Discouraging Deviant Behavior in Monetary Economics
Lawrence Christiano and Yuta Takahashi
Northwestern and Hitotsubashi

May 27, 2019

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Multiple Equilibria Standard NK Model• Standard, New Keynesian (NK) Monetary Model:
I

Interest rate rule with big coefficient on inflation (‘Taylor rule’) and passive fiscal policy:
I

Big coefficient on inflation: ‘Taylor Principle’.

Multiple Equilibria Standard NK Model• Standard, New Keynesian (NK) Monetary Model:
I

Interest rate rule with big coefficient on inflation (‘Taylor rule’) and passive fiscal policy:
I

Big coefficient on inflation: ‘Taylor Principle’.

• Literature focuses on unique equilibrium local to unique interior steady state.
I

Referred to as ‘desired equilibrium’ here.
I

In practice, that equilibrium is ‘pretty good’ in a welfare sense.

Multiple Equilibria Standard NK Model• Standard, New Keynesian (NK) Monetary Model:
I

Interest rate rule with big coefficient on inflation (‘Taylor rule’) and passive fiscal policy:
I

Big coefficient on inflation: ‘Taylor Principle’.

• Literature focuses on unique equilibrium local to unique interior steady state.
I

Referred to as ‘desired equilibrium’ here.
I

In practice, that equilibrium is ‘pretty good’ in a welfare sense.

• But, we have reasons to think that there are other equilibria in NK model:
I

BSGU(01,JET) showed there are two steady states.

Multiple Equilibria Standard NK Model• Standard, New Keynesian (NK) Monetary Model:
I

Interest rate rule with big coefficient on inflation (‘Taylor rule’) and passive fiscal policy:
I

Big coefficient on inflation: ‘Taylor Principle’.

• Literature focuses on unique equilibrium local to unique interior steady state.
I

Referred to as ‘desired equilibrium’ here.
I

In practice, that equilibrium is ‘pretty good’ in a welfare sense.

• But, we have reasons to think that there are other equilibria in NK model:
I

BSGU(01,JET) showed there are two steady states.

I

In simple monetary models there are also other equilibria:
I

Hyperinflation, deflation, cycling, and chaos.

Multiple Equilibria Standard NK Model• Standard, New Keynesian (NK) Monetary Model:
I

Interest rate rule with big coefficient on inflation (‘Taylor rule’) and passive fiscal policy:
I

Big coefficient on inflation: ‘Taylor Principle’.

• Literature focuses on unique equilibrium local to unique interior steady state.
I

Referred to as ‘desired equilibrium’ here.
I

In practice, that equilibrium is ‘pretty good’ in a welfare sense.

• But, we have reasons to think that there are other equilibria in NK model:
I

BSGU(01,JET) showed there are two steady states.

I

In simple monetary models there are also other equilibria:
I

Hyperinflation, deflation, cycling, and chaos.

• Message from models: Taylor rule not sufficient to stabilize inflation globally.

Implementation of Desired Equilibrium by Escape ClauseImplementation of Desired Equilibrium by Escape Clause• Intuitive motivation used in Taylor (1996), Christiano-Rostagno (2001), and BSGU.

Implementation of Desired Equilibrium by Escape Clause• Intuitive motivation used in Taylor (1996), Christiano-Rostagno (2001), and BSGU.
I

In high inflation, money growth high.

Implementation of Desired Equilibrium by Escape Clause• Intuitive motivation used in Taylor (1996), Christiano-Rostagno (2001), and BSGU.
I

In high inflation, money growth high.
I

Just declare ‘we refuse to allow high money growth’.

Implementation of Desired Equilibrium by Escape Clause• Intuitive motivation used in Taylor (1996), Christiano-Rostagno (2001), and BSGU.
I

In high inflation, money growth high.
I

I

Just declare ‘we refuse to allow high money growth’.

In deflation, money growth slow.
I

Just declare ‘we refuse to allow slow (negative) money growth’.

Implementation of Desired Equilibrium by Escape Clause• Intuitive motivation used in Taylor (1996), Christiano-Rostagno (2001), and BSGU.
I

In high inflation, money growth high.
I

I

In deflation, money growth slow.
I

I

Just declare ‘we refuse to allow high money growth’.

Just declare ‘we refuse to allow slow (negative) money growth’.

While inside an inflation monitoring range, follow Taylor rule.

Implementation of Desired Equilibrium by Escape Clause• Intuitive motivation used in Taylor (1996), Christiano-Rostagno (2001), and BSGU.
I

In high inflation, money growth high.
I

I

In deflation, money growth slow.
I

I

Just declare ‘we refuse to allow high money growth’.

Just declare ‘we refuse to allow slow (negative) money growth’.

While inside an inflation monitoring range, follow Taylor rule.

• There exists a unique equilibrium under this policy.

Implementation of Desired Equilibrium by Escape Clause• Intuitive motivation used in Taylor (1996), Christiano-Rostagno (2001), and BSGU.
I

In high inflation, money growth high.
I

I

In deflation, money growth slow.
I

I

Just declare ‘we refuse to allow high money growth’.

Just declare ‘we refuse to allow slow (negative) money growth’.

While inside an inflation monitoring range, follow Taylor rule.

• There exists a unique equilibrium under this policy.
• Practical examples of escape clauses:

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Implementation of Desired Equilibrium by Escape Clause• Intuitive motivation used in Taylor (1996), Christiano-Rostagno (2001), and BSGU.
I

In high inflation, money growth high.
I

I

In deflation, money growth slow.
I

I

Just declare ‘we refuse to allow high money growth’.

Just declare ‘we refuse to allow slow (negative) money growth’.

While inside an inflation monitoring range, follow Taylor rule.

• There exists a unique equilibrium under this policy.
• Practical examples of escape clauses:
I

Exigent circumstances clause 13.3 in Federal Reserve Act.

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Implementation of Desired Equilibrium by Escape Clause• Intuitive motivation used in Taylor (1996), Christiano-Rostagno (2001), and BSGU.
I

In high inflation, money growth high.
I

I

In deflation, money growth slow.
I

I

Just declare ‘we refuse to allow high money growth’.

Just declare ‘we refuse to allow slow (negative) money growth’.

While inside an inflation monitoring range, follow Taylor rule.

• There exists a unique equilibrium under this policy.
• Practical examples of escape clauses:
I

Exigent circumstances clause 13.3 in Federal Reserve Act.

I

European Central Bank Two Pillar Policy.
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Push Back Against Dramatic Conclusions in Two Papers

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Push Back Against Dramatic Conclusions in Two Papers• Cochrane, Journal of Political Economy, 2011.

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Push Back Against Dramatic Conclusions in Two Papers• Cochrane, Journal of Political Economy, 2011.
I

Uniqueness proof with the escape clause is correct.

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Push Back Against Dramatic Conclusions in Two Papers• Cochrane, Journal of Political Economy, 2011.
I
I

Uniqueness proof with the escape clause is correct.
Undesired equilibria ruled out by govt. commitment to do something impossible.
I

I

Commitment to ‘blow up the economy.’

The policy delivering uniqueness is of no economic interest.

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Push Back Against Dramatic Conclusions in Two Papers• Cochrane, Journal of Political Economy, 2011.
I
I

Uniqueness proof with the escape clause is correct.
Undesired equilibria ruled out by govt. commitment to do something impossible.
I

I

Commitment to ‘blow up the economy.’

The policy delivering uniqueness is of no economic interest.

• Our finding is that Cochrane’s conclusion is not correct in a production economy.
I

While correct in his endowment economy.

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Push Back Against Dramatic Conclusions in Two Papers (See paper)

Push Back Against Dramatic Conclusions in Two Papers (See paper)• ACK suggest shrinking the monitoring range to a singleton and letting the escape clausedo all the work to uniquely implement desired equilibrium.

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Push Back Against Dramatic Conclusions in Two Papers (See paper)• ACK suggest shrinking the monitoring range to a singleton and letting the escape clausedo all the work to uniquely implement desired equilibrium.
• ACK conclude: Taylor principle irrelevant to implement desired equilibrium.

5/34

Push Back Against Dramatic Conclusions in Two Papers (See paper)• ACK suggest shrinking the monitoring range to a singleton and letting the escape clausedo all the work to uniquely implement desired equilibrium.
• ACK conclude: Taylor principle irrelevant to implement desired equilibrium.
• Equilibrium with ACK policy is knife-edge:

Push Back Against Dramatic Conclusions in Two Papers (See paper)• ACK suggest shrinking the monitoring range to a singleton and letting the escape clausedo all the work to uniquely implement desired equilibrium.
• ACK conclude: Taylor principle irrelevant to implement desired equilibrium.
• Equilibrium with ACK policy is knife-edge:
I

Lacks robustness to trembles.

Push Back Against Dramatic Conclusions in Two Papers (See paper)• ACK suggest shrinking the monitoring range to a singleton and letting the escape clausedo all the work to uniquely implement desired equilibrium.
• ACK conclude: Taylor principle irrelevant to implement desired equilibrium.
• Equilibrium with ACK policy is knife-edge:
I

Lacks robustness to trembles.

I

Tiny trembles activate escape clause,Push Back Against Dramatic Conclusions in Two Papers (See paper)• ACK suggest shrinking the monitoring range to a singleton and letting the escape clausedo all the work to uniquely implement desired equilibrium.
• ACK conclude: Taylor principle irrelevant to implement desired equilibrium.
• Equilibrium with ACK policy is knife-edge:
I

Lacks robustness to trembles.

I

Tiny trembles activate escape clause,I

Negative consequences for welfare if there are money demand shocks.

Bigger Question

Bigger Question• What makes agents to think that other allocations don’t realize under a certain policy?
I

Competitive equilibrium concept is silent about these types of questions.

Bigger Question• What makes agents to think that other allocations don’t realize under a certain policy?
I

Competitive equilibrium concept is silent about these types of questions.

• We approach this question by reformulating economy as game.
I

We can formally ask “what makes you think other equilibria do not arise?”.

Bigger Question• What makes agents to think that other allocations don’t realize under a certain policy?
I

Competitive equilibrium concept is silent about these types of questions.

• We approach this question by reformulating economy as game.
I

We can formally ask “what makes you think other equilibria do not arise?”.

• We use a refinement of rationalizability to answer the big question.

Bigger Question• What makes agents to think that other allocations don’t realize under a certain policy?
I

Competitive equilibrium concept is silent about these types of questions.

• We approach this question by reformulating economy as game.
I

We can formally ask “what makes you think other equilibria do not arise?”.

• We use a refinement of rationalizability to answer the big question.
I

Rationalizable implementation is more desirable for policy design.
I

Bergemann, Morris, and Tercieux(2011).

Roadmap• ModelRoadmap• Model• Background results:
I

Multiple equilibria with Taylor rule, uniqueness when escape clause is added.

Roadmap• Model• Background results:
I

Multiple equilibria with Taylor rule, uniqueness when escape clause is added.

• How does the escape clause eliminate the non-desired equilibria?

Roadmap• Model• Background results:
I

Multiple equilibria with Taylor rule, uniqueness when escape clause is added.

• How does the escape clause eliminate the non-desired equilibria?
I

How does it discourage deviant behavior?

Roadmap• Model• Background results:
I

Multiple equilibria with Taylor rule, uniqueness when escape clause is added.

• How does the escape clause eliminate the non-desired equilibria?
I

How does it discourage deviant behavior?

• Conclusion

Government

Government• Government levies taxes, provides monetary transfers:(µ̄t − 1) M̄t−1 ,and balances budget in each period.

µ̄t = M̄t /M̄t−1 ,Government• Government levies taxes, provides monetary transfers:(µ̄t − 1) M̄t−1 ,µ̄t = M̄t /M̄t−1 ,and balances budget in each period.
• Monetary policy: {µ̄t }∞t=0 selected so that, in equilibrium,R̄t = R̄ ∗



π̄t
π̄ ∗

φ

Government• Government levies taxes, provides monetary transfers:(µ̄t − 1) M̄t−1 ,µ̄t = M̄t /M̄t−1 ,and balances budget in each period.
• Monetary policy: {µ̄t }∞t=0 selected so that, in equilibrium,R̄t = R̄ ∗



π̄t
π̄ ∗

φ
,

π̄t+1 ≡Pt+1
Pt

Government• Government levies taxes, provides monetary transfers:(µ̄t − 1) M̄t−1 ,µ̄t = M̄t /M̄t−1 ,and balances budget in each period.
• Monetary policy: {µ̄t }∞t=0 selected so that, in equilibrium,R̄t = R̄ ∗



π̄t
π̄ ∗

φ
,

π̄t+1 ≡

Pt+1,
PtR̄ ∗ ≡ π̄ ∗ /β,

where π̄ ∗ = µ̄∗ ≥ 1 and R̄ ∗ are desired inflation and interest rate.

Representative Household

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Representative Household• A version of ‘Limited participation model’:9/34

Representative Household• A version of ‘Limited participation model’:I

Lucas (1990), Fuerst (1993), Christiano-Eichenbaum (1992,1995), CEE (1997).

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Representative Household• A version of ‘Limited participation model’:I

Lucas (1990), Fuerst (1993), Christiano-Eichenbaum (1992,1995), CEE (1997).

I

Household gets wage at start of t, in time to satisfy cash in advance constraint.

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Representative Household• A version of ‘Limited participation model’:I

Lucas (1990), Fuerst (1993), Christiano-Eichenbaum (1992,1995), CEE (1997).

I

Household gets wage at start of t, in time to satisfy cash in advance constraint.

• Household first order conditions:Wt= ctγ ltψ ,Pt−γ
ct−γ = βct+1

R̄t
,
π̄t+1

‘Euler equation’plus transversality and cash in advance conditions.

9/34

Firms• Competitive, final good firm production and profits:
Z 1
Yt =
0

ε−1
ε

Yi,t di

ε
 ε−1

,

ε > 1.

Firms• Competitive, final good firm production and profits:
Z 1
Yt =
0

ε−1
ε

ε
 ε−1

Yi,t di• i th intermediate good firm production: Yt,i = lt,i .

,ε > 1.

Firms• Competitive, final good firm production and profits:
Z 1
Yt =
0

ε−1
ε

ε
 ε−1

Yi,t di,ε > 1.

• i th intermediate good firm production: Yt,i = lt,i .
• Demand curve:Yi,t = Yt

pi,t
Pt

−ε

Z 1
,

Pt ,
0

1−ε
pi,t
di

1
 1−ε

.

Firms• Competitive, final good firm production and profits:
Z 1
Yt =
0

ε−1
ε

ε
 ε−1

Yi,t di,ε > 1.

• i th intermediate good firm production: Yt,i = lt,i .
• Demand curve:Yi,t = Yt• Optimizing price:

pi,t
Pt

−ε

Z 1
,

Pt ,
0

1−ε
pi,t
di

1
 1−ε

.

Firms• Competitive, final good firm production and profits:
Z 1
Yt =
0

ε−1
ε

ε
 ε−1

Yi,t di,ε > 1.

• i th intermediate good firm production: Yt,i = lt,i .
• Demand curve:Yi,t = Yt• Optimizing price:pi,t =

pi,t
Pt

−ε

Z 1
,

Pt ,
0

1−ε
pi,t
di

1
 1−ε

.

Firms• Competitive, final good firm production and profits:
Z 1
Yt =
0

ε−1
ε

ε
 ε−1

,

Yi,t diε > 1.

• i th intermediate good firm production: Yt,i = lt,i .
• Demand curve:Yi,t = Yt

pi,t
Pt

−ε

Z 1
,

Pt ,
0

1−ε
pi,t
di

• Optimizing price:pi,t =

ε
×
− 1}
|ε {z

markupR̄t|{z}interest rate distortion

×

Wt
|{z}

nominal MC× (1 − τt )| {z }
tax

1
 1−ε

.

Firms• Competitive, final good firm production and profits:
Z 1
Yt =
0

ε−1
ε

ε
 ε−1

,

Yi,t diε > 1.

• i th intermediate good firm production: Yt,i = lt,i .
• Demand curve:Yi,t = Yt

pi,t
Pt

−ε

Z 1
,

Pt ,
0

1−ε
pi,t
di

1
 1−ε

.

• Optimizing price:pi,t =

ε
×
− 1}
|ε {z

markupR̄t|{z}interest rate distortion

×

Wt
|{z}

nominal MC× (1 − τt ) = Wt
| {z }
tax

Firms• Competitive, final good firm production and profits:
Z 1
Yt =
0

ε−1
ε

ε
 ε−1

,

Yi,t diε > 1.

• i th intermediate good firm production: Yt,i = lt,i .
• Demand curve:Yi,t = Yt

pi,t
Pt

−ε

Z 1
,

Pt ,
0

1−ε
pi,t
di

1
 1−ε

.

• Optimizing price:pi,t =

ε
×
− 1}
|ε {z

markupR̄t|{z}interest rate distortion

×

Wt
|{z}

nominal MC× (1 − τt ) = Wt =⇒ Pt = Wt .
| {z }
tax

Market Clearing and other Equilibrium Conditions• Labor/goods market clearing and firm optimality:
1=

Wt
Pt

=
|{z}

ctγ ltψ

MRS

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Market Clearing and other Equilibrium Conditions• Labor/goods market clearing and firm optimality:
1=

Wt
Pt

=
|{z}
MRS

ctγ ltψ

=
|{z}

ctγ+ψ

ct =lt11/34

Market Clearing and other Equilibrium Conditions• Labor/goods market clearing and firm optimality:
1=

Wt
Pt

=
|{z}
MRS

ctγ ltψ=|{z}

ctγ+ψ =⇒ ct = 1.

ct =lt11/34

Market Clearing and other Equilibrium Conditions• Labor/goods market clearing and firm optimality:
1=

Wt
Pt

=
|{z}

ctγ ltψ=|{z}

ctγ+ψ =⇒ ct = 1.

ct =ltMRS• In equilibrium, the Euler equation is the Fisher equation:−γ
ct−γ = βct+1

R̄t
π̄t+1

=⇒

1=β

R̄t
.
π̄t+1

Scaling

Scaling• Scaled, logged Fisher equation β R̄t = π̄t+1 :Scaling• Scaled, logged Fisher equation β R̄t = π̄t+1 :
β R̄t
π̄t+1
= ∗
π̄
β R̄ ∗

Scaling• Scaled, logged Fisher equation β R̄t = π̄t+1 :
β R̄t
π̄t+1
= ∗ → Rt = πt+1 ,π̄
β R̄ ∗


(∗)

where

Rt ≡ ln

R̄t
R̄ ∗




, πt+1 ≡ ln

π̄t+1
π̄ ∗


.

Scaling• Scaled, logged Fisher equation β R̄t = π̄t+1 :
β R̄t
π̄t+1
= ∗ → Rt = πt+1 ,π̄
β R̄ ∗


(∗)

where

Rt ≡ ln

R̄t
R̄ ∗




, πt+1 ≡ ln

π̄t+1
π̄ ∗


.

• Monetary policy in scaled terms:
R̄t = R̄

∗



π̄t
π̄ ∗

φ

12/34

Scaling• Scaled, logged Fisher equation β R̄t = π̄t+1 :
β R̄t
π̄t+1
= ∗ → Rt = πt+1 ,π̄
β R̄ ∗


(∗)

where

Rt ≡ ln

R̄t
R̄ ∗




, πt+1 ≡ ln

π̄t+1
π̄ ∗


.

• Monetary policy in scaled terms:
R̄t = R̄

∗



π̄t
π̄ ∗

φ

R̄t
→ ∗ =
R̄



π̄t
π̄ ∗

φ

12/34

Scaling• Scaled, logged Fisher equation β R̄t = π̄t+1 :
β R̄t
π̄t+1
= ∗ → Rt = πt+1 ,π̄
β R̄ ∗


(∗)

where

Rt ≡ ln

R̄t
R̄ ∗




, πt+1 ≡ ln

π̄t+1
π̄ ∗


.

• Monetary policy in scaled terms:
R̄t = R̄

∗



π̄t
π̄ ∗

φ

R̄t
→ ∗ =
R̄



π̄t
π̄ ∗

φ
→ Rt

= φπt

(∗∗).

12/34

Scaling• Scaled, logged Fisher equation β R̄t = π̄t+1 :
β R̄t
π̄t+1
= ∗ → Rt = πt+1 ,π̄
β R̄ ∗


(∗)

where

Rt ≡ ln

R̄t
R̄ ∗




, πt+1 ≡ ln

π̄t+1
π̄ ∗


.

• Monetary policy in scaled terms:
R̄t = R̄

∗



π̄t
π̄ ∗

φ

R̄t
→ ∗ =
R̄



π̄t
π̄ ∗

φ
→ Rt

= φπt

(∗∗).

• Combining (∗) and (∗∗), yields equilibrium difference equation:
πt+1 = φπt .
12/34

Scaling• Scaled, logged Fisher equation β R̄t = π̄t+1 :


β R̄t
π̄t+1
= ∗ → Rt = πt+1 ,π̄
β R̄ ∗(∗)

whereRt ≡ ln

R̄t
R̄ ∗




, πt+1 ≡ ln

π̄t+1
π̄ ∗


.

• Monetary policy in scaled terms:
R̄t = R̄

∗



π̄t
π̄ ∗

φ

R̄t
→ ∗ =
R̄



π̄t
π̄ ∗

φ
→ Rt

= φπt

(∗∗).

• Combining (∗) and (∗∗), yields equilibrium difference equation:
πt+1 = φπt .
• Scaled money growth: µt = ln

µ̄t 

π̄ ∗

12/34

Properties of Taylor Rule Equilibrium

13/34

Multiplicity and Local Uniqueness of Desired Equilibrium
πt+1
π t+

• Multiple equilibria, {πt } , each

1

=

φπ

t

◦

45

indexed by π0 .
• Desired equilibrium is unique

πl

πu

πt

equilibrium that never violatesmonitoring range, [πl , πu ].
I

If π0 6= 0, then |πt | → ∞.

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Taylor rule with Escape ClauseTaylor rule with Escape Clause• Keep using Taylor rule while inflation remains inside monitoring range, πt ∈ [πl , πu ],πl ≤ 0 ≤ πu < ∞.

Taylor rule with Escape Clause• Keep using Taylor rule while inflation remains inside monitoring range, πt ∈ [πl , πu ],πl ≤ 0 ≤ πu < ∞.
• Activate escape clause: if for some t, πt ∈/ [πl , πu ] ,Taylor rule with Escape Clause• Keep using Taylor rule while inflation remains inside monitoring range, πt ∈ [πl , πu ],πl ≤ 0 ≤ πu < ∞.
• Activate escape clause: if for some t, πt ∈/ [πl , πu ] ,Ithen, in t + 1 switch forever to constant money growth, µ = 0.
I

Equilibrium is unique after the activation of the escape clause. (See paper)

Taylor rule with Escape Clause• Keep using Taylor rule while inflation remains inside monitoring range, πt ∈ [πl , πu ],πl ≤ 0 ≤ πu < ∞.
• Activate escape clause: if for some t, πt ∈/ [πl , πu ] ,Ithen, in t + 1 switch forever to constant money growth, µ = 0.
I

Equilibrium is unique after the activation of the escape clause. (See paper)• Result: under Taylor rule with escape clause, desired equilibrium is the globally uniqueequilibrium.

15/34

Uniqueness of Equilibrium Under Escape Clause
πt+1
π t+

 If π0 6= 0, then |πt | → ∞.

1

=

φπ

t

◦

45

• Activation of escape clause is
not consistent with the

πl

πu

πt

equilibrium conditions.
• Unique equilibrium associatedwith π0 = 0.

16/34

Activation of Escape Clause Not an Equilibrium

Activation of Escape Clause Not an Equilibrium• Suppose πT > πu .

Activation of Escape Clause Not an Equilibrium• Suppose πT > πu . Then,
Taylor rule : RT = φπT > πu , because φ > 1

Activation of Escape Clause Not an Equilibrium• Suppose πT > πu . Then,
Taylor rule : RT = φπT > πu , because φ > 1
Fisher equation : RT = πT +1 = 0 ≤ πu
| {z }
Escape clauseActivation of Escape Clause Not an Equilibrium• Suppose πT > πu . Then,
Taylor rule : RT = φπT > πu , because φ > 1
Fisher equation : RT = πT +1 = 0 ≤ πu
| {z }
Escape clause• So,
RT > πu and RT ≤ πu ,contradiction!

Uniqueness of Equilibrium Under Escape Clause
πt+1
π t+

 If π0 6= 0, then |πt | → ∞.

 Activation of escape clause is
not consistent with the

πl

πu

1

=

φπ

t

◦

45

πt

equilibrium conditions.
• Unique equilibrium associatedwith π0 = 0.

18/34

Cochrane’s Critique of Implementation Result

19/34

Cochrane’s Critique of Implementation Result• Cochrane concludes uniqueness is achieved by “blow-up-the-economy threat.”

19/34

Cochrane’s Critique of Implementation Result• Cochrane concludes uniqueness is achieved by “blow-up-the-economy threat.”• Reaches this conclusion by studying the question: ‘what would happen if theout-of-equilibrium event, πT > πu occurred?’

19/34

Cochrane’s Critique of Implementation Result• Cochrane concludes uniqueness is achieved by “blow-up-the-economy threat.”• Reaches this conclusion by studying the question: ‘what would happen if theout-of-equilibrium event, πT > πu occurred?’I

In his endowment economy, ct = y always, in and out of equilibrium

19/34

Cochrane’s Critique of Implementation Result• Cochrane concludes uniqueness is achieved by “blow-up-the-economy threat.”• Reaches this conclusion by studying the question: ‘what would happen if theout-of-equilibrium event, πT > πu occurred?’I

In his endowment economy, ct = y always, in and out of equilibrium

I

Household Euler equation reduces to Fisher equation in and out of equilibrium.

19/34

Cochrane’s Critique of Implementation Result• Cochrane concludes uniqueness is achieved by “blow-up-the-economy threat.”• Reaches this conclusion by studying the question: ‘what would happen if theout-of-equilibrium event, πT > πu occurred?’I

In his endowment economy, ct = y always, in and out of equilibrium

I

Household Euler equation reduces to Fisher equation in and out of equilibrium.
Concludes that under escape clause monetary policy commits to setting RT to two different
values:I

19/34

Cochrane’s Critique of Implementation Result• Cochrane concludes uniqueness is achieved by “blow-up-the-economy threat.”• Reaches this conclusion by studying the question: ‘what would happen if theout-of-equilibrium event, πT > πu occurred?’I

In his endowment economy, ct = y always, in and out of equilibrium

I

Household Euler equation reduces to Fisher equation in and out of equilibrium.
Concludes that under escape clause monetary policy commits to setting RT to two different
values: Impossible!!!

I

I

RT implied by Fisher equation and RT implied by Taylor rule.

19/34

Cochrane’s Critique of Implementation Result• Cochrane concludes uniqueness is achieved by “blow-up-the-economy threat.”• Reaches this conclusion by studying the question: ‘what would happen if theout-of-equilibrium event, πT > πu occurred?’I

In his endowment economy, ct = y always, in and out of equilibrium

I

Household Euler equation reduces to Fisher equation in and out of equilibrium.
Concludes that under escape clause monetary policy commits to setting RT to two different
values: Impossible!!!

I

I
I

RT implied by Fisher equation and RT implied by Taylor rule.

No equilibrium exists if πT > πu .

19/34

Cochrane’s Critique of Implementation Result• Cochrane concludes uniqueness is achieved by “blow-up-the-economy threat.”• Reaches this conclusion by studying the question: ‘what would happen if theout-of-equilibrium event, πT > πu occurred?’I

In his endowment economy, ct = y always, in and out of equilibrium

I

Household Euler equation reduces to Fisher equation in and out of equilibrium.
Concludes that under escape clause monetary policy commits to setting RT to two different
values: Impossible!!!

I

I
I

RT implied by Fisher equation and RT implied by Taylor rule.

No equilibrium exists if πT > πu .

• Cochrane’s answer:

19/34

Cochrane’s Critique of Implementation Result• Cochrane concludes uniqueness is achieved by “blow-up-the-economy threat.”• Reaches this conclusion by studying the question: ‘what would happen if theout-of-equilibrium event, πT > πu occurred?’I

In his endowment economy, ct = y always, in and out of equilibrium

I

Household Euler equation reduces to Fisher equation in and out of equilibrium.
Concludes that under escape clause monetary policy commits to setting RT to two different
values: Impossible!!!

I

I
I

RT implied by Fisher equation and RT implied by Taylor rule.

No equilibrium exists if πT > πu .

• Cochrane’s answer:
I

Escape clause achieves uniqueness by blowing up the economy if πT ∈/ [πl , πu ].

19/34

Cochrane’s Critique of Implementation Result• Cochrane concludes uniqueness is achieved by “blow-up-the-economy threat.”• Reaches this conclusion by studying the question: ‘what would happen if theout-of-equilibrium event, πT > πu occurred?’I

In his endowment economy, ct = y always, in and out of equilibrium

I

Household Euler equation reduces to Fisher equation in and out of equilibrium.
Concludes that under escape clause monetary policy commits to setting RT to two different
values: Impossible!!!

I

I
I

RT implied by Fisher equation and RT implied by Taylor rule.

No equilibrium exists if πT > πu .

• Cochrane’s answer:
I

Escape clause achieves uniqueness by blowing up the economy if πT ∈/ [πl , πu ].

I

No one would believe the escape clause so that hyperinflation is still a valid equilibrium.

Uniqueness by Threatening to Blowing up Economy Not InterestingUniqueness by Threatening to Blowing up Economy Not Interesting• Diamond and Dybvig (1983) model of bank runs.

Uniqueness by Threatening to Blowing up Economy Not Interesting• Diamond and Dybvig (1983) model of bank runs.
I

In absence of regulation, two equilibria: run, no-run.

Uniqueness by Threatening to Blowing up Economy Not Interesting• Diamond and Dybvig (1983) model of bank runs.
I

In absence of regulation, two equilibria: run, no-run.

• Implementation problem:

Uniqueness by Threatening to Blowing up Economy Not Interesting• Diamond and Dybvig (1983) model of bank runs.
I

In absence of regulation, two equilibria: run, no-run.

• Implementation problem:
I

Design policy that rules out run equilibrium and keeps no-run equilibrium.

Uniqueness by Threatening to Blowing up Economy Not Interesting• Diamond and Dybvig (1983) model of bank runs.
I

In absence of regulation, two equilibria: run, no-run.

• Implementation problem:
I

Design policy that rules out run equilibrium and keeps no-run equilibrium.

• Answer to the problem: deposit insurance.

Uniqueness by Threatening to Blowing up Economy Not Interesting• Diamond and Dybvig (1983) model of bank runs.
I

In absence of regulation, two equilibria: run, no-run.

• Implementation problem:
I

Design policy that rules out run equilibrium and keeps no-run equilibrium.

• Answer to the problem: deposit insurance.
I

Everyone’s dominant strategy is no-run.

Uniqueness by Threatening to Blowing up Economy Not Interesting• Diamond and Dybvig (1983) model of bank runs.
I

In absence of regulation, two equilibria: run, no-run.

• Implementation problem:
I

Design policy that rules out run equilibrium and keeps no-run equilibrium.

• Answer to the problem: deposit insurance.
I

Everyone’s dominant strategy is no-run.

• The answer is uninteresting if govt.’s deposit insurance is not feasible.
I

Then no one would believe the insurance, and they might run.

Uniqueness by Threatening to Blowing up Economy Not Interesting• Diamond and Dybvig (1983) model of bank runs.
I

In absence of regulation, two equilibria: run, no-run.

• Implementation problem:
I

Design policy that rules out run equilibrium and keeps no-run equilibrium.

• Answer to the problem: deposit insurance.
I

Everyone’s dominant strategy is no-run.

• The answer is uninteresting if govt.’s deposit insurance is not feasible.
I

Then no one would believe the insurance, and they might run.

• Cochrane calls such implementation Blowing up the Economy.

Uniqueness by Threatening to Blowing up Economy Not Interesting• Diamond and Dybvig (1983) model of bank runs.
I

In absence of regulation, two equilibria: run, no-run.

• Implementation problem:
I

Design policy that rules out run equilibrium and keeps no-run equilibrium.

• Answer to the problem: deposit insurance.
I

Everyone’s dominant strategy is no-run.

• The answer is uninteresting if govt.’s deposit insurance is not feasible.
I

Then no one would believe the insurance, and they might run.

• Cochrane calls such implementation Blowing up the Economy.
I

In the monetary model, no one would believe such policy, and hyperinflation is not excluded!

Cochrane’s Critique in Our Production Economy

21/34

Euler Equation in our Production Economy

22/34

Euler Equation in our Production Economy• Euler Equation in our model:
RT = πT +1 + γ log (cT +1 /cT ) .

22/34

Euler Equation in our Production Economy• Euler Equation in our model:
RT = πT +1 + γ log (cT +1 /cT ) .
I

In equilibrium,I

our Euler equation reduces to Fisher equation because ct = 1 all t ≥ 0.

22/34

Euler Equation in our Production Economy• Euler Equation in our model:
RT = πT +1 + γ log (cT +1 /cT ) .
I

In equilibrium,I

I

our Euler equation reduces to Fisher equation because ct = 1 all t ≥ 0.

Out of equilibrium,I

our Euler equation depends on the value of cT +1 /cT .

22/34

Euler Equation in our Production Economy• Euler Equation in our model:
RT = πT +1 + γ log (cT +1 /cT ) .
I

In equilibrium,I

I

our Euler equation reduces to Fisher equation because ct = 1 all t ≥ 0.

Out of equilibrium,I

our Euler equation depends on the value of cT +1 /cT .

• Euler equation in Cochrane’s endowment economy:
RT = πT +1
I

in and out of equilibrium because ct = Y for all t ≥ 0 (Cochrane (2010,p.574).

Cochrane’s Critique in our Production Economy

23/34

Cochrane’s Critique in our Production Economy• The critique is only valid in Cochrane’s endowment model.

23/34

Cochrane’s Critique in our Production Economy• The critique is only valid in Cochrane’s endowment model.
• Suppose πT > πu in our production economy.

23/34

Cochrane’s Critique in our Production Economy• The critique is only valid in Cochrane’s endowment model.
• Suppose πT > πu in our production economy. Then,
Taylor rule : RT = φπT > πu , because φ > 1

23/34

Cochrane’s Critique in our Production Economy• The critique is only valid in Cochrane’s endowment model.
• Suppose πT > πu in our production economy. Then,
Taylor rule : RT = φπT > πu , because φ > 1
Euler equation : RT =π
| T{z+1}

low, by escape clause+γlog (cT +1 /cT ){z}|endogenously determined

23/34

Cochrane’s Critique in our Production Economy• The critique is only valid in Cochrane’s endowment model.
• Suppose πT > πu in our production economy. Then,
Taylor rule : RT = φπT > πu , because φ > 1
Euler equation : RT =π
| T{z+1}

low, by escape clause+γlog (cT +1 /cT ){z}|endogenously determined• Apparently consistent with a familiar and coherent narrative:

23/34

Cochrane’s Critique in our Production Economy• The critique is only valid in Cochrane’s endowment model.
• Suppose πT > πu in our production economy. Then,
Taylor rule : RT = φπT > πu , because φ > 1
Euler equation : RT =π
| T{z+1}

low, by escape clause+γlog (cT +1 /cT ){z}|endogenously determined• Apparently consistent with a familiar and coherent narrative:I

if πT > πu then real rate, RT − πT +1 , very high and cT very low.

23/34

Cochrane’s Critique in our Production Economy• The critique is only valid in Cochrane’s endowment model.
• Suppose πT > πu in our production economy. Then,
Taylor rule : RT = φπT > πu , because φ > 1
Euler equation : RT =π
| T{z+1}

low, by escape clause+γlog (cT +1 /cT ){z}|endogenously determined• Apparently consistent with a familiar and coherent narrative:I

if πT > πu then real rate, RT − πT +1 , very high and cT very low.

I

looks like a stylized Volcker recession.

23/34

Cochrane’s Critique in our Production Economy• The critique is only valid in Cochrane’s endowment model.
• Suppose πT > πu in our production economy. Then,
Taylor rule : RT = φπT > πu , because φ > 1
Euler equation : RT =π
| T{z+1}

low, by escape clause+γlog (cT +1 /cT ){z}|endogenously determined• Apparently consistent with a familiar and coherent narrative:I

if πT > πu then real rate, RT − πT +1 , very high and cT very low.

I

looks like a stylized Volcker recession.

Iescape clause looks like an (out-of-equilibrium) Taylor Principle.

23/34

Cochrane’s Critique in our Production Economy• The critique is only valid in Cochrane’s endowment model.
• Suppose πT > πu in our production economy. Then,
Taylor rule : RT = φπT > πu , because φ > 1
Euler equation : RT =π
| T{z+1}

low, by escape clause+γlog (cT +1 /cT ){z}|endogenously determined• Apparently consistent with a familiar and coherent narrative:I

if πT > πu then real rate, RT − πT +1 , very high and cT very low.

I

looks like a stylized Volcker recession.

Iescape clause looks like an (out-of-equilibrium) Taylor Principle.

• So, Cochrane’s blow-up-the-economy argument fails in production economy.

How Do We Answer Cochrane’s Question?

How Do We Answer Cochrane’s Question?

• What is it about the escape clause that implies πT > πu cannot occur in equilibrium?

How Do We Answer Cochrane’s Question?

• What is it about the escape clause that implies πT > πu cannot occur in equilibrium?
• We need an equilibrium concept which allows for out-of-equilibrium.

Exit Ramp Off Equilibrium
Competitive
EQM

Deviation

25/34

Equilibrium Concept that Allows for Out-of-Equilibrium Events

26/34

Equilibrium Concept that Allows for Out-of-Equilibrium Events• Our ‘Strategy Equilibrium’ related to Bassetto (2002,2005) and ACK (2010):

26/34

Equilibrium Concept that Allows for Out-of-Equilibrium Events• Our ‘Strategy Equilibrium’ related to Bassetto (2002,2005) and ACK (2010):
I

Reinterpret rational expectations equilibrium as a fixed point of a best response function.
I

Nash Equilibrium.

26/34

Equilibrium Concept that Allows for Out-of-Equilibrium Events• Our ‘Strategy Equilibrium’ related to Bassetto (2002,2005) and ACK (2010):
I

Reinterpret rational expectations equilibrium as a fixed point of a best response function.
I

I

Nash Equilibrium.

Then we can understand the economics of why a non-fixed point fails to be an equilibrium.

26/34

Equilibrium Concept that Allows for Out-of-Equilibrium Events• Our ‘Strategy Equilibrium’ related to Bassetto (2002,2005) and ACK (2010):
I

Reinterpret rational expectations equilibrium as a fixed point of a best response function.
I

I

Nash Equilibrium.

Then we can understand the economics of why a non-fixed point fails to be an equilibrium.

• Best response analysis goes back at least to Diamond and Dybvig (1983)
I

Describe what would happen, off-equilibrium paths, and discourage undesirable actions.

26/34

Introduce Firms’ Best Response Function

27/34

Introduce Firms’ Best Response Function• To set a price, intermediate firms need a belief about Wt . Why?

27/34

Introduce Firms’ Best Response Function• To set a price, intermediate firms need a belief about Wt . Why?
I

Wt is jointly determined in labor market and labor supply depends on Pt .

27/34

Introduce Firms’ Best Response Function• To set a price, intermediate firms need a belief about Wt . Why?
I

Wt is jointly determined in labor market and labor supply depends on Pt .

I

So, intermediate firms need a conjecture, Ptc , about aggregate prices, Pt .
pi,t = Ptc ×

Wt
.
Ptc

27/34

Introduce Firms’ Best Response Function• To set a price, intermediate firms need a belief about Wt . Why?
I

Wt is jointly determined in labor market and labor supply depends on Pt .

I

So, intermediate firms need a conjecture, Ptc , about aggregate prices, Pt .
pi,t = Ptc ×

Wt
.
Ptc

• We divide the period into morning and afternoon.
I

In the morning, intermediate firms set pi,t simultaneously given conjecture Ptc .

27/34

Introduce Firms’ Best Response Function• To set a price, intermediate firms need a belief about Wt . Why?
I

Wt is jointly determined in labor market and labor supply depends on Pt .

I

So, intermediate firms need a conjecture, Ptc , about aggregate prices, Pt .
pi,t = Ptc ×

Wt
.
Ptc

• We divide the period into morning and afternoon.
I

In the morning, intermediate firms set pi,t simultaneously given conjecture Ptc .

I

In the afternoon, the rest happens so Wt /Ptc is determined as a function of “history,”(ht−1 , Ptc ).
pi,t = Ptc ×

γ+ψ
γ+ψ
Wt
= Ptc ctb
= Ptc ctb (ht−1 , Ptc )
.
c
Pt
27/34

Best Response Function

28/34

Best Response Function• Scaling and logging, we get the individual best response F .
γ+ψ 
pi,t
Pt
b
c
= ln
ln
≡ F (ht−1 , πtc ) .
× ct (ht−1 , Pt )Pt−1 µ̄∗Pt−1 µ̄∗| {z }
xi,t28/34

Best Response Function• Scaling and logging, we get the individual best response F .
γ+ψ 
pi,t
Pt
b
c
= ln
ln
≡ F (ht−1 , πtc ) .
× ct (ht−1 , Pt )Pt−1 µ̄∗Pt−1 µ̄∗| {z }xi,t• F (ht−1 , πtc ) is the best response function
xi,t = F (ht−1 , πtc ) .

Continuation Equilibrium• Let
at = lt , πt , ct , Rt , Wt , µ, M̄t

ht−1 = (a0 , a1 , ..., at−1 ) .

29/34

Continuation Equilibrium• Let
at = lt , πt , ct , Rt , Wt , µ, M̄t

ht−1 = (a0 , a1 , ..., at−1 ) .

Definition
A continuation equilibrium conditional on (ht−1 , πtc ) is a sequence, at+s , for s ≥ 0, with two
properties:(a) at+s , s > 0 satisfies all t + s equilibrium conditions.
(b) at satisfies all time t equilibrium conditions except intermediate good firm optimality.
29/34

Strategy Equilibrium
Definition
A strategy equilibrium is a competitive equilibrium with the property that for each possible
history ht−1 : (i) there is a well-defined continuation equilibrium corresponding to any value ofπtc and (ii) there exists a πtc that is a fixed point:
πtc = F (ht−1 , πtc ) .

30/34

Strategy Equilibrium
Definition
A strategy equilibrium is a competitive equilibrium with the property that for each possible
history ht−1 : (i) there is a well-defined continuation equilibrium corresponding to any value ofπtc and (ii) there exists a πtc that is a fixed point:
πtc = F (ht−1 , πtc ) .
Comment:• Property: for on-path ht−1 and when competitive equilibrium unique, then πtc equals
competitive πt .

30/34

Strategy Equilibrium
Definition
A strategy equilibrium is a competitive equilibrium with the property that for each possible
history ht−1 : (i) there is a well-defined continuation equilibrium corresponding to any value ofπtc and (ii) there exists a πtc that is a fixed point:
πtc = F (ht−1 , πtc ) .
Comment:• Property: for on-path ht−1 and when competitive equilibrium unique, then πtc equals
competitive πt .
• Part (i) provides an exit-ramp from the competitive equilibrium in each t.
I

Allows us to think coherently about why people privately choose not to take the exit ramp.

I

Can ask ‘why does the escape strategy’ trim non-desired equilibria?
30/34

Why is πTc > πu not an Equilibrium Under Escape Clause?
• Easy to show that actual inflation would be:
ln cT

F (hT −1 , πTc ) = πTc + (γ + ψ)
|

z

}| {
φ
πc .
1−γ T
{z
}

real wage• Intermediate firms expect govt. to depress economy (i.e., reduce cT ) by raising real rate.

31/34

Why is πTc > πu not an Equilibrium Under Escape Clause?
• Easy to show that actual inflation would be:
ln cT

F (hT −1 , πTc ) = πTc + (γ + ψ)
|

z

}| {
φ
πc .
1−γ T
{z
}

real wage• Intermediate firms expect govt. to depress economy (i.e., reduce cT ) by raising real rate.
• With low output, labor demand is low

31/34

Why is πTc > πu not an Equilibrium Under Escape Clause?
• Easy to show that actual inflation would be:
ln cT

F (hT −1 , πTc ) = πTc + (γ + ψ)
|

z

}| {
φ
πc .
1−γ T
{z
}

real wage• Intermediate firms expect govt. to depress economy (i.e., reduce cT ) by raising real rate.
• With low output, labor demand is low → WT /PT low.

31/34

Why is πTc > πu not an Equilibrium Under Escape Clause?
• Easy to show that actual inflation would be:
ln cT

F (hT −1 , πTc ) = πTc + (γ + ψ)
|

z

}| {
φ
πc .
1−γ T
{z
}

real wage• Intermediate firms expect govt. to depress economy (i.e., reduce cT ) by raising real rate.
• With low output, labor demand is low → WT /PT low.
• So, intermediate firms post lower prices, and actual inflation is low,
πTc > F (πTc )• No fixed points.

Why Can Agents Come Up with a Rational Expectation?

Why Can Agents Come Up with a Rational Expectation?
• We use a refinement of “rationalizability ” for a theory of expectation.

Why Can Agents Come Up with a Rational Expectation?
• We use a refinement of “rationalizability ” for a theory of expectation.
I

Pick an arbitrary big compact set Π ⊂ R for firms’ action space.

Why Can Agents Come Up with a Rational Expectation?
• We use a refinement of “rationalizability ” for a theory of expectation.
Pick an arbitrary big compact set Π ⊂ R for firms’ action space.
I Firms are certain that other firms only choose their action from F (Π) .
I

I

A firm knows others are rational.

Why Can Agents Come Up with a Rational Expectation?
• We use a refinement of “rationalizability ” for a theory of expectation.
Pick an arbitrary big compact set Π ⊂ R for firms’ action space.
I Firms are certain that other firms only choose their action from F (Π) .
I

I
I

A firm knows others are rational.

Then firms are now certain that other firms only choose from F (F (Π)) .
I

A firm knows others knows firms are rational.

Why Can Agents Come Up with a Rational Expectation?
• We use a refinement of “rationalizability ” for a theory of expectation.
Pick an arbitrary big compact set Π ⊂ R for firms’ action space.
I Firms are certain that other firms only choose their action from F (Π) .
I

I
I

I
I

A firm knows others are rational.

Then firms are now certain that other firms only choose from F (F (Π)) .
A firm knows others knows firms are rational.

Keep continuing this forward induction...
I

Firms only play an action from F ∞ (Π).

Why Can Agents Come Up with a Rational Expectation?
• We use a refinement of “rationalizability ” for a theory of expectation.
Pick an arbitrary big compact set Π ⊂ R for firms’ action space.
I Firms are certain that other firms only choose their action from F (Π) .
I

I
I

I
I

A firm knows others are rational.

Then firms are now certain that other firms only choose from F (F (Π)) .
A firm knows others knows firms are rational.

Keep continuing this forward induction...
I

Firms only play an action from F ∞ (Π).

Proposition
γ−1
If γ > 1 and 1 < φ ≤ 2 γ+ψ
, then for any large compact set Π, F ∞ (Π) = {0} .

• Rational firms convince themselves that desired equilibrium occurs!
I

A desired property for policy design.
32/34

Put Simply

33/34

Put Simply• Escape clause prevents undesired inflation by a feasible threat to crash the economy (likeVolcker did) if it happened.

33/34

Put Simply• Escape clause prevents undesired inflation by a feasible threat to crash the economy (likeVolcker did) if it happened.

• Logic by which it works looks like an ‘Out-of-equilibrium Taylor Principle’.

33/34

Put Simply• Escape clause prevents undesired inflation by a feasible threat to crash the economy (likeVolcker did) if it happened.

• Logic by which it works looks like an ‘Out-of-equilibrium Taylor Principle’.

• Common knowledge of rationality is enough to ensure that firms spontaneously come up
with the rational expectation.

33/34

Concluding Observations• Taylor Principle: When inflation is high, raise Rt sharply and (hopefully) this will slow
down the economy and stabilize inflation around desired rate.

34/34

Concluding Observations• Taylor Principle: When inflation is high, raise Rt sharply and (hopefully) this will slow
down the economy and stabilize inflation around desired rate.
• Often, φ > 1 is referred to as the ‘Taylor Principle’.
I

But, only seems to deliver on its promise in neighborhood of desired equilibrium.

I

Does not rule out other, non-desired, equilibria.

Concluding Observations• Taylor Principle: When inflation is high, raise Rt sharply and (hopefully) this will slow
down the economy and stabilize inflation around desired rate.
• Often, φ > 1 is referred to as the ‘Taylor Principle’.
I

But, only seems to deliver on its promise in neighborhood of desired equilibrium.

I

Does not rule out other, non-desired, equilibria.

• We showed that the Taylor rule with φ > 1 and an escape clause:

Concluding Observations• Taylor Principle: When inflation is high, raise Rt sharply and (hopefully) this will slow
down the economy and stabilize inflation around desired rate.
• Often, φ > 1 is referred to as the ‘Taylor Principle’.
I

But, only seems to deliver on its promise in neighborhood of desired equilibrium.

I

Does not rule out other, non-desired, equilibria.

• We showed that the Taylor rule with φ > 1 and an escape clause:I

Rules out non-desired equilibria by an off-equilibrium version of Taylor Principle.

34/34

Concluding Observations• Taylor Principle: When inflation is high, raise Rt sharply and (hopefully) this will slow
down the economy and stabilize inflation around desired rate.
• Often, φ > 1 is referred to as the ‘Taylor Principle’.
I

But, only seems to deliver on its promise in neighborhood of desired equilibrium.

I

Does not rule out other, non-desired, equilibria.

• We showed that the Taylor rule with φ > 1 and an escape clause:I

Rules out non-desired equilibria by an off-equilibrium version of Taylor Principle.

I

Caveat: regime-shift to constant money rule does not always work when money demand isinterest elastic.

34/34

Concluding Observations• Taylor Principle: When inflation is high, raise Rt sharply and (hopefully) this will slow
down the economy and stabilize inflation around desired rate.
• Often, φ > 1 is referred to as the ‘Taylor Principle’.
I

But, only seems to deliver on its promise in neighborhood of desired equilibrium.

I

Does not rule out other, non-desired, equilibria.

• We showed that the Taylor rule with φ > 1 and an escape clause:I

Rules out non-desired equilibria by an off-equilibrium version of Taylor Principle.

I

Caveat: regime-shift to constant money rule does not always work when money demand isinterest elastic.

I

Need to revisit New Keynesian canon that thinking about money demand is unnecessary.
34/34