The Application of the Kalman Filter to the Fisher Equation: Italian and German Term Structure of Interest Rates

Generalizing the Fisher equation for the term structure of interest rates, we analyse the influence of the premium risk on the long-run interest rate. The existence of the risk premium causes an inequality between the forward interest rates and the expected interest rates. We give an alternative view of the Fisher theory in which the interest rate is explained by the expected inflation rate and the variable component of the real interest rate. We estimate the regression using the Kalman filter, under the hypothesis that the agents' expectations are adaptive rather than rational. We analyse the Italian interest rates and the German interest rates over the period 1980:1-1998:1. We find that in the financial markets the monetary policy influences the agents' expectations. Credible monetary policies create rational expectations and low volatility of the interest rates. Non-credible monetary policies make the agentsÍ expectations adaptive and volatility of the interest rates high: the agentsÍ expectations change with the risk premium and with the uncertainty. The comparative analysis between the German and Italian results explains clearly the different impacts of monetary policy on expectations and volatility of interest rates. Low volatility is associated with a low risk premium (calculated as a component of the interest rate): under these conditions it is not possible to hypothesize adaptive expectations, and the Kalman filter is not useful. High volatility is associated with higher risk premium, and the agents could have adaptive expectations rather than rational expectations.