monetary base by $1,000. We can easily verify that no matter
how much cash Bob decides to keep, we will always see an increase in the monetary base by
Chapter 8-4
$1,000. Keep in mind that the results from this analysis can also be applied to the situation when
Bob receives a check from the Fed and he decides to withdraw some of it.
Based on the different scenarios we have looked at, the Fed’s action on the reserves and currency
in circulation depends on how an individual keeps the proceeds: checkable deposit, cash or a
combination of both. Hence, the Fed’s OMO action has an uncertain impact on the reserves and
the currency. However, we know that the Fed’s action has a certain (or definite) impact on the
monetary base since it is define as the sum of reserves and currency. We know that no matter
what an individual prefers, the monetary base will always increase by $1,000 in the above
scenario. This $1,000 increase in monetary base can be either a $1,000 increase in reserves or
$1,000 increase in currency.
So far, we have seen that the Fed’s discount window operation (if it is successful) has a definite
impact on the banking system’s reserves, but the impact of the Fed’s open market operation on
the reserves depends on individual’s behaviors. However, we have seen that the Fed does have a
definite impact on the monetary base. Hence, it is better for the Fed to target changing the
monetary base rather than changing the reserves since it has a better control over the monetary
base.
The Fed’s control over the monetary base
It is important to know that it is true that the Fed has better control over the monetary base than
the reserves. However, the Fed does not have full (or total) control over the monetary base. The
Fed has full control over its open market operation, but not necessarily over its discount window
operation. It is true that the Fed can recall the discount loans it made to banks, but it cannot force
banks to take out discount loans from it. Hence, we can reclassify the monetary base into two
categories: one that is fully controlled by the Fed (through its open market operation), and one
that is partially controlled by the Fed (through its discount window operation).
MB  MBn  DL
where
MB n  Non-borrowed monetary base (fully controlled by the Fed through its open
market operation)
DL  Borrowed monetary base, i.e. discount loans (partially controlled by the Fed
through its discount window operation)
Chapter 8-5
A more complicated money supply model
In an earlier section, we have developed a simple model that attempts to explain some of the
factors that affect the money supply (or deposits). That simple model assumes that (i) banks hold
no excess reserves, and (ii) all the deposits created are kept in checking account and are not
withdrawn as cash. As a result, the Fed has sole control over the money supply (or deposits). It is
solely responsible for expanding and shrinking the economy’s money supply. However, this is
not true in real world situations: Banks and individuals can also influence the economy’s money
supply through their behaviors.
In this section, we will develop a money supply model that takes the behaviors of banks and
individuals into consideration. First, we need to define the relationship between the economy’s
money supply (M) and the monetary base (MB):
M  m  MB
where m = money multiplier.
The money multiplier represents the impact of a $1 change in the monetary base on the
economy’s supply. For example, if m = 4 that means a $1 increase in monetary base will lead to a
$4 increase in the money supply. It is key to remember that the money multiplier is always
greater than one, hence any increase in the monetary base will always lead to a much bigger
increase in the money supply. As a result, the monetary base is also known as high-powered
money.
Deriving the money multiplier
From the above section, we know that the money multiplier represents the impact of a $1 change
in the monetary base on the money supply. In this section we will derive the formula for the
money multiplier, and determine the factors that affect the money multiplier.
Before we proceed, we need to first make two assumptions regarding the behaviors of banks and
individuals. It is assumed that:
(1) Individuals hold a constant proportion of cash (i.e. currency) relative to their deposits, i.e. a
constant currency ratio:
Currencyratio 
C
D
Chapter 8-6
For example, if an individual’s currency ratio is 0.5 that means the individual will keep $5 in
cash if there is $10 in a checkable deposit. And if the individual’s checkable deposit rises to
$100, his/her cash holding will also rise to $50 to keep a 0.5 currency ratio.
(2) Banks hold a constant proportion of excess reserves relative to their deposits, i.e. a constant
excess reserves ratio:
Excess reservesratio 
ER
D
For example, if a bank’s excess reserves ratio is 0.15 that means the bank will keep $150 in
excess reserves if there is $1000 in checkable deposits. And if the bank’s checkable deposit rises
to $10,000, its excess reserves holding will also rise to $1,500 to keep a 0.15 excess reserves
ratio.
We know the banking system’s total reserves (R) is made up of two components: required
reserves (RR) and excess reserves (ER):
R  RR  ER
(1)
In addition, we know that the banking system’s required reserves is determined by the required
reserves ratio ( rD ) set by the Fed:
RR  rD  D
(2)
Substituting the required reserves from equation (2) into equation (1), we can rewrite the banking
system’s reserves as follows:
R  (rD  D)  ER
(1’)
Since we know the monetary base is made up of currency in circulation and the banking system’s
reserves:
MB  C  R
 C  ER  (rD  D)
(3)
It is important to note that the first two components of the monetary base defined in equation (3)
represent the nonexpansionary components, and the last component (actually the deposits)
represents the expansionary component. When an individual holds cash (or currency), that part of
Chapter 8-7
the individual’s wealth is not kept in his/her checkable deposits and the bank cannot use them to
create loans. Similarly, if a bank decides to keep a part of its deposits as excess reserves, there
will be a smaller available pool of resources to make loans. Hence, cash and excess reserves do
not contribute to the process of money creation.
We can incorporate the currency and excess reserves ratios into equation (3) and rewrite the
formula for the monetary base as follows:
C
  ER

MB    D   
 D   rD  D 
D
D

 

 C ER

 
 rD   D
D D

(4)
We can rewrite the above equation to express D in terms of MB:
D
1
 MB
(C / D)  ( ER / D)  rD
(5)
Using a simplified M1 as the representation for the economy’s money supply, we can define the
money supply as the sum of currency and checkable deposits:
M C  D
C
C


   D   D  1    D
D
D


(6)
Substituting the formula for D from equation (5), we can rewrite the formula for the money
supply as:
M
1  (C / D)
 MB
(C / D)  ( ER / D)  rD
(7)
Since we know the relationship between the money supply and the monetary base is defined by:
M  m  MB  M  m  MB
Comparing that relationship with equation (7), we know that the formula for the multiplier is:
m
1  (C / D)
(C / D)  ( ER / D)  rD
Chapter 8-8
(8)
The money multiplier of the more complex model is related to the money multiplier of the simple
model we have derived in the previous example. If you recall, we have the following conditions
in the simple model:
(i)
Excess reserves is zero, ER  0 .
(ii)
Currency in circulation is zero, C  0 .
When we substitute these conditions into the complex money multiplier as defined by equation
(8), we will have the simple money multiplier as follows:
m
1 0
1

0  0  rD rD
Factors affecting the money multiplier
Based on the complex money multiplier that we have derived above, we know that it is affected
by three factors:
(1) The currency ratio (C/D)
(2) The excess reserves ratio (ER/D)
(3) The required reserves ratio ( rD )
It is important that we know the intuitions of how each one of those factors affect the money
multiplier.
(1) Currency ratio (C/D)
The currency ratio represents the amount of cash individuals hold relative to the amount of
checkable deposits they have with the banking system. To simplify our analysis, let us assume
that individuals store their wealth either with cash or checkable deposits. If an individual has
currency ratio of 0.8, that means he/she keeps $80 of cash for every $100 he/she has in a
checking account.
Suppose the individual’s currency ratio increases to 0.9, and his/her wealth level remains at
$180. In this case, the individual will hold approximately $85.26 in cash and $94.74. We have
seen that given everything else remains the same, as an individual’s currency ratio increases, that
simply means that the individual is transferring more of his/her wealth from checkable deposit to
currency holding. Since individuals are holding more currency and less deposits (i.e. currency
Chapter 8-9
ratio increases), less “money” can be created by the banking system. As a result, the money
multiplier and the money supply shrink.
(2) Excess reserves ratio (ER/D)
The excess reserves ratio represents the amount of excess reserves a bank with keep for every $1
of deposits it accepts. It is important to remember that this is the amount of reserves a bank keeps
in addition to those that it is required to keep by law (i.e. required reserves). As a bank keeps
more of the deposits as excess reserves (i.e. excess reserves ratio increases), that means there will
be a smaller pool of resources available to make loans. This will lead to shrinkage of the money
multiplier, which in turn leads to shrinkage of the money supply.
(3) Required reserves ratio ( rD )
The required ratio indicates the amount of reserves a bank is required to keep for every $1 of
deposits it accepts. It is important to point out that as of 1993, the reserve requirement is 10% on
transaction deposits (such as checking accounts) and zero on time deposits. The reserve
requirement represents the portion of the deposits that is not available to a bank to make loans.
Hence, as the required reserves ratio increases, the amount of loans a bank can make decreases.
As a result, the money multiplier and the money supply shrink.
Other factors affecting the money supply
We know that changes in currency ratio, required reserves ratio and excess reserves ratio affect
the money multiplier, which in turns affect the money supply. However, those are not the only
factors that affect the money supply. There are other factors that influence the money supply in
the economy. If you recall, the formula for determining the economy’s money supply is as
follows:
M  m  ( MB n  DL )
From the above formula, we know that changes in the nonborrowed monetary base ( MB n ) and
discount loans (DL) will also have an impact on the money supply.
(1) Nonborrowed monetary base ( MB n )
The non-borrowed monetary base is influenced by the Fed’s open market operation. Assuming
that everything else remains the same, we know that a sale of government securities by the Fed
Chapter 8-10
will lead to a reduction in the non-borrowed monetary base, and a purchase of government
securities by the Fed will lead to an increased in the nonborrowed monetary base. As a result,
any decrease (increase) in the nonborrowed monetary base due to an open market sale (purchase)
of government securities will lead to a fall (rise) in money supply (assuming that behaviors of
banks and individuals do not change as a result of the Fed’s actions).
(2) Discount loans (DL)
As a bank borrows more from the Fed, that means the bank will have a larger pool of funds
available to make loans. Assuming that everything else remains the same, this will lead to an
increase in deposits in the economy (through the banking system’s money creation process).
Hence an increase (decrease) in banks’ borrowing from the Fed will lead to an increase
(decrease) in monetary base which in turn results in an increase (decrease) in money supply.
It is important to point out that the Fed’s actions through its discount window and open market
operations will have an impact on the money supply if the banks and individuals do not alter their
behaviors as a result of the Fed’s actions. If this is not the case, then the Fed’s actions might not
have the same desirable effect or any effect at all on the money supply. For example, suppose the
Fed increases its discount loan to LaSalle Bank by $1,000. However, if LaSalle decides to keep
the loan as excess reserves rather than use it to make more loans, then no additional deposits will
be created by the banking system as a result of the increase in discount loan. In other words, the
Fed’s action has a positive impact on the monetary base but LaSalle has altered its behavior in
such a way that it has a negative effect on the money multiplier. In this case, the monetary base
increases as a result of the Fed’s action but the money multiplier decreases as a result of
LaSalle’s action. Those two actions cancelled each other and the money supply remains
unchanged in the economy.
So far, we have examined how changes in certain variables, such as required reserves ratio,
influence the money multiplier and the economy’s monetary base. However, we have not
determined what are some of the factors that influence those variables. To be more specific, we
would like to know:
(1) What affects an individual’s preference for his/her cash and deposits holdings?
(2) What affects a bank’s desire to hold excess reserves?
(3) What affects a bank’s preference to borrow from the Fed?
Chapter 8-11
We will address each one of those questions in the next section.
Chapter 8-12