The Economics of Money , Banking and Financial Markets

1. The Determinants of the Money Supply
The money multiplier, reserve and
currency ratios, and borrowed reserves

2. M1 and the Monetary Base
• Recall our definition of M1 as currency in circulation plus
checkable deposits
• Recall our definition of MB as currency in circulation plus
reserves
• The Fed has greater control over MB than it does over
M1
– Checkable deposits are influenced by a number of factors that
the Fed does not have direct control over.
• We link MB and M1 together through the money
multiplier
– M1 = m*MB
– For every $1 increase in the MB, the money supply (M1)
increases by m*$1
– m is almost always greater than 1.

3. The Currency Ratio
• How much currency does the public hold
relative to their checkable deposits?
– We assume that the desired level of currency
(C) is a constant fraction of checkable
deposits
– The currency ratio is a constant (in
equilibrium) defined as:
• c = C/D
– C can change, but only in constant proportion
to D

4. Reserve Ratios
• What fraction of checkable deposits do banks hold in
reserve?
– Banks are required by the Fed to hold a minimum fraction in
reserve defined as the reserve requirement ratio (rr)
– Banks may choose to hold excess reserves (i.e. a fraction of
deposits held in reserve above and beyond the minimum
required by the fed).
• Let RR be the required reserves held by banks
– RR = rr*D, where rr is a parameter set by the Fed
• Let ER be the excess reserves held by banks
– ER = e*D, where e is assumed to be a constant proportion set
by banks
• Total reserves (R) = RR + ER = rr*D + e*D = (rr+e)*D
– Note that we have been assuming so far that ER=0 (i.e. the
reserve requirement is binding).

5. Deriving the Money Multiplier
• We define MB as currency (C) plus reserves (R)
• Using our definitions:
– MB = C + R
– MB = c*D + rr*D + e*D
– MB = (rr + e + c)*D
• The monetary base is equal to the fraction of
deposits allocated to required reserves, excess
reserves, and currency in circulation

6. Deriving the Money Multiplier
• MB = (rr + e + c)*D
• Rearranging gives:
• Recall M1 = C + D = (c*D) + D = (1+c)*D
• Plugging in our definition of D:
• Since M1 = m*MB:
MB
cerr
D
++
=
1
MB
cerr
c
++
+
=
1
M1
cerr
c
++
+
=
1
m

7. The Money Multiplier
• The money multiplier is defined as:
m = (1+c)/(rr+e+c)
• If no currency is held and banks hold no excess
reserves, then the money multiplier is simply the inverse
reserve ratio
– A 10% rr will produce a multiplier of 10
– A 20% rr will produce a multiplier of 5
• In reality, people do hold currency and banks do hold
excess reserves.
• As a result, the banking system is limited in the amount
of money it creates through fractional reserve banking
(i.e. multiple deposit creation)
– Money held as currency or in reserve is not being loaned out.

8. Example 1
• Suppose the desired currency ratio is 40%, the
reserve requirement is 10% and the excess
reserve ratio is 0.5%
• The money multiplier is
– m = (1+0.4)/(0.1 + 0.4 + 0.005) = 2.77
– A one dollar increase in the monetary base will lead to
a $2.77 increase in the money supply
• Note that if c = e = 0, then the money multiplier
would have been 10.
• Accounting for currency and excess reserves is
clearly important.

9. Example 2
• Let c = 0.25, e = 0.001, and rr = 0.1.
Compute the money multiplier
– m = (1+0.25)/(0.1+0.001+0.25) = 3.56
• The Fed decides to increase rr to 20%.
What happens to the money multiplier
(and the money supply as a result?)
– m = 1.25/0.456 = 2.74
– A smaller multiplier means that banks create
less money through lending and therefore the
money supply will fall.

10. Example 3
• What happens to the money multiplier when the
desired currency ratio rises?
• Let c = 0.2, rr = 0.25, and e = 0.05
– m = (1+0.2)/(0.25+0.05+0.2) = 1.2/0.5 = 2.4
• Now suppose c rises to 0.3, while all other
variables remain constant
– m = (1+0.3)/(0.25+0.05+0.3) = 1.3/0.6 = 2.17
• Increasing the fraction of deposits held as
currency causes the money supply to fall
– Money is being taken out of the banking system
where it could have been used to make loans.

11. Factors that Determine
the Money Multiplier
• Changes in the required reserve ratio r
– The money multiplier and the money supply are
negatively related to r
• Changes in the currency ratio c
– The money multiplier and the money supply are
negatively related to c
• Changes in the excess reserves ratio e
– The money multiplier and the money supply are
negatively related to the excess reserves ratio e

12. Changes in the Currency Ratio
• We have assumed that the constant currency
ratio is an independent parameter for simplicity.
• A more complete analysis would examine the
factors that cause c to change.
– Changes in income/wealth
• Larger proportions of currency are held by people with low
income/wealth
• As income/wealth rises, the ratio of currency to deposits falls
– Changes in expected returns
• As the interest rate on deposits rises, c falls
• As the cost of acquiring currency falls, c rises
• Fears of bank insolvency (i.e. bank panics) cause c to rise
sharply
• Increases in illegal activity cause c to rise

13. The Currency Ratio Over Time
ATM’s lower
the cost of
acquiring
currency
Series of bank
panics
Increased
illegal drug
trade
Big tax
increases

14. Changes in the Excess Reserve Ratio
• What are the costs and benefits to banks of holding
excess reserves?
• Market Interest Rates (-)
– Every dollar held as an excess reserve has an opportunity cost
equal to the interest rate it could have earned as a bank loan
– As market interest rates rise, this opportunity costs increases
and banks hold fewer excess reserves
– e is negatively related to market interest rates
• Expected Deposit Outflows (+)
– The main benefit of holding excess reserves is that they insulate
the bank (somewhat) from sudden deposit outflows
– With excess reserves, banks do not have to call in loans, sell off
other assets, or borrow from the Fed to cover deposits being
withdrawn
– If banks think that deposit outflows will increase, they would be
wise to increase their excess reserve ratio
– e is positively related to expected deposit outflows.

15. Excess Reserves and Market Interest Rates

16. The Decline of the Reserve Ratio as a Policy Tool
• The preceding analysis suggests that the Fed can
increase/decrease the money supply by lowering/raising
the reserve ratio.
– While the Fed used this policy tool in the past, it has become
ineffective in the past decade or so.
– The Fed allows banks to classify some of their membership
deposits at the Fed as required reserves
– Banks have found that they need to keep extra currency in
ATM’s over weekends and holidays. This currency is classified
as vault cash and counts toward required reserves
• With these two developments, banks actually hold more
reserves than the minimum required by the Fed
• If rr is not binding, then any change in rr will have little to
no effect. (only works if you significantly increase rr!)

17. • Open market operations are controlled by the Fed, but the
Fed does not directly control the amount of borrowing by
banks from the Fed
• We split the monetary base into two components, the non-
borrowed monetary base (MBn) and borrowed reserves by
banks (BR)
– MBn= MB – BR  MB = MBn + BR
– M1 = m*MB = m*(MBn + BR)
• The money supply increases with both the non-borrowed
base and with borrowed reserves
– An increase in BR frees up more bank deposits for loans
– BR tends to be very small since the Fed keeps the discount rate
above the market interest rate.
Borrowed Reserves

18. Factors that Change the Money Supply

19. Changes in the Money Supply, 1980-2006

20. Explains long
run movements
Explains short
run fluctuations

21. • The model we have developed here can be used to explain the sharp
reduction in the money supply during the Great Depression
– Prior to FDIC, there was no publicly provided insurance for bank deposits
– With the Great Depression, many bank loans failed
– People worried (rightfully) that their bank did not have enough in reserves
to cover all deposits
– They rushed to their bank to withdraw their money while their was still
something left in reserve
– This sparked a series of bank panics where even financially stable banks
were affected
• These bank panics directly led to a reduction in the money supply,
even though the Fed would have actually preferred an increase in M1
at this time
– Fears of bank insolvency caused c to rise
– Increases in expected deposit outflows caused e to rise
– The multiplier declined sharply
The Bank Panics of the Great Depression

22. Currency and Excess Reserve Ratios
During the Great Depression

23. M1 and MB during the Great Depression