Jéssica Regina Santos Dutra

Transcription

1 Jéssica Regina Santos Dutra Econometric Forecasting The University of Kansas Brazilian Monetary Policy Introduction Whenever someone tries to determine whether something is a good investment, it is natural to compare the return of investment with the interest rate of the risk-free benchmark plus a risk premium. Government bonds are usually good benchmarks for the basis interest rate in the market. This matter is especially true when dealing with emerging economies, such as Brazil. The country depends widely on foreign direct investment, and in order to attract those, they must guarantee an average return of investment greater than developed economies. On the other hand, interest rates are also tools for monetary policy, and should be analyzed as such, helping balance the short-term tradeoff between inflation and unemployment. Taylor (1993) showed that a simple monetary policy rule was able to describe well the interest rate pattern, determined by the US Federal Reserve Bank (FED) in between 1987 and The rule shows the weight policymakers attribute to inflation and GDP gap when formulating policies. Brazil has lived a period of Hyperinflation from 1982 to 1994, when the problem was finally solved with the Real Plan, which changed the currency and reestablished price stability within the country. In 1999, to ensure price stability would endure as the focus of Brazilian Central Bank (BACEN), Brazil adopted inflation targets. The Brazilian Consumption Price Index 1, calculated by Brazilian Institute of Geography and Statistics (Instituto Brasileiro de Geografia e Estatística IBGE) was the chosen one to be the benchmark by which target would refer to. The 12 months accumulated inflation targets established were 8% for 1999, 6% for 2 and 4% for 21. A tolerance band of ±2 p.p. for each year was also determined. 1 The price index selected IPCA covers a wide sample of Brazilian households, with income between one and forty minimum wages. Includes nine metropolitan regions (São Paulo, Rio de Janeiro, Belo Horizonte, Porto Alegre, Recife, Belém, Fortaleza, Salvador e Curitiba), as well as Goiânia and the federal district.

2 Even though Brazil has come a long way, not only controlling inflation, but also experiencing significant economic growth on the past two decades, the short term interest rate is still very high, which can give potential investors perverse incentives to speculate rather than invest on Fixed Capital. Throughout this project, the short term interest rate in Brazil will be estimated using both ARMA(p,q) and VAR(p) models, seeking to capture their dynamics over time. For the VAR model, a Taylor rule based model will be estimated, having as auxiliary variable thus the deviation of inflation from its target and GDP gap. Writing the Taylor rule as a VAR, we have: (1) where is the short term interest rate; is the deviation of twelve-months accumulated inflation from its target; is GDP gap; is the long term interest rate at equilibrium; and, are the error terms of this equation system and s is the lag length,. Table 1 Data Description Symbol Description Data Origin/ Calculus rational Period Freq. Unit Short term interest rate, monetary policy tool (CDI) CETIP 199/1 213/12 Monthly % a.a. Long term interest rate, equilibrium. Estimated as the models intercept

3 IPCA twelve months accumulated IBGE National Consumption Price Index System (Sistema Nacional de Índices de Preços ao Consumidor (IBGE/SNIPC)) 199/1 213/12 Monthly % a.a. GDP Gross Domestic Product (GDP) Brazilian Bank, Economic Section Central Bulletin, Activity 199/1 213/12 Monthly R$ MM Potential GDP Production capacity of an economy in full use of its factors Inflation deviation from its target (backwardlooking) GDP gap Trend of GDP series, to be estimated through HP filter Twelve months accumulated IPCA s deviation from its target GDP deviation from its potential Source: Author s construction Where short-term interest rate is expressed by the Brazilian Interbank Deposit Certificate (Certificado de Depósito Interbancário CDI), inflation deviation is calculated by the difference between the twelve months accumulated IPCA and inflation target; GDP gap is calculated by the difference between actual GDP and its potential (estimated through Hodrick-Prescott filter); long term interest rate is estimated as the model s intercept. CDI was created on mid 198 s, and guides the title emission of financial institutions that ballast interbank market allowing the resource transfer between them. Thus, CDI determines the lending parameters for short-term in Brazil, and diary CDI rate is also used as benchmark for short term application funds. The IPCA (Brazilian Consumption Price Index) is calculated by the IBGE (Brazilian Institute of Geography and Statistics), and it is the index used to monitor inflation by the monetary authorities. The IPCA has as population target those whose revenue is in between one and forty minimum wage, who live in urban area. When graphing the data from 199M1 to 213M12, it becomes very clear the existence of a structural breakpoint. This is due to the successful monetary policy called

4 the Real Plan established in Brazil in 1994, which changed the currency and was finally able to combat hyperinflation. 5, 4, 3, 2, , Interest rate (% per month) Inflation (% per month) GDP (Nominal MM R$) The series to be forecasted is the interest rate starting on 1999M7 all the way through 213M12 (monetary policy after the adoption of inflation targets), as shown on graph below. 5, 4, 3, 4 3 2, 1, GDP INFLATION SELIC Beginning with an ARMA(p,q) model for the Short term interest rate, estimating all models from ARMA(,) to ARMA(3,3) with a constant, and then ARMA(,) to

5 ARMA(3,3) with a constant and a deterministic linear trend, the best model chosen my Schwarz info criterion was an ARMA (3,1) with a constant and a trend. All of the estimated parameters seem to be statistically significant (we fail to reject the null hypothesis that those parameters are statistically equal to zero at 5% significance). Nevertheless, once we look at this variable overtime, even though it has gone down significantly over the chosen time period, it wouldn t seem reasonable to assume a negative trend behavior for much longer, without incurring in liquidity trap. Looking at the normality of the residuals, we reject the null hypothesis of normality, given that the Jarque-Bera statistics is greater than the 5.99 critical value, as shown below.

6 Series: Residuals Sample 1999M1 213M2 Observations 161 Mean.2818 Median.1893 Maximum Minimum Std. Dev Skewness Kurtosis Jarque-Bera Probability. Also seeking to verify the residuals behavior of the regression, the correlogram and its Q-statistics is reported below. We reject the null hypothesis of the Q-statistics, showing that the residuals aren t white-noise.

7 Using the model to forecast, we have the following scenario: I II III IV I II III IV I II III IV I SELIC SELIC_UP SELIC_DOWN SELICF In fact, due to the deterministic linear trend, the forecast was consistently below the actual data. As a matter of fact, the trend coefficient has shown to be relevant is likely due to the fact that monetary policy has consistently lowered the short term interest rate up until now, but it cannot go on forever. Thus, I decided to pick up the second best model, which is an ARMA(3,1) with constant. Below is the estimation output.

8 The forecast with those parameters appears to fit the data much better than previous one I II III IV I II III IV I II III IV I SELICFC SELIC_DOWNC SELIC_UPC SELIC

9 Seeking to structure the Taylor Rule within a VAR(p) model, and then better understand a possible Brazilian Central Bank reaction function to economic conjecture, it is necessary first to construct such variables that shall reflect the economic environmental, as well as check for stationarity. In order to compute GDP gap, a Hodrick Prescott filter was applied at the series GDP, fixing a lambda=16 2, and the distance between GDP and it potential estimated by the HP filter is going to be our gap, as shown on graph below. Hodrick-Prescott Filter (lambda=16) 5, 4, 4, 2, 3, 2, 1, -2, -4, GDP Trend Cycle Running Augmented Dickey Fuller and Elliot-Rothemberg-Stock tests, we reject both tests null-hypothesis of GDP gap containing a unit root. 2 See Cusinato, Minella & Pôrto Junior (21)

10 Once we look at inflation s behavior since the adoption of inflation targets in Brazil, the scenario is as reported on the graph below. Throughout the whole period, inflation has been consistently on the upper band of the targets. The spike in 22 was due to political uncertainty on the presidential succession and power shift within the country UPPER INFLATION LOWER INFLATION_TARGET

11 According to both ADF and ERS tests, we fail to reject the null of unit root on inflation deviation from its target series, thus this series will be estimated in differences. So the VAR(p) will be restructured as shown below. p p p i t r ρ i s i t s s p ρ s π π t s s p ρ s y y t s s p ε i t π t β ρ s π π t s s p s p ρ i s i t s ρ s y y t s s p ε π t y t φ ρ s y y t s s ρ s π π t s s ρ i s i t s s ε y t VAR models from VAR(1) to VAR(8) with a constant and alternatively with a constant and a trend were tested. According to the Schwarz info criterion for VARs, the best model was a VAR(2) with a constant and a trend.

12 The VAR(2) with a constant and a trend estimation output is described below. Coefficients for lagged values of inflation deviation from its target in differences shows itself to be statistically significant in determining Selic. The result in enhanced by the Granger causality test reported as follows, although the intensity in which it happens isn t as great as expected, which can be seen in the impulse response graphs.

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15 Response to Cholesky One S.D. Innovations ± 2 S.E. Response of SELIC to SELIC Response of SELIC to D(INF_DEV) Response of SELIC to GDP_GAP Response of D(INF_DEV) to SELIC Response of D(INF_DEV) to D(INF_DEV) Response of D(INF_DEV) to GDP_GAP Response of GDP_GAP to SELIC Response of GDP_GAP to D(INF_DEV) Response of GDP_GAP to GDP_GAP 1, 1, 1, 8, 8, 8, 6, 6, 6, 4, 4, 4, 2, 2, 2, -2, , , The forecast using VAR(2) with a constant and a trend is also systematically below the actual values within the last year, even though it is within the 95% confidence bands I II III IV I II III IV I II III IV I SELIC SELIC_UPVAR SELIC_DOWNVAR SELIC (vscen Mean)

16 Thus, the second best model chosen was a VAR(2) with a constant, and no trend, as shown on the Lag length criteria below.

17 And with this VAR(2) with constant model, the forecast shows itself to be better than the one with a trend. The hypothesis for why this happens is the same as it was on the ARMA(3,1) model I II III IV I II III IV I II III IV I SELIC_DOWNVAR_C SELIC_UPVAR_C SELIC SELIC (vscen Mean) Taking into consideration the poor contribution of GDP gap and inflation deviation from its target on the VAR model, it is better to keep estimating Brazilian short term interest rate as an ARMA model, since less parameters are estimated, generating a more

18 parsimonious model. This also reveals the high discretionary character of the Brazilian monetary policy. Possible extensions of this work include: Estimation of a Threshold Auto Regressive (TAR) model, trying to capture whether the policymakers are less sensitive with inflation deviation below its target than when it is above. Estimation of backward vs. forward-looking models, as suggested by Carvalho & Moura (21) when estimating the central banks reaction functions on LAC-7 (seven greater economies in Latin America). Brazil has the advantage of estimating expected inflation on 12 months by the Brazilian Institute of Geography and Statistics IBGE. Estimation of the Taylor Rule including Exchange Rates, since it is very important on determining Foreign Investment within the country. Testing possible political effects within monetary policy. o Does change in Central Bank Presidency affect Monetary Policy? o Does change in Presidential parties change Monetary Policy? This last one has serious implications, since the foundation of the COPOM as an instrument of dissociation between fiscal and monetary policy, seeking to avoid moral hazard with regards to Seigniorage. CARVALHO, A. d.,; Moura, M. L. (21). What can Taylor Rules Say About Monetary Policy in Latin America? Journal of Macroeconomics, 2, pp CUSINATO, R. T., Minella, A., & Pôrto Junior, S. d. (21). Hiato do Produto e PIB no Brasil: uma Analise de Dados em Tempo Real. Trabalhos para Discussão - Departamento de Estudos e Pesquisas (Depep), 23, pp