WEEK 1 - Rules V Discretion: The Barro-Gordon Model Flashcards
What is Simons view on the need for rules V Discretion in Monetary Policy?
Proposed RULE that targeted constant price level in SR
What is Friedman’s view on the need for rules V Discretion in Monetary Policy?
rule that targeted a constant rate of growth of the money supply (the k-percent rule).
What are the recent developments behind the Rules V Discretion in Monetary policy debate?
Bernanke - Favouring constrained discretion (judgement of policy maker)
John Taylor - Rules based monetary policy
According to Cecchetti and Schoenholtz what is the problem of time consistency?
The effectiveness of a policy depends upon the credibility of the commitment - Things change over time
What is the Barro- Gordon model?
Focuses on whether policymakers should adhere to rules or conduct policy according to discretion.
What are the two elements of the model?
(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.
How do you calculate the Phillips Curve in this model?
U = Un - α (Π - Πe)
Reworded comes to:
Π = Πe - 1/α (U-Un)
Where:
Un is Natural Rate of unemployment
How do you calculate the Loss Function in this model?
L = {b(U - kUn)2 + Π)
0 < (or equal to) b < (or equal to) Infinity
0
What does the Loss Function measure?
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
How do we then calculate inflation in the Barro-Gordon model?
Π = ab(1-k)Un/ 1+a2b + a2b/1+a2bΠe = Φ(Πe)
Where:
Φ(Πe) is the best response function (BRF)
How do we then calculate the expected inflation in the Barro- Gordon model?
Πe = ab(1-k)Un
Private Sector Expectations
What outcome will occur if monetary authorities set inflation to zero and it is believed by the private sector? (Authorities cheat/ Surprise Inflation)
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
What outcome will occur if monetary authorities set inflation to zero and it is believed by the private sector? (Authorities don’t cheat)
Abides by rule to set Π = 0
Unemployment equal to natural rate
U = Un - a (0-0) =Un
What overall outcome will occur if monetary authorities set inflation to zero and it is believed by the private sector?
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
What outcome will occur if monetary authorities set inflation to zero and it is not believed by the private sector? (PT 1)
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
What outcome will occur if monetary authorities set inflation to zero and it is not believed by the private sector? (PT 2)
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
What is the overall outcome if monetary authorities set inflation to zero and it is not believed by the private sector?
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
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?
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
What does each scenario show us about their respective loss functions?
Ls
What is the best solution for governments to reduce unemployment below its natural rate?
To generate a monetary surprise which the private sector believes
Impossible as private sector has complete info and structure of PC and rational expectations
What is the order of the differing solutions posed by the Barro-Gordon model?
Ls < Lrule
What is the solution posed by the Barro-Gordon model?
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
