eeEstudos Econômicos (São Paulo)Estud. Econ.0101-41611980-5357Faculdade de Economia, Administração e Contabilidade da Universidade
de São Paulo (FEA-USP)10.1590/0101-416147232aecfArticlesMonetary policy in Brazil: Evidence from new measures of monetary
shocks♦CostaAdonias Evaristo daFilhoUniversidade de BrasíliaBraziladoniasevaristo@hotmail.comDoutor em Economia - Universidade de
Brasília (UnB). E-mail: adoniasevaristo@hotmail.comUniversidade de BrasíliaApr-Jun20174722953280804201619122016This is an Open Access article distributed under the terms of the
Creative Commons Attribution Non-Commercial License which permits
unrestricted non-commercial use, distribution, and reproduction in any
medium provided the original work is properly cited.Abstract
This paper derives new measures of monetary policy shocks for Brazil. First, one
set of shocks is built inspired by Romer and
Romer (2004) methodology, using official and private forecasts.
Central Bank staff forecasts were collected from the technical presentations of
monetary policy meetings, released after the introduction of the Access of
Information Law, while private forecasts come from the Focus survey. Second, a
yield curve shock is constructed for the Brazilian case, based on the Barakchian and Crowe (2013) methodology.
Equipped with the shocks measures, I include them on VARs (Vector
Autoregressions) and analyze the effects on inflation and output. A standardized
monetary policy shock is found to reduce real GDP in up to 0.5%. In all but the
yield curve shock case, it is found evidence of a price puzzle in the estimated
models.
Resumo
Este artigo deriva novas medidas de choques de política monetária para o Brasil.
Em primeiro lugar, um conjunto de choques é construído inspirado na metodologia
de Romer e Romer (2004), utilizando tanto
previsões públicas quanto privadas. As previsões do Banco Central foram
coletadas a partir das apresentações técnicas das reuniões de política
monetária, que vêm se tornando públicas após a Lei de Acesso à Informação,
enquanto as previsões do setor privado vêm da pesquisa Focus. Em segundo lugar,
uma série de choque na curva de juros foi construída para o Brasil, baseada na
metodologia de Barakchian and Crowe
(2013). De posse das medidas de choques, foram estimados VARs (Vetores
Autorregressivos), e analisados os efeitos na inflação e no produto. Encontra-se
que um choque padronizado de política monetária reduz o PIB real em até 0,5%.
Exceto para o caso do choque na curva de juros, para os demais casos são
encontradas evidências de um "price puzzle" nos modelos estimados.
This paper derives new measures of monetary policy shocks for Brazil, aiming to shed
light on the effects of monetary policy on the Brazilian economy. Recently, there
has been a renewed effort to analyze the effects of monetary policy shocks, with
some authors trying to reconcile the evidence (Coibon, 2012) or obtaining new measures of monetary policy shocks, as
shown in the studies of Barakchian and Crowe
(2013) for the United States and Cloyne
and Hurtgen (2014) for the UK.
Following the approach of the aforementioned articles, this research employs a
comprehensive view of monetary policy shocks, investigating the effects on GDP and
inflation of a total of three measures of shocks. Two shocks are derived in the
spirit of the narrative approach introduced by Romer
and Romer (RR) (2004). This method of obtaining monetary policy shocks
consists in a regression of the change in the policy rate on the forecasts of
inflation and GDP growth. The residuals from this regression are taken as the
measure of monetary policy shocks. By using forecasts to estimate the effects of
monetary policy, the methodology pursued here bears a strong resemblance to the one
undertook by Thapar (2008), who used Federal
Reserve's Greenbook forecasts and expectations embedded in financial contracts to
analyze the effects of monetary policy for the US economy. Brissimis and Magginas (2006) also argue for the use of
expectations variables to take into account the forward-looking behavior of central
banks, including an index of leading indicators and federal funds futures in their
models.
For the Brazilian case, the forecasts were collected from different sources. Both
official and private forecasts were used. The official forecasts data come from the
presentations of the Central Bank staff for the monetary policy committee (COPOM)
meetings. These presentations became available after the Access of Information
Law1 was introduced in 2011, which required
that the content of the technical presentations of the first day of COPOM meetings
would be available to the public after four years the meeting took place. Using
these presentations, it was possible to build a new dataset of forecasts of GDP and
inflation from the Central Bank staff at the time of each meeting.2 As of 2016, the presentations of COPOM meetings
from 1999 to 2011 were available. Due to the period required for disclosure by the
law-4 years- it was not possible to obtain data for the more recent years. The
database is presented in the Appendix. On the other hand, private forecasts came
from the Focus survey conducted by the Central Bank, which are available on a daily
basis.
Besides the monetary policy measures obtained through forecasts, an additional
monetary policy shock was obtained from a factor analysis on the difference of the
interest rate swap curve after and before the monetary policy meetings, following
closely the approach of Barakchian and Crowe
(2013). With the new measures of monetary policy shocks at hand, they
were included in a standard VAR, under the recursive assumption, as in much of the
vast literature on the effects of monetary policy shocks, surveyed, for example, in
Christiano et al.
(1999). It is then analyzed the consequences of monetary policy shocks on
output and inflation, at the quarterly frequency.
In terms of content, this paper is related to Vieira
and Gonçalves (2008), who analyzed the consequences of monetary policy
surprises on economic activity measures, finding a larger effect for the unexpected
component of monetary policy. This paper substantially expands the analysis of Viera and Gonçalves (2008),3 not only with the inclusion of new measures of monetary
policy shocks, which have not been done previously but also regarding the
methodology. While the findings of the authors were based on regressions, I follow
the long tradition of using VAR models in studies about monetary policy. Previously
studies using VARs with the recursive identification include Minella (2003), Cysne
(2004, 2005) and Luporini (2008). Signs restrictions (Uhlig, 2005) were employed in Mendonça et al. (2010) and
Bezerra et al. (2014).
Vector error correction models were estimated in Fernandes and Toro (2005) and structural VARs in Céspedes et al. (2008). The FAVAR approach of
Bernanke et al. (2005)
was employed in Carvalho and Rossi Júnior
(2009), with monthly data from 1995 to 2009.
From an international point of view, this paper is related to the large literature on
the effects of monetary policy using VARs and the price puzzle (Sims, 1992; Eichenbaum, 1992), which could be defined as an increase in the price
level after a contractionary monetary policy shock.
The literature on the effects of monetary policy shocks using VARs is large. Bernanke and Blinder (1992) identified the
federal funds rate as the monetary policy instrument, considering it as the
appropriate measure of the stance of monetary policy, and investigated the
composition of US banks' balance sheets and unemployment after a monetary policy
shock using VARs. Bernanke and Mihov (1998)
examined the effects of monetary policy estimating VARs with bank reserves and
federal funds rate, along with commodity prices, inflation, and real GDP, trying to
find an appropriate measure of US monetary policy stance for the period 1965-1996.
Christiano et al. (1996)
use two measures of monetary policy shocks (the federal funds rate and the level of
nonborrowed reserves) to study the response of firm's financial assets and
liabilities in the United States. Cochrane
(1998) distinguishes between the anticipated and non-anticipated effects
of monetary policy, finding a much smaller effect for the former relative to the
latter.
Leeper (1997) criticizes the use of VAR models
and the narrative approach of Romer and Romer
(1989), arguing that the narrative approach does not yield purely
exogenous monetary policy shocks, and suffer from the same identification and
misspecification problems as the ones from monetary VARs, that produce a price
puzzle. By the same token, Rudebusch (1998)
sharply criticizes the use of VARs for the analysis of monetary policy shocks, on
the grounds of the linear structure of the models, limited information set usually
employed by many authors and potential pitfalls caused by the employment of revised,
instead of preliminary data, which usually are the kind of information available for
policymakers. He shows that measures of monetary policy shocks across different
papers are little correlated, and defends measures of monetary policy shocks that
are extracted from financial markets, due to its forward-looking nature. Bagliano and Favero (1999) also use information
from financial markets in a monetary VAR, including the one-month Eurodollar forward
rate as an exogenous variable.
Regarding the price puzzle, the standard solution to solve it has been the inclusion
of a commodity price index in the estimated models. The main reason for this was
that the estimated VARs lacked forward-looking variables that helped to predict
inflation, and that the empirical evidence was consistent with the behavior of a
central bank that decides to raise rates in anticipation of an increase in
inflation. Since commodities prices presumably helped to forecast inflation, their
inclusion in the system was sufficient to eliminate or attenuate the puzzle.
Hanson (2004) cast doubt on the alleged
connection between the price puzzle and the absence of variables that help to
predict inflation, finding that the inclusion of variables that are helpful in
predicting inflation does not solve the puzzle. Giordani (2004) argues that the price puzzle is due to lack of measures
of output gap in the VARs, while Bernanke et
al. (2005) suggest the inclusion of factors to properly
identify the effects of monetary policy shocks, therefore summarizing the
information of a large number of variables in the factors and better reflecting the
information set available for the central bank. More recently, Barakchian and Crowe (2013) developed a new measure of monetary
policy shock, based on a factor extracted from federal fund futures contracts,
following the branch of the literature that uses financial information to identify
monetary policy shocks. They include their measure in a small VAR, with the results
still displaying a price puzzle. Dias and Duarte
(2016) examined whether the price puzzle is due to the shelter share in
the consumer price index (CPI) for the United States-around 30%, arguing that a
contractionary policy shock leads to a decline in the prices of houses and an
increase in rents. They find that measures of inflation that exclude the shelter
component deliver a substantially smaller price puzzle in the estimated models.
Finally, Cochrane (2016) reviews a variety of
monetary models and the empirical evidence based on VARs that usually finds a price
puzzle, arguing for the possibility that inflation rises after an increase in
interest rates, in the context of the zero lower bound on nominal interest rates in
some developed economies after the financial crisis of 2007/2008. Ramey (2016) also reviews many papers about the
effects of monetary policy on prices and inflation, in terms of methodology, maximum
impact on activity, the share of the variability of output explained by monetary
policy shocks and the existence of a price puzzle.4 She comments that the price puzzle continues to pop up in some
specifications over the years (Ramey 2016,
p.27).
Previous studies for Brazil have found that monetary policy impacts economic
activity, as expected. But for inflation, the evidence is less clear, with many
studies showing evidence of a price puzzle, especially when taking into account the
reported confidence intervals, along with the baseline response. For instance,
results obtained by Minella (2003) show a
price puzzle. Similarly, Cysne (2004) found
evidence for a small and temporary (around one-quarter) price puzzle in Brazil,
reporting 90% confidence bands, while for some specifications in Cysne (2005) the price puzzle remains for two
or three quarters. Céspedes et al.
(2008) report 68% confidence intervals and inflation takes a long time to
decline, with the response to a monetary policy shock not being statistically
significant for two quarters after the shock. Carvalho and Rossi Júnior (2009) argue that no price puzzle was found in
their FAVAR estimates. Although the baseline responses were indeed negative, the
reported 90% confidence intervals of the response of IPCA to a monetary shock
include the zero. Luporini (2008) reports 95%
confidence intervals, which includes the zero in all impulse responses of inflation
to a shock in the interest rate. Mendonça et
al. (2010, p.379), using sign restrictions, notice that the
price puzzle appears when their models allow for the possibility that inflation
increases after a monetary policy shock.5
Finally, Bezerra et al.
(2014) use the same methodology, finding few evidences of a price
puzzle.
This paper is organized as follows. Section 2 describes and derives the new measures
of monetary policy shocks. Section 3 describes the data. Section 4 analyses the
effects of monetary policy shocks on inflation and output, through a small VAR,
which includes output, inflation, and the shocks measures. Section 5 proceeds with
the analysis, including three measures of commodity prices in the baseline
specification. Section 6 investigates the consequences of opening up the model, with
the inclusion of gross debt, the exchange rate and variables associated with the
world economy. Section 7 then concludes. Appendix
A shows the autocorrelation tests on the estimated models and Appendix B presents the database constructed,
collecting data from the technical presentations of COPOM meetings.
2. Measures of monetary policy shocks2.1 Measures inspired by <xref ref-type="bibr" rid="B36">Romer and Romer's
(2004)</xref> narrative approach
Romer and Romer (2004) ran the following
regression:
Where Δff_{m} is the change in the funds rate at
meeting m, ffb_{m} is the level of the funds rate
before any changes associated with meeting m, included to capture any mean
reversion behavior from the FOMC, and π and Δy
refer to the forecasts of inflation and real output growth. In their
specification, the unemployment rate was also included. Finally, the i
transcript refers to the horizon of the forecast: -1 is the previous quarter; 0
is the current quarter; and 1 and 2 are one and two quarters ahead. This
equation can be thought as a sort of Taylor Rule
(1993), in which the interest rates changes are regressed on
expectations of inflation and output growth available for the monetary
authority.
Romer and Romer (2004) used forecasts from
the Greenbook, and then proceed in their analysis identifying the residuals from
the estimated equation as a measure of monetary policy shocks, i.e., changes in
the funds rate that could not the accounted for by information of future
economic conditions, which were available for the committee at the time of the
meetings. Basically, the same specification was employed by Cloyne and Hürtgen (2014) for the UK, who
define the shock series as "an unpredictable surprise that is not taken in
response to information about current and future economic developments" (Cloyne and Hürtgen 2014, pg. 8). Thapar (2008) and Brissimis and Magginas (2006) defend a methodology based on
forecasts to study monetary policy since it provides all the information
available for the policymakers and private agents at a given period of time.
The same equation was estimated for Brazil, with some slight changes due to data
limitations. As mentioned in the introduction, I collect data on forecasts of
inflation and GDP growth from the Central Bank of Brazil staff. These forecasts
appear in the technical presentations of the COPOM meetings, available from 1999
to 2011. The inflation forecasts used are those from the economic department of
the Central Bank ("DEPEC"), as they appear in the presentations, as explained in
footnote 2. Usually only forecasts of inflation and GDP growth for the current
year-from the point of view of each meeting- are available. Nonetheless, in the
final meetings of each year, forecasts for the next year begin to appear in the
presentations. In order to capture this feature, the following variable was
constructed, mixing the forecasts for the current and next year in the following
way, in which the month and year refer to that of each COPOM meeting:
The intention of this equation was to smooth the information available for the
Central Bank. Intuitively, at the end of the year, the monetary authority starts
to pay more attention to what the forecasts are showing for the next year
relative to the current. An advantage of using the forecasts of inflation and
output growth from the technical presentations of COPOM meetings is that by
doing so we can get forecasts for every Central Bank decision.
Results for the regressions are shown in Table
1. The sample comprises 125 COPOM meetings, from July 28, 1999 to
November 30, 2011. The forecasts explain more than 40% of the change in the
Selic rate. In comparison to other studies, this value is higher than those
found for the US and UK. Romer and Romer
(2004) original study found a R2 of 0.28 for their equation, while
Cloyne and Hürtgen (2014) report a
figure of 0.29.
Romer and Romer equation with Central Bank forecasts
(1)
(2)
VARIABLES
Δ Selic
Δ Selic
Selic _{t–1}
0.0014
(0.016)
Weighted IPCA Forecast
-0.44***
-0.42***
(0.13)
(0.12)
Weighted GDP Forecast
-0.18
(0.15)
Current IPCA Forecast
0.45***
0.44***
(0.12)
(0.11)
Current GDP Forecast
0.33**
0.17***
(0.13)
(0.037)
ΔCurrent IPCA Forecast
0.024
(0.067)
ΔCurrent GDP Forecast
-0.058
(0.042)
ΔWeighted IPCA
Forecast
0.56***
0.55***
(0.11)
(0.097)
ΔWeighted GDP Forecast
0.28**
0.13**
(0.14)
(0.059)
Constant
-0.80**
-0.87***
(0.32)
(0.23)
Observations
125
125
R-squared
0.441
0.429
Robust standard errors in parentheses
p<0.01,
p<0.05,
* p<0.1
The second column on Table 1 shows the
results considering all explanatory variables, while on the third column I keep
only the statistically significant ones. Overall the results show a strong
reaction to forecasts of GDP growth and inflation for the current year. Changes
in weighted forecasts for GDP and inflation were also significant, and also the
level of the weighted forecast for inflation. The negative sign of the constant
indicates a downward trend in the Selic rate over the period.
As in Romer and Romer (2004, p. 1062), the
goal of the regression is not to estimate the reaction function as well as
possible, but to eliminate movements in the policy rate in response to future
economic developments. The use of forecasts to identify monetary policy shocks
is justified by the need to enlarge the information set of the monetary
authority. Arguably, results like the price puzzle are due to the limited
information set in estimated VARs. Since forecasters use all available
information to forecast, regressions as those in Tables 1 and 2 control the
information available to policymakers at the time of each COPOM meeting. This
information is reflected in all variables that help to forecast inflation and
output growth, that usually appear in the reaction function of the Central Bank.
These likely include the expected path of fiscal policy variables and also the
exchange rate over the forecast period. Even studies for Brazil that allowed for
a larger information set, as the FAVAR estimated by Carvalho and Rossi Júnior (2009), did not include
expectations, due to the small number of observations at the time (Carvalho and Rossi Júnior 2009, pg.
291).
Romer and Romer equation with Focus expectations
(1)
(2)
VARIABLES
Δ Selic
Δ Selic
Selic _{t–1}
-0.056***
-0.038***
(0.017)
(0.011)
1y Inflation Exp
0.22
0.19***
(0.17)
(0.024)
2y Inflation Exp
0.21
(0.48)
2y Inflation Exp
-0.48
(0.42)
1y Growth Exp
0.39***
0.39***
(0.064)
(0.063)
2y Growth Exp
-0.62***
-0.52***
(0.12)
(0.074)
Δ1y Inflation Exp
0.98***
0.89***
(0.35)
(0.20)
Δ2y Inflation Exp
-0.55
(0.67)
Δ3y Inflation Exp
0.49
(0.97)
Δ1y Growth Exp
-0.30*
(0.18)
Δ2y Growth Exp
0.43
(0.35)
Constant
1.66
(1.15)
Observations
108
108
R-squared
0.553
0.543
Robust standard errors in parentheses
p<0.01,
** p<0.05,
p<0.1
A second set of forecasts, also employed in the analysis, comes from the Focus
survey, which on a daily basis disclosures forecasts for growth and inflation
for several years ahead. The end of year forecasts were transformed on constant
maturity forecasts. For each date in which the forecasts were available, I
collect the forecasts for up to the longest year available.
Where j = 0,1,2 for the growth and inflation forecasts. This equation builds the
constant maturity forecast as a weighted average of the forecasts of two
subsequent years. For a given date, we have forecasts for up to four years ahead
for the growth and inflation projections. The equation is used for each pair of
subsequent years to create the constant maturity forecasts for one, two and
three years ahead. The constant maturity expectations series, constructed from
the Focus survey are shown in Figures 1
and 2.
These forecasts series are then used in the Romer
and Romer (2004) specification, taking the residuals as another
measure of monetary policy shock. For the regression, I considered the
expectations for growth and inflation from the business day immediately before
the meetings.
Results for this regression are shown in Table
2, estimated with 108 observations, also at the meeting's frequency.
The estimation period comprises the meetings from January 22, 2003 and December
3, 2014.
Thus, the estimation period does not coincide with the one when a similar
equation was estimated using Central Bank forecasts, which are available until
2011. The second column on Table 2
presents the results considering all explanatory variables, while in the third
column only the significant ones remained.
The negative sign for the initial policy rate reflects a downward trend in the
path of the Selic rate over time, showing statistical significance. Inflation
expectations for one year ahead are significant, along with changes in inflation
expectations. Finally, both growth expectations for one and two years ahead are
significant. The negative sign for output growth expectations for two years
ahead is somehow puzzling. All in all, private sector expectations explain
roughly 54% of the changes in the Selic rate over the sample period, showing,
therefore, a larger explanatory power in comparison to the one obtained using
Central Bank forecasts.
2.2. Yield curve shock
Finally, the last measure of monetary policy shocks follows closely Barakchian and Crowe (2013). These authors
use factors extracted from Fed Funds futures to measure exogenous changes in
policy, arguing that monetary policy became more forward-looking since 1988. The
idea of using information from financial markets to investigate the effects of
monetary policy shocks, particularly futures contracts, can be traced back to
Rudebusch (1998), Bagliano and Favero (1999), Kuttner (2001), Cochrane and Piazzesi (2002), Faust, Swanson and Wright (2004) and Brissimis and Magginas (2006).
Following the identification scheme of Barakchian
and Crowe (2013), I use constant maturity fixed rate-CDI 6 swap contracts. The dataset consists of a
total of seven tenors: three months, six months, and one to five years
ahead.7,8Vieira and Gonçalves (2008) employed the
30 and 360-days swap. Therefore, I substantially expand the analysis, in order
to capture the full impact of monetary policy on the term structure.
As argued by the Barakchian and Crowe
(2013), there are several reasons to take into account a range of
maturities. It helps to minimize noise from a particular tenor, possibly
stemming from term premium, liquidity differences, and also as a measure to
capture both the impact of the change in the policy rate and the effects on
long-term rates through expectations of the future path of short-term rates.
As in their analysis, a simple factor model was estimated via maximum likelihood,
using the change in the swap rates in the neighborhood of each meeting as
inputs, using the difference between the business day immediately after the
meeting relative to the business day immediately before. Specifically, the model
is:
s=ϕΛ′+e
Where s is the vector of the changes in swap rates for all maturities considered
(seven), f is the vector of factors, φ is the factor loading matrix and e
is the vector of unique factors. The factor method is a way to bypass the need
to model the entire yield curve, giving more importance to those maturities that
exhibit a greater degree of comovement in extracting the factors. As in Barakchian and Crowe (2013), I identify the
shock series as the first factor, which has the interpretation of the effect of
monetary policy on the level of the term structure. The dataset used to
construct this factor shock series is comprised of 108 observations (COPOM
meetings) beginning in 2003 and ending in 2014. Even though for the shorter
tenors the data goes back to 1999, for the longer maturities the series begin in
the second half of 2002. This was a very volatile period in financial markets,
due to uncertainty brought by the elections. Thus, I preferred to use 2003 as
the starting point. The swap series which were used as inputs and the cumulated
factors are shown in Figure 3.
Swaps data
I found that two factors explain 92% of the total variance. Alone, the first
factor (yield curve level) explains 75% of the total variance, while the second
factor (yield curve slope) explains 17% of the total variance. As for the
relevance of each variable in the factor, the analysis shows that short-term
maturities account for the bulk of the first factor, while for the second factor
the longest tenors play a more significant role. With the exception of the three
and four year-ahead maturities, the other maturities display a significant
common variability, above 90%, as one can infer from the unique variances in
Table 1. Finally, the loadings
indicate that the first factor exerts a positive influence on all maturities,
whereas the second factor loads negatively the maturities up to two years ahead
and positively from the three year swap onwards, therefore steepening the yield
curve.
Factor Analysis
Factor
Eigenvalue
Difference
Proportion
Cumulative
Factor1
4.36176
3.14576
0.7250
0.7250
Factor2
1.21600
0.77720
0.2021
0.9271
Factor3
0.43880
.
0.0729
1.0000
Variable
Factor1
Factor2
Factor3
Uniqueness
sswap90
0.8029
-0.4345
-0.2570
0.1005
sswap180
0.8883
-0.4109
-0.1259
0.0261
sswap1y
0.9354
-0.2425
0.1225
0.0513
sswap2y
0.8244
-0.1584
0.4709
0.0735
sswap3y
0.6253
0.0853
0.3410
0.4855
sswap4y
0.6932
0.5419
-0.0409
0.2242
sswap5y
0.7085
0.6881
-0.0472
0.0223
Obtained via Maximum Likelihood with 108
observations
2.3. Comparison of the shock series
Figure 4 displays all three shocks series
considered, for the periods in which they overlap (from 2003 to 2011). Based on
the regressions above and departing from the shocks series obtained for each
COPOM meeting, the quarterly averages of each series were taken. It was chosen
to work with quarterly averages, in order to coincide with the frequency of the
real GDP series.
Shocks series
All shocks display a quite similar evolution. The shocks obtained from the
regressions residuals strongly correlate, with a coefficient of 0.87. There is a
mild correlation between the residual of the regression that uses the central
bank expectations and the yield curve factor shock, 0.47. Finally, there is a
poor correlation between the residual of the regression that employs Focus
expectations and the yield curve shock, 0.28.
Before entering the shocks in the VARs, they were cumulated, following the same
procedure as Romer and Romer (2004),
Cochrane (2004) comments on Romer and
Romer (2004) paper, Coibon (2012), Barakchian and Crowe (2013) and Cloyne and Hürtgen (2014). The reason for this is that
usually the interest rate appears in levels in the conventional VARs.
3. Data description
Equipped with the shocks measures, I then proceed to assess the effects of monetary
policy shocks on the Brazilian economy. The cumulated shock measures were used in
standard VARs, under the recursive assumption. The models were estimated at the
quarterly frequency. The variables in the baseline VAR were the log seasonally
adjusted real GDP, quarterly market prices inflation of the IPCA (Índice de Preços
ao Consumidor Amplo) and each measure of monetary policy shock, cumulated. Both
series come from IBGE (Instituto Brasileiro de Geografia e Estatística).
In addition to these series, there is an investigation about how the results change
when the VAR is augmented by the inclusion of the gross debt, the exchange rate,
foreign interest rates and world trade, representing, respectively, fiscal policy
and open economy setting in the system.
For the gross debt, the series 4537 of the Time Series Management System (SGS)9 of the Central Bank of Brazil was used. Since
the gross debt series constructed under the new methodology, adopted since 2008,
begins only in December 2006, it was preferred to use the series based on the old
methodology, due to the larger number of observations. For the BRL/USD exchange
rate, series 3698 of the same system. The foreign interest rate is represented by
the 6-month Libor (series 3841) on US dollars instead of policy rates, due to the
zero lower bound on nominal interest rates after the financial crisis of 2008. World
trade data come from CPB Netherlands Bureau for Economic Policy Analysis. Finally,
it was checked whether commodity price indexes changed the results. The series
employed were the Central Bank of Brazil commodity price index (IC-BR), the
International Monetary Fund (IMF) overall and fuel indexes. All series are quarterly
averaged and, apart from interest rates, in log. Most series are shown in Figure 5. For inflation, quarterly market prices
inflation were employed, since it is important to consider only prices that are
affected by monetary policy to evaluate the effects of the shocks. Thus, an analysis
including regulated prices could be misleading.
Data
All results presented were obtained using the following order: log of real GDP,
quarterly market prices inflation from the IPCA and the measures of monetary policy
shocks (cumulated). This ordering choice basically follows the mentioned papers. As
a robustness exercise, the VARs were also estimated with the monetary policy shock
ordered first, implying a contemporaneous effect on the other variables in the
system, but not the other way around.
The baseline VARs were estimated in levels. Unit root tests indicated that for the
variables, with the exception of the IPCA, it is not possible to reject a unit root.
But I follow the related papers, which also consider the variables in levels. This
procedure is based on the results in Sims et
al. (1990), who put more emphasis on implications for the
distributions of the statistics of interest, rather than the nonstationarity of the
variables. Examples of monetary policy VARs using Brazilian data in levels include
Céspedes et al. (2008),
Mendonça et al. (2010),
some specifications in Minella (2003) and
Bezerra et al.
(2014).
In almost all estimated VARs, stability conditions were satisfied. When that was not
the case, some variables entered the model in first differences, so as to satisfy
stability. Lags were selected based on the AIC and BIC statistics. Appendix A displays the lags for each model,
the p-value at the Lagrange Multipliers statistics, indicating the lack of
autocorrelation, and any transformation to make the model stable.
4. Results
Figures 6 and 7 show the impulse response functions of the estimated VARs, with the
monetary policy shocks ordered first and last, respectively. The baseline response
is showed along with 95% confidence bands in gray.
Impulse Response Functions
Note: The first row shows the responses of the log of real GDP to a
standardized monetary shock, while the second row displays the responses of
inflation to the same shock. From left to right: RR shock with Central Bank
expectations, RR shock with Focus expectations and yield curve factor
shock.
Impulse Response Functions (shocks ordered first)
Note: The first row shows the responses of the log of real GDP to a
standardized monetary shock, while the second row displays the responses of
inflation to the same shock. From left to right: RR shock with Central Bank
expectations, RR shock with Focus expectations and yield curve factor
shock.
In response to the measures of monetary policy shocks, real GDP declines, with a
maximum impact of 0.5% until the fifth month after the shock. For inflation, the
estimation shows a price puzzle for all shocks, with inflation initially increasing
after the shock and then falling. The price puzzle is more pronounced for the
response considering the RR shock with Central Bank expectations and very mild for
the RR shock with market expectations and for the yield curve shock. One possibility
for this behavior might lie in the estimation period of each model. While the VAR
with RR central bank expectations was estimated from the 1999 Q3 to 2011 Q4, the VAR
with RR market expectations was estimated from 2003 Q3 to 2014 Q4. The reason for
the different sample is that the Central Bank of Brazil releases the technical
presentations of COPOM meetings with a delay of four years, being 2011 the last year
with complete data. On the other hand, the period for the model with RR market
expectations was chosen to coincide with the availability of data for the yield
curve, so that the models with RR with market expectations and with the yield curve
shock were estimated using the same period.
Taking into account the confidence bands, the response of inflation is negative only
for the yield curve factor shock, a finding that could link the shape of the yield
curve and the primary goals of the Central Bank under an inflation targeting regime.
For the RR shock with market expectations, the response of inflation in the baseline
is conventional with theory as well, although considering the confidence intervals
it could not be considered statistically significant.
Figure 7 shows that the different ordering does
not affect in a substantial way the results. After a monetary policy shock,
inflation initially increases and then falls, but only for the yield curve shock the
confidence bands remain below zero approximately five quarters after the shocks,
showing a fall in inflation.
5. Including commodity prices
In the next step, commodity price indexes were included in the estimated VARs in
order to check robustness of the results. Traditionally, a commodity price index is
used to "solve" the price puzzle, in the sense that the puzzle is explained by an
anticipation of an increase in inflation, to which the central bank responded by
raising rates, creating a positive correlation between the increase in interest
rates and the increase in inflation. Commodity prices were then used as a variable
that helps to forecast inflation, and including them in the system corrected the
price puzzle. Hanson (2004) examines the link
between indicators that help to predict inflation and their ability to solve the
price puzzle, showing a poor correlation between them, implying that the puzzle
might not be due to a lack of a variable that predicts inflation in the VAR. In our
case, by construction, the RR shocks already excludes the expected component of
inflation and output growth since they are based on the residuals of a regression of
interest rates changes on official and private forecasts. Thus, one could argue that
there is no major reason for including a commodity price index in the estimated
VARs. Regardless of this potential argument, it was done as a robustness
exercise.
In these models, the commodity price index was ordered first in the system, in log
level. The commodity price indexes employed were the IC-BR (Índice de Commodities
Brasil) from the Central Bank of Brazil, the IMF overall and fuel commodity price
index. Thus the VARs were estimated with the following order: each one of the
commodity price indexes, log of real GDP, inflation and one of the three measures of
monetary policy shocks, implicitly implying that the commodity price index is the
most exogenous variable in the system, under the Choleski identification scheme.
The results of the inclusion of commodity price indexes in the models are shown in
Figures 8, 9 and 10. In general, impulse
responses indicate that inflation increases and then declines after the monetary
policy shock hits the economy. For the RR shock with private sector expectations
(Focus), the response is negative considering the baseline response, with the same
continuing to happen for the yield curve shock.
Impulse Response Functions – Model with Commodity Price Index
(IC-BR)Impulse Response Functions – Model with IMF Commodity Price
IndexImpulse Response Functions – Model with IMF Fuel Price Index
Note: The first row shows the responses of the log of real GDP to a
standardized monetary shock, while the second row displays the responses of
inflation to the same shock. From left to right: RR shock with Central Bank
expectations, RR shock with Focus expectations and yield curve factor
shock.
6. Augmenting the VARs with exchange rate, fiscal and external variables
In order to provide additional robustness for the results, VARs including additional
variables were estimated. The first one employed the baseline specification of Luporini (2008), with the following order:
output, inflation rate, nominal exchange rate as measured by the Real/ US Dollar and
the shock series, replacing the interest rate in her paper. This order is also
consistent with the one employed in the comparison of VAR and FAVAR models in Carvalho and Rossi Júnior (2009, p. 297). It was
also included a measure of global trade and US interest rates exogenously in the
VAR, also following Luporini (2008),
intending to see how the results change in an open economy VAR.
Luporini (2008) estimated the model with the
variables in differences, while the models presented here were estimated mostly in
levels, due to reasons presented earlier. The results from this specification are
presented in Figure 11.
Impulse Response Functions – Model Exchange Rate and External
Variables
Note: The first row shows the responses of the log of real GDP to a
standardized monetary shock, while the second row displays the responses of
inflation to the same shock. From left to right: RR shock with Central Bank
expectations, RR shock with Focus expectations and yield curve factor
shock.
The results of the model with the inclusion of the exchange rate and external
variables in the VAR show that the RR shocks measures now lead to a decline in
inflation. One possibility is that, since the model with RR shock with Central Bank
expectation was estimated from data since 1999, it includes a period in which
Brazilian economy was hit by many external shocks, particularly due to the
devaluation in early 1999, terrorist attacks in the US and Argentinean crisis in
2001. Reflecting these events, presumably foreign developments exerted pressure on
Brazilian inflation through the tradeable prices, and the inclusion of the exchange
rate and external variable helps to control for them, ultimately "solving" the price
puzzle.
Finally, fiscal variables, represented by the Gross and Net Debt as a percentage of
GDP, were included in the VAR. Luporini
(2008) reports that the inclusion of the ratio of Net Debt to GDP solved
the exchange rate puzzle in her models, meaning that the inclusion of this variable
warrants an appreciation of the exchange rate after a monetary policy shock. I
report below the results of the model that includes gross debt, due to the greater
emphasis on the evolution of gross debt in recent years, in comparison with net
debt.
For uniformity with Luporini (2008), the debt
variables were included before the monetary policy shocks, with the following
ordering: output, inflation, exchange rate, debt and monetary shocks. As before, it
was also included a measure of global trade and US interest rates exogenously in the
VARs.
Results from this larger model are presented in Figures 12 and 13.
Impulse Response Functions – Model with debt, exchange rate and
external variables
Note: The first row shows the responses of the log of real GDP to a
standardized monetary shock, while the second row displays the responses of
inflation to the same shock. From left to right: RR shock with Central Bank
expectations, RR shock with Focus expectations and yield curve factor
shock.
Impulse Response Functions – Model with debt, exchange rate and
external variables
Note: The first row shows the responses of the log of the exchange rate to a
standardized monetary shock, while the second row displays the responses of
gross debt to the same shock. From left to right: RR shock with Central Bank
expectations, RR shock with Focus expectations and yield curve factor
shock.
The results from this larger VAR, that includes fiscal and external variables, does
not change substantially from those of a model that does not include debt. Real GDP
falls in all cases. The impulse response continue to indicate a fall in inflation
when the RR shocks hit the economy, although in this case, the yield curve factor
does not indicate that inflation drop after the shock. For the exchange rate, the
model indicates an appreciation for the RR with market expectations and the yield
curve shock. Finally, for the gross debt, the responses point to an increase in debt
for the RR shocks, and a fall when the measure of monetary policy shock considered
is the yield curve factor. This might be rationalized by the fact that the yield
curve factor shock reflects the shape of the yield curve, while the RR shocks
reflect the policy rate, by construction. An increase in policy rate exerts an
immediate increase in debt through floating rate notes, while the impact of the
level of the yield curve on debt depends on the participation of fixed rate bonds in
the composition of the debt.
7. Conclusion
The purpose of this paper was to investigate the effects of monetary policy shocks on
the Brazilian economy, taking a comprehensive approach, by using a variety of
monetary policy shocks. The main contribution to the literature was to build new
measures of monetary policy shocks.
Based on expectations for output growth and inflation, both private and official,
measures based on Romer and Romer's (2004)
approach were built for Brazil. Measures of monetary policy shocks based on this
methodology received renewed attention recently in the studies of Coibon (2012) for the US and Cloyne and Hürtgen (2014) for the UK. For the
RR shocks, it was built a new database of forecasts of inflation and GDP growth from
the Central Bank of Brazil staff data. These forecasts appear in the technical
presentations for monetary policy meetings (COPOM) and began to be released after
the Access of Information Law. They are presented in the Appendix for other
researchers. For private forecasts, constant maturity series of expectations of
inflation and output growth were built, shown in Figures 1 and 2.
In addition to the shocks based on Romer and Romer's
(2004) methodology, a yield curve measure of monetary policy shocks was
built, following closely the approach undertaken by Barakchian and Crowe (2013) for the US, intending to see how the yield
curve reaction to monetary policy decisions feeds back into the economy. This
follows the tradition of using financial market data to identify the effects of
monetary policy. This part of the paper thus investigates how the yield curve
reaction to monetary policy reverberates on the Brazilian economy.
Regarding the results, it was found that after a standardized monetary policy shock,
real GDP declines for almost 0.5% after the shock hits the economy. For inflation,
the results show a price puzzle for all RR shocks measures in a small VAR, with
inflation initially increasing and then falling after the shock. Only for the yield
curve shock the response is negative, considering that the 95% confidence bands
remain below zero after the shock. This result could suggest that a monetary policy
strategy that maximizes its impact on the yield curve might produce better outcomes
in terms of reducing inflation, a potential avenue for research in the future. The
inclusion of commodity prices in the models did not change substantially the
results, with inflation falling under the baseline response for the RR with market
expectations and the yield curve shocks. VARs that included the exchange rate,
external variables, and gross debt showed that inflation declined for the RR shocks,
with the response being statistically significant. The exchange rate appreciates for
the RR shocks under the baseline, consistent with theory. Debt increases after the
RR shocks, and it was argued that the different response for the yield curve shocks
might be related to the nature of this shock, which is based on the yield curve.
The price puzzle found in some specifications of this paper could be rationalized, at
least to some extent, by the existence of a cost channel of monetary policy (Barth and Ramey, 2001) operating in Brazil, with
inflation initially increasing and then falling after a monetary policy shock. This
explanation argues that there is nothing wrong with the price puzzle per se, or that
the source of the puzzle in not the misspecification of the models, but only
reflects that firms must finance their wage bill in advance of production. Thus,
after an increase in the interest rate, some production costs also increase,
ultimately leading to an increase in inflation, until the demand effects dominate
and inflation begins to fall. Considering the findings of this paper, a possible
extension of this work could be the estimation of a DSGE model that includes a cost
channel of monetary policy, along the lines of Rabanal (2007) and Henzel et al. (2009).10
Another possible explanation for the price puzzle that emerged recently lies in the
foreign exchange (FX) intervention in Brazil. Tobal
and Yslas (2016) argue that the Brazilian model of FX intervention
entails inflationary costs, creating noise in the relationship between interest
rates and inflation.
Law no 12.527 of 2011, "Lei de Acesso à Informação", in Portuguese.
For GDP, the data collected usually appear on the slide "PIB" on section "Nível
de Atividade", and corresponds to the estimated figure for the end of the 4th
quarter of each year. For IPCA, the figures collected appear on section
"Preços", and correspond to the end of the year value on the slide "Estimativa
de Inflação – IPCA-DEPEC".
These authors considered as measures of monetary policy shocks the difference of
the 30-day and 360-day swap rate before and after the meetings, and the
residuals of a Taylor rule.
See Table 3.1 of Ramey (2016).
See the Appendix D of the paper for this point.
CDI is the one day interbank rate from CETIP, and follows closely the effective
Selic rate, up to a spread. Bets on the path of policy rates in Brazil are most
commonly made through DI futures. I work with constant maturity rates swap
rates, in order to overcome the difficulties posed by the fixed maturity DI
futures.
Barakchian and Crowe (2013) use Fed Funds
futures contracts for up to 5 months ahead. Therefore, I use more contracts and
with longer maturities to build the shock series.
The series were downloaded from Bloomberg Tickers: BCSWEPD, BCSWGPD, BCSWFPD,
BCSWKPD, BCSWLPD, BCSWMPD and BCSWNPD Currency.
Sistema Gerador de Séries Temporais, in Portuguese.
Rabanal (2007) estimates a DSGE model for
the US and the Euro area and finds little evidence of a cost channel of monetary
policy. In his Bayesian estimation of the model, only implausible values of the
parameter associated with the cost channel would lead to a price puzzle. On the
other hand, Henzel et al.
(2009) estimate a DSGE model with a banking sector and a cost channel
for the euro area by minimizing the distance of the impulse responses of a VAR
and those from the model, and show that a parameter configuration without the
cost channel is not successful in replicating the price puzzle observed in the
VAR model.
As opiniões expressas no artigo são exclusivamente do autor.
Appendix A - Autocorrelation Tests
Order of the VAR
Lags
Chi^{2}
Prob>Chi^{2}
Observations
Real GDP -Inflation- RR with CB expectations
2
2,73
0,97
48
Real GDP -Inflation- RR with Focus
expectations
3
9,01
0,44
48
Real GDP -Inflation- Yield Curve Factor
Shock
3
8,05
0,52
48
ICBR-Real GDP -Inflation- RR with CB
expectations
2
17,49
0,35
48
ICBR -Real GDP -Inflation- RR with Focus
expectations
2
13,23
0,66
48
ICBR-Inflation- Yield Curve Factor Shock
2
12,31
0,72
48
IMF Commodity Index-Real GDP -Inflation- RR with
CB expectations
2
10,55
0,84
47
IMF Commodity Index -Real GDP -Inflation- RR with
Focus expectations
2
11,43
0,78
48
IMF Commodity Index-Inflation- Yield Curve Factor
Shock
2
16,33
0,43
48
IMF Fuel Index-Real GDP -Inflation- RR with CB
expectations
2
14,33
0,57
47
IMF Fuel Index -Real GDP -Inflation- RR with
Focus expectations
2
15,34
0,49
48
IMF Fuel Index-Inflation- Yield Curve Factor
Shock
2
19,56
0,24
48
Real GDP -Inflation-Exchange Rate - RR with CB
expectations
2
9,80
0,88
48
Real GDP -Inflation-Exchange Rate - RR with Focus
expectations
2
15,15
0,51
48
Real GDP -Inflation- Exchange Rate -Yield Curve
Factor Shock
2
12,21
0,72
48
Real GDP -Inflation-Exchange Rate-Gross Debt - RR
with CB expectations
2
26,42
0,38
48
Real GDP -Inflation-Exchange Rate-Gross Debt - RR
with Focus expectations
2
32,83
0,14
48
Real GDP -Inflation-Exchange Rate-Gross Debt -
Yield Curve Factor Shock
2
22,38
0,61
48
Note: fd indicates that a first difference was taken the log of the
variable.
Appendix B - Database from the technical presentations of COPOM
meetings
copom
ipca_t
ipca_t+1
ipca_pond
pib_t
pib_t+1
pib_pond
23/06/1999
7,60
7,60
0,7
0,70
28/07/1999
7,90
7,90
0,7
0,70
01/09/1999
7,80
7,80
0,5
0,50
06/10/1999
7,80
4,50
5,05
0,5
0,50
10/11/1999
7,98
5,85
6,03
0,5
0,50
15/12/1999
8,94
6,20
6,20
0,8
0,80
19/01/2000
6,20
6,20
3,3
3,30
16/02/2000
6,20
6,20
3,3
3,30
22/03/2000
6,20
6,20
3,3
3,30
19/04/2000
6,20
6,20
3,6
3,60
24/05/2000
6,00
6,00
3,6
3,60
20/06/2000
5,80
5,80
3,6
3,60
19/07/2000
5,60
5,60
3,6
3,60
23/08/2000
6,54
6,54
3,8
3,80
20/09/2000
6,79
6,79
3,8
3,80
18/10/2000
6,19
6,19
3,8
3,80
22/11/2000
6,28
6,28
3,8
3,9
3,89
20/12/2000
6,06
3,81
3,81
3,8
3,9
3,90
17/01/2001
4,00
4,00
3,9
3,90
14/02/2001
4,09
4,09
3,9
3,90
21/03/2001
4,20
4,20
3,9
3,90
18/04/2001
4,50
4,50
4,3
4,30
23/05/2001
5,63
5,63
2,2
2,20
20/06/2001
5,80
5,80
2,8
2,80
18/07/2001
5,87
5,87
2,5
2,50
22/08/2001
6,32
6,32
2,1
2,10
19/09/2001
6,59
6,59
1,9
1,90
17/10/2001
6,46
6,46
2
2
2,00
21/11/2001
7,35
7,35
2
2,2
2,18
18/12/2001
7,35
4,60
4,60
2
2,5
2,50
23/01/2002
4,49
4,49
2,5
2,50
20/02/2002
4,77
4,77
2,5
2,50
20/03/2002
5,09
5,09
2,5
2,50
17/04/2002
5,56
5,56
2,7
2,70
22/05/2002
5,46
5,46
2,4
2,40
19/06/2002
5,47
5,47
2,2
2,20
17/07/2002
5,81
5,81
1,8
1,80
21/08/2002
6,43
6,43
1,5
1,50
18/09/2002
6,64
4,49
5,03
1,5
1,50
23/10/2002
7,62
5,58
5,92
1,3
2,1
1,97
20/11/2002
9,78
6,54
6,81
1,5
2,7
2,60
18/12/2002
12,48
8,46
8,46
1,6
2,8
2,80
22/01/2003
9,70
9,70
2,8
2,80
19/02/2003
11,28
11,28
2,6
2,60
19/03/2003
11,47
11,47
2,2
2,20
23/04/2003
12,00
12,00
2,2
2,20
21/05/2003
11,96
11,96
2
2,00
18/06/2003
11,48
11,48
1,5
1,50
23/07/2003
9,77
9,77
1,5
1,50
20/08/2003
9,06
9,06
1
1,00
17/09/2003
9,38
9,38
0,6
0,60
22/10/2003
9,52
9,52
0,6
0,60
19/11/2003
9,13
6,43
6,66
0,8
3,5
3,28
17/12/2003
9,17
6,11
6,11
0,3
3,5
3,50
21/01/2004
6,11
6,11
3,5
3,50
18/02/2004
6,49
6,49
3,5
3,50
17/03/2004
6,29
6,29
3,5
3,50
14/04/2004
6,53
6,53
3,5
3,50
19/05/2004
6,44
6,44
3,5
3,50
16/06/2004
6,61
6,61
3,5
3,50
21/07/2004
6,96
6,96
3,75
3,75
copom
ipca_t
ipca_t+1
ipca_pond
pib_t
pib_t+1
pib_pond
18/08/2004
6,96
6,96
3,75
3,75
15/09/2004
7,37
7,37
4,4
4,40
20/10/2004
7,24
7,24
4,4
4,40
17/11/2004
7,28
7,28
4,7
4,70
15/12/2004
7,40
5,81
5,81
5
4
4,00
19/01/2005
5,72
5,72
4
4,00
16/02/2005
5,88
5,88
4
4,00
16/03/2005
5,88
5,88
4
4,00
20/04/2005
6,00
6,00
4
4,00
18/05/2005
6,34
6,34
4
4,00
15/06/2005
6,26
6,26
3,4
3,40
20/07/2005
5,73
5,73
3,4
3,40
17/08/2005
5,50
5,50
3,4
3,40
14/09/2005
5,46
5,46
3,4
3,40
19/10/2005
5,44
5,44
3,4
3,40
23/11/2005
5,61
5,61
3,4
3,40
14/12/2005
5,71
5,71
2,6
2,60
18/01/2006
4,50
4,50
4
4,00
08/03/2006
4,50
4,50
4
4,00
19/04/2006
4,50
4,50
4
4,00
31/05/2006
4,50
4,50
4
4,00
19/07/2006
4,00
4,00
4
4,00
30/08/2006
3,79
3,79
4
4,00
18/10/2006
2,97
2,97
3,5
3,50
29/11/2006
3,20
4,13
4,05
3,5
4,2
4,14
24/01/2007
4,13
4,13
3,8
3,80
07/03/2007
4,00
4,00
4,1
4,10
18/04/2007
4,10
4,10
4,5
4,50
06/06/2007
3,63
3,63
4,7
4,70
18/07/2007
3,72
3,72
4,7
4,70
05/09/2007
4,06
4,06
4,7
4,70
17/10/2007
3,87
3,87
4,7
4,70
05/12/2007
3,99
4,02
4,02
4,7
4,5
4,50
23/01/2008
4,42
4,42
4,5
4,50
05/03/2008
4,33
4,33
4,5
4,50
16/04/2008
4,67
4,67
4,8
4,80
04/06/2008
5,81
5,81
4,8
4,80
23/07/2008
6,54
6,54
4,8
4,80
10/09/2008
6,13
6,13
4,8
4,1
4,28
29/10/2008
6,12
6,12
5
4,1
4,25
10/12/2008
6,19
5,17
5,17
5,6
3,2
3,20
21/01/2009
4,62
4,62
3,2
3,20
11/03/2009
4,59
4,59
2
2,00
29/04/2009
4,42
4,42
0,8
0,80
10/06/2009
4,37
4,37
0,8
0,80
22/07/2009
4,53
4,53
0,8
0,80
02/09/2009
4,26
4,26
0,8
0,80
21/10/2009
4,22
4,22
0,8
0,80
09/12/2009
4,31
4,31
-0,3
5,8
5,80
27/01/2010
4,71
4,71
5,8
5,80
17/03/2010
5,23
5,23
5,8
5,80
28/04/2010
5,51
5,51
6,6
6,60
09/06/2010
5,87
5,87
6,6
6,60
21/07/2010
5,11
5,11
7,3
7,30
01/09/2010
4,83
4,83
7,3
7,30
20/10/2010
5,17
4,59
4,69
7,3
7,30
08/12/2010
5,87
4,59
4,59
7,3
4,5
4,50
19/01/2011
4,93
4,93
4,5
4,50
02/03/2011
5,46
5,46
4
4,00
20/04/2011
6,24
6,24
4
4,00
08/06/2011
6,24
6,24
4
4,00
20/07/2011
6,24
6,24
4
4,00
31/08/2011
6,33
6,33
4
4,00
19/10/2011
6,44
6,44
4
4,00
30/11/2011
6,49
5,27
5,37
3
3,00
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