Implementing Inflation Targeting in Brazil Joel Bogdanski Alexandre Tombini Sérgio Ribeiro da Costa Werlang

1. Implementing Inflation Targeting in Brazil Joel Bogdanski Alexandre Tombini Sérgio Ribeiro da Costa Werlang

2. Macroeconomic Models • Instrumental for managing monetary policy under IT • Powerful tool for communicating monetary policy (inflation fan charts)

3. 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

4. Building 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

5. Demand Side (IS curve) • Non Fiscal IS • Fiscal IS 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.

6. 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 index e log of exchange rate. Et(.)  Expectation on time t. b, f, n white noise.

7. Modeling the passthrough where: pF log of foreign producer price index. e log of exchange-rate. E exchange-rate.

8. Treatment of inflation expectations • Forward-looking Phillips curve • Alternatives • Institutional approach

9. 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.

10. Exchange-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

11. Exchange-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 points PR PSBR/GDP ratio (primary) Zj other risk premium determinants

12. Interest rate rules • Taylor type rules 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

13. Interest 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.

14. Forecasting • 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.

15. Forecasting • 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.