Rafael Santos
.
Vale and Central Bank of Brazil.
In‡ation Targeting with
Imperfect Information
IMF SEMINAR, January 2014
Technical approach: Global Games
De…ned 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 con…dence
– No-common-knowledge prevents self con…rmed equilibrium
– No role for public communication
Angeletos and Werning (AER, 2006)
add
Public Information
– High transparency: self con…rmed 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 in‡ation 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
( % / year)
CPI Inflation
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 in‡ation
Stage 1: CB announces in‡ation target
h
minimizing L ( ; e( a)) + Ik; 6=
n
h
a minimizing E L ( ; e ( a )) + Ik; 6= a
Stage 2: Agent j 2 (0; 1) believes or not in the target: max
j 2f0;1g
E 1
Information set:
private signal:
public signal:
a
i
sj = k + "j ;
> 0 and "j
N (0; 1)
sp = k + p"p ; p > 0 and "p
N (0; 1)
io
j I
c; 6= a
Exploring the third stage
2
2
@ 2L >
Assuming @@ L2 > 0, @@ eL
<
0
;
@
@ 2
P1:
@ 2L
@ e@
:
( e) = e exists and it is unique, named discretionary in‡ation ( D )
( G; G)
arg min L( ; e) s.t.
= e; G named the commitment in‡.
P3: Required k for target achievement depends on the distance btw the a and D
Also is assumed that Loss function becomes less concave as approaches to the discretionary in‡ation level.
EQUILIBRIUM:
such that
such that
e such that
a
solves …rst stage CB problem
solves third stage CB problem
e is de…ned consistent with monotone-bayesian equilibria
a
(j ) attacks , sj
s (sp; a)
“threshold value”
p
e (s ) is computed by aggregating each agent as follow:
D
=
(
s
+
(1
(
s
)
))
e
a
(s )
Z1
0
j sj ; s p ;
a dj
Proposition 4
Given an announced target, if
every public signal
p
@ 2 L(:;:)
2
<
2
@ e@
( a
D)
2
p
then equilibrium is unique for
Transparency on cost k leads to multiplicity
Aggressive targets
a
closer to G fuels multiplicity
Surprise cost (marginal cost of in‡ation higher when expectations are low) fuels multiplicity
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:
2>
p
@ 2 L(:;:) ( Gp D )2
.
@ e@
2
defensible targets improves the target coordination (increases
).
In such a case, more
Barro and Gordon
Loss function:
(y
y )2
= e + ' (y
yn)
L= 2+
Phillips Curve
Alternative application with …scal-monetary trade-o¤
Loss function:
L ( ; e)
+
exp (d
(
e ))
REMARKS
Our results are aligned with the conventional claim on the bene…ts of having low
in‡ation target supported by sound fundamentals.
But still, fundamental improvement might be costly in terms of both time and resources.
Meanwhile, as the public needs to share a precise evidence of weakness to coordinate
against the in‡ation target, central bank should improve coordination
– by adopting a prudent/defensible target
– by avoiding too much transparency
THANK YOU
.
Additional information: [email protected]
Avoid more transparency than
supported by your fundamentals
Avoid more ambitious target than
supported by your fundamentals
http://epge.fgv.br/we/RafaelSantos