The Mechanics of Money:

The Mechanics of The Mechanics of Money:Money:

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

The Banking System

Reserves(Cash in vault…)

T-Bills(Liquidity & i)

Loans(Banks’ B&B)

Demand Deposits (Checking; Transaction)

Equity

Assets

Liabilities & Equity

Accounting Identity: A L + E

M1

The Role of the Fed

The Fed buysbuys/sellssells Treasury securities. This raisesraises/lowerslowers bank reserves. This raisesraises/lowerslowers excess reserves. This causes banks to increaseincrease/decreasedecrease

loans. This will raiseraise/lowerlower measured money, M1.

The Banking System

ReservesT-BillsLoans

Deposits (Transactions)

M1

Grinding it out: TermsTerms TR = Total Reserves RR = Required Reserves

rrD = required reserve ratio ER = Excess Reserves

ER* = Desired excess reserves ERu = Undesired excess reserves e = the desired excess reserve ratio

Grinding it out: TermsTerms

D = (Demand) Deposits C = Currency in circulation

c = desired currency ratio Δ = “Change In …” MB = Monetary Base M1 = Money Supply

From Reserves to Deposits

TR = total reserves = RR + ER RR = Required Reserves = rrD•D

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

ER = ER* + ERu (desired + undesired)where ER* = Desired Excess Reserves = e •D where “e” is the excess reserve ratio (0 to 1).

From Reserves to Deposits

If e=0If e=0, then …

D = (1/rrD) • RR = (1/rrD) • TR

and . . . ΔΔD = (1/rrD = (1/rrDD))··ΔΔTRTR

… and, with any value for ER, we can write

ΔΔD = (1/rrD = (1/rrDD))··ΔΔERERUU

Where it is assumed: No currency is heldNo currency is held by the public.

i.e., all money is held as bank deposits, Banks hold no excess reservesno excess reserves.

Then, (1/rr(1/rrDD) ) is the maximumvalue of the money multiplier (m)money multiplier (m)

From Reserves to Deposits

MB = C + TR C = currency = c •D

where c is the currency ratio.

MB = c •D + rrD•D + e •D = (c+rrD+e) •D M1 = C + D = c •D + D = (1+c) •D Solve to get M1 = [(c+1)/(c+rrD+e)] • MB

where […] is the money multiplier, m*

From Reserves to Money

We can also write this as: M1 = [(1+c)/(c+rrM1 = [(1+c)/(c+rrDD+e)] • +e)] • MBMB

The Fed can change TR. The Fed could change C. The Fed can change rrD. Banks determine e. The public determines c.

From Reserves to Money

M1 = [(1+c)/(c+rrM1 = [(1+c)/(c+rrDD+e)] • +e)] • MBMB Where the system is in disequilibrium…

MB MB can be replaced with ER ERuu

M1 = […] • ERM1 = […] • ERuu

D = [1/(1+c)] • D = [1/(1+c)] • M1M1 C = c • C = c • DD TR = -TR = -CC Loans = Loans = M1 = M1 = D + D + CC

From Reserves to Money

Money Creation Problemrr = 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

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 DataMoney Data

Money DataMoney Data

Money DataMoney Data

The Mechanics of The Mechanics of Money:Money:

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