BMW-Modelmacroeconomics without the LM-curve

Peter Bofinger,Eric Mayer,

Timo Wollmershäuser

Universität Würzburg

BMW-Model

2 20L y 0 0r r e fy

Closed Economy

Optimal

Policy

Taylor Rule

Inflation

bias 2 2

0 ( )L y k

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)

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)

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

Model Aggregate Demand

Phillips Curve

Monetary Policy: Optimal

1dy a br

2e dy

2 2L y 1 2( ; )r r

Policy Outcomes

opt

1 22

a 1 drb b b d

22

dyd

0 22d

Optimal Monetary Policy

Inflation Gap

Output Gap

r

y

y

0

r0

0

d0y r

PC0

1 2r ,

Graphical Analysis: Demand Shock

r

y

y

0

r0

0

d0y r

PC0

d1y r

y1

1

1 2r ,

Graphical Analysis: Demand Shock

1 2r ,

r

y

y

0

r0

0

d0y r

PC0

d1y r

y1

1

r1 1 2r ,

Graphical Analysis: Demand Shock

r

y

y

0

r0

0

d0y r

PC0

d1y r

y1

1

r1

1 2r ,

1 2r ,

Bliss

Point

Graphical Analysis: Demand Shock

r

y

y

0

r0

0

d0y r

PC0

Graphical Analysis: Supply Shock

r

y

y

0

r0

0

d0y r

PC0

PC1

1

Graphical Analysis: Supply Shock

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

The Model with Simple Rules Aggregate Demand

Phillips Curve

Monetary Policy:Simple Rules

1dy a br

2e dy

0 0r r e fy

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

Graphical Analysis: Taylor-Rule

r

y

r0

MP(0)MP(1)

r1

0

r

y

y

0

r0

0

d0y r

PC0

MP(0)

d0y e,f ,

Graphical Analysis: Taylor-Rule: Demand Shock

r

y

y

r0

0

d0y r

PC0

d0y e,f ,

d1y r

MP(0)

0

Graphical Analysis: Taylor-Rule: Demand Shock

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

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

r

y

y

0

r0

0

d0y r

PC0

MP(0)

d0y e,f ,

Graphical Analysis: Taylor-Rule: Supply Shock

r

y

y

0

r0

0

d0y r

PC0

MP(0)

d0y e,f ,

PC1

Graphical Analysis: Taylor-Rule: Supply Shock

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

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

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

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

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

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

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

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

Barro-Gordon: Inflation Bias

0 k

0

y

Central bank with ambitious employment targets

Central bank with stabilization targets

Der Bliss Point of the Central Bank

0

yy=k

01y k

L L

(k;0)

The Reaction Function

0

RF(y)y

y=0 y=k

0 k yd d

Reaction Function of the Central Bank

e=0

RF(y)

0

y=0 y=k

e=0

RF(y)

0

y=0 y=k

Reaction Function of the Central Bank

RF(y)

e=1

0

1

y=0

e=0

Reaction Function of the Central Bank

RF(y)

e=1

2

0

1

y=0

e=0

Reaction Function of the Central Bank

RF(y)

e=1

2

0

1

y=0

e=0

e=2

Reaction Function of the Central Bank

RF(y)

e=1

2

0

1

y=0

e=2

e=0

Reaction Function of the Central Bank

Policy outcomes: Three Scenarios Surprise Inflation

Rational Expectations

Committment

0e

e opt

0e

Surprise Inflation (Point A)

RF(y)

y0

s

PC0(e=)

0

y=kys

A

RF(y)

y0

s

PC0(e=)

0

ys

A

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)

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

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)

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