18.3Determining the Money Supply

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Without banks, there would be no checkable deposits, so the quantity of currency in circulation would equal the money supply. In that case, the money supply would be solely determined by whoever controls government minting and printing presses. But banks do exist, and through their creation of checkable bank deposits they affect the money supply in two ways.

1. Banks remove some currency from circulation: dollar bills that are sitting in bank vaults, as opposed to sitting in people’s wallets, aren’t part of the money supply.

2. Much more importantly, banks create money by accepting deposits and making loans—that is, they make the money supply larger than just the value of currency in circulation.

Our next topic is how banks create money and what determines the amount of money they create.

How Banks Create Money

To see how banks create money, let’s examine what happens when someone decides to deposit currency in a bank. Consider the example of Silas, a miser, who keeps a shoebox full of cash under his bed. Suppose Silas realizes that it would be safer, as well as more convenient, to deposit that cash in the bank and to use his debit card when shopping. Assume that he deposits \$1,000 into a checkable account at First Street Bank. What effect will Silas’s actions have on the money supply?

Panel (a) of Figure 18-4 shows the initial effect of his deposit. First Street Bank credits Silas with \$1,000 in his account, so the economy’s checkable bank deposits rise by \$1,000. Meanwhile, Silas’s cash goes into the vault, raising First Street’s reserves by \$1,000 as well.

Figure 18.4: FIGURE 18-4 Effect on the Money Supply of Turning Cash into a Checkable Deposit
at First Street Bank
Figure 18.4: When Silas deposits \$1,000 (which had been stashed under his bed) into a checkable bank account, there is initially no effect on the money supply: currency in circulation falls by \$1,000, but checkable bank deposits rise by \$1,000. The corresponding entries on the bank’s T-account, depicted in panel (a), show deposits initially rising by \$1,000 and the bank’s reserves initially rising by \$1,000. In the second stage, depicted in panel (b), the bank holds 10% of Silas’s deposit (\$100) as reserves and lends out the rest (\$900) to Maya. As a result, its reserves fall by \$900 and its loans increase by \$900. Its liabilities, including Silas’s \$1,000 deposit, are unchanged. The money supply, the sum of checkable bank deposits and currency in circulation, has now increased by \$900—the \$900 now held by Maya.

This initial transaction has no effect on the money supply. Currency in circulation, part of the money supply, falls by \$1,000; checkable bank deposits, also part of the money supply, rise by the same amount.

But this is not the end of the story because First Street Bank can now lend out part of Silas’s deposit. Assume that it holds 10% of Silas’s deposit—\$100—in reserves and lends the rest out in cash to Silas’s neighbor, Maya. The effect of this second stage is shown in panel (b). First Street’s deposits remain unchanged, and so does the value of its assets. But the composition of its assets changes: by making the loan, it reduces its reserves by \$900, so that they are only \$100 larger than they were before Silas made his deposit. In the place of the \$900 reduction in reserves, the bank has acquired an IOU, its \$900 cash loan to Maya.

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So by putting \$900 of Silas’s cash back into circulation by lending it to Maya, First Street Bank has, in fact, increased the money supply. That is, the sum of currency in circulation and checkable bank deposits has risen by \$900 compared to what it had been when Silas’s cash was still under his bed. Although Silas is still the owner of \$1,000, now in the form of a checkable deposit, Maya has the use of \$900 in cash from her borrowings.

And this may not be the end of the story. Suppose that Maya uses her cash to buy a television from Acme Merchandise. What does Anne Acme, the store’s owner, do with the cash? If she holds on to it, the money supply doesn’t increase any further. But suppose she deposits the \$900 into a checkable bank deposit—say, at Second Street Bank. Second Street Bank, in turn, will keep only part of that deposit in reserves, lending out the rest, creating still more money.

Assume that Second Street Bank, like First Street Bank, keeps 10% of any bank deposit in reserves and lends out the rest. Then it will keep \$90 in reserves and lend out \$810 of Anne’s deposit to another borrower, further increasing the money supply.

Table 18-1 shows the process of money creation we have described so far. At first the money supply consists only of Silas’s \$1,000. After he deposits the cash into a checkable bank deposit and the bank makes a loan, the money supply rises to \$1,900. After the second deposit and the second loan, the money supply rises to \$2,710. And the process will, of course, continue from there. (Although we have considered the case in which Silas places his cash in a checkable bank deposit, the results would be the same if he put it into any type of near-money.)

Table : TABLE 18-1 How Banks Create Money
 Currency in circulation Checkable bank deposits Money supply First stage: Silas keeps his cash under his bed. \$1,000 \$0 \$1,000 Second stage: Silas deposits cash in First Street Bank, which lends out \$900 to Maya, who then pays it to Anne Acme. 900 1,000 1,900 Third stage: Anne Acme deposits \$900 in Second Street Bank, which lends out \$810 to another borrower. 810 1,900 2,710

This process of money creation may sound familiar. In Chapter 17 we described the multiplier process: an initial increase in real GDP leads to a rise in consumer spending, which leads to a further rise in real GDP, which leads to a further rise in consumer spending, and so on. What we have here is another kind of multiplier—the money multiplier. Next, we’ll learn what determines the size of this multiplier.

Reserves, Bank Deposits, and the Money Multiplier

In tracing out the effect of Silas’s deposit in Table 18-1, we assumed that the funds a bank lends out always end up being deposited either in the same bank or in another bank—so funds disbursed as loans come back to the banking system, even if not to the lending bank itself.

In reality, some of these loaned funds may be held by borrowers in their wallets and not deposited in a bank, meaning that some of the loaned amount “leaks” out of the banking system. Such leaks reduce the size of the money multiplier, just as leaks of real income into savings reduce the size of the real GDP multiplier. (Bear in mind, however, that the leak here comes from the fact that borrowers keep some of their funds in currency, rather than the fact that consumers save some of their income.)

Excess reserves are a bank’s reserves over and above its required reserves.

But let’s set that complication aside for a moment and consider how the money supply is determined in a “checkable-deposits-only” monetary system, where funds are always deposited in bank accounts and none are held in wallets as currency. That is, in our checkable-deposits-only monetary system, any and all funds borrowed from a bank are immediately deposited into a checkable bank account. We’ll assume that banks are required to satisfy a minimum reserve ratio of 10% and that every bank lends out all of its excess reserves, reserves over and above the amount needed to satisfy the minimum reserve ratio.

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Frank Cotham, The New Yorker Collection/The CartoonBank

Now suppose that for some reason a bank suddenly finds itself with \$1,000 in excess reserves. What happens? The answer is that the bank will lend out that \$1,000, which will end up as a checkable bank deposit somewhere in the banking system, launching a money multiplier process very similar to the process shown in Table 18-1.

In the first stage, the bank lends out its excess reserves of \$1,000, which becomes a checkable bank deposit somewhere. The bank that receives the \$1,000 deposit keeps 10%, or \$100, as reserves and lends out the remaining 90%, or \$900, which again becomes a checkable bank deposit somewhere. The bank receiving this \$900 deposit again keeps 10%, which is \$90, as reserves and lends out the remaining \$810. The bank receiving this \$810 keeps \$81 in reserves and lends out the remaining \$729, and so on. As a result of this process, the total increase in checkable bank deposits is equal to a sum that looks like:

\$1,000 + \$900 + \$810 + \$729 + . . .

We’ll use the symbol rr for the reserve ratio. More generally, the total increase in checkable bank deposits that is generated when a bank lends out \$1,000 in excess reserves is:

(18-1) Increase in checkable bank deposits from \$1,000 in excess reserves = \$1,000 + (\$1,000 × (1 − rr)) + (\$1,000 × (1 − rr)2) + (\$1,000× (1 − rr)3) + . . .

An infinite series of this form can be simplified to:

(18-2) Increase in checkable bank deposits from \$1,000 in excess reserves = \$1,000/rr

Given a reserve ratio of 10%, or 0.1, a \$1,000 increase in excess reserves will increase the total value of checkable bank deposits by \$1,000/0.1 = \$10,000. In fact, in a checkable-deposits-only monetary system, the total value of checkable bank deposits will be equal to the value of bank reserves divided by the reserve ratio. Or to put it a different way, if the reserve ratio is 10%, each \$1 of reserves held by a bank supports \$1/rr = \$1/0.1 = \$10 of checkable bank deposits.

The Money Multiplier in Reality

In reality, the determination of the money supply is more complicated than our simple model suggests because it depends not only on the ratio of reserves to bank deposits but also on the fraction of the money supply that individuals choose to hold in the form of currency. In fact, we already saw this in our example of Silas depositing the cash under his bed: when he chose to hold a checkable bank deposit instead of currency, he set in motion an increase in the money supply.

The monetary base is the sum of currency in circulation and bank reserves.

To define the money multiplier in practice, it’s important to recognize that the Federal Reserve controls the sum of bank reserves and currency in circulation, called the monetary base, but it does not control the allocation of that sum between bank reserves and currency in circulation. Consider Silas and his deposit one more time: by taking the cash from under his bed and depositing it in a bank, he reduced the quantity of currency in circulation but increased bank reserves by an equal amount—leaving the monetary base, on net, unchanged. The monetary base, which is the quantity the monetary authorities control, is the sum of currency in circulation and reserves held by banks.

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The monetary base is different from the money supply in two ways. First, bank reserves, which are part of the monetary base, aren’t considered part of the money supply. A \$1 bill in someone’s wallet is considered money because it’s available for an individual to spend, but a \$1 bill held as bank reserves in a bank vault or deposited at the Federal Reserve isn’t considered part of the money supply because it’s not available for spending. Second, checkable bank deposits, which are part of the money supply because they are available for spending, aren’t part of the monetary base.

Figure 18-5 shows the two concepts schematically. The circle on the left represents the monetary base, consisting of bank reserves plus currency in circulation. The circle on the right represents the money supply, consisting mainly of currency in circulation plus checkable or near-checkable bank deposits. As the figure indicates, currency in circulation is part of both the monetary base and the money supply. But bank reserves aren’t part of the money supply, and checkable or near-checkable bank deposits aren’t part of the monetary base. In practice, most of the monetary base actually consists of currency in circulation, which also makes up about half of the money supply.

Figure 18.5: FIGURE 18-5 The Monetary Base and the Money Supply
Figure 18.5: The monetary base is equal to bank reserves plus currency in circulation. It is different from the money supply, consisting mainly of checkable or near-checkable bank deposits plus currency in circulation. Each dollar of bank reserves backs several dollars of bank deposits, making the money supply larger than the monetary base.

The money multiplier is the ratio of the money supply to the monetary base.

Now we can formally define the money multiplier: it’s the ratio of the money supply to the monetary base. Before the financial crisis of 2008, the money multiplier was about 1.6; after the crisis it fell to about 0.7. Even before the crisis it was a lot smaller than 1/0.1 = 10, the money multiplier in a checkable-deposits-only system with a reserve ratio of 10% (the minimum required ratio for most checkable deposits in the United States).

The reason the actual money multiplier was so small arises from the fact that people hold significant amounts of cash, and a dollar of currency in circulation, unlike a dollar in reserves, doesn’t support multiple dollars of the money supply. In fact, before the crisis currency in circulation accounted for more than 90% of the monetary base. At the end of 2013, however, currency in circulation was less than a third of the monetary base. What had happened?

The answer is that the financial crisis created an abnormal situation. As explained later in this chapter, a very abnormal situation developed after Lehman Brothers, a key financial institution, failed in September 2008. Banks, seeing few opportunities for safe, profitable lending, began parking large sums at the Federal Reserve in the form of deposits—deposits that counted as part of the monetary base. As a result, currency in circulation no longer dominated the monetary base, and thanks to all those deposits at the Fed the monetary base was actually larger than M1, with the money multiplier therefore less than 1.

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ECONOMICSin Action

Multiplying Money Down

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In our hypothetical example illustrating how banks create money, we described Silas the miser taking the currency from under his bed and turning it into a checkable bank deposit. This led to an increase in the money supply, as banks engaged in successive waves of lending backed by Silas’s funds. It follows that if something happened to make Silas revert to old habits, taking his money out of the bank and putting it back under his bed, the result would be less lending and, ultimately, a decline in the money supply. That’s exactly what happened as a result of the bank runs of the 1930s.

Table 18-2 shows what happened between 1929 and 1933, as bank failures shook the public’s confidence in the banking system. The second column shows the public’s holdings of currency. This increased sharply, as many Americans decided that money under the bed was safer than money in the bank after all. The third column shows the value of checkable bank deposits. This fell sharply, through the multiplier process we have just analyzed, when individuals pulled their cash out of banks. Loans also fell because banks that survived the waves of bank runs increased their excess reserves, just in case another wave began. The fourth column shows the value of M1, the first of the monetary aggregates we described earlier. It fell sharply because the total reduction in checkable or near-checkable bank deposits was much larger than the increase in currency in circulation.

Table : TABLE 18-2 The Effects of Bank Runs, 1929–1933
 Currency incirculation Checkablebank deposits M1 (billions of dollars) 1929 \$3.90 \$22.74 \$26.64 1933 5.09 14.82 19.91 Percent change +31% −35% −25% Data from: U.S. Census Bureau (1975), Historical Statistics of the United States.

Quick Review

• Banks create money when they lend out excess reserves, generating a multiplier effect on the money supply.

• In a checkable-deposits-only system, the money supply would be equal to bank reserves divided by the reserve ratio. In reality, however, the public holds some funds as cash rather than in checkable deposits, which reduces the size of the multiplier.

• The monetary base, equal to bank reserves plus currency in circulation, overlaps but is not equal to the money supply. The money multiplier is equal to the money supply divided by the monetary base.

Question 18.6

1. Assume that total reserves are equal to \$200 and total checkable bank deposits are equal to \$1,000. Also assume that the public does not hold any currency. Now suppose that the required reserve ratio falls from 20% to 10%. Trace out how this leads to an expansion in bank deposits.

Since they only have to hold \$100 in reserves, instead of \$200, banks now lend out \$100 of their reserves. Whoever borrows the \$100 will deposit it in a bank, which will lend out \$100 × (1 − rr) = \$100 × 0.9 = \$90. Whoever borrows the \$90 will put it into a bank, which will lend out \$90 × 0.9 = \$81, and so on. Overall, deposits will increase by \$100/0.1 = \$1,000.

Question 18.7

2. Take the example of Silas depositing his \$1,000 in cash into First Street Bank and assume that the required reserve ratio is 10%. But now assume that each time someone receives a bank loan, he or she keeps half the loan in cash. Trace out the resulting expansion in the money supply.

Silas puts \$1,000 in the bank, of which the bank lends out \$1,000 × (1 − rr) = \$1,000 × 0.9 = \$900. Whoever borrows the \$900 will keep \$450 in cash and deposit \$450 in a bank. The bank will lend out \$450 × 0.9 = \$405. Whoever borrows the \$405 will keep \$202.50 in cash and deposit \$202.50 in a bank. The bank will lend out \$202.50 × 0.9 = \$182.25, and so on. Overall, this leads to an increase in deposits of \$1,000 + \$450 + \$202.50 + . . . But it decreases the amount of currency in circulation: the amount of cash is reduced by the \$1,000 Silas puts into the bank. This is offset, but not fully, by the amount of cash held by each borrower. The amount of currency in circulation therefore changes by −\$1,000 + \$450 + \$202.50 + . . . The money supply therefore increases by the sum of the increase in deposits and the change in currency in circulation, which is \$1,000 − \$1,000 + \$450 + \$450 + \$202.50 + \$202.50 + . . . and so on.

Solutions appear at back of book.