Download Monetary/Fiscal Interactions: Nominal Indeterminacy

Monetary/Fiscal Interactions:
Nominal Indeterminacy
Behzad Diba
University of Bern
May 2011
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
1/7
A Classical Question
Classical economists analyzed long-run equilibrium in models that
incorporated the Classical Dichotomy (long-run neutrality of money):
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
2/7
A Classical Question
Classical economists analyzed long-run equilibrium in models that
incorporated the Classical Dichotomy (long-run neutrality of money):
1
The long-run equilibrium values of real variables (e.g., real wages,
employment, output, real interest rates) don’t depend on monetary
conditions
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
2/7
A Classical Question
Classical economists analyzed long-run equilibrium in models that
incorporated the Classical Dichotomy (long-run neutrality of money):
1
2
The long-run equilibrium values of real variables (e.g., real wages,
employment, output, real interest rates) don’t depend on monetary
conditions
The long-run equilibrium values of nominal variables (e.g., the price
level, nominal wages) are determined by monetary conditions and the
equilibrium values of the relevant real variables
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
2/7
A Classical Question
Classical economists analyzed long-run equilibrium in models that
incorporated the Classical Dichotomy (long-run neutrality of money):
1
2
The long-run equilibrium values of real variables (e.g., real wages,
employment, output, real interest rates) don’t depend on monetary
conditions
The long-run equilibrium values of nominal variables (e.g., the price
level, nominal wages) are determined by monetary conditions and the
equilibrium values of the relevant real variables
Neoclassical models of long-run equilibrium (with no nominal rigidity)
re‡ect the same fundamental view in a more sophisticated setting
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
2/7
A Classical Question
Classical economists analyzed long-run equilibrium in models that
incorporated the Classical Dichotomy (long-run neutrality of money):
1
2
The long-run equilibrium values of real variables (e.g., real wages,
employment, output, real interest rates) don’t depend on monetary
conditions
The long-run equilibrium values of nominal variables (e.g., the price
level, nominal wages) are determined by monetary conditions and the
equilibrium values of the relevant real variables
Neoclassical models of long-run equilibrium (with no nominal rigidity)
re‡ect the same fundamental view in a more sophisticated setting
Classical Monetary Theory was about how monetary conditions pin
down the price level and other nominal variables
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
2/7
A Classical Question
Classical economists analyzed long-run equilibrium in models that
incorporated the Classical Dichotomy (long-run neutrality of money):
1
2
The long-run equilibrium values of real variables (e.g., real wages,
employment, output, real interest rates) don’t depend on monetary
conditions
The long-run equilibrium values of nominal variables (e.g., the price
level, nominal wages) are determined by monetary conditions and the
equilibrium values of the relevant real variables
Neoclassical models of long-run equilibrium (with no nominal rigidity)
re‡ect the same fundamental view in a more sophisticated setting
Classical Monetary Theory was about how monetary conditions pin
down the price level and other nominal variables
The Quantity Theory of Money (MV = PY ) was typically the link
between the money supply and the price level
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
2/7
A Classical Question
Classical economists analyzed long-run equilibrium in models that
incorporated the Classical Dichotomy (long-run neutrality of money):
1
2
The long-run equilibrium values of real variables (e.g., real wages,
employment, output, real interest rates) don’t depend on monetary
conditions
The long-run equilibrium values of nominal variables (e.g., the price
level, nominal wages) are determined by monetary conditions and the
equilibrium values of the relevant real variables
Neoclassical models of long-run equilibrium (with no nominal rigidity)
re‡ect the same fundamental view in a more sophisticated setting
Classical Monetary Theory was about how monetary conditions pin
down the price level and other nominal variables
The Quantity Theory of Money (MV = PY ) was typically the link
between the money supply and the price level
But some classical (neoclassical) economists addressed the question of
price-level determinacy when the central bank sets the nominal interest
rate
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
2/7
Speci…cations of Monetary Policy
We can model monetary policy as a rule for setting either the money
supply or the nominal interest rate
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
3/7
Speci…cations of Monetary Policy
We can model monetary policy as a rule for setting either the money
supply or the nominal interest rate
In our simple cash-in-advance model, a monetary policy that sets an
exogenous path for the money stock pins down the price level
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
3/7
Speci…cations of Monetary Policy
We can model monetary policy as a rule for setting either the money
supply or the nominal interest rate
In our simple cash-in-advance model, a monetary policy that sets an
exogenous path for the money stock pins down the price level
But a policy that sets an exogenous path for the nominal interest rate
(e.g., pegs the nominal rate) does not pin down the price level
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
3/7
Speci…cations of Monetary Policy
We can model monetary policy as a rule for setting either the money
supply or the nominal interest rate
In our simple cash-in-advance model, a monetary policy that sets an
exogenous path for the money stock pins down the price level
But a policy that sets an exogenous path for the nominal interest rate
(e.g., pegs the nominal rate) does not pin down the price level
The same point can be made in an exchange economy with the
ad-hoc speci…cation
mt pt = yt ηit
as the equilibrium condition in the market for money
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
3/7
Speci…cations of Monetary Policy
We can model monetary policy as a rule for setting either the money
supply or the nominal interest rate
In our simple cash-in-advance model, a monetary policy that sets an
exogenous path for the money stock pins down the price level
But a policy that sets an exogenous path for the nominal interest rate
(e.g., pegs the nominal rate) does not pin down the price level
The same point can be made in an exchange economy with the
ad-hoc speci…cation
mt pt = yt ηit
as the equilibrium condition in the market for money
The left-hand side is the (logarithm of the) real money stock
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
3/7
Speci…cations of Monetary Policy
We can model monetary policy as a rule for setting either the money
supply or the nominal interest rate
In our simple cash-in-advance model, a monetary policy that sets an
exogenous path for the money stock pins down the price level
But a policy that sets an exogenous path for the nominal interest rate
(e.g., pegs the nominal rate) does not pin down the price level
The same point can be made in an exchange economy with the
ad-hoc speci…cation
mt pt = yt ηit
as the equilibrium condition in the market for money
The left-hand side is the (logarithm of the) real money stock
The right-hand side is the (logarithm of) demand for real money
balances
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
3/7
Nominal Indeterminacy
With the ad-hoc speci…cation
mt
pt = yt
ηit
a policy that sets an exogenous path for the nominal interest rate pins
down real money balances
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
4/7
Nominal Indeterminacy
With the ad-hoc speci…cation
mt
pt = yt
ηit
a policy that sets an exogenous path for the nominal interest rate pins
down real money balances
And the Fisher equation,
nominal interest rate = (expected) real interest rate
+ (expected) in‡ation
pins down expected in‡ation (because the real rate is determined by
the real side of the model)
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
4/7
Write the Euler equations for real and nominal bonds as
h
u0 (Ct+1
)
1
= Et
0
Rt
u (Cth )
h
u0 (Ct+1
)
0
u (Cth )
1
= Et
It
Pt
Pt+1
where Rt and It are the gross real and nominal interest rates. Rede…ne rt and
it to represent the continuously compounded rates
rt = log(Rt )
De…ne
t+1
let t = log(
bond as
t)
and
=
h
u0 (Ct+1
)
0
u (Cth )
= log(
t
and
t ),
it = log(It )
and
=
t+1
Pt+1
Pt
and write the Euler equation for the nominal
expf it g = Et expf
t+1 g expf
t+1 g
Note that in a steady-state equilibrium, we get
expf ig = expf g expf
g
and the Fisher equation
i=r+
The …rst-order terms in the Taylor approximation satisfy
expf ig[it
i] = expf g expf
gEt ([
t+1
i
t+1
Et
]
which simpli…es to
it =
+ Et
and
it = rt + Et
1
t+1
t+1
[
t+1
])
Nominal Indeterminacy
With the ad-hoc speci…cation
mt
pt = yt
ηit
a policy that sets an exogenous path for the nominal interest rate pins
down real money balances
And the Fisher equation,
nominal interest rate = (expected) real interest rate
+ (expected) in‡ation
pins down expected in‡ation (because the real rate is determined by
the real side of the model)
But the equilibrium price level is not determined (the model exhibits
nominal indeterminacy)
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
4/7
Nominal Determinacy
To get nominal determinacy, we often con…ne our analysis to suitably
bounded equilibria. In this case, the price level is pinned down if we
specify monetary policy as
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
5/7
Nominal Determinacy
To get nominal determinacy, we often con…ne our analysis to suitably
bounded equilibria. In this case, the price level is pinned down if we
specify monetary policy as
an interest-rate rule (reacting to in‡ation) that obeys the Taylor
Principle
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
5/7
Nominal Determinacy
To get nominal determinacy, we often con…ne our analysis to suitably
bounded equilibria. In this case, the price level is pinned down if we
specify monetary policy as
an interest-rate rule (reacting to in‡ation) that obeys the Taylor
Principle
or a policy that sets an exogenous path for the money supply
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
5/7
Nominal Determinacy
To get nominal determinacy, we often con…ne our analysis to suitably
bounded equilibria. In this case, the price level is pinned down if we
specify monetary policy as
an interest-rate rule (reacting to in‡ation) that obeys the Taylor
Principle
or a policy that sets an exogenous path for the money supply
In our simple cash-in-advance model, the determinacy implication of a
money-supply rule is straightforward
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
5/7
Nominal Determinacy
To get nominal determinacy, we often con…ne our analysis to suitably
bounded equilibria. In this case, the price level is pinned down if we
specify monetary policy as
an interest-rate rule (reacting to in‡ation) that obeys the Taylor
Principle
or a policy that sets an exogenous path for the money supply
In our simple cash-in-advance model, the determinacy implication of a
money-supply rule is straightforward
but there are issues, in other models, that are beyond the scope of this
course
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
5/7
Nominal Determinacy
To get nominal determinacy, we often con…ne our analysis to suitably
bounded equilibria. In this case, the price level is pinned down if we
specify monetary policy as
an interest-rate rule (reacting to in‡ation) that obeys the Taylor
Principle
or a policy that sets an exogenous path for the money supply
In our simple cash-in-advance model, the determinacy implication of a
money-supply rule is straightforward
but there are issues, in other models, that are beyond the scope of this
course
and major central banks don’t target the money stock anyway
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
5/7
Nominal Determinacy
To get nominal determinacy, we often con…ne our analysis to suitably
bounded equilibria. In this case, the price level is pinned down if we
specify monetary policy as
an interest-rate rule (reacting to in‡ation) that obeys the Taylor
Principle
or a policy that sets an exogenous path for the money supply
In our simple cash-in-advance model, the determinacy implication of a
money-supply rule is straightforward
but there are issues, in other models, that are beyond the scope of this
course
and major central banks don’t target the money stock anyway
Our discussion will focus on interest-rate rules
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
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The Taylor Principle
An interest-rate rule obeys the Taylor Principle if it responds to
in‡ation with a coe¢ cient greater than unity
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
6/7
The Taylor Principle
An interest-rate rule obeys the Taylor Principle if it responds to
in‡ation with a coe¢ cient greater than unity
this can serve to stabilize aggregate demand in models with nominal
rigidity
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
6/7
The Taylor Principle
An interest-rate rule obeys the Taylor Principle if it responds to
in‡ation with a coe¢ cient greater than unity
this can serve to stabilize aggregate demand in models with nominal
rigidity
it makes in‡ation dynamics explosive and implies a unique bounded
solution for the in‡ation rate
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
6/7
The Taylor Principle
An interest-rate rule obeys the Taylor Principle if it responds to
in‡ation with a coe¢ cient greater than unity
this can serve to stabilize aggregate demand in models with nominal
rigidity
it makes in‡ation dynamics explosive and implies a unique bounded
solution for the in‡ation rate
For concreteness, suppose the central bank has a zero-in‡ation target
in the long run and sets
it = ρ + φπ π t
where ρ is the real interest rate in the steady-state equilibrium
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
6/7
The Taylor Principle
An interest-rate rule obeys the Taylor Principle if it responds to
in‡ation with a coe¢ cient greater than unity
this can serve to stabilize aggregate demand in models with nominal
rigidity
it makes in‡ation dynamics explosive and implies a unique bounded
solution for the in‡ation rate
For concreteness, suppose the central bank has a zero-in‡ation target
in the long run and sets
it = ρ + φπ π t
where ρ is the real interest rate in the steady-state equilibrium
Using, the Fisher equation,
rt = it
Et π t +1 ,
the dynamics of in‡ation are governed by
Et π t + 1 = φ π π t
(Institute)
( rt
ρ)
Monetary/Fiscal Interactions: Nominal Indeterminacy
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Determinacy under the Taylor Principle
The dynamic equation
Et π t + 1 = φ π π t
( rt
ρ)
generates explosive dynamics if φπ > 1
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
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Determinacy under the Taylor Principle
The dynamic equation
Et π t + 1 = φ π π t
( rt
ρ)
generates explosive dynamics if φπ > 1
So, an interest-rate rule that obeys the Taylor Principle implies a
unique bounded solution for the in‡ation rate, and this determines the
price level
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
7/7
Determinacy under the Taylor Principle
The dynamic equation
Et π t + 1 = φ π π t
( rt
ρ)
generates explosive dynamics if φπ > 1
So, an interest-rate rule that obeys the Taylor Principle implies a
unique bounded solution for the in‡ation rate, and this determines the
price level
There are, however, historical episodes (e.g., the US before 1979) for
which the data suggest the Taylor Principle was not satis…ed
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
7/7
Determinacy under the Taylor Principle
The dynamic equation
Et π t + 1 = φ π π t
( rt
ρ)
generates explosive dynamics if φπ > 1
So, an interest-rate rule that obeys the Taylor Principle implies a
unique bounded solution for the in‡ation rate, and this determines the
price level
There are, however, historical episodes (e.g., the US before 1979) for
which the data suggest the Taylor Principle was not satis…ed
We will discuss nominal determinacy during these episodes later
(Institute)
Monetary/Fiscal Interactions: Nominal Indeterminacy
May 2011
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