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BMW-Modelmacroeconomics without the LM-curve
Peter Bofinger,Eric Mayer,
Timo Wollmershäuser
Universität Würzburg
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BMW-Model
2 20L y 0 0r r e fy
Closed Economy
Optimal
Policy
Taylor Rule
Inflation
bias 2 2
0 ( )L y k
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BMW-ModelOpen
Economy
Flexible Exchange
Rates
Fixed Exchange rates
Managed floating
UIP and PPP hold
(r=r*)
UIP holds, PPP
not
UIP and PPP hold
not
UIP hold
UIP and PPP violated
(=currency crisis)
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Problems of the IS/LM Model Monetary Policy depicted as
targeting monetary aggregates No explicit determination of the
inflation rate Inconsistent derivation of
aggregate supply Open economy only depicted as fix
price model (Mundell-Flemming)
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Inconsistent Derivation of Aggregate Demand
P0P1
AD1
i0
i
Y
d0Y i
P
YYF
IS-curve
d1Y i
AD0
0
0
MLMP
0
1
MLMP
i1
Y1
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Model Aggregate Demand
Phillips Curve
Monetary Policy: Optimal
1dy a br
2e dy
2 2L y 1 2( ; )r r
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Policy Outcomes
opt
1 22
a 1 drb b b d
22
dyd
0 22d
Optimal Monetary Policy
Inflation Gap
Output Gap
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r
y
y
0
r0
0
d0y r
PC0
1 2r ,
Graphical Analysis: Demand Shock
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r
y
y
0
r0
0
d0y r
PC0
d1y r
y1
1
1 2r ,
Graphical Analysis: Demand Shock
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1 2r ,
r
y
y
0
r0
0
d0y r
PC0
d1y r
y1
1
r1 1 2r ,
Graphical Analysis: Demand Shock
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r
y
y
0
r0
0
d0y r
PC0
d1y r
y1
1
r1
1 2r ,
1 2r ,
Bliss
Point
Graphical Analysis: Demand Shock
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r
y
y
0
r0
0
d0y r
PC0
Graphical Analysis: Supply Shock
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r
y
y
0
r0
0
d0y r
PC0
PC1
1
Graphical Analysis: Supply Shock
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r
y
y
A
rB
d0y r
PC0(e=0, 2=0)PC1(e=1, 2>0)
rA
B
A
B
RF , y
yB=0yA
1 2r ,
1 2r ,
Graphical Analysis: Demand Shock
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The Model with Simple Rules Aggregate Demand
Phillips Curve
Monetary Policy:Simple Rules
1dy a br
2e dy
0 0r r e fy
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Policy Outcomes Optimal Policy
Inflation Gap
Output gap
0 0r r e fy
2 1be 1y
1 bf dbe 1 bf dbe
0 1 2d 1 bf
1 bf dbe 1 bf dbe
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Graphical Analysis: Taylor-Rule
r
y
r0
MP(0)MP(1)
r1
0
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r
y
y
0
r0
0
d0y r
PC0
MP(0)
d0y e,f ,
Graphical Analysis: Taylor-Rule: Demand Shock
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r
y
y
r0
0
d0y r
PC0
d0y e,f ,
d1y r
MP(0)
0
Graphical Analysis: Taylor-Rule: Demand Shock
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r
y
y
r0
0
d0y r
PC0
d0y e,f ,
d1y r
d1y e,f ,
MP(0)
0
y‘
r‘
Graphical Analysis: Taylor-Rule: Demand Shock
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r
y
y
r0
0
d0y r
PC0
d0y e,f ,
d1y r
d1y e,f ,
MP(0)MP(1)
01
y1
r1
Graphical Analysis: Taylor-Rule: Demand Shock
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r
y
y
0
r0
0
d0y r
PC0
MP(0)
d0y e,f ,
Graphical Analysis: Taylor-Rule: Supply Shock
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r
y
y
0
r0
0
d0y r
PC0
MP(0)
d0y e,f ,
PC1
Graphical Analysis: Taylor-Rule: Supply Shock
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r
y
y
0
r0
0
d0y r
PC0
MP(0)
d0y e,f ,
PC1
y1
r1
MP(1)
1
Graphical Analysis: Taylor-Rule: Supply Shock
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Graphical Analysis: Taylor Rule and Optimal Monetary Policy: Supply Shock
r
y
y
0
r0
0
PC0
y1
1
r1 1 2r , 1 2r ,
0IS
PC1
yd()
Taylor RuleTaylor Rule
T
yT
rT
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r
y
y
r0
0
d0y r
PC0
d0y
d1y r
d1y
MP(0)MP(1)
01
y1
r1
Graphical Analysis: Taylor-Rule: Demand Shock
1 2r ,
1 2r , r1
Optimal Monetary
Policy
Taylor Rule
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A Comparison: Optimal versus simple Rules: Analytical Although the Taylor rule is a linear
relationship between two endogenous variables (output gap; inflation rate), it can be transformed in a way that shows the implicit reaction of the central bank to exogenous demand and supply shocks.
Taylor0 1 2
ed f er r1 bf bed 1 bf dbe
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A Comparison: Optimal versus simple Rules: Demand Shocks Optimal and simple monetary policy can
only be identical if:
Which translates into:
However this is only true for values of e and/or f approaching infinity
opt
1 22
1ab b
drb d
Taylor0 1 2
ed f1 bf
ebed
r r1 bf dbe
1 1
b 1 ed f b
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A Comparison: Optimal versus simple Rules: Supply Shocks Equivalence can hold if
Which translates into:
Thus, under certain conditions a Taylor rule can lead to an optimum response to supply shocks.
2
d e1 bf dbeb d
d(1 bf )eb
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Optimale Politik versus einfacheRegel
Optimale Politik
Taylor-Regel
0 1 2
2 20
dr
22
0
2
22
L y
einsetzen der Phillipskurve und
der y Kuve, dann ableiten nach r:
Politikergebnisse:dy
1 dr=rb b
, d
d
d
0
1 2
0
1 2
0
Politikergebnisse:1 bey= ε - ε ,
1+bf+dbe 1+bf+dbed 1+bfπ=π + ε + ε
1+bf+db
r r e f
e 1+bf+d
y
be
Determination desZinssatzes
•Als Funktion der Schocks
•Als Funktion der Zielvariablen
Vorgehen Heuristik
Determination desZinssatzes
Vorgehen
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Barro-Gordon-Model: Central bank with employment targets
L = (-0)2+(y-k)2 with k>0 = e+dy Optimal Inflation rate: opt > 0, in
order to reduce unemployment
Time Consistent Monetary Policy
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Barro-Gordon: Inflation Bias
0 k
0
y
Central bank with ambitious employment targets
Central bank with stabilization targets
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Der Bliss Point of the Central Bank
0
yy=k
01y k
L L
(k;0)
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The Reaction Function
0
RF(y)y
y=0 y=k
0 k yd d
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Reaction Function of the Central Bank
e=0
RF(y)
0
y=0 y=k
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e=0
RF(y)
0
y=0 y=k
Reaction Function of the Central Bank
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RF(y)
e=1
0
1
y=0
e=0
Reaction Function of the Central Bank
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RF(y)
e=1
2
0
1
y=0
e=0
Reaction Function of the Central Bank
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RF(y)
e=1
2
0
1
y=0
e=0
e=2
Reaction Function of the Central Bank
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RF(y)
e=1
2
0
1
y=0
e=2
e=0
Reaction Function of the Central Bank
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Policy outcomes: Three Scenarios Surprise Inflation
Rational Expectations
Committment
0e
e opt
0e
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Surprise Inflation (Point A)
RF(y)
y0
s
PC0(e=)
0
y=kys
A
RF(y)
y0
s
PC0(e=)
0
ys
A
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RF(y)
y0
s0
y=kys
A
y
PC
s
0e
y
0 ( )dy r
ZL(r0)r0
r
ZL(r1)r1
Surprise Inflation (Point A)
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Rational Expectations (Point B)
RF(y)
y
rat
0
PC0(e=)B
PC1(e=rat )
0
y=kys
A
C
RF(y)
y
rat
0
PC0(e=)B
PC1(e= )
0
ys
As
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RF(y)
y0
B
y=kys
A
C
ys
As
0e PC0
PC1 1
e
rat
0 ( )dy r
ZL(r0)r0
r
ZL(r1)r1
Rational Expectations (Point B)
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Commitment-Solution (Point C)
RF(y)
y
rat
0
s
PC0(e=)B
PC1(e=rat )
0
y=kys
A
C
RF(y)
y
rat
0
s
PC0(e=)B
PC1(e= )
0
ys
A
C