L7 The Taylor Equation & Expanded Loanable Funds Model

taylor eqn

i_f = pi + a(pi - pi*) + b(U* - U) + r_f*

i_f is recommended nominal federal funds rate

pi is inflation rate

pi* is inflation target

U is unemployment rate

U* is natural unemployment rate (aka NAIRU)

r_f* is neutral real federal funds rate

a is the weight on the inflation gap

b is the weight on the unemployment gap

three policy stances and their relation to r_f*

restrictive: rf > rf* so you slow demand and reduce inflationary pressure

neutral: rf = rf* so you are supporting sustainable growth with stable inflation (neutral)

easy/expansionary: rf<rf* so you’re encouraging spending investment and employment

what is the neutral real interest rate rf* meaning

the policy rate consistent with the economy remaining at potential GDP with inflation and unemployment at target

at neutral, monetary policy is neither stimulating or restraining

what does the taylor equation look like when unemployment and inflation are at target

i_f = pi + rf*

why does inflation compensation appear twice in the taylor equation

recall the eqn:

i_f = pi + a(pi - pi*) + b(U*-U) + rf*

see how you add pi, and then you also have the a(pi-pi*) term

it’s because you have the first one for if inflation increases the nominal interest rate must also increase to keep the real rate unchanged

and then the second one is to describe the affect that above target inflation would have on the intended target interest rate.

why doesn’t the taylor eqn make a policymakers job super easy

bc U*, rf*, alpha, and beta are all estimated, we don’t know the true values so you have to constantly guess and change them

even the inflation rate pi that you use could be expected or last years for baseline

how would a tech breakthru affect the neutral rate

tech means there are many highly profitable investment opportunities

businesses eager to borrow and invest

upward pressure on interest rates

signs of the modifiers in the taylor eqn

for inflation it’s pi - pi* where pi* is desired inflation

for u its u* - u

if real interest rate is less than neutral, is that expansionary or stimulative

it is expansionary because it stimulates more borrowing

how does corporate pessimism affect the corporate bonds graph

corporations want to invest less so the downward sloping demand curve shifts left

means at equil., r_c is lower and so is Qc

What happens to the attractiveness of short-term Treasury bills when the Fed raises \(r_f\)?

Short-term T-bills become more attractive because they offer higher real returns. Households may shift funds away from long-term government and corporate bonds.

How does an increase in \(r_f\) affect the household funding-supply curves?

• \(S_g\) shifts LEFT.

• \(S_c\) shifts LEFT.

Households prefer higher-yielding short-term Treasury bills, putting upward pressure on \(r_g\) and \(r_c\).

How does a decrease in \(r_f\) affect the household funding-supply curves?

• \(S_g\) shifts RIGHT.

• \(S_c\) shifts RIGHT.

Short-term T-bills become less attractive, encouraging households to purchase long-term bonds. This puts downward pressure on \(r_g\) and \(r_c\).

During a financial panic, how do household funding-supply curves shift?

• \(S_g\) shifts RIGHT because households seek safer government bonds.

• \(S_c\) shifts LEFT because households avoid risky corporate bonds.

Consequently, \(r_g\) falls, while \(r_c\) faces upward pressure.

What happens when businesses become pessimistic about future profitability?

Corporate financing demand \(D_c\) shifts LEFT.

At unchanged supply, both \(r_c\) and \(Q_c\) decrease.

What happens when technological innovation increases expected investment profitability?

Corporate financing demand \(D_c\) shifts RIGHT.

At unchanged supply, both \(r_c\) and \(Q_c\) increase.

What happens when the government increases long-term borrowing?

Government financing demand \(D_g\) shifts RIGHT.

At unchanged household funding supply, \(r_g\) increases and government borrowing \(Q_g\) increases.

If corporate funding supply shifts LEFT and corporate financing demand shifts RIGHT, what happens?

• \(r_c\) definitely INCREASES.

• \(Q_c\) is AMBIGUOUS.

Both shifts raise the interest rate, but they have opposing effects on borrowing quantity.

If corporate funding supply and corporate financing demand BOTH shift LEFT, what happens?

• \(Q_c\) definitely DECREASES.

• \(r_c\) is AMBIGUOUS.

Both shifts reduce borrowing, but supply contraction pushes rates up while demand contraction pushes rates down.

If corporate funding supply and corporate financing demand BOTH shift RIGHT, what happens?

• \(Q_c\) definitely INCREASES.

• \(r_c\) is AMBIGUOUS.

Both shifts increase borrowing, but they have opposing effects on interest rates.