[Notes on Mishkin Ch.15 - P.1]

Chapter 15: The Fed-Funds Market (“Tools of Monetary Policy” working in the Fed Funds market)

between banks = Buying and selling reserve balances held at the Fed. - Overnight loans, unsecured, OTC. Symbol:

i ff = Fed Funds rate.

- Key point: Trading does not change total reserves.

Supply of Reserves

1. Supply through open market operations:

NBR = Non-borrowed. 2. Supply through discount loans:

BR = borrowed at interest rate

id , provided to banks on demand, only for as long as discount loans are outstanding.

- Write as function

BR = BR(i ff − id ). Zero for

i ff < id . - Interest-elastic for

i ff ≥ id . Extreme case in Mishkin: horizonal at

i ff = id.

the Fed Funds rate

Rs(i ff ) = NBR+BR(i ff − id ) Shape: Corner at

i ff = id . Vertical for

i ff < id . Elastic for

i ff ≥ id .

[Notes on Mishkin Ch.15 - P.2]

Demand for Reserves

-

RR = rr ⋅D - Excess reserves:

ER = ERD +ERI => Total reserve demand:

Rd = RR+ER = rr ⋅D+ER

offer interest on reserves (ior).

2. Banks make decisions about excess reserves, multiple motives: - deposit taking – as discussed in the money multiplier model:

ERD = eD ⋅D. - interest on reserves – motivates banks to absorb excess:

ERI = ERI (ior − i ff ) - minimizing cost of reserves within a reserve maintenance period.

- Several arguments …

[Notes on Mishkin Ch.15 - P.3]

The Fed funds rate determines banks’ incentives to attract deposits and make loans => ff.

- cost (consumer interest rates) and transaction needs. Needs:

- Fed funds rate is the opportunity cost of funds for banks Changes in i ff triggers changes in retail interest rates (loans, deposits) =>

D = D(i ff ,Y ,P,...) downward sloping function of iff

- esired deposits depends on real output and prices (like money demand) - esired deposits

2: deposits - reserves are proportional to deposits (by definition) =>

RR = rr ⋅D(i ff ,Y ,P,...) downward sloping function of iff - Excess reserves are small and proportional to deposits, provided

i ff > ior : =>

R = (rr + e) ⋅D(i ff ,Y ,P,...) downward sloping function of iff

[Notes on Mishkin Ch.15 - P.4]

-run argument: - Banks are obliged to hold sufficient reserves over a reserve maintenance

period of 14 days => Incentives to hold more/less reserves on days when the -

elastic than deposits within each reserve maintenance period.

pecial argument : - If

i ff < ior , banks could earn arbitrage profits

ior − i ff by borrowing Fed funds

i ff < ior

i ff = ior (Textbook graph)

- Technical Caveat: Some institutions not eligible to receive interest on reserves => Find that

i ff ≥ ior −Δ with

Δ = small profit margin for intermediaries (Simplify theoretical exposition: assume

Δ ≈ 0 so

i ff ≥ ior.) - Main result: IOR provides a lower bound for the Fed Funds rate.

eserve demand function has two parts: - is decreasing function of the Fed funds rate for

i ff > ior - is horizontal at the lower bound

i ff = ior

[Notes on Mishkin Ch.15 - P.5]

Market Equilibrium :

Rs = NBR+BR(i ff − id ) = Rd (i ff ,ior ,Y ,P,.rr,...) i ff , i

d, and

ior

- iscount rate below the Fed funds target administrative restrictions on discount loans to discourage opportunistic borrowing by banks.

- – iscount rate set above the Fed funds target (penalty rate). No

ior = 0.25%. - Since

i ff ≈ ior.

iff

id

iff

id

iff

ior

[Notes on Mishkin Ch.15 - P.6]

Mishkin’s Diagrams

[Notes on Mishkin Ch.15 - P.7]

2. Impact of an Open Market Operations

Main tool for controlling the Fed Funds rate in normal times. Ineffective when with ample reserves and

i ff ≈ ior.

[Notes on Mishkin Ch.15 - P. ]

3. Impact of a reduced discount rate

[Notes on Mishkin Ch.15 - P.9]

Rd ≈ rr ⋅D => —similar answers)

[Notes on Mishkin Ch.15 - P. ]

5. Impact of a higher interest rate on reserve balances

Main tool for controlling the Fed Funds rate with ample reserves. Ineffective when

i ff > ior .

[Notes on Mishkin Ch.15 - P.11]

Fluctuations in the Demand for Reserves

, subject to shocks. - Macro disturbances: changes in Y, P => shifts in Md d - Financial disturbances: seasonal changes (holiday cash needs), banking

: iff

d. No Fed involvement => Loss of control over iff.

[Notes on Mishkin Ch.15 - P.12]

Coping with Fluctuating Reserve Demand

over the money supply. Monetary history = search for solutions. 1. Fed procedures before 2003: set the discount rate below the Fed funds rate

target, use administrative controls to restrict discount loans:

can take out discount loans.

rate effect of shifts in reserve demand.

s flat or more steep.

M1 = m * (MBn

- d: setup induces banks to claim emergencies to obtain “cheap” discount loans.

iff

id

[Notes on Mishkin Ch.15 - P.13]

2. Fed procedures 2003-2008: - Set the discount rate above the Fed funds rate target (penalty rate) -

Normal procedure:

stabilize iff between meetings. ff-the target as needed.

Open market operations that stabilize iff imply that money supply is perfectly elastic when demand shifts: Higher Md d => higher

ff constant => increase in M1 = m * MBn. - Procedures rely on FOMC to adjust the target to avoid excessive M1 growth. d are observed => gives FOMC information about Md

iff

id

[Notes on Mishkin Ch.15 - P.14]

3. Fed procedures since 2008 – -

reserves so that

i ff ≈ ior. Set the discount rate at penalty level.

stabilize iff between FOMC meetings

ff-target as needed.

What could possibly go wrong?

d are unobserved => No information about banks’ desired reserves

to support deposit taking vs. excess reserves held as investments 2. Question about how/if the Fed can control money supply

d includes excess reserves for deposit taking. Flat segment captures reserves held as investment.

-

i ff = ior and

R = ˆ R d = (rr + eD) ⋅D(ior )

iff

id

ior

[Notes on Mishkin Ch.15 - P.15]

Monetary Analysis with Ample Reserves

Rs > ˆ R d . Traditional case when

Rs ≤ ˆ R d.

Rs > ˆ R d :

-

ERI = Rs − ˆ R d > 0 and

e = ERDD + ERI

D > eD. - Open market purchases increase

ERI , increase

e, but have no impact on M1. Though MB increases, higher e reduces m enough to neutralize the effect. - Open market sales reduce

ERI , reduce

e, but have no impact on M1, unless they are large enough that reserve supply falls below

ˆ R d.

-elastic money supply

Term structure: money market rates (i) determined by current & expected iff

=> Fed can fix i=i* by setting ior => Then M = *

d curve shifts, M1 varies => Money supply curve is horizontal at i*

ior, the Fed must rely on term structure linkages and on the downward slope of Md(i)

i

M

i*

[Notes on Mishkin Ch.15 - P.16]

Final Comment: What else could the Fed do? -crisis) used both lower and

upper bounds to control money market interest rates

When reserve demand varies, Fed funds rate would bounce within the interval - Provides information about reserve demand related to deposit taking - Setting tight bounds would allow the Fed to reduce security holdings without

risk of triggering large interest rate changes. => Possible , return to pre-

operation of the Fed Funds market.

iff