How the banking system is used to create money.
Suppose that all banks have zero excess reserves. Suppose that Bank A has
the following balance sheet:
Bank A
Assets
R
RR
ER
Loans
Securities
Total
Liabilities + Net Worth
1000
10000
Deposits
1000
0
8000
1000
10000
0
10000
Net Worth
Now suppose that Bank A sells a security to the Fed for $1000. Bank A’s
balance sheet now has $1000 more reserves.
Bank A
Assets
R
RR
ER
Liabilities + Net Worth
2000
10000
Deposits
1000
1000
Loans
8000
Total
10000
0
10000
Net Worth
In this balance sheet let R = total reserves; RR = required reserves, and ER =
excess reserves. The reserve ration is 0.10. Bank A has $8000 in loans (to
keep the picture fairly simple we will ignore securities and most of the other item
on the balance sheet. All deposits will be demand deposits.
Pay particular attention to the increases in reserves and deposits on the balance
sheets. Demand deposits are part of M1. If demand deposits increase by $1.00
then M1 increases by $1.00 as well.
Now suppose that Bank A lends out the $1000 to a business person who spends
it at the local computer store. This person deposits the proceeds in the stores
demand deposit in Bank B. Bank B’s deposits will increase by $1000 so M1 just
increased by $1000. Likewise Banks B’s reserves increase by $1000. Of this
reserve increase $100 will be in required reserves and $900 will be in excess
reserves.
Bank A
Assets
R
RR
ER
Liabilities + Net Worth
1000
10000
Deposits
1000
0
Loans
9000
Total
10000
0
10000
Net Worth
After the loan Bank A is left with zero excess reserves. We will only record
changes to Bank B’s balance sheet as they affect reserves and deposits.
Bank B
Assets
R
+1000
+100
+900
RR
ER
Liabilities + Net Worth
+1000
Deposits
Bank B now lends $900 and the proceeds wind up in a deposit in Bank C.
Bank B
Assets
R
RR
ER
Loans
+100
+100
0
+900
Liabilities + Net Worth
+1000
Deposits
The total increase in M1 at Bank B is $1000 and the total increase in reserves at
Bank B is $100.
Bank C
Assets
R
Liabilities + Net Worth
+900
Deposits
+900
RR
ER
+90
+810
Bank C will increase its deposits by $900 and its required reserves by $90. It can
now loan $810 out of excess reserves. If it does so the balance sheet will be
Bank C
Assets
R
Liabilities + Net Worth
+900
Deposits
+90
RR
ER
Loans
+90
0
+810
Bank C increases deposits by $900 and reserves by $90. M1 increases by $900.
Suppose the proceeds end up as a deposit in Bank D.
Bank D
Assets
R
Liabilities + Net Worth
+810
Deposits
+810
RR
ER
+81
+729
Now Bank D lends out all of its’ excess reserves
Bank D
Assets
R
RR
ER
Loans
Liabilities + Net Worth
+810
Deposits
+81
+81
0
+729
The proceeds wind up in Bank E.
Bank E.
Assets
Liabilities + Net Worth
+729
+729
Deposits
+72.90
+656.10
R
RR
ER
Bank E lends all of its excess reserves
Bank E
R
RR
ER
Loans
Assets
+72.90
Liabilities + Net Worth
+729
Deposits
+72.90
0
+656.10
The increase in deposits thus far has been $1000+900+810+729 (this is also the
increase in M1). The increase in reserves in $100+90+81+72.90. Note that the
increase in deposits is 10 times the increase in reserves.
Recall that
R  RR  ER
where R = total reserves, RR = required reserves, and ER = excess reserves. If
the banking system is willing to drive excess reserves to zero, then
R  RR  ER  RR  0  RR
and because required reserves are a fraction of deposits
RR  rD D
where D = total demand deposits and rD is the reserve ratio. So the change in
demand deposits will be related to the change is reserves by
RR  rD D
D 
1
1
RR  R
rD
rD
1
is called the simple deposit multiplier. The simple deposit multiplier
rD
determines the maximum amount of deposits that can be created with a change
in reserves.
where
Recall that the initial increase in reserves was $1000 so
R  1000
1
1
D  R 
1000  10000
rD
0.1
So the initial increase of $1000 could create as much as $10000 additional
demand deposits. Again this represents the maximum amount of new deposits.
Because demand deposits are part of M1, this also represents the maximum
increase in the nations money supply brought about by a $1000 increase in
reserves.
How small could the increase be? Suppose Bank A did not make the initial loan.
In that case no additional deposits or money would be created. So the amount of
new deposits and new money created will be somewhere between zero and
$10000. This may give some indication of how difficult the Fed can find it to be
to control the money supply. But the key to Fed money supply creation is the
control of reserves. If the Fed wants to change the money supply it does so by
changing reserves.
Money supply contraction
Money supply contraction is a bit more difficult to explain. Actually money supply
contraction is pretty rare.
Figure 1. Money supply growth rates
Figure 1 shows growth rates for M1, M2 and M3 since 1960. Most of the time the
growth rate has been positive. Generally the Fed has reduced the rate of growth
of the money supply rather than actually decreasing it. Rates of growth are
harder to understand than absolute values.
Consider a bank with inadequate excess reserves. This bank may try to build up
excess reserves by calling in loans. When the loan is repaid with a demand
deposit that reduces M1. If the bank does not issue a new loan, then M1 stays
reduced.
If the Fed sell a bond to a bank, this will reduce a banks excess reserves and
starts the process by which the bank builds up its excess reserves. If the Fed
sell a bond to a member of the public who pays with a demand deposit that
reduces deposits but increases currency. These offset one another. But the
demand deposit reduction also decreases excess reserves which starts off the
process described above.
Assets
+1000
R
RR
-1000
-100
Liabilities + Net Worth
Deposits
ER
Loans
+1100
-1000 +1000
Net worth
When a depositor pays off a loan, deposits fall in the banking system and this will
reduce the money supply if the bank does not re—lend the money taken in when
the loan is repaid.
The Fed’s balance sheet and the monetary base
The monetary base is a convenient way of viewing how the Fed might control
reserves. First consider the Fed’s balance sheet:
The Fed’s balance sheet (end of 1999)
Assets
Securities
Discount loans
Gold and SDRs
Coin
Items in process of
collection
Other assets
490.7
0.2
18.2
0.3
6.0
528
15.5
4.5
0.2
4.9
56.8
19.1
Total
572.2 572.2
Liabilities + Net Worth
Federal Reserve Notes
outstanding
Bank deposits (reserves)
U.S Treasury deposits
Foreign deposits
Deferred availability cash
items
Other liabilities and
capital
Total
Assets
1. Securities: These are mostly government securities that the Fed has
purchased. Usually these are Treasury securities.
2. Discount loans: Loans the Fed has made to banks.
3. Gold and SDRs. SDRs are special drawing rights that have been issued
by the International Monetary Fund. They have generally replaced gold as
a means of settling international transactions.
4. Coin. Coins are issued by the Treasury. The Fed holds some.
5. Cash item in the process of collection. Check that have not yet cleared
the bank of the check writer. The Fed takes the checks in and these are
an asset until the proceeds have been collected.
6. Other Federal Reserve Assets: The Fed’s physical assets (computers,
buildings, etc) pus holding of foreign currency and government bonds.
Liabilities.
1. Federal Reserve notes outstanding: These are the bills in your wallet.
They have printed “Federal Reserve note” on them. This is cash in the
hands of the nonbank public.
2. Reserves: These are mostly deposits that member banks have made with
the Fed. The member make deposits with the Fed just like we make
deposits with our banks. The member banks must have deposits as least
as large are required reserves with the Fed. The reserves also consists of
vault cash—that is cash in the hands of banks.
3. Treasury deposits: The Fed serves as the Treasury’s bank. The Treasury
writes checks on the Fed.
4. Foreign and other deposits: Deposits made by foreign governments,
foreign central banks, and international agencies such as the U.N. and by
U.S. government agencies such as the FDIC.
5. Deferred—availability cash items. Remember the cash items in the
process of collection? The Fed does not immediately credit the receiving
bank.
6. Other Federal Reserve liabilities and capital accounts. The member
banks are required to buy shares in the Fed. This is the capital.
Monetary Base
The monetary base (MB) consists of the Fed’s monetary liabilities (Federal
Reserve notes + Reserves in the banking system) plus the Treasury’s monetary
liabilities (Treasury notes + coins). The monetary base is also called high power
money.
MB = (Federal Reserve notes + Treasury liabilities – coins owned by Fed) +
reserves
MB = C + R
Where C is currency in the hands of the nonblank public, that is Federal reserve
notes, Treasury currency and coins in the hands of the non bank public (Note
that the coins in the expression above are coins that the Fed owns, not
coins in the hands of the nonblank public). Another way of looking at this is
that the money base is equal to vault cash, deposits at the Fed, and currency in
circulation. Note that vault cash is part of a banks reserves. We can do a little
accounting
Assets = Liabilities = Federal Reserve notes + reserves + [U.S. Treasury
deposits + Foreign and other deposits + Deferred availability cash items + other
Federal Reserve liabilities and capital].
Or
Federal Reserve notes + reserves = (Assets) – [U.S. Treasury deposits - Foreign
and other deposits - Deferred availability cash items - other Federal Reserve
liabilities and capital].
Now put in the items that make up assets.
Federal Reserve notes + reserves = (Securities + discount loans + gold and
SDRs + coins +cash items in the process of collection + other Federal
Reserves assets) - [U.S. Treasury deposits - Foreign and other deposits Deferred availability cash items - other Federal Reserve liabilities and
capital].
Now some arranging
Float = cash items in the process of collection – deferred availability cash items
Move coins to the left hand side
Add Treasury currency to both sides
MB = Federal Reserve notes +Treasury currency – coins + reserves
MB = Securities + discount loans + gold and SDRs +Float + other Federal
Reserves assets + Treasury currency - U.S. Treasury deposits - Foreign
and other deposits - other Federal Reserve liabilities and capital.
Now we can determine things that will increase or decrease MB
Factor
Securities
Discount loans
Gold and SDRs
Float
Other Federal Reserve
assets
Treasury currency
Change in Factor





Change in MB







Treasury deposits with
Fed
Foreign and other
deposits
Other Fed liabilities and
capital






Controlling the monetary base versus controlling reserves
Open market operations
Suppose that the Fed buys a $1000 security from a bank.
The banks balance sheet before the sale of the security
Assets
R
1000
10000
1000
0
RR
ER
Loans
Securities
Total
8000
1000
10000
Liabilities + Net Worth
Deposits
0
10000
Net Worth
The banks balance sheet after the sale
Assets
R
2000
10000
1000
1000
RR
ER
Loans
Securities
Total
8000
0
10000
Liabilities + Net Worth
Deposits
0
10000
Net Worth
The bank deposits the reserves with the Fed.
The change in the Fed’s balance sheet
Assets
Securities
Liabilities
+1000
+1000
Reserves
MB = C + R and reserves have increased by $1000 so MB increases by $1000
as well.
Suppose that the security had been owned by a member of the nonblank public
(us). If we deposit the Fed’s check in our bank
Change in our bank’s balance sheet
Assets
Reserves
Liabilities
+1000
+1000
Deposits
Change in the Fed’s balance sheet
Assets
Securities
Liabilities
+1000
+1000
Reserves
In this case R increases and so does the monetary base MB=C+R.
Suppose rather than deposit the proceeds with our bank we take out $1000 in
cash. The banks reserves are unchanged. It gets $1000 from the Fed which is
an increase in reserves but loses $1000 in vault cash (a decrease in reserves).
The Fed gets the security, but now has an additional $1000 liability in the form of
currency in circulation (the bank will likely ask the Fed to replenish the vault
cash).. We get $1000 in cash. So C increases and MB = C+R increases but R
does not change. The Fed’s balance sheet is
Changes in the Fed’s balance sheet.
Assets
Securities
+1000
+1000
Liabilities
Currency in circulation
The Fed was able to increase the monetary base by $1000 in both cases.
Reserves increased by $1000 only in the case where the individual deposits the
Fed’s check with his bank.
The public decides to hold more currency
Suppose that a person decides to take out $1000 in cash from his checking
account
The banks balance sheet
Assets
Reserves
Liabilities
-1000
-1000
Deposits
The Fed’s balance sheet
Assets
Liabilities
-1000
+1000
Reserves
Currency in circulation
From MB = C+R we see that C has increased by $1000 while R has decreased
by $1000. So MB remains unchanged while there has been a decrease in
reserves. NOTE: the decrease in reserves will tend to reduce the money supply
however.
Class I
Discount loans
Suppose that a bank wishes to build up its reserve position by borrowing from the
Fed. If the Fed agrees it will give the bank a discount loan.
The bank’s balance sheet
The Fed’s balance sheet
MB = C+R and both MB and R increase by $1000