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. — game S 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
Brazil - Inflation Targeting Regime Target 14 Re-Target Re-Re-Target (Jan/03) 11 CPI Inflation ( % / year) 8 5 2 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008
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, π e ( π a )) + I k,π � = π a � � �� Stage 1 : CB announces inflation target π a minimizing E L ( π, π e ( π a )) + I k,π � = π a � 1 − α j � Stage 2 : Agent j ∈ (0 , 1) believes or not in the target: max α j ∈{ 0 , 1 } E I c,π � = π a Information set: s j = k + σε j ; σ > 0 and ε j ∼ N (0 , 1) private signal: s p = k + σ p ε p ; σ p > 0 and ε p ∼ N (0 , 1) public signal:
Exploring the third stage Assuming ∗ ∂ 2 L ∂π e ∂π < 0 , ∂ 2 L ∂ 2 L ∂π 2 > − ∂ 2 L ∂π 2 > 0 , ∂π e ∂π : • P1: π ∗ ( π e ) = π e exists and it is unique, named discretionary inflation ( π D ) • ( π G , π G ) ≡ arg min L ( π, π e ) s.t. π = π e , π G named the commitment infl. • P3: Required k for target achievement depends on the distance btw the π a and π D ∗ Also is assumed that Loss function becomes less concave as approaches to the discretionary inflation level.
EQUILIBRIUM: π ∗ π ∗ a such that a solves first stage CB problem π ∗ such that π ∗ solves third stage CB problem π ∗ π ∗ e such that e is defined consistent with monotone-bayesian equilibria ( j ) attacks ⇔ s j ≤ s ∗ ( s p , π a ) ≡ “threshold value” π e ( s p ) is computed by aggregating each agent as follow: π ∗ e = α ( s ∗ ) π ∗ a + (1 − α ( s ∗ )) π D 1 � α j � � α ( s ∗ ) ≡ s j , s p , π a dj 0
Proposition 4 � σ 2 � √ Given an announced target, if − ∂ 2 L ( .,. ) 2 π p ∂π e ∂π < then equilibrium is unique for ( π a − π D ) 2 σ every public signal • Transparency on cost k leads to multiplicity � π a closer to π G � • Aggressive targets 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 � � ( π G − π D ) 2 − ∂ 2 L ( .,. ) signals and for all target-candidates: σ 2 p > σ √ . In such a case, more ∂π e ∂π 2 π defensible targets improves the target coordination (increases α ∗ ).
Barro and Gordon Loss function: L = π 2 + λ ( y − y ∗ ) 2 Phillips Curve π = π e + ϕ ( y − y n )
Alternative application with fiscal-monetary trade-off Loss function: η L ( π, π e ) ≡ π η + λ exp ( d − ( π − π e ))
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
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