The money multiplier, re-examined
Philip George
Abstract: The idea of the money multiplier is unhesitatingly accepted by all schools of
economics. So non-controversial is the idea that it finds a place in nearly every
undergraduate economics text. In recent times a few economists like Prof Steve Keen
have cast doubts on it but only to suggest that multiple deposit expansion can take place
even before required reserves are in place. This paper argues that the idea of money
multiplication is based on a simple error and that the multiplier can never be greater than
1.
JEL: E4, E5, E51
Keywords: Money multiplier, credit deposit expansion
Correspondence: 17 Kairali Nagar, Upper Meridian Road, Kuravankonam, Trivandrum
695003, Kerala, India
[email protected]
Introduction
There are not many things that Keynesians and Austrians agree upon today but the money
multiplier is one of them. This modern-day agreement is a little strange when you
consider that John Maynard Keynes did not mention the money multiplier in The General
Theory of Employment, Interest and Money and that Ludwig von Mises "resisted basing
his analysis on the study of the credit expansion multiplier".
The fact that both Keynes and Mises found no use for the deposit expansion multiplier
suggests that the idea is of recent vintage. Thomas M. Humphrey has, however, showed
that the kernel of the idea dates back to 1826 and that it found mathematical expression as
the sum of a geometrical series as early as the 19th century in Alfred Marshall. After
money supply began to be defined in terms of various deposits, the credit-deposit
multiplier was extended into a money multiplier, notably by Milton Friedman.
Today the idea is assumed to be a given and is taught to undergraduates as noncontroversial.
1.
Version 1 of the Money Multiplier
In the undergraduate text Economics by Samuelson and Nordhaus the money multiplier is
expounded as follows. The Federal Reserve buys a $1000 government bond from Ms
Bondholder, who deposits the $1000 in her checking account at Bank 1. Banks are
required to keep a reserve requirement of 10 per cent, hence Bank 1 must set aside $100
of the $1000 deposit. But the bank now has $900 of excess reserves, so it makes a loan of
an equal amount. The person who borrows the money takes the $900 (in cash or check)
and deposits it in her account in Bank 2.
If we calculate the amount of money at this stage, we are in for a big surprise. In addition
to the original $1000 of deposits there is $900 of demand deposits in another account (i.e.
in the checking account of the person who got the $900). The total amount of money is
therefore $1900. Bank 1's activity has created $900 of new money.
Now Bank 2 which receives the $900 of new deposits needs to keep only $90 as required
reserves and extends $810 as a new loan which is deposited in Bank 3. At this point the
original $1000 has produced a total of $2710 ($1900 + $810) of money. Now Bank 3
which receives the $810 sets aside $81 as required reserves and lends $729, thus creating
$729 in new money. The process ends when new money equal to $10,000 has been
created. This figure is arrived at as the sum of a geometric series and is equal to the initial
money injection divided by the reserve ratio 0.1.
The above exposition of the money multiplier has been uncritically accepted for nearly a
century. But it is not too difficult to identify the holes in it. To begin with, a person does
not take a loan of $900 from Bank 1 after paying interest on it in order to leave it unspent
in his bank account in Bank 2 that pays a lower interest rate so that the latter can lend it.
He spends the $900 and if he spends the $900 then Bank 2 cannot lend it. It may be
argued that even if the $900 is spent it lands up as a deposit in another account in another
bank which can then lend it. But the same argument applies in the case of this bank: if the
$900 is spent it cannot be lent.
In other words, the amount of money that the banking system can lend has nothing to do
with the reserve ratio but is equal to the quantum of money that remains unspent. We
shall return to this principle (which we have here demonstrated analytically) later in this
paper and verify it empirically using data for the United States. Note that spending is
completely different from cash leakage, which is introduced into more sophisticated
versions of the money multiplier.
If the initial recipient of the $1000 injection by the Fed spends the money then the
banking system has no money to lend. It is instructive, however, to follow the trail of
spending, taking care also to introduce an element of time. Let us assume that the first
recipient, Ms Bondholder in the text by Samuelson and Nordhaus, receives the money
initially in Deposit D1 on Day 1. She spends the money which lands in Deposit D2
owned by A on Day 2. A spends the money which then lands in Deposit D3 owned by B
on Day 3. B spends the money which then lands in Deposit D4 owned by C on Day 4.
The process continues ad infinitum until one of the recipients decides not to spend part of
his receipts. At this stage his bank can lend the unspent money.
The spending by Ms Bondholder gives rise to a chain of deposits: Deposit D1 on Day 1,
Deposit D2 on Day 2, Deposit D3 on Day 3, Deposit D4 on Day 4 and so on. This chain
of deposits and spending is not, however, equal to a chain of money creation. Money is a
stock, not a flow. It is a snapshot of deposits at a particular point of time. On Day 2, there
is $1000 in Deposit D2, but no money anywhere else in the chain. On Day 3 there is
$1000 in Deposit D3 but nowhere else. So it is incorrect to add all the deposits that are
formed over a period of time and equate that with the amount of money created. What
interests us is the amount of money at a particular instant of time, and this can never be
greater than $1000.
For the calculation of the money multiplier in Economics to be correct, the deposit of
$1000 in Bank 1, the deposit of $900 in the account of the borrower in Bank 2, the
deposit of $810 in the account of the borrower in Bank 3, $729 in the account of the
borrower in Bank 4, and so on have to coexist at the same moment of time. And this, as
we have shown before, is not possible because the borrower of $900 does not borrow the
money to leave it unspent, the borrower of $810 does not borrow the money to leave it
unspent and so on. If money is defined as that which is available for spending it can never
be greater than $1000.
2.
Version 2 of the Money Multiplier
There is another version of the money multiplier that looks more sophisticated at first
glance because it incorporates spending. We use the description on the Economic
Education Web site of the University of Nebraska at Omaha.
http://ecedweb.unomaha.edu/ve/library/hbcm.pdf
XYZ Securities Dealer sells $20,000 worth of securities to the Fed. It deposits the money
in First Bank of the US. First Bank sets aside $2,000 worth of required reserves (the
reserve ratio is 10%) and approves a $18,000 loan for Gordo's Tequeria which wants to
remodel its restaurant. First Bank credits Gordo's checking account for $18,000.
Gordo's writes a check on this account payable to Able Construction Company, the
remodeling contractor. Able Construction in turn deposits the check into its account at
Second Bank. Second Bank's deposits now have increased by $18,000. Out of this
$18,000, Second Bank must hold $1,800 as required reserves and may lend an amount
equal to its $16,200 remaining excess reserves.
Second Bank approves a loan for one of its customers, Amen Tires, which has decided to
purchase another truck for its mobile tire repair fleet. Second Bank credits Amen Tires'
checking account for $16,200. Amen, in turn, writes a check on its account payable to T2 Trucks, which deposits its check into Third Bank.
Third Bank sets aside $1,620 as required reserves and lends an amount equal to its
remaining excess reserves of $14,580.
The total amount of newly created checkbook money resulting from the Federal
Reserve's security purchase and three rounds of lending equals $68,780 with First Bank
contributing $18,000, Second Bank contributing $16,200, and Third Bank contributing
$14,580. In addition to the $48,780 of new checkbook money, the money supply
increased by the $20,000 deposit in XYZ's checking account which resulted from the
Fed's securities purchase. The multiple expansion process continues until the total new
money created is equal to $200,000 which is the initial injection $20,000 divided by the
reserve ratio 0.1.
At first glance this seems to take care of the problems that we pointed out in Economics.
But on a closer look we see that here too the success of the model depends on the initial
$20,000 and then amounts of $18,000 in Second Bank, $16,200 in Third Bank etc
remaining unspent. If these amounts are spent the model collapses.
We again arrive at the principle we formulated earlier: the banking system can only lend
money that is unspent.
3.
Banks can lend only money that is unspent
It is possible to verify the above principle empirically using some simplifying but very
reasonable assumptions.
The first assumption is that M1 represents money that is spent or held to be spent shortly.
The reasoning is that if it were not intended to be spent it would not have been held as
currency or a checkable deposit but have been moved to a savings or time deposit paying
a higher rate of interest. Apart from currency and checkable deposits, M2 includes
savings and time deposits that pay a higher rate of interest. These represent money that is
not intended to be spent in the immediate future and can therefore be lent by banks. Thus
M2-M1 represents money that is not spent and can therefore be lent by banks. In the US,
since 1994, banks have been allowed to "sweep" part of demand deposits held by
customers into "sweep deposits" on which reserves need not be maintained. These too
must be added to M2-M1 to get the amount of money that is not spent and can therefore
be lent by banks.
We compare this amount with the total amount of loans and leases made by commercial
banks.
The resulting graph is as in Figure 1 below.
Fig 1. Total loans and leases versus money available to lend
It can be seen that for more than half a century the graph of total loans and leases runs
below the graph for M2-M1+sweeps. The exception is such a brief period in1995 that it
can safely be attributed to a reporting error.(The probable reason is underreporting of
sweeps. From December 1994 to April 1995, the sweeps for each month were zero,
according to Fed data.)
This is strong support for the commonsensical principle that was formulated earlier viz.
that the amount of loans that banks can make is constrained by the amount of money that
is unspent.
4.
The role of reserves
Several countries have reserve ratios equal to zero or close to zero, suggesting indirectly
that the role of reserves in controlling money supply has been vastly exaggerated.
A look at the figures shows why reserves are more or less meaningless. In May 2012, the
gap between loans made and money available to lend in Fig 1 was 16% of money
available for lending. In absolute terms, the gap was about $1,400 billion dollars. At this
point M1 was about $2,300 billion and the currency component of M1 was about $1,000
billion dollars, so checkable deposits amounted to about $1,300 billion. If the Fed wanted
to reduce bank lending to any extend it would have had to impose a 100%-plus reserve
ratio on demand deposits. Reducing the reserve ratio to encourage lending would of
course be meaningless because it would merely free more money for lending at a time
when the gap between loans and money available to lend was already larger than the
quantum of demand deposits.
Thus Fig 1 shows that reserve ratios can have an impact on bank lending only when the
gap between money available to lend and loans actually made is close to zero.
CONCLUSION
The paper above argued, and we hope proved conclusively, that the well-known idea of
the money multiplier is incorrect because it rests on the impossible assumption that loans
are not spent.
In Austrian economics the multiplier plays an important role in showing that booms and
busts are caused by unrestrained credit expansion owing to fractional reserve banking.
Disproving the idea of the multiplier thus deals a death-blow to a key contention of the
Austrians. In the Keynesian scheme of things the multiplier does not play much of a
direct role. It can, however, be showed that disproving the idea of the money multiplier
has implications which question key tenets of Keynesianism although the limited
objective of this brief paper prevents us from exploring this at any length.
References
Samuelson, Paul. A and Nordhaus, William D. (2005). Economics, 18th edition, The
McGraw Hill Companies
De Soto, Jesus Huerta (2009), Money, Bank Credit and Economic Cycles, 2nd edition,
Ludwig von Mises Institute
Humphrey, Thomas M. (March/April 1987), The Theory of Multiple Expansion of
Deposits: What It Is and Whence It Came, Economic Review, Federal Reserve Bank of
Richmond
Beale, Lyndi, How Banks Create Money, Economic Education Web site of the University
of Nebraska at Omaha, URL: http://ecedweb.unomaha.edu/ve/library/hbcm.pdf