تجزیه و تحلیل میزان بازده به عنوان پیش بینی نرخ تورم در برزیل: شواهدی از یک رویکرد موجکها

In the present paper we apply multiresolution decomposition in order to test if the Brazilian yield spread has informational content in the prediction of inflation. Additionally, we investigate the effect of the implementation of inflation targeting regime over this relation. The results suggest that the predictive power of the spread varies across time patterns. Inasmuch, the results indicate that the implementation of the inflation target regime was a sine qua non condition for a substantial increase in the predictive power of inflation. Overall, results suggest that wavelets transformations may be very useful in the building of forecasts of important financial variables.

A large body of empirical evidence suggests that the yield curve is a significant predictor of inflation (Berk and Van Bergeijk, 2000, Berk and Van Bergeijk, 2001, Estrella, 2005, Mishkin, 1990a, Mishkin, 1990b, Mishkin, 1991 and Schich, 1999).1 This evidence is important for financial regulators, practitioners, portfolio and risk managers as it may help in the development of forecasting models. Nonetheless, most research has applied linear regressions to study this relationship. Recent research in econometrics and statistics has shown that wavelets may be employed to unveil such relationships and empirical results have been favorable to the use of such methods in the analysis of economic phenomena.2 This paper contributes to the literature by employing such recent wavelets techniques to the analysis of inflation forecasts for the Brazilian economy.3 Estrella (2005) developed an analytical model that shows that the yield curve should help predict output and inflation under most circumstances. However, the usefulness of the yield curve as a predictor depends on the monetary policy framework under place. If monetary policy reacts to deviations of inflation from the target, then the predictive relationship would depend on the magnitudes of the reaction parameters. It is not clear whether the yield curve contains relevant information that can be helpful in forecasting inflation for emerging markets. Many emerging markets have had structural changes in monetary policy in recent years, adopting inflation targeting (IT) frameworks. An important question is whether the adoption of such regimes has provoked any changes in the predictive power of the yield curve. This is an important issue that deserves special attention. Recent literature has shown that emerging countries adopting IT regimes have experienced greater drops in inflation and in growth volatility if compared to non-targeters (Goncalves and Salles (2008)), and therefore that the adoption of IT regimes imply in concrete welfare gains. Furthermore, inflation uncertainty has been shown to have negative and significant effects on growth (Grier and Grier (2006)). Therefore, an important issue is whether with the implementation of an IT regime inflation predictability increases (inflation uncertainty decreases).4 The Brazilian case seems to be an interesting case study as it has implemented an IT framework for monetary policy in the mid 1999s. With the implementation of the IT the main concern of monetary policy was to deliver an inflation target. Brazil also let the currency float in the IT regime and employs short-term interest rates as the main instrument of monetary policy. The main contribution of this paper is that it shows that with the adoption of the IT framework in Brazil the yield curve seems to increase its forecasting power for the evolution of future inflation employing a wavelets approach. Inasmuch, the results indicate that the implementation of the IT regime was a sine qua non condition for a substantial increase in the predictive power of inflation. This result is in line with the reasoning of Estrella (2005) and sheds some light on why the predictive power may change from country to country and within samples. It seems to depend on the monetary policy framework under place. Furthermore, the paper employs a novel methodology (wavelets) and shows that the predictive power of the yield spread varies across time patterns. The remainder of the paper is structured as follows. Section 2 introduces an overview of the literature. Section 3 describes the methodology while Section 4 discusses the empirical results. Finally, a summary of important findings and key issues is offered in Section 5.

In this section we present a discussion and the results of the regression between the yield curve and inflation. In the first test, we intend to investigate the predictive power of the yield spread in a period that includes either the pre or post inflation target implementation. This way, we can make preliminary conclusions about the informational content of the yield curve in a period of almost eleven years. Our sample spans from April 1995 to March 2007, in a total of 147 observations. In this multiresolution approach, the size of the sample is a fundamental issue since the wavelet decomposition can only be applied to sample sizes that are multiple of m power of 2. Since we use 147 observations, a level 4 decomposition is feasible (9×249×24). We apply the wavelet decomposition to the level of the inflation and to each interest rate separately, and then estimate the following regression: equation(10) View the MathML source1200h(lnπt+h-lnπt)=α+βspreadt+εt+h Turn MathJax on where h is the time horizon used in the estimation. Table 2 and Table 3 content the results for the three and six-month horizon forecasts. These results indicate that for the unfiltered series, the spread is not significant for both horizons. We can affirm that this lack of informational content of the unfiltered series is related to the higher frequency components, since for the 1, 2 and 3 detail levels, the spread is not significant for both horizons. On the other hand, the results for the long-run trend present a high predictive power and also an elevated adjusted R2, suggesting that, for the studied period, we must look at the long-term relationship in order to use the spread as a predictor of inflation.From these results we can infer that the spread do not capture in its predictions short-term oscillations of inflation. The link of inflation and the term structure is related to long and consistent changes. This result can also be related to the delayed effects of monetary policy over inflation. Since inflation has a lagged response, the perception of the effect of a monetary policy change by the yield spread can only perceived after a determined period. Consequently, the short-term oscillation of inflation is not predicted by the spread. The impact of structural changes in the predictive power of the yield curve is an issue tested and defended by some authors. Benati and Goodhart (2008), testing for the ability of the spread to predict GDP growth, found a variation of the predictive power through time, and they indicate a link between this variation and structural breaks. Nakaota (2003) testing for Japan also found that a break point in July 1991, where after this point, there is an increase in the predictive ability of the spread. In order to investigate the role that the implementation of the inflation target regime in Brazil played in the predictive power of the yield spread, we use two sub-samples: one that spans from January 1995 to December 1998 in a total of 48 monthly observations, and the other from April 1999 to March 2007, in a total of 96 observations. This way, in the first sub-sample the level 4 decomposition is feasible (3×243×24), while in the second sub-sample the series is decomposed up to level 5 (3×253×25). Fig. 1 shows the wavelet decomposition of the yield spread and Fig. 2 presents the decomposition of the second sub-sample for inflation.It is worth mentioning that as a proxy for inflation we use the Brazilian CPI. Furthermore, the spread is considered as the difference between the six and one-month interest rates.10 Table 3 presents the estimation results for the first sub-sample. What can be noticed is that the significance level is very low for both time horizons, with the exception of the level 3 decomposition, that presents an unexpected high significance, which can be seen by the elevated value of the adjusted R2. Overall we can infer that for this period the yield spread is not relevant in the prediction of inflation independently if we are investigating the unfiltered series, its trend or its higher frequencies decomposition. On the other hand, Table 4, which presents the regression results for sub-sample 2 presents different results. It can be noticed that the predictive power of the yield spread is significant for both time horizons, and the estimated coefficient is significant in almost all cases. It is interesting to notice that, differently from the industrial production, the results for the three-month horizon are more relevant than the ones for the six-month.Both the unfiltered series and the trend present an elevated adjusted R2, suggesting that in case of using the yield spread in the prediction of inflation, both are more indicated relatively to the high frequency elements. Nevertheless, the results for levels 5, 4 and 1 suggest that the high-resolution properties of the series can also be useful, but in a lower level, in the prediction of inflation. It is possible to infer from the results that the response of inflation to changes in monetary policy before the IT regime was almost insignificant. This can be affirmed since the yield spread is a variable indicated to capture such response. Inasmuch, the target regime acted as an efficient link between inflation and monetary policy. After the IT, the yield spread is significant for both studied horizons, and more specifically, the long-term changes in inflation are well captured by the yield curve. It can be also affirmed that the term spread can be used, not only as a predictor of inflation, but also as a variable that measures the response of inflation to changes in monetary policy.