Inflation Targeting with Imperfect Information IMF SEMINAR, January - - PowerPoint PPT Presentation

Rafael Santos

.

Vale and Central Bank of Brazil.

Inflation Targeting with Imperfect Information

IMF SEMINAR, January 2014

Technical approach: Global Games

• Defined by Hans Carlsson and Eric van Damme (1993)
• "Global Games and Equilibrium Selection", Econometrica 61 (5): 989-1018.

— gameS from individual perspective — global output

• Morris and Shin (AER, 1998)
• Angeletos and Werning (AER, 2006)
• Araujo, Berriel and Santos (Revised-resubmitted to the IER)

Morris and Shin (AER, 1998)

• Information and speculative attacks

— Uniqueness: crises depends only on fundamentals — Crises cannot be triggered by lack of confidence — No-common-knowledge prevents self confirmed equilibrium — No role for public communication

Angeletos and Werning (AER, 2006)

• add Public Information

— High transparency: self confirmed crises are possible — Even under no-common-knowledge — Currency value may depend on equilibrium selection

This paper

• Adapts Angeletos and Werning (2006)

— one stage added — exogenous public information

• We then study the role of inflation targeting announcement:

— Aggressive targets hurt coordination and may open the door to ME — Noisy information helps to coordinate expectations around the announced target — There are limits to IT announcements and transparency reinforce such limits

• Some data before model ...

The case of Brazil-2002

• In Brazil, the target for the year (t + 2) is decided in the year (t)
• Luiz Inácio Lula da Silva was elected president of Brazil at the end of 2002 (October)
• At that time, expectations about keeping currency stability in next years were really

low

• They were grounded on a fear of Lula’s innovation in monetary policy making

2 5 8 11 14 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Target Re-Target Re-Re-Target (Jan/03) CPI Inflation ( % / year)

Brazil - Inflation Targeting Regime

Cross country evidence ?

Model based on 3-stage-game with 2 type of players Static monetary model with imperfect information

Stage 3: CB decides actual inflation π minimizing L (π, πe(πa)) +

• Ik,π=πa
• Stage 1: CB announces inflation target πa minimizing E
• L (π, πe(πa)) +
• Ik,π=πa
• Stage 2: Agent j ∈ (0, 1) believes or not in the target: maxαj∈{0,1} E
• 1 − αj

Ic,π=πa Information set: private signal: sj = k + σεj ; σ > 0 and εj ∼ N(0, 1) public signal: sp = k + σpεp ; σp > 0 and εp ∼ N(0, 1)

Exploring the third stage

Assuming∗ ∂2L

∂π2 > 0, ∂2L ∂πe∂π < 0, ∂2L ∂π2 > − ∂2L ∂πe∂π :

• P1: π∗ (πe) = πe exists and it is unique, named discretionary inflation (πD)
• (πG, πG) ≡ arg min L(π, πe) s.t. π = πe, πG named the commitment infl.
• P3: Required k for target achievement depends on the distance btw the πa and πD

∗Also is assumed that Loss function becomes less concave as approaches to the discretionary inflation level.

EQUILIBRIUM:

π∗

a such that

π∗

a solves first stage CB problem

π∗ such that π∗ solves third stage CB problem π∗

e such that

π∗

e is defined consistent with monotone-bayesian equilibria

(j) attacks ⇔ sj ≤ s∗(sp, πa) ≡ “threshold value” πe(sp) is computed by aggregating each agent as follow: π∗

e = α (s∗) π∗ a + (1 − α (s∗))πD

α (s∗) ≡

1

• αj

sj, sp, πa

• dj

Proposition 4

Given an announced target, if −∂2L(.,.)

∂πe∂π < √ 2π (πa−πD)2

σ2

p

σ

• then equilibrium is unique for

every public signal

• Transparency on cost k leads to multiplicity
• Aggressive targets
• πa closer to πG

fuels multiplicity

• Surprise cost (marginal cost of inflation higher when expectations are low) fuels mul-

tiplicity

Proposition 5

Let the variance of the public signal be high enough to ensure the uniqueness for all public signals and for all target-candidates: σ2

p > σ

• −∂2L(.,.)

∂πe∂π

• (πG−πD)2

√ 2π

. In such a case, more defensible targets improves the target coordination (increases α∗).

Barro and Gordon

Loss function: L = π2 + λ (y − y∗)2 Phillips Curve π = πe + ϕ (y − yn)

Alternative application with fiscal-monetary trade-off

Loss function: L (π, πe) ≡ π

η

η + λ exp (d − (π − πe))

REMARKS

• Our results are aligned with the conventional claim on the benefits of having low

inflation target supported by sound fundamentals.

• But still, fundamental improvement might be costly in terms of both time and re-

sources.

• Meanwhile, as the public needs to share a precise evidence of weakness to coordinate

against the inflation target, central bank should improve coordination — by adopting a prudent/defensible target — by avoiding too much transparency

THANK YOU

.

Additional information: rafael.santos@bcb.gov.br Avoid more transparency than Avoid more ambitious target than supported by your fundamentals supported by your fundamentals http://epge.fgv.br/we/RafaelSantos