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# Determinants of the Money Supply by sdaferv

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```									      Econ 210 Money and Banking
Determinants of the Money Supply

Haitao Xiang

Simon Fraser University

July 22, 2009
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I   The simple deposit multiplier ∆D/∆R = 1/r
I   It seems that the Bank of Canada can control deposits (and
hence the money supply) by adjusting reserves
I   Problems:
1. The Bank of Canada cannot exert as precise control over
reserves as over the monetary base
2. Critique of the simple model: ignore decisions of depositors
holdings
I   An improved model of money supply:
1. Link the money supply (M) to the monetary base (MB) with a
money multiplier (m): M = m MB
2. Money multiplier m re‡ects the e¤ect on the money supply of
other factors besides MB: decisions of depositors about
currency holdings and decisions of banks about reserve holdings
Deriving the Money Multiplier
I   De…ne money M as currency plus chequable deposits
I   corresponds to M1+: currency in circulation plus chequable
deposits at all depository institutions (chartered banks and
near banks)
I   Assume the desired level of currency (C ) and desired reserves
(DR) both grow proportionately with chequable deposits (D)
currency ratio :       c = C /D
desired reserve ratio :       r = DR/D
I   Total reserves in the banking system equal desired reserves
(assume all reserves are held voluntarily, i.e., all reserves are
desired):
R = DR
I   By de…nition,
DR = r      D
)R=r         D
Deriving the Money Multiplier II

MB = C + R = C + (r       D)
I   The currency component (C ) of monetary base does not lead
to multiple deposit creation; the reserves component (R) does

MB    =   (c D ) + (r D )
=   (c + r ) D
1
)   D=           MB
c +r
M    =   C +D
=   c D +D
=   (1 + c ) D
1+c
=             MB
c +r
M      1+c
m   =        =
MB      c +r
Intuition behind the Money Multiplier
I   An numerical example:
I   r = desired reserve ratio = 0.05
I   C = currency in circulation = \$40 billion
I   D = chequable deposits = \$160 billion
I   M = money supply (M1+) = C + D = \$200 billion

C    \$40 billion
c   =      =               = 0.25
D    \$160 billion
1+c       1 + 0.25
m =            =               = 4.2
c +r    0.25 + 0.05
I   Money multiplier is smaller than the simple deposit multiplier:
m = 1 +c < 1
c +r   r
I   Although there is multiple expansion of deposits, there is no
such expansion for currency. If some portion of the increase in
high-powered money …nds its way into currency (c > 0), this
portion does not undergo multiple deposit expansion, and the
overall deposit expansion must be lower, meaning a smaller
multiplier
Factors that Determine the Money Multiplier

I   Changes in the currency ratio c:
I   The money multiplier and the money supply are negatively
related to c
1+c    c + r + (1     r)          1 r
m=         =                     = 1+
c +r        c +r                  c +r
I   Intuition: An increase in c means that depositors are
converting deposits into currency. Then there is a switch from
a component of the money supply that undergoes multiple
expansion to one that does not. The overall level of multiple
expansion declines, and so must the multiplier.
Factors that Determine the Money Multiplier II

I   Changes in the desired reserve ratio r :
I   The money multiplier and the money supply are negatively
related to r
1+c
m=
c +r
I   Intuition: An increase in r means that banks will reduce their
loans, causing a decline in the level of chequable deposits and a
decline in the money supply, and the money multiplier will fall.
I   Two primary factors a¤ecting r :
I   Market interest rates: higher market interest rates, higher
opportunity cost of holding reserves, lower r
I   Expected deposit out‡ows: higher expected deposit out‡ows,
higher expected bene…ts from holding reserves, higher r
Additional Factors that Determines the Money Supply

I   The Bank of Canada do not have full control over the
monetary base: cannot unilaterally determine the amount
banks borrow from the Bank - advances
I   Split the monetary base into two components:
I   nonborrowed monetary base (MBn ), which is directly
controlled by the Bank through open market operations.
I   borrowed monetary base or borrowerd reserves (BR),which also
depend on banks’borrowing decisions.

MB = MBn + BR

I   The money supply is positively related to both MBn and BR

M=m        (MBn + BR )
Overview of the Money Supply Process
Application

1+c
M=m        MB =             (MBn + BR )
c +r
I   c and r depend on the decisions made by households, …rms
and banks.
I                                     s
MBn and BR depend on central bank’ monetary policy
conduct and banks’decisions
I   All these decisions are in‡uenced by market condition and
government policy
I   Example 1: the Great Depression: c " r " m # M #
I   Example 2: recent U.S. recession: MB "" r " m # M "
http://research.stlouisfed.org/publications/review/09/03/Gavin.pdf
Application: the Great Depression
Application: the Great Depression
Application: Recent U.S. Recession
Application: Recent U.S. Recession II
Application: Recent U.S. Recession III
Application: Recent U.S. Recession IV

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