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Barro – Gordon – Model. How to avoid the inflation bias? 1. Reputation: Barro-Gordon (1983b). 2. Delegation: Rogoff (1985). 3. Central bank contract.
Typology: Lecture notes
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min L s. t. N Nn c(- e ),
min b ( *^ )^2 ( N c( e) N *)^2
2 goals of monetary policy:
Static Phillips curve: N = Nn + c ( π – π e),
Loss function L = b ( π – π )^2 + (N – N)^2
2
Response of the central bank on given expectations
2
b c
b c N N c E
e e n
e * ( N * N n ) b
c
c
Inflation bias
3
Response of central bank to inflation expectations π ( π e) without commitment
π
π *
π for π e= π *
Iso-loss curves
Phillips curve for π e= π *
Equilibrium with rational expectations:
π *
π equilibrium
Phillips curve for π e^ = π equilibrium
Iso-loss curve
equilibrium
Discretionary solution =
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For avoiding the inflation bias and stabilizing the economy in an efficient way,
With L = b ( π – π *)^2 + (N – N (^) n)^2 and π e^ = π *. we get L = b E( π – E( π ))^2 + E(N – E(N))^2 = b Var( π ) + Var(N).
Stochastic economy:
policy.
inflation, output and employment are stabilized as well.
have real effects.
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8.1 Stabilizing supply shocks
What is the optimal response of monetary policy to
shocks in productivity?
production function y = a N + θ
Productivity shock θ : E( θ ) = 0 Var( θ ) = σ^2
Labor demand N = Nn + c ( π – w + θ )
Wages w = π e
All variables may be interpreted as growth rates.
Phillips curve
a c 1
1
Stabilizing supply shocks
π
π e
N = N (^) n + c ( π – π e^ + θ )
1/c
Phillips curve für θ = 0
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Stabilizing supply shocks
Solving the trade-off between stabilizing inflation and
employment.
Min b ( π – π *)^2 + (N – Nn)^2
= Min b ( π – π *)^2 + ( c ( π – π e^ + θ ) )^2
Since N*=N (^) n, the inflation bias is zero, so that π e^ = π *.
=> 2 b ( π – π *) + 2 c^2 ( π – π * + θ ) = 0
=> (b+c^2 ) ( π – π *) = – c^2 θ
2
c
b c
Stabilizing supply shocks
π
Min b ( π – π *)^2 + (N – N (^) n)^2
N = N (^) n + c ( π – π e^ + θ )
Phillips curve for θ = 0
employment fluctuations
fluctuations of inflation
1/c
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8.2 Rules versus Discretion
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What are optimal rules in the face of demand and supply
shocks?
production function y = a N + θ
Productivity shock θ : E( θ ) = 0 Var( θ ) =
Labor demand N = Nn + c ( π – w + θ ),
Wages w = π e
Demand side (quantity theory) μ + η = π + y
Demand shock η : E( η ) = 0 Var( η ) =
Phillips curve
2
Loss function L = b ( π – π )^2 + (N – N)^2
a
c
1
1
Rules versus Discretion
Rule 1: constant rate of inflation, π = π *
=> π e^ = π * => N = N (^) n + c θ
( *^ )^222 N (^) n N c
Rules versus Discretion
Comparing welfare loss for rule 1 versus rule 2
2
2
2 2
2 2
( 1 ( 1 ) )
2
2 2
2
1 ( 1 )
b
b
Constant money supply growth leads to higher expected costs than constant inflation, if (i) the weight on pricestability is sufficiently large, or (ii) the variance of demand shocks is large compared to the variance of supply shocks.