The development of forecasting models for short and long-term interest rates has been in the research agenda for the past years and is crucial for policy modeling, portfolio and risk management and for macroeconomists (See Fletcher and Gulley, 1996). The dynamics of interest rates have important implications for the economy and its forecasts are necessary for almost all economic activities. Furthermore, long-term interest rate forecasts are useful as economic agents consider them to make decisions regarding investment and savings levels.
It is consensus in the economics literature that monetary policy matters for explaining movements in real output (short run) and inflation (long run). However, the transmission mechanism through which monetary policy affects the economy is more controversial. Central banks define short-term interest rates in the conduct of monetary policy, but it is generally accepted that aggregate-spending decisions are more closely related to long-term interest rate behavior. In other words, central banks set up short-term interest rates, which affect longer-term interest rates, which by its turn influences aggregate-spending decisions affecting real output and inflation. For this reason, understanding the relationship between short and longterm interest rates is crucial for macroeconomic modeling and the conduct of monetary policy.
In this paper we study the relationship between short and long-term interest rates for Brazil. To accomplish this purpose we estimated a vector autoregression (VAR) and a vector error correction (VEC) between the short-term interest rate SELIC, which is determined by the Monetary Policy Committee (COPOM), and the medium-term interest rate, performing out-of-sample forecasts of these variables. We then compared the forecasts from these models with the results presented by a random walk to evaluate their accuracy.
The main contribution of the paper is to evaluate whether simple VAR and VEC models can be helpful in forecasting medium-term interest rates. Besides, differently from previous literature, we test whether knowledge of the future path of short-term interest rates is useful in forecasting medium-term interest rates. It is widely perceived that central banks wish to smooth interest rates and therefore determine paths for short-term interest rates. We test whether knowledge of this future path may improve forecasting. Additionally, we test for both predictive and directional accuracy. Our main results suggest that such models perform poorly in terms of predictive accuracy but are helpful in terms of directional accuracy. Therefore, they are helpful in building qualitative scenarios for policy modeling.
The rest of the paper will be structured as follows: In section 2 we present a brief review of the literature, section 3 describes the data we used in our estimations, section 4 is the methodology, in 5 we present the empirical results and, finally, section 6 concludes the paper.
2. BRIEF LITERATURE REVIEW
The link between short and medium-term interest rates is given by the Expectations Hypothesis (EH) which suggests that monetary policy affects medium-term interest rates by directly influencing short-term rates and by altering market expectations of future short-term rates. This hypothesis is important since the term structure is one of the most relevant channel of the transmission of the monetary policy.
The equation for the EH is presented below:
[R.sup.n.sub.t] = 1/k [k-1.summation over (i=0)] E[[R.sup.m.sub.t+m]] + [[phi].sub.n.m]
where n > m, n and m stand for long and short-term, k = n / m is an integer, [R.sup.n.sub.t] is the n-period …