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Introduction to the Money Supply Process - maxwell.syr


									Introduction to the
Money Supply Process

z Fundamental Property -- Money
  supply expands when banks make
  loans (or more generally, expand
  loans or buy bonds)
Deposit Expansion:
The Individual Bank
Consider the following example.
(rD = 0.10, rT = 0.05)

R     $20000 D $70000
L     $90000 T $80000
Bonds $50000 E $10000
Computing Required and
Excess Reserves
          Chase              rD = 0.10
R     $20000 D $70000        rT = 0.05
L     $90000 T $80000
Bonds $50000 E $10000

RR = rDD + rTT = (0.10)($70000) +
     (0.05)($80000) = $11000
ER = R - RR = $20000 - $11000 = $9000
Loan of $9000
Step #1 -- Loan is Approved

R     $20000 D $79000
L     $99000 T $80000
Bonds $50000 E $10000

Borrower signs loan contract,
receives check from bank.
Step #2 -- Loan is Spent

R     $11000 D $70000
L     $99000 T $80000
Bonds $50000 E $10000

Seller deposits check in her bank.

DR    + $9000 DD + $9000
Bank Loaning and
Money Supply Expansion
Consider: M2 = C + D + T + MMMF

Þ DM2 = DC + DD + DT + DMMMF

Our example:
    DM2 = $0 + $9000 + $0 + $0 = $9000

(Chase’s loan leads to
  new deposits for HSBC.)
Key Concepts:
Money Supply Expansion

z Key is step #1, Chase expands its
  deposit commitments without
  changing its reserves.

z Note -- Process is symmetric.
  Repayment or liquidation of loan
  leads to decrease in M2 (by the
  amount of the loan).
Deposit Expansion:
The Banking System

z Multiple Expansion -- An initial
  change in bank reserves prompted
  by the Federal Reserve leads to an
  eventual increase in the money
  supply which is a multiple of that
  initial change.
Developing a Formula
for Multiple Expansion

z Define -- The Monetary Base, or
  High Powered Money (H)

Key Properties:
The Monetary Base

z The monetary base (H) is unaffected by
  changes in public asset holdings.
z The monetary base (H) is also
  unaffected by bank loaning.
z Important factors that change H: Open
  Market Operations and Discount Loans
Discount Loans
and the Monetary Base

z Example 1 -- Chase borrows $100
  from the Federal Reserve.

  DR    + $100 DDL + $100

  DH = DC + DR = $0 + $100 = $100
Open Market Operations
and the Monetary Base
z Example 2 -- The Federal Reserve
  buys a $100 bond from Chase.

  DBonds     - $100
  DR         + $100

  DH = DC + DR = $0 + $100 = $100
The Nonborrowed Base

z The Nonborrowed Base (HNON)

 HNON = H - DL

z Key property -- The nonborrowed
  base is only affected by open
  market operations.
A Formula for Money
Supply Determination

z Define the following variables.

   k = C/D
   t = T/D
   e = ER/D
Money Supply
Determination: The Formula

M2 =      (1 + k + t)    (HNON + DL) + MMMF
       (k + rD + rTt + e)

  The money multiplier (m2)
Computing the Money
Multiplier: An Example

Suppose that:
  C = 550          rD = 0.10
  D = 600          rT = 0.03
  T = 3000
  ER = 10.
Compute the money multiplier (m2).
Computing the Ratios

k = C/D = 550/600 = 0.917

t = T/D = 3000/600 = 5.000

e = ER/D = 10/600 = 0.0167
Plugging Into
The Multiplier Formula
m2 =           1+k+t
             k + rD + rT t + e

m2 =          1 + 0.917 + 5.0
       0.917 + 0.10 + (0.03)(5.0) + 0.0167

m2 =                5.84
Effects of HNON and DL
on M2 Determination
z Since M2 = (m2)(HNON + DL),
       DM2 = (m2)(D HNON),
       DM2 = (m2)(DDL).
z In other words,
       HNON­Þ M2­
       DL­ Þ M2­
z Changes in HNON or DL give banks
  reserves, greater ability to loan.
Effects of Reserve Ratios
on M2 Determination
z Increases in reserve ratios hinder
  bank loaning, thereby decreasing
  the multiplier and M2.

   m2 =     1+k+t
          k + r D + r Tt + e

   rD­ Þ m2¯ Þ M2¯
   rT­ Þ m2¯ Þ M2¯
Effects of k (C/D) and t (T/D)
on M2 Determination
z Changes in k and t (public’s desire to
  reallocate assets) have different effects on
  bank loaning, the multiplier, and M2.

   m2 =     1+k+t
          k + r D + r Tt + e

   k­ Þ m2¯ Þ M2¯
   t­ Þ m2­ Þ M2­
Effects of e (ER/D) on M2
z Changes in e (banks desire to hold
  more excess reserves) affect the
  multiplier, which affects M2.

  m2 =      1+k+t
          k + r D + r Tt + e

   e­ Þ m2¯ Þ M2¯
M2 Determination: Summary

First, the formula again.

M2 =      (1 + k + t) (HNON + DL) + MMMF
       (k + rD + rTt + e)
A Summary Table

    HNON­   Þ   M2­
    DL­     Þ   M2­
    r D­    Þ   M2¯
    r T­    Þ   M2¯
    k­      Þ   M2¯
    t­      Þ   M2­
    e­      Þ   M2¯
The Multiplier -- Trying to
Control the Money Supply
M2 =      (1 + k + t)    (HNON + DL) + MMMF
       (k + rD + rTt + e)

z Federal Reserve controls HNON, rD, and
  rT and uses them as policy tools.
z But M2 is also determined by public
  asset holding (k, t, MMMF) and bank
  behavior (e, DL).
Can the Federal Reserve
Control the Money Supply?

z Practical Solution -- The Federal
  Reserve tries to control money
  supply growth within a given
  target range. If actual M2 growth
  falls within the range, M2 is
  considered controlled.
The Multiplier Effect and
Controlling M2

z Consider formula for M2
  determination (apart from MMMF),
  written as follows (recall that H =
  HNON + DL).

  M2 = (m2)(H)
M2 Determination in
Growth Rates

z Since the levels are multiplicative,
  the growth rates are additive

z Growth in M2 @
    (Growth in m2) + (Growth in H)
Implications for M2 Control

z Growth in M2 @
    (Growth in m2) + (Growth in H)

z If the multiplier is roughly constant
  over time (growth in m2 » 0), then
  the growth rate of M2 will
  approximate closely the growth
  rate of the monetary base.
Difficulties in M2 Control

z Growth in M2 @
    (Growth in m2) + (Growth in H)

z But if the multiplier changes over
  time (growth rate either positive or
  negative), then the growth rate of
  M2 will deviate from the growth
  rate of the monetary base.
Non-Federal Reserve
Changes in M2

z Best solution: constant multiplier,
  zero DL. Unfortunately, not true.
z Second best solution: predictable
  multiplier and DL.
z How to predict non-Fed controlled
  changes in M2? What determines
  movements in the components
  (k, t, e, DL, MMMF)?

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