WEEK 1 - Rules V Discretion: The Barro-Gordon Model

Question 1

What is Simons view on the need for rules V Discretion in Monetary Policy?

Answer 1

Proposed RULE that targeted constant price level in SR

Question 2

What is Friedman’s view on the need for rules V Discretion in Monetary Policy?

Answer 2

rule that targeted a constant rate of growth of the money supply (the k-percent rule).

Question 3

What are the recent developments behind the Rules V Discretion in Monetary policy debate?

Answer 3

Bernanke - Favouring constrained discretion (judgement of policy maker)

John Taylor - Rules based monetary policy

Question 4

According to Cecchetti and Schoenholtz what is the problem of time consistency?

Answer 4

The effectiveness of a policy depends upon the credibility of the commitment - Things change over time

Question 5

What is the Barro- Gordon model?

Answer 5

Focuses on whether policymakers should adhere to rules or conduct policy according to discretion.

Question 6

What are the two elements of the model?

Answer 6

(i)A Phillips curve the relationship between
unemployment and inflation,
(ii) a loss function, shows preferences of monetary
authorities (or society) over inflation and unemployment.

Question 7

How do you calculate the Phillips Curve in this model?

Answer 7

U = Un - α (Π - Πe)

Reworded comes to:
Π = Πe - 1/α (U-Un)

Where:
Un is Natural Rate of unemployment

Question 8

How do you calculate the Loss Function in this model?

Answer 8

L = {b(U - kUn)2 + Π)

0 < (or equal to) b < (or equal to) Infinity

0

Question 9

What does the Loss Function measure?

Answer 9

Measures amount of dis utility felt by monetary authorities

The higher the L, higher lvl of disutility and vice versa. Aim to make L as low as possible

Question 10

How do we then calculate inflation in the Barro-Gordon model?

Answer 10

Π = ab(1-k)Un/ 1+a2b + a2b/1+a2bΠe = Φ(Πe)

Where:
Φ(Πe) is the best response function (BRF)

Question 11

How do we then calculate the expected inflation in the Barro- Gordon model?

Answer 11

Πe = ab(1-k)Un

Private Sector Expectations

Question 12

What outcome will occur if monetary authorities set inflation to zero and it is believed by the private sector? (Authorities cheat/ Surprise Inflation)

Answer 12

In this scenario:
Πe = 0
Π = 0

If Πe = 0, then inflation positive

Π = ab(1 - k)Un / 1 +a2b
Πe = 0

See effects on unemploy sub Π = ab(1 - k)Un / 1 +a2b and Πe = 0 into Phillips Curve to show:

U = Un - a2b(1-k)Un / 1+a2b

So, unemployment below natural lvl

Question 13

What outcome will occur if monetary authorities set inflation to zero and it is believed by the private sector? (Authorities don’t cheat)

Answer 13

Abides by rule to set Π = 0

Unemployment equal to natural rate

U = Un - a (0-0) =Un

Question 14

What overall outcome will occur if monetary authorities set inflation to zero and it is believed by the private sector?

Answer 14

In the interests of the govt to announce 0 inflation and cheat then adhere to rules as loss function is smaller under Ls(urprise)

Ls < Lrule

Question 15

What outcome will occur if monetary authorities set inflation to zero and it is not believed by the private sector? (PT 1)

Answer 15

Private sector - Rational Expectations and complete info (Loss function and Phillips)

• Private sector see that if not bound by a rule than Monetary authorities will cheat on their promise to set 0 inflation, so private sector expects positive inflation of:
• > Π = ab(1 - k)Un

Monetary authorities also know of private sector expectations, so inflation equals (Plugging in positive inflation and inflation calculation):
Π = ab(1 - k)Un/1 + a2b +a2b/1+a2bΠe = ab(1-k)Un

Question 16

What outcome will occur if monetary authorities set inflation to zero and it is not believed by the private sector? (PT 2)

Answer 16

Plugging the values of π and πe into the PC gives unemployment, U:

U = Un - a(π - πe)
= Un - a(ab(1-k)Un - ab(1-k)Un)
= Un

Question 17

What is the overall outcome if monetary authorities set inflation to zero and it is not believed by the private sector?

Answer 17

when the monetary authorities set inflation in
accordance with the private expectation of inflation, unemployment remains at its natural level.

Plugging the PC and inflation into loss function yields the following expression, where LRat denotes the RE solution.
LRat = b[(1 + a2b)(1 - k)Un]2

Question 18

What is the overall outcome if monetary authorities set inflation to zero and are bound by a rule to do so given private sector’s rational expectation of positive inflation?

Answer 18

In short the economy will be disinflated: realised inflation will be below what the private sector expects.

Unemployment pushed above its natural rate, while inflation positive.
Can be seen by plugging π =0 and πe = ab(1 k)Un
into Phillips curve

This gives:
U = Un - a(π - πe)
= Un (1+ab(1-k)

Loss Function:
LDis = b(1 + a2b)2[(1 k)Un]2

Question 19

What does each scenario show us about their respective loss functions?

Answer 19

Ls

Question 20

What is the best solution for governments to reduce unemployment below its natural rate?

Answer 20

To generate a monetary surprise which the private sector believes

Impossible as private sector has complete info and structure of PC and rational expectations

Question 21

What is the order of the differing solutions posed by the Barro-Gordon model?

Answer 21

Ls < Lrule

Question 22

What is the solution posed by the Barro-Gordon model?

Answer 22

Despite Ls having lowest loss function cannot be chosen as private sector cannot be fooled.

Lrule cannot be chosen in the event where private sector do not believe the authorities will set inflation to 0 (Results in disinflation)

So, L rat(ional expectations) best choice