GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No.35

Endogenous Policy Announcement andAccountability for Inflation Target

Keiichi Morimoto

February 2009GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Endogenous Policy Announcement andAccountability for Inflation Target
Keiichi Morimoto∗February, 2009

Abstract
In this paper, I show that accountability for inflation target will improve social welfare when the central bank makes transparency-opaqueness choices endogenously. The key elements are uncertainty of the firms’ informational quality, theopacity bias of constrained discretionay monetary policy under noisy information,and the role of harmful noisy public information. Based on the qualitative andquantitative result, I present a policy recommendation as to policy announcements
and inflation targeting regime.

JEL Classification: D82, E52, E58
Keywords: asymmetric information, economic transparency, inflation targeting∗

Graduate School of Economics, Osaka University, 1-7, Machikaneyama, Toyonaka,Osaka 560-0043,
Japan. (E-mail address: gge014mk@mail2.econ.osaka-u.ac.jp) I am grateful to Takushi Kurozumi andall participants of Macroeconomics Conference for Young Professionals, Osaka (February 8, 2009). Remaining errors are my own.

1

Introduction

In recent years, the role of information in monetary policy analysis has been one of themost important issues in monetary economics. The problems about the ambiguous effectsof transparency on social welfare have been focused. For example, see Morris and Shin
(2002).
In this paper, I show that accountability for inflation target will improve social welfare
when the central bank makes the transparent-opaqueness choice endogenously. Amongthe five kind of transparency classified by Geraats (2002), I focus on economic transparency. I explore the relationship between the central bank’s announcement undernoisy information and social welfare, how the central bank decides to make policy announcements and the design of the mechanism to implement the announcement actions.
The problem of endogenous regime choice by the central bank has not been argured
yet. In the literature, using a traditional Phillips curve, Faust and Svensson (2002) analyze endogenous (continuous) choice of degree of control and transparency under bothcommitment and discretion. They emphasizes the importance of commitment mechanisms and policy objectives in treating central bank transparency. The meaning oftransparency in the model of Faust and Svensson (2002) is not a provision of the central
bank’s forecast of future economic developmets.
In the model of this paper, transparency means that the central bank gives announcements on its outlook for future economic shocks. Opaqueness means that the central bankmakes no announcements on its information. Since whether the central bank announce
its information to the public can be thought as a classification criterion of monetary policy regimes, the decision-makings about transparecy or opaqueness is a kind of monetary
policy regime choices. Another feature of my analysis is that the central bank’s choice isdiscrete. There are only two alternatives, transparency and opaqueness. This generates
difficulty of the central bank’s approapriate decision-making because failure in judgement
generated by imperfect information would tend to bring larger losses than in continuous
choice cases. I treats the problem in this paper.
Section 2 describes the basic model with exogenous policy announcement. Section 3
1

quickly reviews the basic model’s welfare implications which is necessary to understandthe main result of this paper. Section 4 presents the main result of the relationshipbetween the endogenous policy announcements and accountability for inflation target.
Section 5 concludes.

2

The Model

I use the model of Walsh (2007b) and Walsh (2008). I abstract from Morris and Shin’s(2002) informational heterogeneity of firms in the base model since that is not an important assumption for the main result of this paper.
There are a continuum of monopolistic competitive firms. Their price-setting behavior
is characterized by Calvo-type staggered pricing, which introduces nominal rigidity to themodel. Each firm and the central bank receive private signals on the fundamental shocks.
I assume that each firm’s signal is identical, so that, there is informational asymmetry
only between the private sector and the central bank.

2.1

Timing and Infomational Structure

In the model economy there are the three fundamental shocks; cost, demand and welfare
gap shocks, denoted by u, v, w respectively. I assume that the central bank’s policy
instrument is the intended next-period output gap.
The timing is as follows:
1. To begin with, the central bank chooses between the transparent regime and theopaque regime. The transparent (opaque) regime is one in which the central bankmakes (no) announcements on its forecast of future economic shocks. The differenceof the model of this paper and Walsh (2008) is this dicision-making of the centralbank.
2. At the end of period t − 1, the central bank receives its signals on the shocks inperiod t and sets the value of its policy instrument.

2

3. The private sector receives the signals on the shocks in period t and the value ofpolicy instrument the central bank set.
4. The firms which can adjust their price set prices in period t.
5. At the beginning of period t, the three shocks are realized and then the inflation
rate and output gap in period t are determined.
At the end of period t − 1, each firm receives the signals, uft , vtf , wtf , on the shocks inperiod t in the following form.
uft = ut + εfu,t ,vtf = vt + εfv,t ,wtf = wt + εfw,t ,where ut , vt and wt are the realization of the shocks in period t, and εfu,t and εfv,t are thefirms’ measurement errors.
In the same way, the central bank receives signals on the three shocks byucb= ut + εcb
t
u,t ,

(1)

vtcb = vt + εcb
v,t ,

(2)

wtcb = wt + εcb
w,t .

(3)

I assume that all shocks and measurement errors are independent and serially uncorrelated and follow the normal distribution with mean zero.
The key elements of the informational structure are
γsf =

σs2
σs2
cb
, γs = 2(s = u, v, w),22
σs2 + σf,sσs + σcb,s22and σcb,sare the variance of εfs,t and εcb
where σs2 is the variace of shock st and σf,ss,trespectively. The noise ratios above are the measure of quality of the firms’ and thecentral bank’s information on the future economic shocks. For example, when γucb is high,the central bank has precise outlook for future cost shock. If γscb = 1, then the central
bank’s information on shock s is perfect and if γscb < 1 , then it is imperfect.
3

In the line of rational expectations, I assume that the private sector knows γscb (s =u, v, w). Thus, since the central bank’s forecast of the shock s is given by (see (1),(2),(3))1cb
Et−1
st = γscb scb
t ,the private sector is able to observe the central bank’s forcasts if the central bank reveals
its signals. Therefore, the transparent regime of monetary policy is one in which thecentral bank announces its signals to the private sector.

2.2

Supply and Demand Sides

As in Walsh (2007a), by the standard assumption of Calvo-pricing and monopolisticcompetition, the AS relation (supply side) of the model is represented by the following
New-Keynesian Phillips curve:f
πt+1 +
πt = βEt−1(1 − ω)(1 − βω)
f
f
ut ),
xt + Et−1(κEt−1
ω(4)

where πt and xt are inflation rate and output gap in period t and the parameter β, ωand κ represents the discount factor, the probability which each firm can not adjust its
price and the elasticity of inflation with respect to output gap respectively. For details,
see Appendix.
I specify the AD relation (demand side) by
xt = θt−1 + vt ,(5)

where θt−1 is the central bank’s policy instrument in period t − 1 (the intended output
gap).

2.3

Monetary Policy Objectives

To measure social welfare, I adopt the standard social loss function such that∞
1 X t 2
L = E0β [πt + λ(xt − wt )2 ],
2
t=0
1

(6)

cb
Et−1
st means the expectation of shock st based on the centrtal bank’s information in period t − 1.

4

where the parameter λ represents the social preference relation between inflation andoutput gap.
When the monetary policy regime is inflation targeting, the central bank is accountable for the inflation target to some extent. Thus, as in Walsh (2003), I set the loss
function of the central banker to∞i
1 cb X t h 2
2
T 2
L = E0β πt + λ(xt − wt ) + τ (πt − π ) ,
2
t=0
cb

(7)

where π T is the (non-state-contingent) target value of inflation rate and the parameterτ ≥ 0 is the degree of accountability for the target. Since there is no average inflation
bias in this model, the appropriate inflation target is zero. Hence, by (5), the central
bank’s loss function is reduced to∞i
1 cb X t h
L = E0β (1 + τ )πt2 + λ(xt − wt )2 .
2
t=0
cb

3

(8)

Opaque and Transparent Regimes

The qualitative welfare implication of the opaque and transparent monetary policy issimilar to Walsh (2008) but I quickly review them for convienience to understand thebackground of the results in the next section.

3.1

Opaque Regime and Optimal Degree of Accountability

In opaque regimes, the central bank does not announce the signals it receives, Ωcb
t =
cb
cb 0
[ucb
t , vt , wt ] . Thus, the private sector will set their optimal prices by infering the central

bank’s information Ωcbt through the revealed value of the policy instrument θt−1 .
Let Ωft = [uft , vtf , wtf ]0 . Then, each firm’s information vector in period t − 1 is[Ωft , θt−1 ]0 . By using the method of minimal state variables, the equilibrium pricing
strategy will be of the form such asπt∗ = Ao Ωft + B o θt−1 ,5(9)Table 1: Optimal Policy Responses in the opaque regime ( σu2 = σv2 = σw2 = 1 )
γscb
∗

γsf
1

πθ
E cb u0.474 -0.452

E cb v-1.000E cb w
0.36340.4 0.4
0.8

0.122 -0.126
0.265 -0.301-1.017-1.0240.86210.50220.8 0.4
0.8

0.043 -0.058
0.162 -0.279-1.006-1.011

0.94210.6439where Ao is 1 × 3 and B o is 1 × 1.2 Aggregate inflation rate isπt = (1 − ω)πt∗ = (1 − ω)(Ao Ωft + B o θt−1 ).
The reponse of the inflation rate to the policy instrument is
πθ ≡

∂πt
(1 − ω)(1 − βω)=κ(1 + C o E f Sθ ),∂θt−1ωwhere C o is 1 × 3 and E f Sθ is impact which observing θt−1 has on firms’ expectation of
the vector of fundamental shocks, St ≡ [ut , vt , wt ]0 . 3 The first and second term in thebracketed part of the right-hand side of (12) are the direct effect and the informational
effect on inflation. Note that if πθ is high, then given a degree of inflation volatility, thecentral bank can make output gap volatility small.
In the following analysis, I specify the value of parameters. 4 The baseline values ofparameters are as follow: β = 0.99, ω = 0.75, κ = 1.8, λ = 0.0625, σu2 = σv2 = 1. I set
σw2 = 0.001 to make the model close to the standard model in which there are no welfare
gap shocks.
The key findings in Table 1 are the next two points. First, given γscb , πθ is increasing in
γsf . In the opaque regime, under imperfect information (γsf < 1), θ conveys information2 ∗πt = p∗t − pt−1 . p∗t is the optimal price of each firm which can adjust their prices and pt is aggregate(log) price level.
3
The concrete definition of E f Sθ lies in the appendix.
4
These values are consistent with standard New Keynesian models. See Walsh (2008).

6

Table 2: Optimal Accountability in the opaque regime = τo∗ ( σu2 = σv2 = σw2 = 1 )γscb γsf
τo∗0.4 0.4 3.34
0.6 1.86
0.8 0.67
10
0.8 0.4 4.76
0.6 3.98
0.8 1.63
1
0

on the central bank’s forecast to the private sector. A rise in θ lowers the firms’ forecastsof demand shocks and also reduces their forcasts of cost shocks, so that the expected
inflation decreases. Second, imperfect information reduces the optimal policy responses
to the central bank’s signals on the cost and demand shock. This is the immediate resultof the first point.
The second point above suggests that positive degree of accountability for inflation
target is optimal. The reason is that it makes the central bank stabilize inflation volatility
in the face of cost shocks and this means monetary policy is closer to the perfect information case. In fact, Table 2 supports such a conjecture. Note that given the qualityof the central bank’s information, the optimal degree decreases with the quality of theprivate sector’s information. A rise in γsf reduces inefficient informational effect which
the policy instrument makes. Note also that in the perfect information case, there is no
inefficient informational effect and so the optimal degree of accountability is zero.

3.2

Transparent Regime

In a transparent regime, the central bank announces its signals on the fundamental shocks.
Thus, the information vector of the firms in period t − 1 is [Ωft , Ωcbt , θt−1 ]. Hence, the7

firms’ equilibrium pricing strategy is of the form such astπt∗ = At Ωft + Dt Ωcb
t + B θt−1 ,At and Dt are 1 × 3 and B t is 1 × 1. As shown in Appendix,
πθ =

∂πt
(1 − ω)(1 − βω)
=
κ,
∂θt−1
ω

which suggests that there is no informational effect of the policy instrument in the transparent regime. Therefore, the optimal degree of accountability for inflation target is zero
whatever the values of noise ratios are. That is, Rogoff’s (1985) conservative central
banker reduces social loss under imperfect information. In this model, the cost shocks
are serially uncorrelated. Hence, without any infomation effect, there is no reason toconsider the positive degree of accountability. See Clarida et al.(1999)

3.3

Transparency versus Opaqueness

Figure 1 presents welfare comparison between the transparent and opaque regime withthe optimal degree of accountability. The key parameters are γucb and γsf . The intuition isclear. If γ f is large, then the quality of the central bank’s information on demand shock ishigh. Thus, the central bank can set the policy instrument and the gain of transparency
dominates that of opaqueness.

4

Endogenous Policy Announcement and Accountability

This section is the main body of the paper. In the last section, it is exogenous whether
the central bank announces its forecast for the future economic development. In thissection, I will endogenize the central bank’s choice between the transparent and opaqueregime. I call it transparent-opaqueness choice. Since I assume that the monetary policy
regime is constrained discretion, the central bank have to make transparency-opaquenesschoices before it actually conducts monetary policy and commits it through the future. 5
5

See King (2002).

8

The simulation result of the last section suggests that a key element to determine whichof transparent and opaque regime is desirable is the quality of the firm’s information, γsf .

4.1

Endogenous Policy Announcement

I add the following assumptions. The central bank chooses whether to announce to the
public its information of the future economic development. Before the decision-making
above, the central bank receives signal γ̃sf on γsf . The signal γ̃sf is assumed to be uniformly
distributed on the interval [γsf − as , γsf +as ], where as is a positive parameter. It considers
both the opaque and transparent regimes. About the opaque regime, given a degree τ ofthe accountability for inflation target, it anticipates the coefficients A, B of the private
sector’s response such thatπt = (1 − ω)(AΩft + Bθt−1 ),its own response coefficient Θ such that θt−1 = ΘΓcb Ωcbt and equilibrium dynamics of themodel economy, and then estimates expected value of its loss function Lcb in the opaqueregime. The case of the transparent regime is analogously calculated. 6 The transparent
regime is chosen if the expected value is smaller in transparent regime than in the opaqueregime.
With large measurement error of the quality of the firms’ information, |γsf − γ̃sf |, thecentral bank might make a mistake on TOCs and leads catastrophic social loss. Since results of transparency-opaqueness choices crucially depend on the degree of accountability
for the inflation target, I explore the role of accountability for beneficial implementationof transparency-opaqueness choices. In general, if τ is small, then the central bank will
be tend to choice transparent regime. However, this does not necessarily improve social welfare since the opaque regime is desirable when γsf is low. Thus, there is room
to optimize the expected social welfare with respect to τ with the quality of the firms’
information given.
6

In the transparent regime, the private sector’s response is of the form such as πt = (1 − ω)(AΩft +DΩcbt + Bθt−1 ).

9I formulate this problem. Before the beginning of the period 0, the central bankreceive the signalγ̃sf ∼ U ([γsf − as , γsf + as ]), s = u, v, w.
The central bank chooses between the transparent and opaque regime to minimize its
loss function subject to that it must subsequently conduct monetary policy under theconstrained discretionary regime it chooses. That is, the behavior of the central bank ismini∈{0,1}∞i
1 cb X t h
E0
β (1 + τ )πt2 (i, τ ) + λ(xt (i, τ ) − wt )2 ,2t=0

where 0 and 1 indicate the transparent and opaque regime respectively and {πt (i, τ ), xt (i, τ )}∞t=0
is equilibrium dynamics of the model when the degree of accountability for the inflation
target is τ and the central bank chooses regime i. Because the central bank chooses eithertransparent regime or opaque regime, the choice can be represented by a function
C : (γ̃uf , γ̃vf , γ̃wf , τ ) 7→ {0, 1},
Once the central bank makes a transparency-opaqueness choice, the monetary policy
regime is determined and optimal monetary policy is conducted under the regime. Eventually, given the actual firms’ infomational quality, the social loss L depends on the resultof the transparency-opaqueness choice, which is given by a function
L( · |γuf , γvf , γwf ) : {0, 1} → R.
Thus, the optimal degree τ ∗∗ of accountability for inflation target is written by
¯
´i
h ³
¯
τ ∗∗ (γuf , γvf , γwf ) ∈ argmin E L C(γ̃uf , γ̃vf , γ̃wf , τ )¯γuf , γvf , γwf ,τ ≥0where γ̃sf ∼ U ([γsf − as , γsf + as ]), s = u, v, w.
For simplicity, I consider the case where γuf = γvf = γwf (= γ f ) and au = av = aw (= a).
Hence, the expectations will be taken with repect to γ̃ f ∼ U ([γ f − a, γ f + a]). For
numerical calculation, I set the baseline values such that a = 0.2, γucb = γvcb = γwcb = 0.8.
10Figure 2 shows the simulation result. It is intuitively plausible. When the firms’
informational noise is strong (γ f ≤ γ0 ), τ ∗∗ is identical to τ ∗ , the optimal degree ofaccountability without parameter uncertainty for the central bank. In this case, τ ∗ islarge and so the central bank will definitely choose the opaque regime if the optimal
accountability τ ∗ is assigned since monetary policy under transparent regime is intensely
distorted by strong accountability τ ∗ . 7
When γ0 < γ f < γ1 , τ ∗∗ > τ ∗ . Since τ ∗ is somewhat small, under τ ∗ , there ispossibility that the central bank chooses the transparent regime. The quality of theprivate sector’s information is not high, so that the private sector’s response to noiseof the central bank information is sensitive. Accountability for inflation target helps tomake the cetnral bank choose the transparent regime. Intuitively, it is optimal to escapeloss of inflation volatility under the transparent regime stochastically by imposing strong
accountability for inflation target on the central bank when it might fail in transparencyopaqueness choices since announcing inaccurate information generates crucial social loss.
When γ f > γ1 , τ ∗∗ = τ ∗ again. Since τ = 0 brings large opacity bias under opaqueregime, assigning it makes the central bank choose the transparent regime definitely.
To summerize, the policy implication of the analysis above is:Result 1
Assume that welfare gap shocks are very small (i.e. σw ≈ 0). If the central bank makes
transparency-opaqueness choices and there is uncertfuture economic developments, thenit is optimal to impose higher (or equal) degaincy about the central bank’s informationon the quality of firms’ outlook for ree of accountability for inflation target on the central
banker than in the case of certainty.
By Figure 1, the optimal degree of accountability for inflation target jumps at γ1 ,which is the threshold of welfare comparison between transparency and opaqueness under certainty about the firms’ informational quality. This is a difficulty of the suboptimal
implementation of transparency-opaqueness choices. Discreteness of announcement policy regimes generate the problem.
7

Note that the optimal degree of accountability under transparent regime is 0 independent of noise
ratios γ.

115Conclusion

Transparency does not necessarily improve social welfare. This fact plays a significant
role in the design of an optimal monetary policy regime. In this paper, I show that
accountability for the inflation target can exclude harmful central bank transparency
which confuses the private sector.
There are two remaining problems. First, another process of the central bank’stransparency-opaqueness choices should be considered. In the model, the central bank isassumed to make transparency-opaqueness choices according only to its anticipation of
the private sector’s response. Second, the central bank makes transparency-opaquenesschoices when it conducts commitment policy. Under commitment, the opacity bias will
disappear but the loss generated from noisy central bank’s informaiton will not and so it
is meaningful to investigate how to implement the suboptimal transparency-opaquenesschoices.

12

References
Clarida, R., Galı́, J. and M. Gertler (1999), ”The Science of Monetary Policy: A New
Keynesian Perspective”, Journal of Economic Literature, 37, 1661-1707.
Faust, J. and L. Svensson (2002), ”The Equilibrium Degree of Transparency and Control
in Monetary Policy”, Journal of Money, Credit and Banking, 34, 520-539.
Geraats, P. (2002), ”Central Bank Transparency”, Economic Journal, 112, 532-565.
King, M. (2004), ”The Institutions of Monetary Policy”, American Economic Review,
94, 1-13.
Morris, S. and H. Shin (2002), ”Social Value of Public Information”, American Economic Review, 92, 1521-1534.
Rogoff, K. (1985), ”The Optimal Degree of Commitment to an Intermediate Monetary
Target”, Quarterly Journal of Economics, 100, 1169-1189.
Walsh, C. (2003), ”Accountability, Transparency, and Inflation Targeting”, Journal of
Money, Credit, and Banking, 35, 829-849.
Walsh, C. (2007a), ”Optimal Economic Transparency”, International Journal of Central
Banking, 3, 5-36.
Walsh, C. (2007b), ”Announcement and the Role of Policy Guidance”, Unpublished
Manuscript.
Walsh, C. (2008), ”Transparency, the Opacity Bias and Optimal Flexible Inflation Targeting”, Unpublished Manuscript.
Woodford, M. (1999), ”Optimal Monetary Policy Inertia”, NBER Working Paper No.
7261.
Woodford, M. (2003), ”Interest and Prices”, Princeton University Press.

13Appendix
Derivation of the New Keynesian Phillips curve
In the standard assumption of the Calvo-pricing, firm j’s price adjustment strategy is
∞
³
´
X
j
j
j
j
s
(βω) Et−1 M Ct+s + Et−1 pt+s + Et−1 ut+s ,p∗j,t = (1 − βω)

s=0where M Ct+s denotes nominal marginal cost in period t + s. By this equation, we obtain³

p∗j,t = (1 − βω)

j
j
j
Et−1
pt + Et−1
M Ct + Et−1
ut´j+ βωEt−1p∗j,t+1 .

(10)Aggregate price level in period t is given by
pt = (1 − ω)p∗t + ωpt−1 ,which implies
πt = pt − pt−1 =1−ω ∗(pt − pt ),ω(11)where p∗t is the average of p∗j,t over price-adjusting firm j. Since all firms are symmetricin this model, p∗j,t = p∗t . Assuming M Ct = κxt , from (17) and (18),πt∗ =1 − βω fβ
1 − βω f
κEt−1 xt +Et−1 ut +E f πt+1 .
ωω
1 − ω t−1

(12)Hence, from (17) and (19), I obtain the New Keynesian Phillips curve.

Solving the Model under Opaque Regime
Assume that the private sector’s belief about monetary policy isθt−1 = Θo Γcb Ωcbt ,where Θ is 1 × 3 undetermined coefficient and

 cb
0
γu 0
Γcb =  0 γvcb 0  .
00 γwcb14(13)

The private sector’s expectation of the aggregate shock vector St = (ut , vt , wt ) and thefirms price-adjustment strategy are of the forms such asf
Et−1
St = Ψ01 Ωft + Ψo2 θt−1 ,(14)πt∗ = Ao Ωft + B o θt−1 .

(15)

fSince Et−1
πt+1 = 0 by πt = (1 − ω)πt∗ , (20) and (22), (19) is

1 − βω
1 − βω 1κθt−1 +
(e + κe2 )(Ψo1 Ωft + Ψo2 θt−1 )
ω
ω
1
−
βω
1 − βω
f=⇒ πt∗ =(e1 + κe2 )Ψo1 Ωt +(κ + (e1 + κe2 )Ψo2 )θt−1 .
ω
ω
πt∗ =

(16)

Comparing the coefficients of (22) and (23), I obtain
1 − βω 1(e + κe2 )Ψo1 ,ω
1 − βω
=(κ + (e1 + κe2 )Ψo2 ),
ω

Ao =
Bo

where ei is normal unit vector with i-th element 1. By (22), equilibrium inflation rate is
πt+1 = (1 − ω)(Ao Ωft + B o θt−1 ). Thusπθ = (1 − ω)B o .
Put C o = κ−1 (e1 κ−1 + e2 ) and E f Sθ = Ψo2 .
By (7) and (11), in equilibrium, optimal monetary policy rule under discretion iscbcbcb(1 + τ )(1 − ω)B o Et−1
πt + λ(θt−1 + Et−1
vt − Et−1
wt ) = 0
h
i
o
cb
cb
=⇒ (1 + τ )(1 − ω)B o (1 − ω)Ao Γcb Ωcb
+
(1
−
ω)B
θ
t−1 + λ(θt−1 + Et−1 vt − Et wt ) = 0
t
³
´
1
3
2
2 o o
λe
−
λe
−
(1
+
τ
)(1
−
ω)
B
A
Γcb Ωcb=⇒ θt−1 =t .
λ + (1 − ω)(1 + τ )(B o )2Comparing the coefficients of (20) and (24), I can calculate the undetermined coefficients.
8

8

In precise, I first guess the value of Ψ, calculate Ao , B o and find new value of Ψ. Iterating untilconvergence, I obtain the true value of the coefficients.

15

Solving the Model under Transparent Regime
The solution method is analogous to that of the opaque regime. Assume that the firms’
belief about monetary policy isθt−1 = Θt Γcb Ωcbt .
In this regime, firms receive the central bank’s information Ωcb
t . Thus, the private sector’s
expectation of the aggregate shock can be written by
µ f ¶
Ω
f
t
E St = Ψ.
ΩcbFirms’ pricing strategy is of the form such astπt∗ = At Ωft + Dt Ωcb
t + B θt−1 .

Using these equations, by the same way in the opaque regime, I obtain the following
relation:
At = [(1 − βω)(e1 + κe2 )]Ψt1 , B t =Kt =1 − βω 1(e + κe2 Ψt2 + βAt Ψt2 ).
ω(1 − βω),ωIn equilibrium, inflation rate ist
πt+1 = (1 − ω)(At Ωft + Dt Ωcb
t + B θt−1 ).

The first order condition of the discretionary monetary policy has the same form as
before. Hence, eventually, I obtainθt−1 =

h
i
1
3
2
t 4
t
t
t
cb −1
(1
+
τ
)λ(e
−
e
)
+
(1
−
ω)(B
e
−
(1
−
ω)B
(A
+
K
(Γ
)
)
Γcb Ωcbt .
λ + (1 − ω)(1 + τ )(B t )216

1transparent regime

0.9

0.8

0.7

γ cv b0.6

0.5

opaque regime

0.4

0.3

0.2

0.1

0

0

0.1

0.2

0.3

0.4

0.5

γ

0.6

0.7

0.8

0.9

1

f

Figure 1: One of the key elements for welfare comparison is the firms’ informational
quality.

17

7

∗

τ , τ∗∗

τ∗

τ∗∗

6

5

4

3

Opaque Regime

Transparent Regime

2

γ0

1

γ1

0

0.2

0.3

0.4

γf

0.5

0.6

0.7

0.8

Figure 2: τ ∗∗ = τ ∗ if γ f ≤ γ0 and γ f > γ1 . τ ∗∗ > τ ∗ if γ0 < γ f < γ1 .

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