This document contains material from the 6th (next) edition of your textbook, Chapter 13, which won’t be
in print until some time next year. It has a different approach to changes in the money supply, which is
the approach I’ll be using in lecture. If you want a source for the approach in lecture, read these pages in
place of pp. 365 – 372 in your textbook.
The Fed and the Money Supply
The main type of Fed action that changes the money supply is called an open market operation.
In an open market operation, the Fed buys or sells government bonds in the
bond market.
When the Fed buys government bonds, it conducts an open market purchase. Selling government bonds is an
open market sale. Let’s consider open market purchases first.
How Open Market Purchases can Increase the Money Supply
How might an open market purchase cause the nation’s money supply to increase? We’ll make two
special assumptions for now to keep our analysis as simple as possible:
1. Banks never hold excess reserves (i.e., they never hold reserves beyond the minimum legal or
necessary amounts)
2. Households and businesses are satisfied holding the amount of cash they are currently holding
(that is, households do now withdraw from or deposit cash into their banks).
We’ll also assume that the required reserve ratio is 0.1, so that each time checking deposits rise by $1,000
at a bank, its reserves must rise by $100.
With these assumptions, let’s see what happens when the Fed purchases government bonds. Specifically,
we’ll suppose the Fed buys $100,000 worth of bonds from Acme Bond Company, a bond trading firm that
has its own checking account with Mid-Size national bank.
When the Fed buys the bonds from Acme, it will pay with a $100,000 check. Acme, in turn, will deposit
this check into its account at Midsize National Bank. Midsize will immediately transmit an image of the
check to the Fed, which will credit Midsize’s reserve account for $100,000 million. Starting from the
initial balance sheet you saw earlier in Table 1, Midsize’s balance sheet will now undergo the following
changes:
Changes in Midsize National Bank’s Balance Sheet:
Action
Change in Assets
Acme deposits $100,000
check from Fed
+ $100,000 in reserves
Change in Liabilities
+ $100,000 in checking accts
Notice that in the table above, we show only changes in Midsize’s balance sheet. Other balance sheet
items—such as property and buildings, loans, government bonds, or shareholder’s equity—do not change,
so they are not listed here.
As you can see, Midsize has gained an asset—reserves—so we enter “+$100,000 in reserves” on
the left side of the table. But Midsize also has a new liability: $100,000 in Acme’s checking account.
Since Midsize’s balance sheet was in balance before Acme’s deposit, and since assets and liabilities both
grew by the same amount ($100,000), we know that the balance sheet still balances. As before, total assets
are equal to total liabilities plus shareholder’s equity.
Before we go further, let’s take note of two important things that have happened. First, the Fed, by
conducting an open market purchase, has injected $100,000 in reserves into the banking system. So far,
these reserves are being held by Midsize Bank in its reserve account at the Fed.
The second thing to notice is easy to miss: The money supply has already increased. Why?
Because checking accounts are part of the money supply, and they have increased by $100,000. As you
are about to see, even more money will be created before our story ends.
To see what will happen next, let’s take the point of view of Midsize’s manager. She might reason
as follows: “Our checking accounts have just increased by $100,000. So our reserves must rise by 10
percent of that amount, or $10,000. But our actual reserves have gone up by much more than that:
$100,000. Therefore, we now have excess reserves equal to $100,000 - $10,000 = $90,000. Since the Fed
is paying such a low interest rate on these excess reserves, it would be more profitable to lend them out.”
So Midsize will want to lend out $90,000.
Midsize could lend out $90,000 in cash from its vault. It would be more typical, however, for the
bank to issue a $90,000 check to the borrower. Let’s suppose the borrower is Paula, who wants a loan to
buy new ovens for her restaurant, Paula’s Pizza. When Paula deposits the $90,000 check from Midsie into
her own bank account (at a bank we’ll call “Second Bank”), the Federal Reserve—which keeps track of
these transactions for the banking system—will transfer $90,000 from Midsize’s reserve account to
Second Bank’s reserve account. The loan and the loss of reserves at Midsize will cause further changes in
its balance sheet, as follows:
Changes in Midsize National Bank’s Balance Sheet:
Action
Change in Assets
Midsize Lends out Excess
Reserves of $90,000
Change in Liabilities
- $90,000 in reserves
+ $90,000 in loans
By making the loan, Midsize has given up $90,000 in reserves in exchange for an asset of equal value—
the $90,000 loan. (Remember: While loans are liabilities to the borrower, they are assets to banks.) Both
changes are seen on the assets side of the balance sheet.
Let’s now combine everything that has happened to Midsize’s balance sheet, from the moment it
got Acme’s deposit to the lending out of its excess reserves. Reserves first rose by $100,000, then fell by
$90,000, so their final change was +$10,000. Midsize also has $90,000 more in loans on the asset side,
and $100,000 more in checking accounts on the liabilities side. From beginning to end, these are the net
changes that have taken place on Midsize’s balance sheet:
Changes in Midsize National Bank’s Balance Sheet:
Action
Change in Assets
Change in Liabilities
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Combined Effect of Acme’s
+$10,000 in reserves
+ $100,000 in checking accts
Deposit and Midsize’s Loan
+ $90,000 in loans
Notice that Midsize no longer has excess reserves: Compared to its initial situation, Midsize’s now has
$100,000 more in checking accounts, and is holding $10,000 more in reserves. Its reserves rose by 10
percent of its checking accounts—just what a 10 percent required reserve ratio calls for. When a bank has
no excess reserves, we say that it is “fully loaned up.”
But there is still more to our story. Recall that when Midsize lent money to Paula, and she
deposited the loan proceeds into her checking account at Second Bank, the Fed added $90,000 to Second
Bank’s reserve account. So now Second Bank has excess reserves. Because its checking accounts rose by
$90,000, it needs to hold 10 percent of that (or $9,000) as reserves, leaving it free to lend out the
remaining $81,000. After making the loan, Second Bank will be left with a net increase of $9,000 in
reserves ($90,000 minus the $81,000 loaned out), and its own balance sheet changes as follows:
Changes in Second Bank’s Balance Sheet:
Action
Change in Assets
Combined Effect of Paula’s
Deposit and Second Bank’s
Loan
+$9,000 in reserves
Change in Liabilities
+ $90,000 in checking accts
+ $81,000 in loans
As you might have guessed, this isn’t the end of the story either. Now some other bank (Third
Bank) has just received the proceeds of the $81,000 loan made by Second Bank. Third Bank’s reserves
will rise by $81,000, it will hold onto $8,100 of those reserves, and lend out the excess ($72,900). And the
process will continue. At each bank, more checking accounts are created, so the money supply increases
at each stage. But each bank gets less in reserves, and creates less new checking accounts, than the bank
before. Eventually, the newly created checking accounts are so small that we can safely ignore them.
Table 2 summarizes the increases in checking accounts, reserves and loans that will occur
throughout the entire banking system. Notice that, at each bank checking accounts have increased by 10
times the increase in reserves, so no bank is holding excess reserves.
Now note the total increase in checking accounts in the entire banking system: $1,000,000. How
did we get this number? We know the $100,000 of reserves the Fed injected into the system are all being
held by one bank or another, and all are required (there are no excess reserves). But with a required
reserve ratio of 0.1, an additional $100,000 in total reserves will be required only if banks have, in total,
an additional $1,000,000 in checking accounts.
Table 2: Effects of a $100,000 Open Market Purchase
Bank
Midsize National
Second Bank
Third Bank
Fourth Bank
…
Total Increase at
Checking
Accounts
+$100,000
+$90,000
+$81,000
+$72,900
…
+$1,000,000
Reserves
Loans
+$10,000
+$9,000
+$8,100
+$7,290
…
+$100,000
+$90,000
+$81,000
+$72,900
+$65,610
…
+$900,000
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All Banks
The Money Multiplier
Let’s go back and summarize what happened as a result of the Fed’s open market purchase in our
example. The Fed injected $100,000 in reserves into the banking system. As a result, checking deposits
and the money supply rose by $1 million—10 times the injection in reserves. As you can verify, if the Fed
had injected twice the amount of reserves ($200,000), the money supply would have increased by 10
times that amount ($2 million). In fact, whatever the injection of reserves, total checking deposits and the
total money supply will increase by a factor of 10, so we can write:
∆Money Supply = ∆Checking Deposits = 10 x (reserve injection)
The injection of reserves must be multiplied by the number 10 in order to get the change in the money
supply that it causes. For this reason, we can say 10 is the money multiplier in this example.
The money multiplier is the number by which we multiply the injection of
reserves to get the total change in the money supply.
The size of the money multiplier depends on the value of the required reserve ratio (RRR). If the RRR
had been 0.20 instead of 0.10, then each dollar of checking deposits would require 20 cents in reserves, or
each dollar of additional reserves would support an additional $5 in deposits. In that case, our formula
would be
∆ Money Supply = 5 x (reserve injection)
You may have already spotted the pattern here: In each case, the money multiplier is one divided by the
required reserve ratio.
For any value of the required reserve ratio (RRR), the formula for the money
multiplier is 1/RRR.
In our example, the RRR was equal to 0.1, so the money multiplier had the value 1/0.1 = 10.
Using our general formula for the money multiplier, we can state what happens when the Fed injects
reserves into the banking system as follows:
∆ Money Supply = [1/RRR] x (∆Reserves)
How an Open Market Sale Can Decrease the Money Supply
Just as the Fed can increase the money supply by purchasing government bonds, it can also decrease the
money supply by selling government bonds—an open market sale. Where does the Fed get the
government bonds to sell? It has hundreds of billions of dollars worth of government bonds from open
market purchases it has conducted in the past. On average, the Fed tends to increase the money supply
each year, so it conducts more open market purchases than open market sales, and its supply of bonds
keeps growing. So, except in unusual circumstances, we needn’t worry that the Fed will run out of bonds
to sell.
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The effects of an open market sale are very similar to the effects of an open market purchase, but in
the opposite direction. However, keeping track of what happens can be a bit tricky, so let’s look at the
first few steps. We’ll suppose that the Fed now sells $100,000 in government bonds to Acme bond dealers.
Acme will pay with a $100,000 check drawn on its account at Midsize. When the Fed gets the check, it
will settle with Midsize by deducting $100,000 from the bank’s reserve account. Midsize’s balance sheet
will thus change as follows:
Changes in Midsize National Bank’s Balance Sheet:
Action
Change in Assets
Change in Liabilities
Acme writes a check for
$100,000 to pay the Fed
- $100,000 in
reserves
- $100,000 in checking
accts
Now Midsize’s manager reasons as follows: “Our checking accounts have just decreased by $100,000.
So our required reserves are $10,000 less than before. But our actual reserves have dropped by much more
than that: $100,000. Therefore, we now have deficient reserves equal to $100,000 - $10,000 = $90,000.
We’ll have to somehow get another $90,000 in reserves to meet our requirements.” A bank that needs to
acquire additional reserves has a few different options. But here, we’ll explore just one of them: calling
in loans.
In theory, calling in a loan means the bank would tell borrowers such as Paula’s Pizza, “You know that
new loan we gave you? Actually, we need it back.” But in reality, bank loans are for specified time
periods, and a bank cannot actually demand that a loan be repaid early. Our conclusion still holds,
however. Most banks have a large volume of loans outstanding, with some being repaid each day.
Typically, the funds will be lent out again the very same day they are repaid. A bank that needs to acquire
reserves will simply reduce its rate of new lending on that day, thereby reducing its total amount of loans
outstanding. This has the same effect as “calling in a loan.”
The resulting changes for Midsize’s balance sheet are as follows:
Changes in Midsize National Bank’s Balance Sheet:
Action
Change in Assets
Change in Liabilities
Midsize “calls in” $90,000 + $90,000 in reserves
in loans (reduces its - $90,000 in loans
outstanding loans volume
by $90,000)
What happens next? The $90,000 in loans paid back to Midsize came from checking accounts at some
other bank, Second Bank. So now Second bank has lost $90,000 in reserves and checking accounts, and
will have to “call in” loans equal to $81,000. And the process continues.
Keeping in mind that a withdrawal of reserves is a negative change in reserves, we can still use the
money multiplier:
∆Money Supply = [1/RRR] x (∆Reserves)
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Applying it to our example, we have:
∆Money Supply = [1/0.1] x (-$100,000) = -$1 million
In other words, the Fed’s $100,000 million open market sale causes a $1 million decrease in the money
supply.
Some Important Provisos about the Money Multiplier
The process of money creation and destruction as we’ve described it illustrates some basic ideas. But our
formula for the money multiplier—1/RRR—is oversimplified. Among other things, it ignores changes in
the behavior of the public and the banks that can reduce the value of the money multiplier.
Changes in the Public’s Cash Holdings
In our simple story, we’ve assumed that the public does not change its cash holdings as the money supply
changes. But as the money supply increases, the public will usually want to hold part of the increase in
checking accounts, and part of the increase in cash. As a result, in each round of the money-creation
process, some reserves will leak out of the banking system in the form of cash. This will lead to a smaller
increase in lending and checking accounts than in our simple story.
Increased Reserve Holdings
Another assumption we’ve made in our simple story of money creation is that banks are always “fully
loaned up”; that is, they hold the minimum required amount of reserves, and create the maximum amount
of new checking deposits (the maximum amount of new loans). In reality, as we discussed earlier, banks
sometimes hold excess reserves. If banks decide to increase their excess reserves as the Fed is injecting
new reserves, each bank will lend out less than in our simple story, and the money supply will increase by
less. This tends to make the money multiplier smaller than it would otherwise be.
It is even possible for the money multiplier to be zero. If, for example, interest rates dropped so low –
say, down to the interest rate the Fed pays on reserves—then any new reserves injected into the system
will be held by banks as excess reserves. Every bank manager would reason, “Why should we lend out
funds if we can earn the same rate of return – with no risk—by holding the funds as reserves at the Fed?”
Without new lending, the injection of reserves cannot create new money, so the money multiplier would
be zero.
Other Fed Actions That Change the Money Supply
Open market purchases and sales are the most common way the Fed changes the money supply. But there
are three additional Fed actions that can, at least in theory, change the money supply as well.
Changes in the Required Reserve Ratio
As long as banks are bound by legal reserve requirements, the Fed can set off the same process of deposit
we’ve been describing by lowering the required reserve ratio. For example, suppose the Fed lowered the
required reserve ratio from 0.10 to 0.05. Suddenly every bank in the system would find that its reserves—
which used to support 10 times their value in checking deposits—could now support 20 times their value.
To earn the highest profit possible, banks might then increase their lending, creating new checking
deposits in the process. The money supply would increase.
On the other side, if the Fed raised the required reserve ratio, the process would work in reverse: All
banks would suddenly find that—given their reserves—their checking accounts exceed the legal
maximum. They would be forced to reduce their volume of outstanding loans, and the money supply
would decrease.
For a variety of reasons, however, the Fed cannot count on the effectiveness of this tool. For example,
suppose banks are already holding excess reserves. Then lowering the required reserve ratio will only
make the bank regard more of its existing reserves as “excess,” while raising the ratio will just make the
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bank regard less of its reserves as “excess.” Neither action would change the amount of lending or total
checking deposits.
Not surprisingly, changes in the required reserve ratio are rare in the United States. The most recent
change was in April 1992, when the Fed lowered the ratio for most checking deposits from 12 percent to
10 percent. But in some countries—such as China—the ratio is changed much more often, and is one of
the key tools of the central bank.
Changes in the Discount Rate
The discount rate, mentioned earlier, is the rate the Fed charges banks when it lends them reserves. In
principle, a lower discount rate that enables banks to borrow reserves from the Fed more cheaply, might
encourage banks to borrow more of them. Borrowed reserves works just like any other injection of
reserves into the banking system: They increase the money supply.
On the other side, a rise in the discount rate would make it more expensive for banks to hang on to
borrowed reserves, so they would pay back some reserves they had borrowed. This withdrawal of reserves
from the banking system would lead to a decrease in the money supply.
So much for the theory. In reality, except during periods of great financial turmoil, banks have been
hesitant to borrow from the Fed at all. They fear that potential investors will see such borrowing as a sign
of weakness. After all, if the bank is turning to the Fed, it must be having trouble raising funds through
customer deposits or other privately available means. Because of this hesitancy to borrow from the Fed,
changes in the discount rate typically have little effect on bank borrowing, bank reserves, or the money
supply. Although the Fed changes the discount rate often, it is usually combined with other, more
powerful Fed actions (such as open market operations) to achieve the Fed’s goals.
Changes in the IOR Rate
Before the Fed began paying interest on reserves (IOR) in 2008, a bank’s opportunity cost for holding
reserves was the interest it could earn by lending them out. But once the Fed started paying IOR, the
opportunity cost of holding reserves was reduced. If the Fed lowers the IOR rate, the opportunity cost of
holding excess reserves rises. So lowering the IOR rate is another tool the Fed can use to encourage bank
lending, and in the process, increase the money supply. Similarly, an increase in the IOR rate would
reduce the opportunity cost of holding excess reserves; banks would decrease their volume of loans and
hold more excess reserves instead. The money supply would shrink.
From 2008 to 2011, the Fed kept the IOR rate very low (0.25 percent), and did not use changes in the
IOR rate as a policy tool. In the future, however, many economists believe that changes in IOR rate will
become one of the Fed’s major policy tools.
***
In the next chapter, we’ll be combining what you’ve learned about banks, the Fed, and the money
supply to explore how the Fed guides the macroeconomy. But what you’ve already learned about these
topics can help you understand a potential threat to the financial system: bank failures and banking panics.
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