Master Thesis - Humboldt-Universität zu Berlin

5.5 Monetary and fiscal policy
Finally,we write the equations for fiscal and monetary policy. In steady-state
government consumption is assumed to be 0, so the transfers equal the tax
revenues:
¯ T R
Ȳ
= τ c ¯C
Ȳ
+ τ
l ¯w ¯L
Ȳ
+ τ k (r k − δ) ¯K
Ȳ
(111)
In this equation we know ¯CȲ
¯w ¯L
; Ȳ
= 1−α, r k −δ = ( 1 −1) 1 and ¯KȲ = ĪȲ β 1−τ k δ
follow from FOC equalities of respective variables in the steady state.
Expressing government as percentage deviation from the steady state
output G t = Ȳ Ĝt we have the log-linearized budget constraint:
Ĝ t = τ ¯C c
Ȳ (ˆτ t c +Ĉt)+τ l (1−α))(ˆτ l c +ˆL t +ŵ t )+τ k (r k −δ) ¯K
Ȳ (ˆτ t k +
T R
TˆR t
Ȳ
(112)
rk
r k − δ ˆrk t + ˆ˜Kt )− ¯
With some allowance for interest rate smoothing introduced by parameter
ρ, monetary policy is described by the following interest rate reaction
function:
ˆR t = ρ ˆR
{
t +(1−ρ) r πˆπ t
C
+ r y (Ŷ D
t
{
− Ŷ D,flex
t )
}+r dy (Ŷ t
D
− Ŷ D,flex
t ) − (Ŷ t−1 D − Ŷ D,flex
(113)
t−1 )
}
+ɛ ms
t
ɛ ms
t = ρɛ ms
t−1 + ηt
ms , with ηt
ms an i.i.d. - Normal error term
The interest rate reacts on current inflation, lagged interest rate, current
and lagged output gap, expressed as the difference between real and potential
output.
6 Impulse response functions for the shocks
In this section we analyze the impulse-response functions obtained from the
implementation in the Toolkit and Dynare.
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