Chapter 14

1. Chapter 14 Determinants of the Money Supply

2. Introduction • In Ch 13, we developed a simple model of multiple deposit creation which showed that the Central Bank can influence MONEY SUPPLY through monetary base. This is by using OMOs and discount loans. • However, the model assumes unrealistically that: 1) the public holds no cash (C) and; 2) banks hold no excess reserves (ER).

3. THE MONEY SUPPLY 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 and banks can hold excess reserves.  • We link the monetary base, which the central bank can better control, to the money supply (M for M1), using themoney multiplier (m).

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

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 the money multiplier (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

6. 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.

7. 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

8. 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 the central bank.

9. Example Given: RRR = 10%, ER = $0.8 billion, C = $400 billion , D = $800 billion, ………………Calculate m? • We can calculate the currency and excess reserve ratios: C/D = / = ER/D = / = • The money multiplier is calculated as follows: m = Given -----------------M= m(MB) The multiplier shows that an increase in MB by( $ 1) leads to an increase in money supply by $____.

10. 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.

11. 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 (MB)}. • In other words, if RRR is higher, less multiple expansion of checkable deposits occur which means that (m) must fall.

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

13. 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.

14. 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 0.001 to 0.005. m = Result: The money multiplier and the money supply are __________related to the excess reserve ratio.

15. SUMMARY VARIABLE   CHANGE         REPSONSE IN MS  MB               Increase               ________  RRR           Increase               ________  C/D              Increase               ________  ER/D           Increase ________