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Monetary and fiscal policy interactions with central bank

transparency and public investment

Meixing Daia and Moïse Sidiropoulosb

Abstract: In this paper, we study how the interactions between central bank transparency and

fiscal policy affect macroeconomic performance and volatility, in a framework where

productivity-enhancing public investment could improve future growth potential. We analyze the

effects of central bank’s opacity (lack of transparency) according to the marginal effect of public

investment by considering the Stackelberg equilibrium where the government is the first mover

and the central bank the follower. We show that the optimal choice of tax rate and public

investment, when the public investment is highly productivity-enhancing, eliminates the effects

of distortionary taxation and fully counterbalance both the direct and the fiscal-disciplining

effects of opacity, on the level and variability of inflation and output gap. In the case where the

public investment is not sufficiently productivity-enhancing, opacity could still have some

disciplining effects as in the benchmark model, which ignores the effects of public investment.

Keywords: Distortionary taxes, output distortions, productivity-enhancing public investment,

central bank transparency (opacity), fiscal disciplining effect.

JEL classification numbers: E52, E58, E62, E63, H21, H30.

________________________________________

aBETA, University of Strasbourg, 61, avenue de la Forêt Noire – 67085 Strasbourg Cedex – France; Tel (33) 03 68

85 21 31; Fax (33) 03 68 85 20 71; e-mail : dai@unistra.fr.

bLEAP, Department of Economics, Aristotle University of Thessaloniki, Thessaloniki, Greece 54124, E-mail:

msidiro@econ.auth.gr, Phone: (30) 23 10 99 87 10; and BETA, University of Strasbourg, 61, avenue de la Forêt

Noire – 67085 Strasbourg Cedex – France; Tel (33) 03 68 85 20 85 ; Fax (33) 03 68 85 20 71; e-mail:

sidiro@cournot.u-strasbg.fr.

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1. Introduction

Over the past two decades, an increasing number of central banks have become more transparent

about their objectives, procedures, rationales, models and data. This has stimulated an intensive

ongoing research about the effects of central bank transparency.1 Most economists agree that

openness and communication with the public are crucial for the effectiveness of monetary policy,

because they allow the private sector to improve expectations and hence to make better-informed

decisions (Blinder, 1998). Counterexamples have been provided, with addition of distortions,

where information disclosure reduces the ability of central banks to strategically use their private

information, and therefore, greater transparency may not lead to welfare improvement (e.g.,

Sorensen (1991), Faust and Svensson (2001), Jensen (2002), Grüner (2002), Morris and Shin

(2002)).2 In effect, according to the second best theory, the removal of one distortion may not

always lead to a more efficient allocation when other distortions are present.

Typical models on monetary policy transparency usually consider two players, the monetary

authority and the private sector. Departing from this approach, several authors introduce

monetary and fiscal policy interactions.3 In a framework where the government sets a

distortionary tax rate, it was shown that uncertainty (or opacity) about the “political” preference

parameter of the central bank, i.e. the relative weight assigned to inflation and output gap targets,

could reduce average inflation as well as inflation and output variability (Hughes Hallett and

Viegi (2003), Ciccarone et al. (2007), Hefeker and Zimmer (2010)). Higher distortionary taxes

1 Pioneered by Cukierman and Metzler (1986), transparency issue has been examined both theoretically and

empirically by Nolan and Schaling (1998), Faust and Svensson (2001), Chortareas et al. (2002), Eijffinger and

Geraats (2006), Demertzis and Hughes Hallet (2007), among others. See Geraats (2002) and Eijffinger and van der

Cruijsen (2010) for a survey of the literature.

2 See Dincer and Eichengreen (2007) for a short survey about these models including distortions.

3 Some researchers study the relationship between central bank transparency and the institutional design (Walsh,

2003; Hughes Hallett and Weymark, 2005; Hughes Hallett and Libich, 2006, 2009; Geraats, 2007).

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necessary for financing higher public expenditures will induce lower output gap and higher

unemployment. Thus, central bank increases the inflation rate and workers claim higher nominal

wages. In terms of macroeconomic volatility, less central bank political transparency has a

disciplining effect on the fiscal authority, which could dominate the direct effect of opacity when

the government cares less about the public expenditures, and the central bank is quite populist

whilst the initial degree of central bank opacity is sufficiently high.4

However, the aforementioned studies do not distinguish the different components of public

expenditures by separating public consumption (e.g. public sector wages and current public

spending on goods) from public investment (e.g., infrastructure, health and education). A

substantial theoretical and empirical research has been directed towards identifying the

components of public expenditure that have significant effects on economic growth (Barro

(1990)). The introduction of both public capital (infrastructures) and public services (education)

as inputs in the production of final goods, theoretical models suggested that public investment

generates higher growth in the long run through raising private sector productivity (e.g. Futagami

et al. (1993), Cashin (1995), Glomm and Ravikumar (1997), Ghosh and Roy (2004), Hassler et

al. (2007), Klein et al. (2008), Azzimonti et al. (2009)). In addition, empirical studies confirm the

positive impact of public investment on productivity and output (e.g. Aschauer (1989), Morrison

and Schwartz (1996), Pereira (2000), and Mittnik and Neuman (2001)).

Usually, the frameworks used in theoretical studies on public investment ignore the effects

due to monetary and fiscal interactions. Cavalcanti Ferreira (1999) examines the interaction

between public investment and inflation tax and has found that the distortionary effect of

4 The term “political transparency” used here corresponds to the information disclosure about the weights assigned

by the central bank to the output gap and inflation stabilisation. Five motives for central bank transparency (i.e.

political transparency, economic transparency, procedural transparency, policy transparency and operational

transparency) are defined in Geraats (2002).

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inflation tax is compensated by the productive effect of public expenditures. Ismihan and Ozkan

(2004) consider the relationship between central bank independence and productivity-enhancing

public investment, and argue that although central bank independence delivers lower inflation in

the short term, it may reduce the scope for productivity-enhancing public investment and so harm

future growth potential. Ismihan and Ozkan (2007) extend the previous model by taking into

account the issues of public debt, and have found that, under alternative fiscal rules (balanced-

budget rule, capital borrowing rule), the contribution of public investment to future output plays a

key role in determining its effects on macroeconomic performance.

The distinction between public consumption and public investment could allow us to

introduce in the literature of central bank transparency the effects of public investment on the

aggregate supply. These effects could correct the distortionary effects of taxation and therefore

interact with central bank transparency. For this purpose, we re-examine in this paper the

interaction between central bank political transparency and fiscal policies in a two-period model,

similar to Ismihan and Ozkan (2004), where the public investment is productivity-enhancing and

could compensate, partially or totally, the distortions generated by the taxes on revenue. The aim

of the paper is to investigate to what extent the disciplining effect of opacity could be generalized

to a framework where the government has more than one policy instrument.

The paper is organized as follows. The next section presents the model. Section 3 presents the

benchmark equilibrium where there is no productivity-enhancing public investment. Section 4

examines how the inclusion of public investment affects the effects of opacity according to the

marginal effect of public investment on the aggregate supply. The last section summarizes our

findings.

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2. The model

The two-period model of discretionary policy making is similar to the one presented by Ismihan

and Ozkan (2004). To model the effects of distortionary taxes and public investment on the

supply, we consider a representative competitive firm, which chooses labor to maximize profits

by taking price (or inflation rate

t π ), wages (hence expected inflation

e

t π ), and tax rate (

tτ ) on

the total revenue of the firm in period t as given, subject to a production technology with

productivity enhanced by public investment in the previous period (

i

tg

1

−). The normalized

output-supply function is:

i

tt

e

ttt

gx

1

−

+−−=ψτππ

,

2 , 1

=

t

; (1)

where

tx (in log terms) represents the normalized output (or output gap). Equation (1) captures

the effects of supply-side fiscal policies on the aggregate supply of output, with the effect of

distortionary taxes being clearly distinguished from that of public investment.5

The public expenditures are composed by public sector consumption (

0

>

c

tg

) and investment

(

0

≥

i

tg

), both expressed as percentages of the output. The public investment consists of

productivity-enhancing expenditures on infrastructure, health, education etc. However, as its

favorable consequences indirectly affect the consumers’ utility, this type of expenditure is not

taken into account in the policy maker’s utility function. On the contrary, public consumption

made up of public sector wages, current public spending on goods and other government

spending is assumed to yield immediate utility to the government. The fiscal authority’s loss

function is

5 The variable τ allows covering a whole range of structural reforms. In effect, τ could also represent non-wage costs

associated with social security (or job protection legislation), the pressures caused by tax or wage competition on a

regional basis or the more general effects of supply-side deregulation (Demertzis et al., 2004).

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∑

=

t

−

−++=

2

1

2

2

2

t

2

t

1

1

0

2

1

0

])([E

c

t

c

t

t

G

G

ggxL

δπδβ

, (2)

where

0

E is an operator of mathematical expectations,

G

β the government’s discount factor,

1 δ

and

2

δ the weights assigned to the stabilization of inflation and public consumption respectively,

while the output-gap stabilization is assigned a weight equal to unity.

The government’s objectives are the stabilization of the inflation rate and the output gap

around zero, and of the public consumption around its target

c

tg . The government minimizes the

above two-period loss function subject to the following budget constraint:

t

c

t

i

t

gg

τ

=+

, with

2 , 1

=

t

. (3)

Equation (3) is a simple form of the budget constraint since public debt and seigniorage revenue

are not taken into account. Even though

i

tg enhances the productivity in the future, it is

implemented and financed in the current period.

The government delegates the conduct of the monetary policy to the central bank while it

retains control of its fiscal instruments. The central bank sets its policy in order to minimize the

loss function

∑

=

t

−

++−=

2

1

2

t

2

t

1

0

2

1

0

]) 1 ()[(E

t

CB

CB

xL

επεμβ

,

0

>μ

, (4)

where

CB

β

is the central bank’s discount factor. The parameter μ is the expected relative weight

that the central bank assigns to the inflation target and it could be equal or different from

1 δ . It is

therefore an indicator of central bank conservatism (larger μ values) versus liberalism or

populism. According to the literature, we assume that the central bank can fully neutralize the

effects of policy shocks (including public spending) or exogenous demand shocks affecting the

goods market through appropriate setting of its policy instrument π .

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The weights assigned by the central bank to the inflation and output-gap targets are more or

less predictable by the government and private sector, meaning that ε is a stochastic variable.

The fact that ε is associated to both inflation and output objectives is adopted for avoiding the

arbitrary effects of central bank preference uncertainty on average monetary policy (Beetsma and

Jensen, 2003). The distribution of ε is characterized by 0)(

=

ε

E

,

2

ε

2)() var(

σεε== E

and

] , 1

−

[

με∈

. Variance

2

ε

σ represents the degree of opacity about central bank preferences. When

0

2=

ε

σ

, the central bank is completely predictable and hence, completely transparent. As the

random variable ε is taking values in a compact set and has an expectation equal to zero,

Ciccarone et al., (2007) have proved that

2

ε

σ has an upper bound so that

], 0 [

2

μσε∈

.

The timing of the game is the following. First, the private sector forms inflation expectations,

then, the government sets the tax rate and public investment, and finally the central bank chooses

the inflation rate. The private sector composed of atomistic agents plays a Nash game against the

central bank. The government, as Stackelberg leader, plays a Stackelberg game against the

central bank. The game is solved by backward induction.

3. The benchmark equilibrium without public investment

First, we consider a benchmark case where the public investment has no supply-side effect.

Therefore, it is optimal for the government to set its level at zero. This benchmark case is drawn

directly from Hefeker and Zimmer (2010). It is different from Ciccarone et al. (2007) who also

introduce distortions in the labor market through the wage determination by an all-encompassing

monopoly union, as well as from Hughes Hallett and Viegi (2003) who consider a Nash game

between the fiscal and monetary authorities, both concerned by distortionary taxes.

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Equations (1) and (3) are rewritten as:

t

e

tttx

τππ−−=

, (5)

t

c

tg

τ=

. (6)

The central bank minimizes the loss function (4) subject to (5). Its reaction function is:

μ

τπ

+

ε

π

++

=

1

) )( 1 (

t

e

t

t

. (7)

Equations (5)-(7) allow us to express the output gap as:

μ

τπε

1

μ

(

+

+−−

=

) )(

t

e

t

tx

. (8)

The government has only one instrument to choose between the tax rate and public

consumption due to the budget constraint (6). Setting its fiscal policy, the government cannot

predict (7)-(8) with precision due to imperfect disclosure of information about the central bank

preferences. Substituting

c

tg ,

t π and

tx given by (6)-(8), the government’s constrained

minimization problem is rewritten, after rearranging the terms, as an unconstrained minimization

problem:

∑

=

t

+

++−

−

⎭⎬⎫

⎩⎨⎧

−++=

2

1

2

2

2

)1 (

)1 (

2

)(

1

0

2

1

0

)()(E min

τ

2

1

2

c

ttt

e

t

t

G

G

gL

t

τδτπβ

μ

εδμε

. (9)

Using the second-order Taylor approximation to obtain

][E

2

2

1

)

2

1 (

)1 ()(

μ

εδμε

+

++−

=Θ

2

ε

)1 (

)

2

1 (

)1 (

1

2

1

2

μ

δ

μ

δμ

σ

+

+

+

+

+≈

,

the government’s loss function is rewritten as

∑

=

t

−

−++Θ≅

2

1

2

2

21

2

1

0

])()([

c

ttt

e

t

t

G

G

gL

τδτπβ

. (10)

Proposition 1. For given expected inflation and tax rate, an increase in central bank’s opacity

generally induces higher social welfare loss.

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9

Proof. Deriving (10) with respect to

2

ε

σ yields 0])([

2

1

2

) 1 (

1

1

2

1

2

1

2

0

>+≅ ∑

=

+

+

−

∂

∂

t

t

e

t

t

G

LG

τπβ

μ

δ

σε

if

0

≠+

t

e

t

τπ

. ■

As the government has an objective of public consumption,

tτ cannot be fixed in a way to

completely neutralize the effects of central bank’s opacity in the social loss function. If the

government sets

e

tt

π

−

τ

=

to neutralize the effects of opacity on the social loss function, it will

suffer from high marginal cost due to insufficient public consumption. Hence, the optimal level

of the tax rate depends on the degree of opacity. From the first-order condition of the

government’s minimization problem we obtain:

2

2

2

ε

11

2

2

ε

1

μ

1

22

2

2

2

) 1 () 1 (

]) 1 (

δ

)

+

[( ) 1

+

(

σδδμ

πσδ

+

δμ

+

μδ

δ

πδ

τ

+

+++−+

=

+Θ

Θ−

=

e

t

c

t

e

t

c

t

t

gg

. (11)

Substituting

tτ given by (11) into (7) and imposing rational expectations yields:

2

ε

11

2

2

2

2

2

Θ

)1 ()1 (

)1 (

μ+

)1 (

σδδμμδ

μ

+

δ

μμδ

δ

+

π

+++

+

=

+

=

c

t

c

t

e

t

gg

. (12)

Substituting

e

t π given by (12) into (11) and taking account of (6) lead to:

2

ε

11

2

2

2

+

2

2

) 1 ()1 (

)1 (

μ

)1 (

σδδμμδ

μ

+

μδ

μμδ

μ

Θ

δ

+

τ

+++

+

=

+

==

c

t

c

t

c

tt

gg

g

. (13)

Using (12)-(13) into (7)-(8) and the budget constraint (6) yields:

2

ε

11

2

2

2

2

2

)1 ()1 (

)1 (

+

)

μ

1 (

μ

+

)1 (

) 1 (

μδ

σδδμδ

μ

+

δε

+

μ

δε

Θ+

π

+

++

=

+

+

=

c

t

c

t

t

gg

, (14)

2

ε

11

2

2

2

1 (

+

2

2

)) 1 (

)1)(

μ

(

) 1 (

)(

σδδμμδ

δμμ

+

ε

μμδ

δμ

Θ+

ε

+++

+−

=

+

−

=

c

t

c

t

t

gg

x

, (15)

2

ε

11

2

2

2

ε

+

1

+

1

2

2

) 1 () 1 (

]) 1 (

+

[

) 1 (

)

+

1 (

+

σδδμμμδ

σδδ

+

μ

+

μμδ

μ

+++−

=

Θ

+Θ−

=−

c

t

c

t

c

t

c

t

gg

gg

. (16)

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10

Calculating the variance of

t π and

tx results to:

22

ε

11

2

2

2

ε

+

2

2

2

2

2

ε

μ

2

2

+

]) 1 ()1 ([

]

+

) 1 (

+

[

μ

)]1 ([

)(

μ

)var()var(

σδδμμδ

σμ

+

δ

δ

σ

+

δ

π

+

+

=

Θ

==

c

t

c

t

tt

gg

x

. (17)

From (13)-(17), we observe that the denominator increases as the degree of opacity

2

ε

σ , while

the numerator of (16) decreases as

2

ε

σ and the numerator of (17) is increases as

2

ε

σ . It follows

that

tτ ,

c

tg ,

t π and

tx are all decreasing in

2

ε

σ . On the other hand, ) var(

t π and )var(tx could be

both increasing or decreasing in

2

ε

σ , as shown by the results of Hefeker and Zimmer (2010) that

we reformulate in the following proposition.

Proposition 2. An increase in central bank’s opacity reduces the tax rate, inflation and output

distortions but increases deviations of public consumption from its target level. It reduces the

variability of inflation and output gap if the initial degree of opacity is sufficiently high and vice

versa.

Proof. Deriving

tτ ,

t π ,

tx and

c

t

c

t

gg −

given by (13)-(16) with respect to

2

ε

σ , leads to the first

part of Proposition 2. Deriving )var(

t π and )var(tx given by (17) with respect to

2

ε

σ , yields:

32

ε

11

2

2

2

2

)

2

ε

+

1

+

1

μ

2

2

2

ε

2

ε

]1 () 1 ([

])1 (

σ

][

δ

)1 (

+

)1 ([)var(

σ∂

)var(

σ∂δμμδ

μδσδδ

+

μ

+

μμδπ++−+++

=

∂

=

∂

c

ttt

gx

.

It follows that

0

)var(

∂

σ

)var(

∂

σ

2

ε

2

ε

>

∂

=

∂

π

tt

x

if

1

1

2

2

2

1

)1 (

δ

δμμ

+

μδ

σε

+++

<

and vice versa. ■

Distortions introduced by taxes used to finance public expenditures imply higher current and

expected inflation rates. Brainard’s (1967) conservatism principle implies that the government is

incited to adopt a less aggressive fiscal policy (“disciplining effect”) because the perceived

marginal costs associated with higher taxes are higher under central bank opacity. This stance of

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fiscal policy leads to lower output gap and inflation rate at the cost of larger deviation of public

consumption from its target level. In terms of macroeconomic volatility, opacity triggers two

opposing effects. The first corresponds to the direct effect of opacity on the variability of

inflation and output gap for a given tax rate (or given level of distortions). The second refers to

the disciplining effect, since uncertainty about the central bank preference leads to greater fiscal

discipline, contributing to the reduction of inflation and output volatility. The disciplining effect

is more likely to dominate the direct effect of opacity if the central bank is less averse to inflation

(smaller μ ) and the government is less concerned with the public consumption deviations

(smaller

2

δ ).

Using the property

] , 0 [

2

μσε∈

, shown by Ciccarone et al. (2007), we extend the previous

results in the following proposition.

Proposition 3. If the government assign a sufficiently high weight to the public consumption, i.e.

) 1 (

)()

μ

1 (

2

1

2

1

μ

δμμδ

δ

+

+−+

>

, the disciplining effect of central bank’s opacity will always be dominated by

the direct effect of opacity on the variability of inflation and output gap and vice versa.

Proof. We obtain 0

2

ε

2

ε

) var(

∂

σ

) var(

∂

σ

<=

∂∂

π

tt

x

,

)

1

1 (

) 1 (

2

)

1

2

(

2

ε

δ

μμδδμ

σ

+

+++

>∀

. According to Ciccarone et al.

(2007), there exists an upper bound on

2

ε

σ so that

] , 0 [

2

μσε∈

. Thus, the previous lower bound on

2

ε

σ is valid only when

μ

δ

μμ

)

δδμ

<

+

+++

1

1 (

)1 (

2

)

1

2

(

. This leads to

) 1 (

)()

μ

1 (

2

1

2

1

μ

δμμδ

δ

+

+−+

<

. If

) 1 (

)()

μ

1 (

2

1

2

1

μ

δμμδ

δ

+

+−+

>

, the only possible case is that we have always

)

1

1 (

)1 (

2

)

1

2

(

2

ε

δ

μμδδμ

σ

+

+++

<

. In this

case, the direct effect of opacity will always dominate the disciplining effect. ■

In the following, we examine the validity of the previous results in the case where the public

investment is productivity-enhancing.

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4. Effects of productivity-enhancing public investment

Consider that the public investment is productivity-enhancing. However, according to the

marginal effect of such investment, the government might be incited to implement positive, zero

or even negative public investment in period 1 or/and 2. Even though negative public

investments, such as privatization of infrastructure and education institutions, are possible in

practice, they cannot be captured in the present model. That is because such disinvestments are

considered to generate a negative effect on the productivity while the privatization suggests a

transfer of property but not an inversion of effects of such investments on the productivity. Thus,

we assume that negative public investments are not allowed. This implies that we must introduce

two supplementary constraints for the government, i.e.

0

1≥

ig

and 0

2≥

ig

.

Minimizing the central bank’s loss function (4) subject to the economic constraint (1) yields

the central bank’s reaction function:

μ

ψ−τπε

π

+

++

=

−

1

) )(1 (

1

i

tt

e

t

t

g

, with 2 , 1

=

t

. (18)

Using (1)-(3) and (18), we rewrite the government’s loss function as:

} ])()([)()({

2

2222

2

122

2

1112

2

011

2

1

0

ciie

G

ciieG

ggggggL

−−+−+Θ+−−+−+Θ=τδψτπβτδψτπ

. (19)

Proposition 4. For given

tτ ,

c

tg and

i

tg , if

0

1≠

−

−+

i

tt

e

t

g

ψτπ

, an increase in central bank’s

opacity induces a higher social welfare loss.

Proof. Deriving the loss function given in (19) with respect to

2

ε

σ and using the definition of Θ ,

we obtain:

0])()( [

2

122

2

011

) 1 ( 2

)1 (

2

1

2

0

>−++−+=

+

+

∂

∂

ie

G

ie

L

gg

G

ψτπβψτπ

μ

δ

σε

if

0

1≠

−

−+

i

tt

e

t

g

ψτπ

. ■

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Opacity has negative effects on the social welfare. In the absence of productivity-enhancing

public investment, the government has incentive to reduce the tax rate but at the risk of increasing

the deviation of public consumption from its target level. In the case of productivity-enhancing

public investment, when positive interior solutions exist for public investment in two periods, the

effects of past public investment allow a complete compensation of the distortions introduced by

the taxes. Thus, the government is enabled to set a tax rate to ensure that the objective of public

consumption is realized. Since the distortions disappear, the central bank has no incentive to set

an inflation rate higher than zero. In contrast, the distortions will only be partially compensated

when such interior solutions do not exist. In the following we consider the case where positive

interior solutions exist for public investment and two cases of corner solutions.

4.1. The case where positive interior solutions exist for public investment

This is the case where the public investment is sufficiently productivity-enhancing, such that

public investments are set optimally by the government at a strictly positive level in two periods.

The first-order conditions of the minimization problem (19) are:

0)()(

1112011

1

=−−+−+Θ=

∂

∂

ciie

G

t

ggg

L

τ

τδψτπ

, (20)

0)()(

1221112

1

=−+Θ−−−−=

∂

∂

ie

G

ci

i

G

t

ggg

g

L

ψτπψβτδ

, (21)

0)()(

2222122

2

=−−+−+Θ=

∂

∂

ci

G

ie

G

G

t

ggg

L

τ

τδβψτπβ

, (22)

0)(

2222

2

=−−−=

∂

∂

ci

G

i

G

t

gg

g

L

τδβ

. (23)

Solving (20)-(23) gives the government’s reaction functions:

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14

ie

1

g01

ψ+π−τ=

, (24)

i

0

e

1

c

1

i

ggg

1

ψ π +−−=

, (25)

e

1

e

2

ci

0

gg

1

2

2

ψπ−πψ−ψ=τ−

,

(26)

e

1

e

2

c

2

c

1

i

0

i

2

gggg

2

ψπ−πψ−ψ−−=

. (27)

To determine the expected inflation rates, we substitute

1τ ,

ig1 and

2 τ respectively, given by

(24)-(26) into (18). Imposing rational expectations yields:

0

21

==

ee

ππ

. (28)

Using the results given by (28) into (24)-(27) leads to the equilibrium solutions

ig01

ψτ =

, (29)

c

1

i

0

i

ggg

1

−=ψ

, (30)

c

1

i

0

gg

2

2

ψ

−

ψτ

=

, (31)

c

2

c

1

i

0

i

2

gggg

2

−−=

ψψ

. (32)

From (30) and (32), we deduce the minimal value of ψ for ensuring that the optimal public

investment is strictly positive in two periods, as follows:

i

0

c

2

i

0

c

1

2

c

1

g

gggg

2

4

+±

>

ψ

.

Under this condition, we have simultaneously 0

1>

ig

and 0

2>

ig

.

Using (29)-(32) into (3), we get the public consumptions:

c

t

c

t

gg =

, with 2 , 1

=

t

. (33)

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15

Compared to the benchmark solution (13), the solutions of tax rate and public consumption given

by (29), (31) and (33), are extremely simple. They depend only on the initial public investment,

the marginal effect of public investment and the targets of public consumption.

Proposition 5. If the public investment is sufficiently productivity-enhancing, i.e.

i

0

c

2

i

0

c

1

2

c

1

g

gggg

2

4

+±

>ψ

, the government will optimally set the tax rate and public investment such as

to neutralize the effects of central bank preferences and hence the effects of opacity on its

decisions.

Proof. It follows straightforward from (29)-(33). ■

We remark that the government’s decisions given by (29)-(33) are not dependent on central

bank preferences. The central bank’s “type” (more or less conservative) has neither effect on the

tax rate and public investment nor on their variability. Thus, the degree of transparency has no

impact on these decisions. The introduction of sufficiently productivity-enhancing public

investment incites the government to increase the tax rate to finance higher investment in period

1, but not necessarily in period 2. In effect, the government can collect more taxes, given the

higher productivity in period 2. But, as the benefits of public investment in period 2 will be

attributed to the next government, the government has no incentive to increase public investment

in this period. However, the government is not urged to set the public investment in period 2 at

zero, since the tax rate which neutralizes the distortions could generate more tax revenue than

what is optimal to spend on the public consumption. The current government is elected on a

mandate which implies that it should not set a too high public consumption to avoid the

deterioration of the social welfare.

We notice that the tax rate and public investment in the two periods do not depend on the

preferences of fiscal authorities. In effect, when the government, whatever are the government