Monetary Policy (Stabilisation Policy, Optimal MP, Interest Rate Rules (big)) (not technical, just equations to rmb)

Question 1

Over long run - what is the cause of high inflation

Answer 1

Excessive money creation

Question 2

Short run action for monetary policy makers

Answer 2

Want to know how policy makers should respond to various shocks

Question 3

Main macro model used:

Answer 3

COMPASS - a New Keynesian general equilibrium model

Question 4

Assumptions of COMPASS New Keynesian model

A) Prices and wages are sticky. What does this mean

B) role of expectations - they impact what? (2)

Answer 4

Prices and wages sticky, so MP affects output and employment in the short to medium term

Expectations also impact current output and inflation

Question 5

So we said how in the long run high inflation is caused by misguided MP; we can show this by

Quantity theory of money - expression

B) logged version

Answer 5

MV = PY

B)
Take logs of it to get
m+v = p+y (Lower case represents logged version)

Question 6

Then add growth rates
∆𝑚 + ∆𝑣 = ∆𝑝 + ∆𝑦

Given V is stable. What do we get (final QToM eq)

Answer 6

𝜋 = 𝜎 − 𝑔

Inflation = money supply growth rate - GDP growth rate

I.e inflation is caused by money supply growing faster than GDP. Hence why Friedman’s k% rule to ensure 𝜎=𝑔 to have no inflation.

Question 7

That was long run considerations. (Short, we focus on short run)

What do policymakers consider in the short run? (4)

Answer 7

Stabilisation policy and inflation targets

Optimal MP

Interest rates rules

Zero lower bound and liquidity traps

Question 8

Policymakers need to consider stabilisation policy:

Why does high inflation need stabilising (why is it costly for a) households and b) firms c) tax system

Answer 8

Households - waste time/resources economising on their holdings of cash; (banking time or shoe leather costs)

B) Firms waste time/resources trying to calculate price (menu costs)

C) Fiscal drag - more in higher tax bands if tax bands don’t rise with it

Question 9

What has happened to income tax in UK

Answer 9

Income tax threshold frozen until 2027/28

Bad for households, good for government (earn more tax revenue without actually rising taxes - a stealth tax!)

Question 10

So those are 3 negatives to households, firms and tax system (but gov benefit from fiscal drag)

Benefits to inflation (2)

Answer 10

Grease wheels of labour markets - cut real wage cuts stealthily (keeping nominal wage constant while inflation rises)

Higher inflation target = higher interest rates = less likely to hit the ZLB nominal interest rates

Question 11

Conclusion on inflation - good or bad

Answer 11

Little bit of inflation might be healthy and useful, but too much is destabilising with costs to society.

(Healthy as shows people are buying stuff - zero inflation can mean 0 growth like Japan had 0 inflation because of 0 growth!)

Question 12

So incentive to control inflation from being too high as destabilising. (3 reasons for households, firms, tax system)

What about stabilising output or unemployment?

Compare UK vs US stabilisation policy

Answer 12

UK inflation target

US dual mandate - equal weight on inflation and unemployment

Question 13

We can express this by
Central Bank loss function (a negative utility function, where we want to minimise losses) pg6

Answer 13

L = b(πt - πT)² + (yt - ye)²

πt: actual inflation
πT: inflation target
yt: acutal output
ye: long run output
b: how much CB cares about inflation relative to output

Question 14

Intuition of b:
b=1
b>1
b<1

B) pg6
Diagrams of loss function if b=1 b>1 b<1

Answer 14

b=1 dual mandate (equally weight inflation/output)
b>1 inflation target (weight inflation more)
b<1 output primacy (weight output more - less likely irl)

B) at bliss point L=0 no loss! Unrealistic tho
b>1 = inflation target looks squashed vertically
b<1 = output primacy looks squashed horizontally

Question 15

2nd consideration of policymakers: optimal MC
What does the central bank do to optimise their policy

Answer 15

Minimise their loss function

Question 16

What is the issue with minimising CB loss function

Answer 16

Optimal policy is sensitive to the model specification /misspecification

I.e if model is wrong, which it is often not perfect and mispeciffied, policy recommendations will be wrong

Question 17

Alternative to avoid this

Answer 17

Instead of loss function, add monetary policy rule to the model. E.g Taylor rule, Canonical NK model

This way it still works even if model incorrectly specified

Question 18

Canonical New Keynesian model 3 equations, what is the MP rule

B) General Intuition

Answer 18

Demand side NKIS
Supply side Phillips curve

MP rule:
it = 𝜙𝜋𝐸𝑡𝜋𝑡+1 + 𝜙𝑦𝐸𝑡𝑦𝑡+1 + 𝜀𝑡𝑀𝑃

𝜙π responsiveness of CB with interest rates to inflation
𝜙y responsiveness of CB with interest rates to output

B)
Forward looking - If expected inflation Etπt+1 increases, increase current interest rates now, as know it lags exist - takes time to get desired effects, hence raise now!

Question 19

3 equilibrium types in dynamic models

Answer 19

Unique and stable

Explosive

Multiple equilibria (sunspots)

Question 20

Unique and stable, what happens here (good)

And example

Answer 20

Economy returns to its long-run equilibrium following a shock

E,g with RBC we see shocks, and then come back to LR eq.

Question 21

Explosive equilibrium (not good)

Answer 21

Endogenous variables such as output and inflation, shoot off to + or - infinity following a shock, never come back to LR eq.

Policy tries to stop this from happening e.g stop hyperinflation

Question 22

Multiple equilibria (sunspots) equilbrium

B) example of this equilibrium

Answer 22

Multiple equilibria exist, some may be stable some not. Problematic since equilibrium is whatever agents expect it to be (self-fulfilling!)

B) DD model - 2 possible nash equilibrium:
Socially-optimal outcome: people follow their preferences (Type A withdraw and type B save - this is the stable equilibrium)

But if B believes all types withdraw, all withdraw as don’t wanna end up with nothing. Banks liquidate projects. This is the unstable equilibrium. (Self-fullfilling, not based on economic fundamentals!)

Question 23

Recall Taylor’s interest rate rule:

B) Under this, what equilibrium types we just looked at are possible, and under what conditions

C) why is it not realistic

Answer 23

It = 𝜋𝑡 + p + 𝜃𝜋(𝜋𝑡− 𝜋𝑡*)+ 𝜃𝑌(𝑌𝑡−𝑌bar𝑡)

B)
unique and stable (if 𝜃𝜋>0)
or explosive (if not >0 get hyperinfaltion)

C) as this rule is not forward looking - IRL CB’s look ahead. With a forward looking rule equilibrium type 1 and 3 (multiple equilibria) are possible

Question 24

When we have a forward looking rule, which equilibrium types are possible.

Answer 24

Type 1 and 3
(Unique and stable, multi equilibria - expectations drive outcome i.e selfullfilling like DD model)

(Type 3 when 𝜙𝜋 < 1, type 1 when >1, PTO!)

Question 25

So we use a forward looking (better than Taylor rule which doesn’t include forward looking): Like the previous (or Clarida, next one) it = 𝜙𝜋𝐸𝑡𝜋𝑡+1 + 𝜙𝑦𝐸𝑡𝑦𝑡+1 + 𝜀𝑡𝑀𝑃 Suppose that 𝜙𝑦 = 0 and 𝜙𝜋 > 1 Consider a rise in expected inflation: what do CB’s do?

Answer 25

CB increase it (nominal) by more than the rise in expected inflation, in order to increase the real interest rate!

Question 26

So CB increase real interest rates via overshooting the nominal rate. Main implications - what is no longer possible now, and why? (Good thing)

Answer 26

Type 3 (multiple equilibria) no longer possible! No self-fulfilling expectations, as CB’s have a credible plan (overshoot nominal rates) if expected inflation gets out of control, and agents know this and believe it. Just the threat to raise interest following a rise in expected inflation prevents any increases in the first place. (Like in DD model, all they needed was a credible promise that government would back deposits (in order to prevent type B’s also withdrawing in panic)

Question 27

Clarida rule (i*t) : pg 9 (another forward looking MP rule, slightly diff from the MP rule Canonical NK model one)

Answer 27

𝑖*𝑡= rn + 𝜙𝜋(𝐸𝑡[𝜋𝑡+𝑘]− π*) + 𝜙𝑦𝐸𝑡[ln𝑌𝑡+𝑘− ln𝑌 to the n 𝑡+𝑘] K>0 since forward looking i*t: interest rate CB announces rn: natural/LR real interest rate π*: inflation target 𝜙𝜋: responsiveness of interest rate to expected inflation, if it moves away from inflation target) 𝜙y: responsiveness of interest rate to expected output inflation, if it moves away from long run output) i.e expected output gap

Question 28

Clarida also adds interest rate smoothing. What is meant by this? B) interest rate smoothing expression

Answer 28

Policy makers dont want to scare and do all in one, they spread out changes over multiple policies B) 𝑖𝑡 = 𝜌𝑖𝑡−₁ + (1 − 𝜌)𝑖𝑡* P measures degree of smoothing (0

Question 29

Looked at empirics, A) prevolcker era has 𝜙𝜋= 0.83. Meaning: B) second period 𝜙𝜋= 2.15

Answer 29

𝜙𝜋= 0.83. <1!!! Recall if 𝜙𝜋>1 means self fulfilling i.e multiple equilibria. Since <1, means we get type 3 equilibrium (pg9 or FC27) Second period: 𝜙𝜋 = 2.15, >1 so we get unique and stable!

Question 30

So that was 3rd consideration of policymakers: interest rate rules. Now final short-run consideration: zero lower bound and liquidity traps. Interest rate controls seemed to work well, until GFC. Why?

Answer 30

Interest rates went to 0, but economy still in recession. Hard to lower below 0. So interest rates weren’t effective here.