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Determinants of the Money Supply

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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
             about currency holdings and decisions of banks about reserve
             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 "
          I   recommended reading:
              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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