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Monetary Policy Tradeos by Jordi Gal November 2010 Policy Tradeos - - PowerPoint PPT Presentation
Monetary Policy Tradeos by Jordi Gal November 2010 Policy Tradeos - - PowerPoint PPT Presentation
Monetary Policy Tradeos by Jordi Gal November 2010 Policy Tradeos and the New Keynesian Phillips Curve t = E t f t +1 g + ( y t y n t ) Criticism: no policy tradeos, optimality of strict ination targeting y e t
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The Monetary Policy Problem min E0f
1
X
t=0
t xx2
t + 2 t
- g
(1) subject to: t = Etft+1g + xt + ut where futg evolves exogenously according to ut = uut1 + "t In addition: xt = 1 (it Etft+1g re
t) + Etfxt+1g
(2) Note: utility based criterion requires x =
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Optimal Discretionary Policy Each period CB chooses (xt; t) to minimize xx2
t + 2 t
subject to t = xt + vt where vt Etft+1g + ut is taken as given. Optimality condition: xt = x t (3) Equilibrium t = xut (4) xt = ut (5) it = re
t + [(1 u) + xu]ut
(6) where
1 2+x(1u)
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Implementation: it = re
t + [(1 u)
x + u]t uniqueness condition:
x > 1 (likely if utility-based: > 1)
Alternatively, it = re
t + [(1 u) + xu]ut + (t xut)
uniqueness condition: > 1:
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Optimal Policy with Commitment State-contingent policy fxt; tg1
t=0 that minimizes
E0
1
X
t=0
t xx2
t + 2 t
- subject to the sequence of constraints:
t = Etft+1g + xt + ut Lagrangean: L = 1 2E0
1
X
t=0
t[x x2
t + 2 t + 2t (t xt t+1)]
First order conditions: xxt t = 0 t + t t1 = 0 for t = 0; 1; 2; :::and where 1 = 0.
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Eliminating multipliers: x0 = x (7) xt = xt1 x t (8) for t = 1; 2; 3; :::.. Alternative representation: xt = x b pt (9) for t = 0; 1; 2; :::where b pt pt p1
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Equilibrium b pt = ab pt1 + aEtfb pt+1g + aut for t = 0; 1; 2; :::where a
x x(1+)+2
Stationary solution: b pt = b pt1 +
- (1 u)ut
(10) for t = 0; 1; 2; :::where
1p 14a2 2a
2 (0; 1): ! price level targeting ! xt = xt1
- x(1 u)ut
(11) for t = 1; 2; 3; :::as well as x0 =
- x(1 u) u0