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.