1. Determinants of the Money Supply: The Money Multiplier
Chapter 14
Determinants of the Money Supply: The Money Multiplier
Dr. Reyadh Faras

2. Introduction
In Ch 13, we developed a simple model of multiple deposit creation which showed that the Central Bank can influence the amount of checking deposits (D), bank reserves (R), and the monetary base (MB) by changing the reserve requirement (RRR), discount loans (DL) and OMOs.
However, the model assumes unrealistically that:
1) the public holds no cash (C) and;
2) banks hold no excess reserves (ER).
Dr. Reyadh Faras

3. THE MS MODEL AND THE MONEY MULTIPLIER
We now develop a more realistic money supply model that allows for the fact that the public does hold cash balances. 
We link the monetary base, which the central bank can better control, to the money supply (M for M1), using the money multiplier (m).
Dr. Reyadh Faras

4. Money Multiplier
It is a ratio that shows how much the money supply changes for a given change in the monetary base.
MS = m  x  MB (1)
Because the multiplier is larger than one, the monetary base is called “high powered money”, meaning that a change in MB by 1% leads to a change in MS by more than 1%.
Dr. Reyadh Faras

5. Deriving the Money Multiplier
Here we account for the possibility that depositors hold some cash (outside the banking system) and banks hold excess reserves. These two decisions affect (m).
We assume that holdings of currency (C) and excess reserves (ER) grow proportionally with checkable deposits (D), which means that the following ratios are constants:
{C/D} = currency ratio
{ER/D} = excess reserve ratio
Dr. Reyadh Faras

6. Currency and Excess Reserve Ratios in Kuwait
Currency Ratio
(C/D)
(%)
Excess Reserve Ratio
(ER/D)
Sight
Deposits
(Million KDs)
Currency in
Circulation
Cash with Local Banks
Year
46.8
6.2
758.8
355.2
46.9
1993
45.3
8.3
774.7
351.3
64.1
1994
K-Net
35.7
11.9
873.5
311.5
104.1
1995
20.1
2.8
2643.3
531.0
75.3
2004
18.4
3.4
3148.7
578.7
105.9
2005
22.7
5.1
2893.9
656.3
148.6
2006
18.3
3.3
3505.2
641.5
115.2
2007
19.3
4.4
3662.5
707.8
161.4
2008
19.7
4.3
3938.3
775.7
168.1
2009
17.6
4782.1
842.9
163.7
2010

7. Next, we derive a formula showing how these ratios plus the required reserve ratio affect m.
Total reserves equal the sum of required reserves (RR) and excess reserves (ER): 
R = RR + ER
We know that RR equals checking deposits multiplied by the reserve requirement ratio, thus R equals:
R = ( RRR x D ) + ER
But MB equals to C plus R, thus it can be rewritten using the above equation as follows:
MB = R + C = ( RRR x D ) + ER + C
This equation shows the amount of MB needed to support the existing amounts of checkable deposits, currency and excess reserves.
Dr. Reyadh Faras

8. C as {C / D} X D and ER as {ER / D} X D, as follows:
To derive a formula for m in terms of the currency and excess reserve ratios, we rewrite the above equation specifying
C as {C / D} X D and ER as {ER / D} X D, as follows:
MB = ( RRR x D ) + ({ER / D} X D) + ({C / D} X D)
= ( RRR + {ER / D} + {C / D}) X D
Next, divide both sides of the equation by the term inside the parentheses to get an expression linking checkable deposits (D) to the monetary base (MB):
D = [1 / (RRR + {ER / D} + {C / D})] X MB (2)
Using the definition of money supply as currency plus checkable deposits (M = D + C) and specifying C as {C / D} X D,
M = D + ({C / D} X D)
= (1 + {C/D}) X D
Dr. Reyadh Faras

9. Substituting equation (2) for D in the above equation, we have
M = [(1+{C/D}) / (RRR + {ER / D} + {C / D})] X MB (3)
Equation (3) is a detailed form of equation (1)
(M = m x MB), to get an expression for m, we have to divide both sides of equation (3) by MB:
m = [(1+ {C/D}) / (RRR + {ER / D} + {C / D})] (4)
Clearly, m depends on: {C/D} set by depositors,
{ER/D} set by banks, and {RRR} set by central bank.
Dr. Reyadh Faras

10. Example Assume: RRR = 10% ER = $0.8 billion
C = $400 billion D = $800 billion
Calculate the currency and excess reserve ratios:
C/D = / =
ER/D = / =
The money multiplier is calculated as follows:
m =
The multiplier shows that an increase in MB by % ___ leads to an increase in money supply by %____.
Dr. Reyadh Faras

11. The value of (m) is much smaller than 10, which was expected from the model in chapter 13. There are two reasons for the low value found here:
First, we allow for the possibility that the public hold currency proportional to their holdings of deposits.
Second, banks are also allowed to hold excess reserves proportional to the value of deposits.
Dr. Reyadh Faras

12. Factors that Determine the Money Multiplier
1. Changes in RRR
If RRR increases, more required reserves are needed proportional to the level of checkable deposits.
This reduces the bank’s ability to lend, so loans will decline and as a result (new) deposits decline too.
Finally, money supply has to decline.
But since money supply has declined while MB didn’t change, this means that (m) must have declined (M=m X MB).
In other words, if RRR is higher, less multiple expansion of checkable deposits occur which means that (m) must fall.
Dr. Reyadh Faras

13. If RRR increases from 10% to 15%. m =
Example
If RRR increases from 10% to 15%.
m =
Result:
The money supply and the money multiplier are _________ related to the required reserve ratio.
Dr. Reyadh Faras

14. 2. Changes in {C/D}
An increase in {C/D} means that depositors are converting some of their checkable deposits into currency.
As it was shown in chapter 13, checkable deposits undergo multiple expansion while currency does not.
Therefore, an increase in currency results in a decline in the level of multiple expansion and (m) too.
Example
If {C/D} rises from 0.5 to 0.75.
m =
Result:
The money multiplier and the money supply are _________ related to the currency ratio.
Dr. Reyadh Faras

15. When banks increase their holdings of excess reserves,
3. Changes in {ER/D}
When banks increase their holdings of excess reserves,
this means that for the same level of MB, banks will reduce their loans, causing a decline the level of checkable deposits and a decline in the money supply. As a result, m must fall.
Example
If {ER/D} rises from to
m =
Result:
The money multiplier and the money supply are __________related to the excess reserve ratio.
Dr. Reyadh Faras

16. Factors that Determine the Money Supply
Dr. Reyadh Faras

17. SUMMARY
VARIABLE CHANGE REPSONSE IN MS RRR Increase ________ C/D Increase ________ ER/D Increase ________ MB Increase ________
Dr. Reyadh Faras

18. Excess Reserves Ratio and Interest Rate
Dr. Reyadh Faras

19. {ER/D}, {C/D}: 1929–33
Dr. Reyadh Faras

20. Money Supply and Monetary Base: 1929–33
Dr. Reyadh Faras

21. Required and Excess Reserves in the US: 2007- 2009