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Dimensions of central bank transparency and monetary policy
Helder Ferreira de Mendonça
José Simão Filho
Fluminense Federal University
Department of Economics (Brazil) and
National Council for Scientific and Technological
Development (CNPq)
Postal address: Rua Dr. Sodré, 59 – Vila Suíça
Miguel Pereira – Rio de Janeiro
CEP: 26900-000 – Brazil
Juiz de Fora Federal University
Department of Economics (Brazil)
Postal address: Rua das Orquídeas 55, casa 1Novo Horizonte - Juiz de Fora - MG
CEP: 36038-470 – Brazil
email address: [email protected]
email address: [email protected]
Abstract
The main objective of this paper is to make a theoretical analysis of the impact of the
multidimensionality of the central bank transparency on the effectiveness of monetary
policy. Therefore the effects caused by several types of transparency on macroeconomic
variables are analyzed. The results denote the importance of central bank transparency
in the determination of the main macroeconomic variables and its influence on the
monetary policy effectiveness. Central bank transparency is desirable because it reduces
the asymmetric information between the central bank and the public and it increases the
central bank accountability. A higher degree of central bank transparency implies an
increase in the sensitivity of central bank reputation regarding its actions which in turn
attenuates the inflation bias in the conduction of the monetary policy.
Key words: multidimensionality transparency, monetary policy, inflation rate, interest
rate.
Resumo
O principal objetivo deste artigo é fazer uma análise teórica do impacto da
multidimensionalidade da transparência do banco central sobre a efetividade da política
monetária. Portanto, são analisados os efeitos causados pelos vários tipos de
transparência sobre as variáveis macroeconômicas. Os resultados denotam a
importância da transparência do banco central na determinação das principais variáveis
macroeconômicas e de sua influência sobre a efetividade da política monetária. A
transparência supracitada é importante porque ela reduz a assimetria de informações
entre o banco central e o público e aumenta a responsabilidade do banco sobredito. O
alto grau de transparência do banco central implica um aumento da sensibilidade da
reputação do banco, considerando suas ações que atenuam o viés inflacionário na
condução da política monetária.
Palavras chave: multidimensionalidade da transparência, política monetária, taxa de
inflação, taxa de juros.
JEL N. E52, E43.
1
1. Introduction
In a general way, the transparency can be understood as the existence of
symmetric information between monetary policymakers and other economic agents.
Since the 1990s the growing adoption of inflation targeting by several countries has
contributed to develop the analysis concerning central bank transparency. Transparency
is relevant because it provides the absence of an explicit target and induces the public
expectations to be made based on central bank forecasts. Therefore, transparency
improves the capacity of the economic agents anticipating the actions of the central
bank.
A potential advantage from an increase in transparency in the conduction of the
monetary policy is that it works as a guide for expectations and increases the set of
information related to the duration of the interest rate, and thus improves the efficiency
of the financial market. Furthermore, transparency represents a commitment technology
for the conduction of the monetary policy increasing the accountability of the central
bank in the search for the inflation target, and thus, implies an increase in credibility.
In practice, inflation reports, minutes on meetings of monetary policy
committees, announcements on the target, and publications related to the future inflation
target are the main tools used by central banks for increasing their transparency (Fry et
alii, 2000). Authors such as Bernanke (2004a and 2004b) and Woodford (2005) have
highlighted the importance of the above-mentioned information for the central bank
being able to change the movement in the future interest rates and thus affecting the
decisions of the economic agents.
The literature about transparency is in ebullience and one of the main gaps is the
analysis of the several dimensions of central bank transparency. Geraats (2002)
emphasizes the importance of this study and divides the different dimensions of central
bank transparency: political transparency, economic transparency, procedural
transparency, policy transparency, and operational transparency. Walsh (2001) is
another author who highlights the importance of the different dimensions of
transparency especially economic and political and that dimension related with
decisions of monetary policy.
The main objective of this paper is to make a theoretical analysis of the impact
of the multidimensionality of the central bank transparency on the effectiveness of
monetary policy. Therefore the effects caused by several types of transparency
2
(economic transparency of the central bank, political transparency, transparency of
monetary policy decisions, central bank transparency in relation to financial
innovations, and multidimensionality of central bank transparency) on macroeconomic
variables are analyzed.
2. Economic Transparency1
This section develops a theoretical framework which permits the analysis of the
impact caused by central bank transparency on the effectiveness of the monetary policy.
The focus is on the effect of economic transparency on interest rate taking into
consideration an environment under inflation targeting. Moreover, the consequence of
an increase in transparency on central bank credibility, inflation average, and output gap
is considered.
The private sector is represented by a new Keynesian Phillips curve (which
represents a constraint to the model) where the current inflation (t) depends on the
expected future inflation (Ett+1) due to the presence of two types of firms in the
economy (one with sticky prices and another with flexible prices)2
(1)
 t   xt   Et t 1  et
where,  is the intertemporal utility discount factor; xt is the output gap; >0 is the
sensitiveness of inflation to the output gap; and et is the inflation shock.
It is important to note that the objective functions to the principal (public or
government) and to the agent (central bank) are different. Such as in a delegation model,
the public, through institutional framework, decides the inflation target (T) and the
penalties when the target is not achieved.
The loss function is standard in the literature and considers the relative objective
to the output (>0), an intertemporal discount rate (0<<1), and the number of periods
(n),
(2)
L
1
E
2 t


n 0
n
 xt  n 2   t2 n  .
The central bank loss function (Lcb) takes into consideration the possibility of the
This section is based on de Mendonça and Simão Filho (2007).
Based on Woodford (2003) the justification of the dependence of current inflation on the future inflation
is that the firms cannot readjust their prices during one period. In this sense, the firms take the decision to
anticipate the readjustment of prices.
1
2
3
presence of the inflation bias (ut) in the conduction of the monetary policy. Moreover,
punishment () is assumed for deviations in relation to the inflation target. Therefore,
(3)
Lcb 
n
1 cb 
   x  u  2   2      T 2  .


t n
t n
t n
t n
t n
E


2 t n 0
According to the literature concerning economic transparency there are three
main advantages due to the economic transparency (de Mendonça and Simão Filho,
2007; Walsh, 2003): (i) it increases the speed of market reaction to interest rate
announcements; (ii) the market reaction is decreased in environments that are more
transparent; (iii) it solves the time inconsistency problem creating a high incentive in the
contract between the central bank and the public.
The possibility of a difference between the central bank information and that
observed by the public is assumed. However, a high degree of economic transparency of
the monetary authority allows the public to be more accurate in their perception in
relation to the central bank forecast concerning the inflation shock Etcb  et   e . It is
cb
t
important to note that the political pressures for expanding the output do not influence
the relative weight given to output stabilization versus inflation stabilization (),
therefore these pressures do not change the central bank preferences.
In this analysis economic transparency is defined as the difference between the
observation of the public and of the central bank in relation to supply shocks. As
highlighted by Blinder (2000), de Haan and Eijffinger (2000), some degree of freedom
is necessary for the central bank in the conduction of the monetary policy, which in turn
justifies the partial publication of the central bank forecasts on supply shocks.
Therefore, the supply shock observed by the public (eo) is a result of the sum of the
central bank forecast on supply shocks (ecb) and an error (wt – which represents a
measure of opacity),
(4)
eto  et  wt .
cb
Through equations (3) and (4), a new central bank loss function (5) is obtained.
The main idea is that the central bank minimizes its loss function taking into account
that the public inflation expectation is conditioned by forecasts published by central
bank. In this case, the central bank publishes part of its forecasts on supply shocks and
minimizes the loss function considering that the public forms its inflation expectations
4
conditioned by these forecasts (eo).3 The relative term for the contract of the central
bank with the public reveals that while the deviation of the inflation in relation to the
shock which is observed by the public increases, the loss of reputation of the central
bank also increases. Hence,
(5)
L
n
1 cb 
   x  u  2   2     e o  2 


t n
t n
t n
t n
t n
E


2 t n 0
Minimizing the equation above in relation to the ouput gap, the following
expressions for inflation (πt) and output gap (xt) are achieved: 4

(7)

 cb

2
 2
t 
u  1 
w.
e 
   2 1    t     2 1     t    2 1    t
   1   
   1   
2
etcb 

xt 
2
ut 

(6)
   2 1   
wt ,
The result denotes that an increase in economic transparency (lower wt which
denotes opacity) decreases inflation and output gap.
Due to the fact that one feature of central bank opacity is the persistence over
time an auto-regressive process is assumed, that is,
(8)
wt   wt 1   t ,
where  t is white noise with mean zero and variance equal to 2 ;  is the coefficient
of persistence of the opacity and its values are distributed between zero and one.
With the objective of evaluating the impact of economic transparency on the
interest rate, an intertemporal IS similar to the one obtained by Woodford (2003) which
makes a relation between the interest rate and the inflation expectation is considered.
(9)
1  it 
1
,
 uc  ct 1 , t 1  
 Et 

 uc  ct , t   t 1 
where uc is the marginal utility of consumption; t is the preference shock on
consumption; ct is the consumption in the current period; and it is the nominal interest
rate in the short run.
The combination of equations (7), (8) and (9) allows achieving an equation for
interest rate,
3
It is assumed that the socially optimal inflation target is zero.
4
The derivation of these equations is in de Mendonça and Simão Filho (2007).
5
(10)



 cb

2
 2
it   Et 
u

1

e

 t 1  

 t 1
t 1
2
2
2
   1   
    1   

    1    
 2
w  1.
   2 1    t
Therefore, an increase in the opacity of the central bank ( wt ), in relation to the
publication of it forecasts of supply shocks, increases the nominal interest rate in the
short run.5
As pointed out by Fry et alii (2000) economic transparency is a way to
compensate for the lack of central bank credibility reducing inflation expectation and
social loss. Transparency works as a guide to public expectations. In this sense,
countries where the credibility is being built are more sensitive to the effects caused by
economic transparency (Chortareas, Stasavage and Stern, 2002). Therefore, taking into
account the argument that the quality of information is determinant for the success of
monetary policy, the equations of inflation and output gap are introduced in the social
loss function, and a minimization of it in relation to the punishment for deviations in the
inflation to the target (τ) is made. The result is
         1   

         


2
(11)
2
2
u
2 2
2
w
4
2
ecb
.
2
ecb
The result reveals that an increase in the dispersion of the degree of central bank
opacity (  w2 ) decreases the power of incentive contract (τ) for the accomplishment of
targets. It is important to observe that the opacity reduces the social welfare due to the
increase in inflation and output gap, while  w2 reduces the reputation and increases the
part associated with inflationary bias and thus causes a time inconsistency problem.6 In
addition, it is observed that a lower variance of forecast error implies that the central
bank is more credible, even though it does not publish all information that it has on
supply shocks.
Some authors have criticized the idea that central bank loses flexibility when it
publishes its forecasts. The justification is that the central bank cannot modify its
announced policy in order to face situations that require a change of posture due to a
5
As emphasized by Blinder (2000), the current short-term interest rate affects the future short-term interest
rate, which in turn affects the long-term interest rate.
6
According to Walsh (1995) the time inconsistency problem is due to sub-optimal contracts. Hence,
when
 w2
is minimized, this implies that τ is maximized due to a fall in inflationary bias.
6
loss in credibility. However, equation (11) shows that systematic changes in central
bank strategy (variance in degree of opacity) imply loss of credibility.
With the intention of finding the optimal level of transparency (which minimizes
 w2 and which maximizes the reputation), equation (11) is substituted in the central
bank loss function and the result is minimized in relation to  w2 . Moreover, substituting
e0 for wt  et (equation 4) yields
cb
(12)
wt 
t
2
 et .
cb
The equation above means that the optimal level of opacity ( wt ) corresponds to
 
the CB publishing half of the optimal inflation  t  as a forecast on supply shocks
 2 
(eo). This result is in accordance with Muller and Zelmer (1999) who highlight that
publishing details on future supply shocks implies a high volatility of the nominal shortterm interest rate.
3. Political transparency
The political transparency has as its characteristic the transparency on central
bank objectives and transparency on institutional design between public and central
bank. The transparency concerning objectives in the conduction of the monetary policy
is divided into the publication of the objective and the publication of the importance that
the central bank gives to the output compared to the inflation.
The importance of the political transparency is highlighted by Morris and Shin
(2000). Under this view, feasible and credible numerical inflation targets are powerful
instruments for controlling the public expectation about inflation. In spite of this, the
same authors recognize that inflation targeting is not reduced to the announcement of
the inflation target. A communication framework capable of guiding the inflation
expectation is necessary. Another point is the necessary attention to the explanation of
the past actions because it can cause noise and thus a misleading interpretation by the
public in relation to the conduction of the monetary policy thus damaging the
convergence of the expectations to the inflation target. The public information is very
7
effective in influencing the private actions which in turn can create an overreaction by
the public and thus amplify the adverse effects from noise. Therefore the publication of
the central bank objective helps to attenuate the deviation of prices in the different
markets.
Herrendorf (1998) is another author that is favorable to the announcement of the
inflation target because it avoids the problem of private information (inflation bias) and
creates reputation for the central bank. A credible inflation target improves the central
bank’s control over expected inflation (increase the convergence to inflation target)
which in turn avoids the exaggerated fall in the output in order to restrain the inflation.
Svensson (1999), Eijffinger and Hoeberichts (2000) highlight that central bank
political transparency contributes to the effectiveness of a system with delegation
because the principal (public), knowing the characteristics of the agent (central bank),
can create more efficient mechanisms of incentive. Under this perspective, De Haan,
Amtenbrink and Eijffinger (1999) created a central bank transparency index based on
laws (which made explicit the central bank preferences and its objectives) of each
country. According to this view, a clear central bank preference in the control of
inflation reduces the uncertainty in relation to the future inflation and attenuates the
expected inflation. Therefore, there is an increase in the central bank credibility. This
type of political transparency is denominated as accountability transparency and is
useful for central banks with low credibility. However, it is not indicated for countries
that are very sensitive to shocks and with a low capacity for stabilization.
Geraats (2002) classifies political transparency as everything related with
institutional design of the monetary policy. In this sense, the transparency of central
bank preferences is an important component of political transparency. The presence of
explicit inflation targets, legal contracts between central bank and society, central bank
independence, etc., are other components of the political transparency.
With the intention of analyzing the impact of transparency of central bank
preferences on inflation, output gap, and nominal interest rate, the equations (1), (2) and
(3) are used. The novelty in this model is that there exists a difference between what the
public expects in relation to central bank preferences and the real choices of the
monetary authority. This difference is defined as political opacity and it is represented
by μt in equation below:
8
(13)
t  t  t .
cb
Combining equations (3) and (13), and supposing that social optimal inflation is
zero, then:7
(14)
n
1 cb 
2
L  E   (tcb  t )  xt  n  ut  n   (1  t ) t2 n   t2n  .


t
2
n 0
cb
After defining the main equations in the inflation targeting model, the central
bank minimizes its loss function taking into account t  t  t that is the effective
cb
parameter of preference related to the inflation target and to the output target.
Neglecting the policy independent terms and minimizing the central bank loss function
in relation to the output gap the following is found:
(15)
xt 
 1  t   
(tcb  t )
ut  cb
et .
cb
2
t  t   1  t    
t  t   2 1  t    
Making the substitution of equation (15) into Phillips curve:
(16)


 2 1     
 (tcb  t )ut


 t  cb

1


 et .
2
cb
2
t  t   1       t  t   1      


With the intention of analyzing the impact of political opacity in the output gap
on inflation, it is necessary to study its impact on political shocks  ut  and supply
shocks  et  . The first term of the equations regarding xt and  t relates to the opacity of
central bank preferences (  t ) with the political pressure for expansion of output ( ut ).
Hence, a derivation of the first term of equation (15) in relation to  t is made. In this
case, an increase in political opacity of the central bank increases inflation and output
gap which in turn implies an advantage in increasing the political transparency.
Moreover, the increase in the central bank’s penalty implies a decrease in the first term
of equations (15) and (16) and thus the central bank accountability strengthens the
above-mentioned advantage.
7
It is important to note that Muscatelli (1998) modeled the uncertainty relative to central bank
preferences such as in equation (13) and found a loss function similar to equation (14).
9
Contrary to what was presented above, the second term in equation (15) shows
that an increase in the transparency increases the output gap and thus the inflation.
Hence, an increase in the central bank’s penalty amplifies the effect caused by political
transparency of the central bank on supply shocks. Therefore, incentive contracts which
penalize a central bank that do not achieve the social optimal inflation create problems
for stabilization in the economy. According to Walsh (1995) suboptimal incentive
contracts imply inefficient monetary policies. In this sense, the quality of these contracts
is determinant for the central bank to anchor the public expectation in relation to the
inflation (see Winkler, 2000).
For derivates the influence of the transparency of central bank preferences on the
interest rate, the following equation obtained from intertemporal IS (equation 9) is
assumed:
(17)
1  it   Et t 1 ,
Where  
uc  ct , t 
 Et uc  ct 1 , t 1 
.
Making the substitution of inflation (equation 16) into equation (17) one period
ahead, then:
(18)

 2 1  t 1   
 (tcb1  t 1 )

 
1  it   Et  cb
u

1


 et 1 
t 1
2
cb
2
 t 1  t 1   1  t 1    
 t  t 1   1  t 1      
Due to the fact that opacity is time-dependent, the equation of opacity has as a
characteristic an auto-regressive term, a serial autocorrelation coefficient (  ), and an
error component that is i.i.d. ( E (t )  0 and var(t )  2t ). Thus opacity is given by:
(19)
t 1  t  t .
Combining the equation of political opacity (19) with equation (18) the result is:
(20)

 2 1  t  t   
 (tcb1  t  t )

 
1  it   Et  cb
u

1


 et 1 
t 1
2
cb
2
 t 1  t  t   1  t  t    
 t  t  t   1  t  t      
The equation above reproduces the results in equations (15) and (16), that is, a
more transparent central bank reduces the effect caused by the political shock for the
10
expansion of output on interest rate. In spite of this, a lower  t implies a higher it
because central banks with suboptimal incentive contracts create problems of
stabilization in the economy.
4. Central bank transparency of monetary policy decisions and in relation
to financial innovations
In this section an analysis regarding the importance of central bank to reveal the
shocks on the speed of circulation of money is made. Walsh (1999) highlights the
importance of this type of transparency because the speed of circulation of money is one
of determinants of transmission mechanism in monetary policy. Under this perspective
the growth of money supply and the shocks on speed of circulation of money are the
main determinants of inflation. Unexpected shocks caused by financial innovations on
above-mentioned variables may reduce the central bank reputation and thus lose the
capacity of guiding public expectation.
Based on the above idea, the model takes into consideration an equation (21)
where the inflation is determined by growth of money supply ( mtsCB ), the shocks on the
speed of circulation of money ( vtcb ), and the equations (1), (2), (3), and (4). It is
important to note that the shocks are not completely revealed to the public. As a
consequence there is a term related to the central bank opacity regarding the information
of shocks on the speed of circulation money.
(21)
 t  msCB  v .
t
Making the substitution of equation (4) into equation (3), the central bank loss
function can be written as:
(22)
Lcb 
1 1
2 1 
Etcb   x  u   1    
2
t
t
2
t
 2 t eto  .

Combining equation (21) with equation (1) and substituting the result into
equation (22), then
(23)
1 1
L 
2 1 
cb
2
sCB
cb


cb   mt  vt  et  u   1     2  2 eo  .
t
t
t t
Et  







Therefore, the growth rate of money supply which minimizes the central bank
loss function is given by:
11
(24)
mtsCB 
ut 
    vt    ecb  


t
e
cb
t
 wt 


   1    
.
Due to the hypothesis that the central bank does not publish all information that
it has regarding shocks on speed of circulation of money, the public expectation
concerning these shocks ( vtp ) is a result of two components: the speed which is
observed by the central bank ( vtcb ) and a public’s forecast error (  t ).
(25)
vtp  vtcb   t .
Substituting equation (25) into equation (24), the growth rate of money supply
is:
(26)
sCB
mt

 ut       v p        t   ecb    etcb  wt 
t
   1   
t
.
The equation above shows that higher values of wt and  t imply higher mtsCB .
Hence, there is a higher inflation (  t  mtsCB  v ) and increases in output gap (see
Phillips curve). Since intertemporal IS relates in a direct way to the nominal interest rate
with inflation, a less credible central bank (more discretionary) needs a higher interest
rate for the system. Therefore, central banks which are not transparent in regard to
financial innovations are associated with high inflation rate and high interest rate
because the public embeds an inflation bias in the inflation expectation.
5. Multidimensionality of central bank transparency
The objective of this section is to build a model which considers several
dimensions of the central bank transparency and its effect on macroeconomic variables.
The basic framework of the model is close to that presented in the previous section. The
main difference is the inclusion of political opacity (equation 13).
Through the combination of equation (1) and equation (21), the output gap is
(27)
xt 
mtsCB  vt  etcb

.
12
Making the substitution of equation (13) into equation (3), the central bank loss
function is given by:
(28)
Lcb 
n
1 cb 
  cb     x  u 2  1     2   2  2 e0   e0 2  .


t
t n
t n
t
t n
t n
t n t n
t n
E


2 t n 0
Solving the geometric progression with ratio β, neglecting the policy
independent terms, and making the substitution of equation (27) into equation (28), the
central bank loss function can be rewritten as:
(29)
1 1
L 
2 1 
cb
2
sCB
cb


cb   cb    mt  vt  et  u   1       2  2 e0  .
t
t
t
t
t t
Et 








Deriving the expression above in relation to the growth of money supply the
result is:
(30)
mtsCB 
  cb  t 

   cb  t 

 1  t    




ut 
cb
 t 

   cb  t 

 1  t    




etcb 
 et0
   cb  t 

 1  t    




 vt
Taking into account the central bank opacity regarding the speed of circulation
of money (equation (25)) and the equation regarding the economic transparency
(equation (4)) the above equation can be rewritten as:
(31)
mtsCB 
   t 
    t 

 1  t    

 

  t   
ut 

    t 

 1  t    

 

etcb 

    t 

 1  t    

 

It is observed that the first term of the equation above is close to that related to
political transparency and shows that a higher political opacity increases the output gap.
The second term shows that the adverse effect on the supply shocks are avoided with
13
wt  vtp   t
full transparency. Increases in political transparency (decreases in  t ) decreases the
expectation in regard to mtsCB and thus gives a sign that the central bank does not have a
discretionary procedure. The third term shows that a decrease in the central bank’s
economic opacity (increase in central bank’s economic transparency) implies a fall in
the expectation in regard to the growth rate of money supply. The justification is that
the economic agents have an increase in the set of forward-looking information which
in turn implies that the central bank’s preventive polices are understood avoiding
misleading interpretations regarding the central bank objective. Hence, the
communication about the economic future helps to explain the current decisions
concerning the monetary policy instrument and attenuates the uncertainty in regard to
central bank’s intention.
A peculiar result from equation (31) is that the political opacity (through the first
term of the equation) damages the advantages from economic transparency, that is,
increases in  t decrease the effects of a fall in wt .8 Therefore, the uncertainty regarding
central bank preferences implies that the monetary authority loses the power of
influencing the future interest rate (crucial variable in the public’s making decision).
Hence economic transparency has an important role in avoiding the adverse effects
caused by the increase in central bank’s penalty. A lower wt implies a lower impact of
 on growth rate of money supply and thus on inflation and on output gap. The last
term in the equation reveals that a higher opacity of monetary policy decisions (  t )
implies a higher expectation to mtsCB . Therefore, it is important the central can explain
its monetary policy decisions based on financial innovations because this attenuates the
inflation bias and minimizes the time inconsistency problem.
6. Concluding remarks
Due to the fact that the inflation targeting has been adopted by several central
banks and that the main objective of this monetary regime is to work as a guide for
public’s inflation expectation, the transparency in the conduction of the monetary policy
becomes a necessary condition. One of the main motives for increasing the transparency
is to reduce the uncertainty created by the policymakers. An important point is that a
8
For empirical evidence of this result, see de Mendonça and Simão Filho (2008).
14
higher transparency implies that the market answer to the information disclosure by the
central bank and not to the central banker.
In relation to the analysis of economic transparency it is observed that a higher
central bank’s information quality implies a lower public’s error in predicting the
supply shocks. Moreover a higher volatility in central bank transparency reduces the
sensitivity of central bank’s loss regarding its failure to accomplish the inflation target.
Therefore, a higher volatility for central bank transparency reduces the advantages for
inflation, output gap, and nominal interest rate. Another point is that some central bank
opacity is useful because the financial market needs to believe in the central bank’s
capacity to change the public expectation.
The analysis of central bank’s political transparency, taking into account the
effects on inflation, output gap, and the interest rate, reveals that it is adequate for
economies which are not less subject to supply shocks. Furthermore, the model reveals
that a poor quality in the incentive contract can cause adverse effects for the conduction
of the monetary policy.
The analyses regarding transparency of monetary policy decisions and financial
innovations denote that the explanation of central bank’s decision is relevant (disclosure
of interest rate minutes). The main justification for the advantage from transparency is
that it increases the information quality in the decisions concerning the instrument of
monetary policy.
The analysis of the multidimensionality of central bank transparency reveals the
adverse effects caused by political opacity on economic transparency. The advantages
from central bank’s economic transparency are avoided due to the fact that the public
does not know the central bank preferences. As a consequence evaluations regarding the
economic future are not taken into consideration in the economic agent’s decisions.
In short the results denote the importance of central bank transparency in the
determination of the main macroeconomic variables and its influence on the monetary
policy effectiveness. In other words central bank transparency is desirable because it
reduces the asymmetric information between the central bank and the public and it
increases the central bank accountability. A higher degree of central bank transparency
implies an increase in the sensitivity of central bank reputation regarding its actions
which in turn attenuates the inflation bias in the conduction of the monetary policy.
15
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Appendix
This appendix presents the derivation of the following equations: (15), (17),
(27), (30), and (31).
Considering the equations present in the models:
(1)
 t   xt   Et t 1  et
(2)
L
1
E
2 t


n 0
n
 xt  n 2   t2 n 
n
1 cb 
   x  u  2   2      T 2 


t n
t n
t n
t n
t n
E


2 t n 0
(3)
Lcb 
(4)
eto  et  wt
(13)
t  t  t
(21)
 t  msCB  v
(25)
vtp  vtcb   t
cb
cb
t
Derivation of equations (15) and (17)
Equation (13) reveals the political opacity (μt). Through equations (3) and (13),
and supposing that the optimal inflation target is zero, then
(14)
Lcb 
n
1 cb 
(tcb  t )  xt  n  ut  n 2  (1  t ) t2 n   2 


E
t n 

2 t n 0
Lcb 
n
1 cb 
(tcb  t ) xt2 n  2 xt  nut  n (tcb  t )  (tcb  t )ut2 n  (1  t ) t2 n   t2n 


E
t
2
n 0
1  1  cb
cb
2
cb
cb
2
2
2
Lcb  
 E (t  t ) xt  n  2 xt  nut  n (t  t )  (t  t )ut  n  1  t   t n   tn 
2  1   t 
17
Neglecting the independent terms of policy and minimizing the central bank loss
function in relation to the output gap (xt), then
2(  t ) xt  2(  t )ut 
cb
t
cb
t
 1  t     t2 
xt
tcb  t   2 1  t     xt  (tcb  t )ut   1  t    et
Solving this result for xt then,
(15)
xt 
 1  t   
(tcb  t )
ut  cb
et .
cb
2
t  t   1  t    
t  t   2 1  t    
With the objective to study the effect of political opacity on output gap, equation
(15) is derived regarding the opacity term. The two terms of the equation are analyzed
in a separate way. The derivation related to the first term is given by:

(tcb  t )ut
tcb  t   2 1  t    
t
tcb  t   2 1  t      (tcb  t ) 1   2 


2
tcb  t   2 1  t    
tcb   2   2    2tcb

0
2
tcb  t   2 1  t    
In this case it is observed that a higher  t implies a higher xt .The same
procedure for the second term of the equation is adopted, that is,
 1  t   
  t   2 1  t      .tcb  t   2 1  t      1  t    . 1   2 



2
t
tcb  t   2 1  t    
cb
t

t      t  
cb
t
tcb  t   2 1  t    
2


    

cb
t
tcb  t   2 1  t    
2
.
Therefore an increase in central bank opacity implies a decrease in output gap.
For determination of the nominal interest rate the intertemporal IS is used:
1  it 
1
 u c ,  
 Et  c t 1 t 1 
 uc  ct , t   t 1 
18
1  it 
1  it 
Et  t 1uc  ct , t   uc  ct , t  Et  t 1 
1
 

 Et uc  ct 1 , t 1   Et uc  ct 1 , t 1  
1  uc  ct 1 , t 1  
 Et


 t 1  uc  ct , t  
uc  ct , t  Et t 1
 Et uc  ct 1 , t 1 
, 1  it   Et t 1 (17), where,  
uc  ct , t 
 Et uc  ct 1 , t 1 
.
Derivation of equations (27), (30) and (31)
Equating equation (1) to equation (21), mtsCB  vt   xt  etcb , then xt 
mtsCB  vt  etcb

(27)
Based on equation (3) and defining ecb as the forecast in relation to the shock that the
central bank expects, then
n
1 cb 
  cb     x  u 2  1     2   2  2 e0   e0 2 


t
t n
t n
t
t n
t n t n
t n
E
t n


2 t n 0
1 1
cb   cb    x  u 2  1       2  2 e0 
Lcb 

t
t
t
t
t
t t 
E
2 1  t 
Lcb 
Making the substitution of equation (34) into the above equation gives
1 1
L 
2 1 
cb
2
sCB
cb


cb   cb    mt  vt  et  u   1       2  2 e0  .
t
t
t
t
t t
Et 








Deriving the central bank loss function (Lcb) in relation to the growth rate of
money supply ( mtsCB ), the result is:
 cb
Lcb
   t

0
,
mtsCB


 mtsCB  vt  etcb
 mtsCB
mtsCB 0 
 ut  
1  t     t  
et   0
  
  t 



t


Taking into account that
mtsCB
 t
= 1, then:
 cb

 mtsCB  vt  etcb

 ut   1  t    mtsCB  vt   et0   0
   t  








19

     
cb

(30) m sCB 
cb
 t 
t
    t 

 1  t    




cb
t
ut 

    t 

 1  t    




cb
etcb 

    t 

 1  t    




cb
wt  vt .
Making the substitution of equation (25) into equation (30), the growth rate of
money supply can be rewritten as:
     
cb
mtsCB 

cb
 t 
    t 

 1  t    




cb
t
ut 

    t 

 1  t    




cb
etcb 

    t 

 1  t   




cb
     

wt  vtp   t
cb
mt 
sCB
(31)

cb
 t 
    t 

 1  t   

 

cb
t
ut 

    t 

 1  t   

 

cb
etcb 

    t 

 1  t   

 

cb
wt  vtp   t
With the objective of evaluating the effect of central bank political transparency
on the second term of tha above equation, a derivation in relation to  t is made.
   cb  t    1  t        t   cb  1    



2
2

 


.
2
   cb  t 

 1  t    




With the intention to demonstrate that an increase in opacity implies an increase
in

money
cb
supply
it
is
necessary
to
prove
that
 t    1  t       t   cb  1     0 .
Hence,   cb  t    1  t       t   cb  1    
  cb  t    t      t   cb   2  t   cb 
    2   cb .
Due to the fact that the expression above is greater than zero, it can be affirmed
that the full transparency avoids the adverse effect caused by political transparency on
the term regarding supply shock.
20
.
