Introduction to the Money Supply Process

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)

Chase

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 = 0.05L $90000 T $80000Bonds $50000 E $10000

RR = rDD + rTT = (0.10)($70000) + (0.05)($80000) = $11000ER = R - RR = $20000 - $11000 = $9000

Loan of $9000 Step #1 -- Loan is Approved

Chase

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

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

Seller deposits check in her bank.

HSBCR + $9000 D + $9000

Bank Loaning and Money Supply Expansion

Consider: M2 = C + D + T + MMMF

M2 = C + D + T + MMMF

Our example: M2 = $0 + $9000 + $0 + $0 = $9000 (Chase’s loan leads to new

deposits for HSBC.)

Key Concepts: Money Supply Expansion

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

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

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

Define -- The Monetary Base, or

High Powered Money (H)

H = C + R

Key Properties: The Monetary Base

The monetary base (H) is unaffected by changes in public asset holdings.

The monetary base (H) is also unaffected by bank loaning.

Important factors that change H: Open Market Operations and Discount Loans (DL).

Discount Loans and the Monetary Base

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

Chase

R + $100 DL + $100

H = C + R = $0 + $100 = $100

Open Market Operations and the Monetary BaseExample 2 -- The Federal Reserve buys a

$100 bond from Chase.

Chase

Bonds - $100

R + $100

H = C + R = $0 + $100 = $100

The Nonborrowed Base

The Nonborrowed Base (HNON)

HNON = H - DL

Key property -- The nonborrowed base is only affected by open market operations.

A Formula for Money Supply Determination

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 + rTt + 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

Since M2 = (m2)(HNON + DL),

M2 = (m2)( HNON),

M2 = (m2)(DL).

In other words,

HNON M2

DL M2Changes in HNON or DL give banks

reserves, greater ability to loan.

Effects of Reserve Ratios on M2 DeterminationIncreases in reserve ratios hinder bank

loaning, thereby decreasing the multiplier and M2.

m2 = 1 + k + t

k + rD + rTt + e

rD m2 M2 rT m2 M2

Effects of k (C/D) and t (T/D) on M2 DeterminationChanges 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 + rD + rTt + e

k m2 M2 t m2 M2

Effects of e (ER/D) on M2

Changes in e (banks desire to hold more excess reserves) affect the multiplier, which affects M2.

m2 = 1 + k + t

k + rD + rTt + e

e m2 M2

M2 Determination: Summary

First, the formula again.

M2 = (1 + k + t) (HNON + DL) + MMMF

(k + rD + rTt + e)

A Summary Table

HNON M2

DL M2 rD M2

rT M2

k M2

t M2

e M2

The Multiplier -- Trying to Control the Money Supply

M2 = (1 + k + t) (HNON + DL) + MMMF

(k + rD + rTt + e)

Federal Reserve controls HNON, rD, and rT and uses them as policy tools.

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?

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

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

M2 = (m2)(H)

M2 Determination in Growth Rates

Since the levels are multiplicative, the growth rates are additive

Growth in M2

(Growth in m2) + (Growth in H)

Implications for M2 Control

Growth in M2

(Growth in m2) + (Growth in H)

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

Growth in M2

(Growth in m2) + (Growth in H)

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

Best solution: constant multiplier, zero DL. Unfortunately, not true.

Second best solution: predictable multiplier and DL.

How to predict non-Fed controlled changes in M2? What determines movements in the components (k, t, e, DL, MMMF)?