One Year of Inflation Targeting in Brazil Implementing Inflation Targeting in Brazil Joel Bogdanski...
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One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Implementing Inflation Targeting in
BrazilJoel Bogdanski
Alexandre TombiniSérgio Ribeiro da Costa Werlang
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Macroeconomic Models
Macroeconomic Models
Instrumental for managing monetary policy under IT
Powerful tool for communicating monetary policy (inflation fan charts)
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Challenges for Macro Modeling
Challenges for Macro Modeling
Exchange-rate passthrough Endogeneization of exchange-rate
movements Forward vs. Background-looking
Phillips curve Role of inflation expectations Role of prices set by the public
sector
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Building BlocksBuilding Blocks
Demand (IS Curve) Supply (Phillips Curve)
exchange-rate passthrough forward x backward looking inflation expectation
Exchange-rate (UIP) endogenous x exogenous risk premium
Interest rate rules Taylor type rules predetermined path optimal rules
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Demand Side (IS curve)
Demand Side (IS curve)
Non Fiscal IS
Fiscal IS
where:h log of output gap.r log of (one plus) real interest ratePr log of (one plus) total primary deficit /GDPh,hf white noise.
httttt rhhh 1322110
hftttttt prrhhh 141322110
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Supply Side (Phillips Curve)
Supply Side (Phillips Curve)
Backward-looking
Forward-looking
Combined
where: log of one plus inflation.h log of output gap.pF log of foreign producer price indexe log of exchange rate.
Et(.) Expectation on time t.b, f, n white noise.
btt
Ft
bt
bt
bt
bt eph )(4132211
ftt
Ft
ft
ftt
ft
ft ephE )()( 4131211
ntt
Fttttttt ephE )()( 514231211
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Modeling the passthrough
Modeling the passthrough
where:pF log of foreign producer price index.e log of exchange-rate.E exchange-rate.
constant4
142414 te
))(( 1142414 tFt ep
422
1
422
1414
t
t
E
E
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Treatment of inflation expectations
Treatment of inflation expectations
Forward-looking Phillips curve Alternatives
Institutional approach
i t
E
it
it
it
itt
for target inflation theis where
,
2
1)(
*it
*
*
*
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Treatment of inflation expectations
Treatment of inflation expectations
Alternatives Model Consistent (recursive solution)*
where a b means that b is in a neighborhood of a.* - The convergence is usually achieved in less than 20 iterations.
)1(1
)1(1
)(1
)1(1
)0(
)( until
model the solve
and)(
Do
model theSolve
guess} initial{)(
nt
ntt
nt
ntt
itt
E
E
E
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Exchange-rate determinationExchange-rate determination
Exchange rate follows a UIP:
where:
e log of exchange rate
iF log of foreign interest rate
x log of risk premium
residual including the expectation variations assumed white noise
tttFtt
tFttttt
ixie
xiieeE
1
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Exchange-rate determinationExchange-rate determination
Modeling the risk premium exogenous path endogenous determination
depends on PSBR/GDP ratio (primary) and other risk premium determinants.
where:X risk premium (SOT) in basis pointsPR PSBR/GDP ratio (primary)Zj other risk premium determinants
N
jttjjttt j
ZPRXX3
,3211
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Interest rate rulesInterest rate rules
Taylor type rules
where: log of inflation* log of inflation targeth log of output gapi log of interest rate degree of interest rate smoothing ( = 1, conventional Taylor rule)’s arbitrarily set or obtained through an optimization procedure
Predetermined path fixed nominal rate (fan chart) budget trajectory
))(()1( 32*
11 tttt hii
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
Interest rate rulesInterest rate rules
Optimal rules Non-stochastic simulation: find an interest rate path that
minimizes the following loss-function.
Stochastic simulation: find an interest rate path that minimizes the following loss function. This simulation is more computer demanding than the non-stochastic one.
])()(])[([ 23
22
2*
11 rtrttrt
N
rrtt ihEEL
])()())(([ 23
22
2*
11 rtrttrt
N
rrtt ihEEL
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
ForecastingForecasting
Scenarios Model specification
Copom defines which relations are relevant for the monetary policy decision.
Exogenous variables The most likely path for the exogenous variables are
set by the Copom after interacting with the staff. Shocks
The timing, magnitude, variance and skewness are set by the Copom after interacting with the staff.
One Year of One Year of Inflation Targeting Inflation Targeting in Brazilin Brazil
ForecastingForecasting
Fan Chart Measure of central tendency
median: the model estimate the mean, median is obtained using the variance and skewness of a two-piece normal distribution.
Shocks stylization The magnitudes are obtained from out of model
estimation. The assessment of variance and skewness are subjective.
Variance It is calculated using the historical forecast error
as benchmark. However, it can be adjusted by subjective assessment.