Without banks, there would be no chequeable 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 chequeable deposits they affect the money supply in two ways. First, 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. Second, and 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.

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 $1000 into a chequeable account at First Street Bank. What effect will Silas’s actions have on the money supply?

Figure 14-5a shows the initial effect of his deposit. First Street Bank credits Silas with $1000 in his account, so the economy’s chequeable deposits rise by $1000. Meanwhile, Silas’s cash goes into the vault, raising First Street’s reserves by $1000 as well.

This initial transaction has no effect on the money supply. Currency in circulation, part of the money supply, falls by $1000; chequeable 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 neighbour, Maya. The effect of this second stage is shown in Figure 14-5b. 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.

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 chequeable 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 $1000, now in the form of a chequeable 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 and a DVD player 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 chequeable 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 14-1 shows the process of money creation we have described so far. At first the money supply consists only of Silas’s $1000. After he deposits the cash into a chequeable deposit and the bank makes a loan, the money supply rises to $1900. After the second deposit and the second loan, the money supply rises to $2710. And the process will, of course, continue from there. (Although we have considered the case in which Silas places his cash in a chequeable deposit, the results would be the same if he put it into any type of near-money.)

This process of money creation may sound familiar. In Chapter 11 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.

In tracing out the effect of Silas’s deposit in Table 14-1, 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.)

But let’s set that complication aside for a moment and consider how the money supply is determined in a “chequeable-deposits-only” monetary system, where funds are always deposited in bank accounts and none are held in wallets as currency. That is, in our chequeable-deposits-only monetary system, any and all funds borrowed from a bank are immediately deposited into a chequeable bank account. We’ll assume that banks have a desired (or voluntary) 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 desired reserve ratio.

Now suppose that for some reason a bank suddenly finds itself with $1000 in excess reserves. What happens? The answer is that the bank will lend out that $1000, which will end up as a chequeable deposit somewhere in the banking system, launching a money multiplier process very similar to the process shown in Table 14-1.

In the first stage, the bank lends out its excess reserves of $1000, which becomes a chequeable deposit somewhere. The bank that receives the $1000 deposit keeps 10%, or $100, as reserves and lends out the remaining 90%, or $900, which again becomes a chequeable 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 chequeable deposits is equal to a sum that looks like:

We’ll use the symbol rr for the reserve ratio. More generally, the total increase in chequeable deposits that is generated when a bank lends out $1000 in excess reserves is:

As we saw in Chapter 11, an infinite series of this form can be simplified to:

Given a reserve ratio of 10%, or 0.1, a $1000 increase in excess reserves will increase the total value of chequeable deposits by $1000/0.1 = $10 000. In fact, in a chequeable-deposits-only monetary system, the total value of chequeable 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 chequeable deposits.

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 chequeable deposit instead of currency, he set in motion an increase in the money supply.

To define the money multiplier in practice, it’s important to recognize that the Bank of Canada 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.

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 $10 bill in someone’s wallet is considered money because it’s available for an individual to spend, but a $10 bill held as bank reserves in a bank vault or deposited at the Bank of Canada isn’t considered part of the money supply because it’s not available for spending. Second, chequeable deposits, which are part of the money supply because they are available for spending, aren’t part of the monetary base.

Figure 14-6 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 chequeable or near-chequeable 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 chequeable or near-chequeable 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.

Now we can formally define the money multiplier: it’s the ratio of the money supply to the monetary base. The (actual) money multiplier in Canada, using M1 as our measure of money, has fluctuated between 6.1 and 9.1 from August 2003 to August 2012, with the average being 7.3. On the other hand, using M2+ as our measure of the money supply, during this period, the money multiplier fluctuated between 18.9 and 22.8, with the average being 20.7. How do these numbers compare with our money multiplier formula? The voluntary reserve ratio in Canada during the same time horizon was about 0.04 (i.e., 4%). That implies a money multiplier in a chequeable-deposits-only system of 1/.04, or 25. (Since there is no required reserve ratio, this is the ratio of reserves to deposits that banks desire to hold.) To be precise, that number should be interpreted as the maximum (potential) change in money supply when there is a unit change in monetary base. In this case, with a voluntary reserve ratio of 4%, a unit increase in monetary base will lead to a maximum increase in money supply of 25. As you can see, the actual money multiplier is small because 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, currency in circulation normally accounts for more than 90% of the monetary base.

That describes what happened during normal times, when the economy was not in a crisis. But during “abnormal” times, the money multiplier can fall dramatically. Take the U.S. as an example. Usually the money multiplier in the United States, using M1 as the measure of money, fluctuates between 1.5 and 3.0. During the U.S. recession of 2007–2009, it fell to about 0.7. What happened? As we explain later in this chapter, and at greater length in Chapter 17, a very abnormal situation developed when Lehman Brothers, a key financial institution in the U.S., failed in September 2008. The American banks, seeing few opportunities for safe, profitable lending, began parking large sums at the Federal Reserve, the U.S. central bank, in the form of deposits—deposits that counted as part of the monetary base. As a result, currency in circulation in January 2012 made up only 40% of the monetary base, and in 2011 the monetary base was actually larger than M1, with the money multiplier therefore less than 1.