Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worryDiscussion of Evans and Honkapohja,“Robust Learning Stability.”
James Bullard
President and CEO
Federal Reserve Bank of St. Louis1

28 May 2008
Frontiers in Monetary Theory and Policy—IMES, BOJ

1 Views expressed are those of the author and do not necessarily reflect official positions of the FOMC or theFederal Reserve System.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Learning and monetary policy
Rational expectations is a cornerstone of modern
macroeconomic theory.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Learning and monetary policy
Rational expectations is a cornerstone of modern
macroeconomic theory.
Rational expectations equilibrium is at the heart of thelearning literature.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Learning and monetary policy
Rational expectations is a cornerstone of modern
macroeconomic theory.
Rational expectations equilibrium is at the heart of thelearning literature.
But rational expectations is not a practical assumption.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Learning and monetary policy
Rational expectations is a cornerstone of modern
macroeconomic theory.
Rational expectations equilibrium is at the heart of thelearning literature.
But rational expectations is not a practical assumption.
Actual private sector expectations are unlikely to beprecisely consistent with REE.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Learning and monetary policy
Rational expectations is a cornerstone of modern
macroeconomic theory.
Rational expectations equilibrium is at the heart of thelearning literature.
But rational expectations is not a practical assumption.
Actual private sector expectations are unlikely to beprecisely consistent with REE.
That is still all right ...

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Learning and monetary policy
Rational expectations is a cornerstone of modern
macroeconomic theory.
Rational expectations equilibrium is at the heart of thelearning literature.
But rational expectations is not a practical assumption.
Actual private sector expectations are unlikely to beprecisely consistent with REE.
That is still all right ...
... so long as small expectational deviations from RE
dissipate, instead of accumulating.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Learning and monetary policy
Rational expectations is a cornerstone of modern
macroeconomic theory.
Rational expectations equilibrium is at the heart of thelearning literature.
But rational expectations is not a practical assumption.
Actual private sector expectations are unlikely to beprecisely consistent with REE.
That is still all right ...
... so long as small expectational deviations from RE
dissipate, instead of accumulating.

That condition is known as expectational stability.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

What the literature has shown
REE may or may not be expectationally stable in New
Keynesian models.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

What the literature has shown
REE may or may not be expectationally stable in New
Keynesian models.
In the simplest New Keynesian model, the Taylor Principle
is associated with E-stability.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

What the literature has shown
REE may or may not be expectationally stable in New
Keynesian models.
In the simplest New Keynesian model, the Taylor Principle
is associated with E-stability.
Failure of the Taylor Principle is associated withexpectational instability.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

What the literature has shown
REE may or may not be expectationally stable in New
Keynesian models.
In the simplest New Keynesian model, the Taylor Principle
is associated with E-stability.
Failure of the Taylor Principle is associated withexpectational instability.

That result assumes

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

What the literature has shown
REE may or may not be expectationally stable in New
Keynesian models.
In the simplest New Keynesian model, the Taylor Principle
is associated with E-stability.
Failure of the Taylor Principle is associated withexpectational instability.

That result assumes
contemporaneous data specification of the policy rule.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

What the literature has shown
REE may or may not be expectationally stable in New
Keynesian models.
In the simplest New Keynesian model, the Taylor Principle
is associated with E-stability.
Failure of the Taylor Principle is associated withexpectational instability.

That result assumes
contemporaneous data specification of the policy rule.
decreasing gain in the learning rule.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

What the literature has shown
REE may or may not be expectationally stable in New
Keynesian models.
In the simplest New Keynesian model, the Taylor Principle
is associated with E-stability.
Failure of the Taylor Principle is associated withexpectational instability.

That result assumes
contemporaneous data specification of the policy rule.
decreasing gain in the learning rule.

Comforting.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

What the authors do

Instrument rules plus various forms of “optimal” policy.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

What the authors do

Instrument rules plus various forms of “optimal” policy.
Replace decreasing gain with constant gain.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

What the authors do

Instrument rules plus various forms of “optimal” policy.
Replace decreasing gain with constant gain.
Agents are trying to robustly track the changing
environment in which they operate.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

What the authors do

Instrument rules plus various forms of “optimal” policy.
Replace decreasing gain with constant gain.
Agents are trying to robustly track the changing
environment in which they operate.

Concentrate on operational rules in the sense of McCallum.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

What the authors do

Instrument rules plus various forms of “optimal” policy.
Replace decreasing gain with constant gain.
Agents are trying to robustly track the changing
environment in which they operate.

Concentrate on operational rules in the sense of McCallum.
Keep policymaker information in line with reality.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

What the authors do

Instrument rules plus various forms of “optimal” policy.
Replace decreasing gain with constant gain.
Agents are trying to robustly track the changing
environment in which they operate.

Concentrate on operational rules in the sense of McCallum.
Keep policymaker information in line with reality.

In particular, contemporaneous values of output andinflation are not known when policy decisions are made.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Main findings

There are many recommended good or “optimal” policies
for this model ...

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Main findings

There are many recommended good or “optimal” policies
for this model ...
... but most produce expectational instability in this setting.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Main findings

There are many recommended good or “optimal” policies
for this model ...
... but most produce expectational instability in this setting.

Policymakers following these recommended approaches inthis environment would be surprised to find that theeconomy does not coordinate on the intended equilibrium.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Main findings

There are many recommended good or “optimal” policies
for this model ...
... but most produce expectational instability in this setting.

Policymakers following these recommended approaches inthis environment would be surprised to find that theeconomy does not coordinate on the intended equilibrium.
To obtain expectational stability, use theexpectations-based rules of Evans-Honkapohja (2003,
2006).

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

How to think about E-stability
Stability is not a common mode of analysis inmacroeconomics and monetary policy.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

How to think about E-stability
Stability is not a common mode of analysis inmacroeconomics and monetary policy.
The actual learning dynamics would only be observed in
an unstable situtation.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

How to think about E-stability
Stability is not a common mode of analysis inmacroeconomics and monetary policy.
The actual learning dynamics would only be observed in
an unstable situtation.
Otherwise convergence occurs.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

How to think about E-stability
Stability is not a common mode of analysis inmacroeconomics and monetary policy.
The actual learning dynamics would only be observed in
an unstable situtation.
Otherwise convergence occurs.
We are talking about locally to the REE.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

How to think about E-stability
Stability is not a common mode of analysis inmacroeconomics and monetary policy.
The actual learning dynamics would only be observed in
an unstable situtation.
Otherwise convergence occurs.
We are talking about locally to the REE.
If policy is executed correctly ...

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

How to think about E-stability
Stability is not a common mode of analysis inmacroeconomics and monetary policy.
The actual learning dynamics would only be observed in
an unstable situtation.
Otherwise convergence occurs.
We are talking about locally to the REE.
If policy is executed correctly ...
... observers would see only the REE values of key macro
variables.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

How to think about E-stability
Stability is not a common mode of analysis inmacroeconomics and monetary policy.
The actual learning dynamics would only be observed in
an unstable situtation.
Otherwise convergence occurs.
We are talking about locally to the REE.
If policy is executed correctly ...
... observers would see only the REE values of key macro
variables.
Learning would appear to be unimportant, even though it
is enforcing the REE.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

How to think about E-stability
Stability is not a common mode of analysis inmacroeconomics and monetary policy.
The actual learning dynamics would only be observed in
an unstable situtation.
Otherwise convergence occurs.
We are talking about locally to the REE.
If policy is executed correctly ...
... observers would see only the REE values of key macro
variables.
Learning would appear to be unimportant, even though it
is enforcing the REE.

One analogy: off-equilibrium play in games.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

How to think about E-stability
Stability is not a common mode of analysis inmacroeconomics and monetary policy.
The actual learning dynamics would only be observed in
an unstable situtation.
Otherwise convergence occurs.
We are talking about locally to the REE.
If policy is executed correctly ...
... observers would see only the REE values of key macro
variables.
Learning would appear to be unimportant, even though it
is enforcing the REE.

One analogy: off-equilibrium play in games.
Another analogy: default punishment in models withendogenous debt constraints.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Expectational instability
Some might worry that the unstable case is “not reallyobserved.”

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Expectational instability
Some might worry that the unstable case is “not reallyobserved.”
Indeed, we would not expect to see a lot of these cases ...

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Expectational instability
Some might worry that the unstable case is “not reallyobserved.”
Indeed, we would not expect to see a lot of these cases ...
... policymakers would have to abandon their policies.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Expectational instability
Some might worry that the unstable case is “not reallyobserved.”
Indeed, we would not expect to see a lot of these cases ...
... policymakers would have to abandon their policies.
But consider Figure 2 in the paper.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Expectational instability
Some might worry that the unstable case is “not reallyobserved.”
Indeed, we would not expect to see a lot of these cases ...
... policymakers would have to abandon their policies.
But consider Figure 2 in the paper.
Inflation and the output gap behave as if the REE has been
attained for many periods.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Expectational instability
Some might worry that the unstable case is “not reallyobserved.”
Indeed, we would not expect to see a lot of these cases ...
... policymakers would have to abandon their policies.
But consider Figure 2 in the paper.
Inflation and the output gap behave as if the REE has been
attained for many periods.
But eventually, expectational errors accumulate and drive
the economy away from the targeted equilibrium.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Expectational instability
Some might worry that the unstable case is “not reallyobserved.”
Indeed, we would not expect to see a lot of these cases ...
... policymakers would have to abandon their policies.
But consider Figure 2 in the paper.
Inflation and the output gap behave as if the REE has been
attained for many periods.
But eventually, expectational errors accumulate and drive
the economy away from the targeted equilibrium.
Does it happen?

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Expectational instability
Some might worry that the unstable case is “not reallyobserved.”
Indeed, we would not expect to see a lot of these cases ...
... policymakers would have to abandon their policies.
But consider Figure 2 in the paper.
Inflation and the output gap behave as if the REE has been
attained for many periods.
But eventually, expectational errors accumulate and drive
the economy away from the targeted equilibrium.
Does it happen?
Consider the breakdown of Bretton Woods.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Expectational instability
Some might worry that the unstable case is “not reallyobserved.”
Indeed, we would not expect to see a lot of these cases ...
... policymakers would have to abandon their policies.
But consider Figure 2 in the paper.
Inflation and the output gap behave as if the REE has been
attained for many periods.
But eventually, expectational errors accumulate and drive
the economy away from the targeted equilibrium.
Does it happen?
Consider the breakdown of Bretton Woods.
And maybe we should worry about Sweden, as we will see
below.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Taylor-type rules

Some potential for instability in the calibrated case.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Taylor-type rules

Some potential for instability in the calibrated case.
Taylor rule fairs better than some other recommended
rules studied later in the paper.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Taylor-type rules

Some potential for instability in the calibrated case.
Taylor rule fairs better than some other recommended
rules studied later in the paper.
Instability requires the combination of operational ruleswith constant gain learning.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Duffy and Xiao
The Duffy/Xiao rule is a Taylor-type rule.

Other analyses

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Duffy and Xiao
The Duffy/Xiao rule is a Taylor-type rule.
It represents optimal policy under discretion if thepolicymaker has a preference for interest rate smoothing.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Duffy and Xiao
The Duffy/Xiao rule is a Taylor-type rule.
It represents optimal policy under discretion if thepolicymaker has a preference for interest rate smoothing.
Results for commitment case similar.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Duffy and Xiao
The Duffy/Xiao rule is a Taylor-type rule.
It represents optimal policy under discretion if thepolicymaker has a preference for interest rate smoothing.
Results for commitment case similar.

The rule is
it =

ϕλ
ϕαx
πt +
xt .
αi
αi

(1)

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Duffy and Xiao
The Duffy/Xiao rule is a Taylor-type rule.
It represents optimal policy under discretion if thepolicymaker has a preference for interest rate smoothing.
Results for commitment case similar.

The rule is
it =

ϕλ
ϕαx
πt +
xt .
αi
αi

Produces determinacy if αi sufficiently large.

(1)

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Duffy and Xiao
The Duffy/Xiao rule is a Taylor-type rule.
It represents optimal policy under discretion if thepolicymaker has a preference for interest rate smoothing.
Results for commitment case similar.

The rule is
it =

ϕλ
ϕαx
πt +
xt .
αi
αi

Produces determinacy if αi sufficiently large.
Produces expectational instability if αi sufficiently small.

(1)

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Duffy and Xiao
The Duffy/Xiao rule is a Taylor-type rule.
It represents optimal policy under discretion if thepolicymaker has a preference for interest rate smoothing.
Results for commitment case similar.

The rule is
it =

ϕλ
ϕαx
πt +
xt .
αi
αi

Produces determinacy if αi sufficiently large.
Produces expectational instability if αi sufficiently small.
Similar results for Duffy/Xiao under commitment.

(1)

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Duffy and Xiao
The Duffy/Xiao rule is a Taylor-type rule.
It represents optimal policy under discretion if thepolicymaker has a preference for interest rate smoothing.
Results for commitment case similar.

The rule is
it =

ϕλ
ϕαx
πt +
xt .
αi
αi

Produces determinacy if αi sufficiently large.
Produces expectational instability if αi sufficiently small.
Similar results for Duffy/Xiao under commitment.
Worrisome.

(1)Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Duffy and Xiao
The Duffy/Xiao rule is a Taylor-type rule.
It represents optimal policy under discretion if thepolicymaker has a preference for interest rate smoothing.
Results for commitment case similar.

The rule is
it =

ϕλ
ϕαx
πt +
xt .
αi
αi

Produces determinacy if αi sufficiently large.
Produces expectational instability if αi sufficiently small.
Similar results for Duffy/Xiao under commitment.
Worrisome.
The expectations-based approach of Evans andHonkapohja solves this problem and provides robust
expectational stability.

(1)Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Commitment

No interest rate smoothing, timeless perspective, goal is toimplement the FOC.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Commitment

No interest rate smoothing, timeless perspective, goal is toimplement the FOC.
Svensson and Woodford (2005) recommended rule
equation (18) in the paper.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Commitment

No interest rate smoothing, timeless perspective, goal is toimplement the FOC.
Svensson and Woodford (2005) recommended rule
equation (18) in the paper.
Operational versions can be associated with instability
under learning for reasonable gain parameters.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Commitment

No interest rate smoothing, timeless perspective, goal is toimplement the FOC.
Svensson and Woodford (2005) recommended rule
equation (18) in the paper.
Operational versions can be associated with instability
under learning for reasonable gain parameters.
Worrisome for Sweden? Figure 2?

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Commitment

No interest rate smoothing, timeless perspective, goal is toimplement the FOC.
Svensson and Woodford (2005) recommended rule
equation (18) in the paper.
Operational versions can be associated with instability
under learning for reasonable gain parameters.
Worrisome for Sweden? Figure 2?
There is nothing optimal about instability.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Woodford NRE

Woodford (2008) has considered an alternative approach to
checking the robustness of policy to the possibility that
expectations may not be fully rational.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Woodford NRE

Woodford (2008) has considered an alternative approach to
checking the robustness of policy to the possibility that
expectations may not be fully rational.
Avoids committing to a particular recursive algorithm todescribe learning.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Woodford NRE

Woodford (2008) has considered an alternative approach to
checking the robustness of policy to the possibility that
expectations may not be fully rational.
Avoids committing to a particular recursive algorithm todescribe learning.
But, expectational stability still plays a role in that analysis.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Bayesian approaches

Many feel that recursive learning should be Bayesian.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Bayesian approaches

Many feel that recursive learning should be Bayesian.
Bullard and Suda (2008).

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Bayesian approaches

Many feel that recursive learning should be Bayesian.
Bullard and Suda (2008).
Standard recursive learning exercise, but replace classicaleconometricians with Bayesian econometricians.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Bayesian approaches

Many feel that recursive learning should be Bayesian.
Bullard and Suda (2008).
Standard recursive learning exercise, but replace classicaleconometricians with Bayesian econometricians.
Main results still hold:Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Bayesian approaches

Many feel that recursive learning should be Bayesian.
Bullard and Suda (2008).
Standard recursive learning exercise, but replace classicaleconometricians with Bayesian econometricians.
Main results still hold:“extra” term in the actual law of motion.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Bayesian approaches

Many feel that recursive learning should be Bayesian.
Bullard and Suda (2008).
Standard recursive learning exercise, but replace classicaleconometricians with Bayesian econometricians.
Main results still hold:“extra” term in the actual law of motion.
expectational stability conditions unchanged.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Bayesian approaches

Many feel that recursive learning should be Bayesian.
Bullard and Suda (2008).
Standard recursive learning exercise, but replace classicaleconometricians with Bayesian econometricians.
Main results still hold:“extra” term in the actual law of motion.
expectational stability conditions unchanged.

Stability still an issue.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Responding to expectations

Policymakers seem to do this at times ...

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Responding to expectations

Policymakers seem to do this at times ...
but it is not that clear how to map this idea into reality.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Responding to expectations

Policymakers seem to do this at times ...
but it is not that clear how to map this idea into reality.

Measurement issues.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Responding to expectations

Policymakers seem to do this at times ...
but it is not that clear how to map this idea into reality.

Measurement issues.
Potential games.

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Final thoughts

Very nice paper in a very nice conference.

Other analyses

Why worry

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Final thoughts

Very nice paper in a very nice conference.
Thanks to the Bank of Japan for inviting me to participate.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Final thoughts

Very nice paper in a very nice conference.
Thanks to the Bank of Japan for inviting me to participate.
I appreciate the attention to stability issues, which I think
are insufficiently analyzed in macroeconomics.

Main ideas

What the authors do

Interpretations

Unstable is not optimal

Other analyses

Why worry

Final thoughts

Very nice paper in a very nice conference.
Thanks to the Bank of Japan for inviting me to participate.
I appreciate the attention to stability issues, which I think
are insufficiently analyzed in macroeconomics.
Instability can produce the “big ticket losses” thatpolicymakers really worry about.