The Mechanics of Money:

ECO 473 - Money & Banking - Dr. D. Foster

The Banking System

Reserves(Cash in vault)

T-Bills(Liquidity & income)

Loans(Banks’ earnings)

Demand Deposits (Checking; Transaction)

Equity

Assets

Liabilities & Equity

Accounting Identity: A L + E

M1

+$10,000

+$10,000

+$8,000

+$8,000

+$2,000

The Role of the Fed

The Fed buys/sells Treasury securities.

This raises/lowers bank reserves.

This raises/lowers excess reserves.

This causes banks to increase/decrease loans.

This will raise/lower measured money, M1.

The Banking System

Reserves

T-Bills

Loans

Deposits (Transactions)

M1

Grinding it out: Terms

TR = Total Reserves = RR + ER RR = Required Reserves

rrD = required reserve ratio

ER = Excess Reserves = ER* + ERu

ER* = Desired excess reserves

ERu = Undesired excess reserves

e = the desired excess reserve ratio

The Federal Reserve

determines rrD.

Banks determine

e.

D = (Demand) Deposits C = Currency in circulation

c = desired currency ratio

MB = Monetary Base = C + TR M1 = Money Supply = C + D Δ = “Change In …”

The public determines c.

Grinding it out: Terms

Deriving RR, ER* and C

RR = Required Reserves = rrD•D

where rrD is the required reserve ratio (0 to 1), and it is fixed to the level of demand deposits (D).

ER* = Desired Excess Reserves = e •D where “e” is the excess reserve ratio and is presumed

to be fixed to the level of deposits (D).

Note that ERu = TR – RR – ER* and may be +, 0, -.

C = Desired Currency Holdings = c •D where “c” is the currency ratio and is presumed to be

fixed to the level of deposits (D).

From Reserves to Money

We know that: M1 = C + D MB = C + TR = C + RR + ER* + ERu

In “equilibrium” (no more money creation/destruction): ERu = 0

With some substitution and rearrangement, we get:

where m* is the “money multiplier.”

We can also write this as:

M1 = [(1+c)/(c+rrD+e)] • MB The Fed can change TR. The Fed could change C.

The Fed can change rrD.

Banks determine e. The public determines c.

Who Determines the

Money Supply?

When the banking system is not in equilibrium, we can write this out as:

When ERu is positive, banks will create more money.

When ERu is negative, banks will destroy money.

When ERu is zero, the banking system is in equilibrium.

From Reserves to Money

With a bank holding positive ERu, they will lend these funds out, raising M1. Those funds become part of another bank’s reserves – they will keep some and lend out the rest. This will continue until ERu are zero.

Money Creation:Getting to Equilibrium

With a bank holding negative ERu, they will reduce their loans, lowering M1. [As loans are paid off, deposits fall.] This contraction of the money supply will continue until ERu are zero.

ReservesRR =

ERu =

Loans

Demand Deposits

Assets

Liabilities & Equity

M1

+$10,000

+$8,000

rrD=20%

-$10,000

+$10,000

+$8,000

+$2,000

+$8,000

+$2,000

Money Creation:Getting to Equilibrium

ReservesRR =

ERu =

Loans

Demand Deposits

Assets

Liabilities & Equity

M1

+$10,000

+$8,000

rrD=20%

-$10,000

+$10,000

+$8,000

+$2,000

+$8,000

+$2,000+$8,000

+$8,000

+$6,400

+$6,400

+$1,600

+$1,600

+$6,400

Money Creation:Getting to Equilibrium

ReservesRR =

ERu =

Loans

Demand Deposits

Assets

Liabilities & Equity

M1

+$10,000

+$8,000

rrD=20%

-$10,000

+$10,000

+$8,000

This process will continue until

there are no more undesired excess

reserves.

+$2,000

+$8,000

+$2,000+$8,000

+$8,000

+$6,400

+$6,400

+$1,600

+$1,600

+$6,400

+$5,120

+$6,400

+$6,400

+$5,120

+$1,280

+$5,120

+$1,280

+$19,520

Money Creation:Getting to Equilibrium

Insure Assets = Liabilities

Identify whether there are +/- ERu

M1 = Loans = [m*] • ERu

D = [1/(1+c)] • M1

C = c • D TR = -C Final values = Beginning values + changes

Arriving at Equilibrium

Money = M1 = C + D

Monetary Base = MB = TR + C

m* =

M1 = [m*] • ERu

D = [1/(1+c)] • M1

C = c • D TR = -C Loans = M1 = D + C

Money Creation Formulas

RR = rrD*D

ER* = e*D

ERu = TR-RR-ER*

C = c*D

Money Creation Problem

rr =

e =

c =

$15,000 Deposits $80,000RRDes. ERUndes. ER

$65,000

DepositsRRDes. ERUndes. ER

Money Creation Spreadsheet Form

Loans

Change in L =

Assets LiabilitiesReserves

Change in M1 = Change in D = Change in C =

Change in TR =

Assets LiabilitiesReserves

Loans

Money Creation Problem

rr =

e =

c =

$15,000 Deposits $80,000RRDes. ERUndes. ER

$65,000

DepositsRRDes. ERUndes. ER

Money Creation Spreadsheet Form

Loans

Change in L =

Assets LiabilitiesReserves

Change in M1 = Change in D = Change in C =

Change in TR =

Assets LiabilitiesReserves

Loans

.05

0

0

4,0000

11,000

+220,000

0

0

MS changed

from $80,000

to $300,000

20*11,000

m* = 1/.05 = 20

1*220,0000*220,000

-(0)C+D

+220,00000

+220,000

300,00015,000

+285,000

15,000

Money Creation Problem

rr =

e =

c =

$15,000 Deposits $80,000RRDes. ERUndes. ER

$65,000

DepositsRRDes. ERUndes. ER

Money Creation Spreadsheet Form

Loans

Change in L =

Assets LiabilitiesReserves

Change in M1 = Change in D = Change in C =

Change in TR =

Assets LiabilitiesReserves

Loans

.10

.03

.15

8,0002,400

4,600

+18,893

2,893

0

MS changed

from $92,000

to $110,893

4.107*4,600

m* =1.15/.28 = 4.1071428

.8695*18,893.15*16,429

-(2,464)C+D

+16,4292,464

-2,464+18,893

96,42912,536

83,893

9,643

C changed

from $12,000

to $14,464

Quick Hits

Money multipliers are derived from the data: M1/MB = m*1 and M2/MB = m*2

Fed targets for money depends on: which multiplier is more stable, and which M is a better predictor of GDP.

Quick Hits

Money Data

Money Data

Money Data

The Mechanics of Money:

ECO 473 - Money & Banking - Dr. D. Foster

MB = C + TR = C + RR + ER* in equilibrium

MB = c •D + rrD•D + e •D = (c+rrD+e) •D

Rearrange and solve for D = [1/ (c+rrD+e)]*MB

M1 = C + D = c •D + D = (1+c) •D

Substitute in formula for D into M1 to get: M1 = [(1+c)/(c+rrD+e)] • MB

Appendix – Deriving m*