Download Inflation targeting - Banco Central Do Brasil

One Year of Inflation
Targeting in Brazil
Implementing Inflation
Targeting in Brazil
Joel Bogdanski
Alexandre Tombini
Sérgio Ribeiro da Costa Werlang
One Year of Inflation
Targeting in Brazil
Macroeconomic Models
 Instrumental
for managing monetary
policy under IT
 Powerful
tool for communicating
monetary policy (inflation fan charts)
One Year of Inflation
Targeting in Brazil
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 Inflation
Targeting in Brazil


Demand (IS Curve)
Supply (Phillips Curve)




exchange-rate passthrough
forward x backward looking
inflation expectation
Exchange-rate (UIP)


Building Blocks
endogenous x exogenous risk premium
Interest rate rules



Taylor type rules
predetermined path
optimal rules
One Year of Inflation
Targeting in Brazil


Demand Side (IS curve)
Non Fiscal IS
ht   0  1ht 1   2 ht  2   3rt 1   th
Fiscal IS
ht   0  1ht 1   2 ht  2   3rt 1   4 prt 1   thf
where:
h  log of output gap.
r  log of (one plus) real interest rate
Pr  log of (one plus) total primary deficit /GDP
h,hf white noise.
One Year of Inflation
Targeting in Brazil
Supply Side
(Phillips Curve)

Backward-looking
 t  1b t 1   2b t 2  3b ht 1   4b ( ptF  et )   tb

Forward-looking
 t  1f  t 1   2f Et ( t 1 )   3f ht 1   4f ( ptF  et )   t f

Combined
 t  1 t 1   2 Et ( t 1 )   3 t 2   4 ht 1   5 ( ptF  et )   tn
where:

h
pF
e
Et(.)
b, f, n
 log of one plus inflation.
 log of output gap.
 log of foreign producer price index
 log of exchange rate.
 Expectation on time t.
 white noise.
One Year of Inflation
Targeting in Brazil
Modeling the passthrough
 4  constant
 4  ( 41   42( ptF1  et 1 ))
 4   41   42 et 1
Et21   42
 4   41 2
Et 1   42
where:
pF  log of foreign producer price index.
e  log of exchange-rate.
E  exchange-rate.
Treatment of inflation
expectations
One Year of Inflation
Targeting in Brazil
 Forward-looking
Phillips curve
 Alternatives

Institutional approach
  t*i
 *
Et ( t i )   t i  1 ,
 *  2
 t i
where  t*i is the inflation target for t  i
Treatment of inflation
expectations
One Year of Inflation
Targeting in Brazil
 Alternatives

Model Consistent (recursive solution)*
Et ( t i )( 0)  {initial
guess}
Solve the model
Do
Et ( t 1 )( n1)   t 1( n ) and
solve the model
until Et ( t 1 )
( n 1)
  t 1
( n 1)
where a  b means that b is in a neighborhood of a.
* - The convergence is usually achieved in less than 20 iterations.
One Year of Inflation
Targeting in Brazil
 Exchange
Exchange-rate
determination
rate follows a UIP:
Et et 1  et  it  itF  xt
et  itF  xt  it  t
where:
e
iF
x

 log of exchange rate
 log of foreign interest rate
 log of risk premium
 residual including the expectation variations assumed
white noise
One Year of Inflation
Targeting in Brazil

Exchange-rate
determination
Modeling the risk premium


exogenous path
endogenous determination

depends on PSBR/GDP ratio (primary) and other risk
premium determinants.
N
X t   1X t 1   2PRt 3   j Z j ,t t j
j 3
where:
X  risk premium (SOT) in basis points
PR  PSBR/GDP ratio (primary)
Zj  other risk premium determinants
One Year of Inflation
Targeting in Brazil
 Taylor
Interest rate rules
type rules
it  (1   )it 1   (1 ( t   * )   2 ht   3 )
where:
  log of inflation
*  log of inflation target
h  log of output gap
i
 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
One Year of Inflation
Targeting in Brazil
 Optimal

Interest rate rules
rules
Non-stochastic simulation: find an interest rate path that
minimizes the following loss-function.
N
L   [1 ( Et ( t  r )   t* r ) 2  2 Et (ht  r )  3 (it  r ) 2 ]
2
r 1

Stochastic simulation: find an interest rate path that
minimizes the following loss function. This simulation is more
computer demanding than the non-stochastic one.
N
L   [1 Et [( t  r   t* r ) 2 ]  2 Et (ht2 r )  3 (it  r ) 2 ]
r 1
One Year of Inflation
Targeting in Brazil

Forecasting
Scenarios

Model specification


Exogenous variables


Copom defines which relations are relevant for the
monetary policy decision.
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 Inflation
Targeting in Brazil

Forecasting
Fan Chart
 Measure of central tendency


Shocks stylization


median: the model estimate the mean, median is
obtained using the variance and skewness of a two-piece
normal distribution.
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.