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In Ch 15, we developed a simple model of multiple deposit creation which showed that the Fed can influence the amount of checking deposits (D), bank reserves (R), and the monetary base (therefore the money supply) by changing the reserve requirement (r) and through OMOs.
However, the model assumes unrealistically that: • 1) The public holds no cash (C) • 2) Banks hold no excess reserves (ER).
The MS Model and the Money Multiplier: • Money supply model that allows the public to hold cash balances. We include currency in circulation now. • NOTE: Money = C + D
We link the monetary base, which the central bank can control better than reserves, to the money supply (M for M1), using themoney multiplier (m). M = m x MB (1)
Money Multiplier (m): • It is a ratio that shows how much the money supply changes for a given change in the monetary base. • Because the multiplier is larger than one, the base is called “high powered money”: • A change in MB by 1% leads to a change in M by more than 1%.
Factors affecting the size of (m): 1-Depositor’s decision regarding their holding of currency. 2-Reserve requirement. 3-ER.
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 = {C/D} = C ratio, e = (ER/D) = ER ratio • Next, we derive a formula showing how these ratios plus the required reserve ratio (r) affect m. • Total reserves (R) equals the sum of required reserves (RR) and excess reserves (ER): R = RR + ER
RR equals checking deposits (D) multiplied by the reserve requirement ratio (r): RR = r x D • Thus R equals: R = (r x D) + ER • Since (r < 1), then a ($1) of reserves can support more than ($1) of deposits and the multiple expansion of deposits occurs.
Example: if (ER=0), (r =10%), (D=$800): Then the amount of reserves needed: = (0.10) (800) = ($80). The ($80) of reserves can support ($800) in checkable deposits (multiple deposit creation). Recall: R = (r x D) + ER But MB = C + R; can rewrite the above equation as follows: MB = R + C = RR + ER + C = (r x D) + ER + C
This equation shows: 1) The amount of MB needed to support the existing amounts of checkable deposits, currency and excess reserves. 2) An additional ($1) of MB arises from an additional ($1) of currency does not support any additional deposits (No changes in D). • Result: An increase in the MB that goes into C is not multiplied, but an increase that goes into supporting D is multiplied.
3) An additional ($1) of MB that goes into (ER) doesn’t support any additional (D) or (C). • This is because when a bank decides to hold (ER), it doesn’t make additional loans, so (ER) do not lead to the creation of deposits. • This means that for a given level of (R), a higher amount of (ER) implies that the banking system has fewer reserves to support (D).
m = 1 + c/ r + e + c • And (m) is a function of (c, e, r): m depends on: {C/D} set by depositors, {ER/D} set by banks, and (r) set by the central bank.
r = 0.1, ER = $0.8 billion, C= $400, D= $800, and M = $1200 billion. • We can calculate the values of the currency and excess reserve ratios (c, e): • c = C/D = 400 / 800 = 0.5, e = ER/D = 0.8 / 800 = 0.001 • The money multiplier is calculated as follows: • m = (1+0.5) / (0.1 + 0.001 + 0.5) = 1.5 / 0.601 = 2.5
The multiplier shows that, given the r = 10%, and the behavior of depositors represented by c = 0.5, and banks as represented by e 0.001, a ($1) increase in MB leads to an increase in money supply by ($2.5) • The value of (m) is much smaller than (10), which was expected in chapter 15.
There are two reasons for the low value found here. 1) The possibility that the public hold currency proportional to their holdings of deposits. 2) Banks are also allowed to hold excess reserves proportional to the value of deposits.
Factors that Determine the Money Multiplier 1- Changes in r: • If (r) increases, leaving all other variables unchanged, more required reserves • are needed to support 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 (r) is higher, less multiple expansion of checkable deposits occur which means that (m) must fall.
Example • If (r) increases from (10%) to (15%): • m = (1+0.5) / (0.15 + 0.001 + 0.5) = 1.5 / 0.651 = 2.3 • Result: • The money supply and the money multiplier are negatively related to the required reserve ratio.
2- Changes in the currency ratio c = {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 15, 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 = (1+0.75) / (0.15 + 0.001 + 0.75) = 1.75 / 0.851 = 2.06 • Result: • The money multiplier and the money supply are negatively related to the currency ratio.
3- Changes in {ER/D}: • When banks increase their holdings of excess reserves relative to checkable deposits, the banking system has fewer reserves to support checkable deposits. • This means that for the same level of MB, banks will reduce their loans, causing a decline in 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 = (1+0.5) / (0.15 + 0.005 + 0.5) = 1.5 / 0.605 = 2.48 • Result: • The money multiplier and the money supply are negatively related to the excess reserve ratio.
