A theory of the relationship between interest rates and expected inflation is contained in the well-known hypothesis expounded by Irwin Fisher in 1930. According to the Fisher hypothesis the nominal interest rate determined by the market is made up of the expected real rate and a premium for the expected inflation rate. Furthermore, changes in nominal interest rates over time adjust to changes in expected inflation while the expected real rate remains constant. More than half a century after it was first enunciated, the Fisher hypothesis continues to be regarded as a major paradigm in economic theory.
Despite its wide acceptance by the economic community, empirical support for the Fisher hypothesis has been mixed. Initial support was provided by Fama (1975), who showed that if the expected real rate is assumed to be constant the nominal rate has a roughly one to one correspondence with the inflation rate. Subsequent researchers have, however, challenged the assumption of a constant real rate and provided alternative interpretations for the time-varying behavior of the expected real rate. For example, Nelson and Schwert (1977) show that Fama’s empirical evidence is also consistent with a process in which the real rate follows a random walk. Further evidence that the ex ante real rate follows a non-stationary stochastic process which is therefore inconsistent with Fama’s assumption of a constant real rate is provided by Cheung (1993). Carmichael and Stebbing (1983) present arguments against the Fisher hypothesis; they refer to an “inverted Fisher hypothesis,” according to which the expected after-tax real rate on financial assets moves inversely in a one to one correspondence with expected inflation, while the nominal rate remains constant over the long run. Thus, while the challenges to the constant expected real rate assumption appear to be strong, the theoretical explanation for the interest rate-inflation rate relationship is still an unsettled issue.
While the exact nature of the interest rate-inflation rate relationship is being debated, many of the competing theories acknowledge the notion that the nominal rate and future inflation rates have some systematic relationship. Empirical researchers have recognized that any such systematic relationship has useful practical implications, since the nominal interest rate observed in the market can then be used to derive information on the market’s assessment of future inflation. Mishkin (1990) formulated a model for deriving information on future inflation changes from the yield spread of the t erm structure rather than from the interest rate of a single instrument. If the term spread has information on future inflation, Mishkin’s model is very appealing because the term structure is readily observable and lends itself as a very convenient forecasting tool. Mishkin’s formulation is based on a combination of the Fisher equation with the rational expectations hypothesis. It says that the spread between the long and short rate is directly related to the expected inflation differential between the corresponding long and short horizon. He refers to the derived relation between the term spread and future inflation rates as the “inflation-change equation,” which he uses in a regression framework as a forecasting equation. The intuition for the relation between the term spread and future inflation can also be seen in a different light. Previous research has provided evidence of a relationship between the term structure and future interest rates based on the expectations theory, as in Fama (1984) . A second set of relationships exists between interest rates and future inflation, which we alluded to in the first paragraph. If these two relationships are combined, the relation between the term structure and future inflation can be viewed as the indirect link in a chain that links the term structure to changes in interest rates and changes in interest rates to future inflation. Mishkin’s tests of his “inflation-change equation” are based on US markets. He found that when the yield spread is constructed from the short end of the term structure, that is from yields of less than six months maturity, the yield spread provides no information on changes in future inflation rates. However, spreads constructed from maturities beyond nine months do have the ability to predict changes in inflation rates. On a similar note, Mishkin and Simon (1994) report on the existence of a Fisher effect in Australia. Using cointegration-based analysis they find no evidence of a short-run Fisher effect, that is short-run changes in interest rates do not indicate inflationary expectations. They find evidence, however, that longer-run levels of short-term interest rates reflect inflationary expectations.
In deriving his regression model Mishkin imp oses the restriction that the spread of the real term structure is held constant over time. But if the expected real rate is time varying, as argued in the literature cited above, the real term spread may not necessarily be a constant over time. Alles and Bhar (1995) modify Mishkin’s forecasting model by allowing the real term spread to vary over time in a random fashion. They then use the Kalman filter technique to estimate the model using Australian data. The Kalman filter commonly refers to estimation of state-space models where there are two parts, the transition equation and the measurement equation. The transition equation describes the evolution of the state variables (i.e. the parameters) and the measurement equation describes how the observations are actually generated from the state variables. Regression estimates for each time period in this case are based upon previous periods’ estimates and data up to and including the current time period. In their Kalman filter model, Alles and Bhar (1 995) specify a simple stochastic model for the expected real rate spread – the random walk. Such a specification is consistent with the arguments of Nelson and Schwert (1977) and the evidence provided by Cheung (1993). Alles and Bhar (1995) further consider the possibility that the parameter estimate of the regressor may not be constant and also may vary with time. To allow for such a variation they introduce a further modification to the inflation estimation model by allowing the parameter estimate of the yield spread to vary with time in accordance with the random walk model.
The results of the Alles and Bhar (1995) paper includes a comparative evaluation of the forecasting ability of different formulations of the inflation change equation and an assessment of the efficacy of the constant real rate assumption in the forecasting equation. They show that the Kalman filter estimations in all cases present significantly reduced sum-of-square residuals, suggesting the suitability of such models in capturing the time-varying dynamics of the system. This establishes the fact that the real rate is not constant over the period analyzed. A similar result has also been specified by Cheung (1993). However, when the coefficient of the yield spread is allowed to vary as a random walk, the coefficients lose significance, suggesting the inappropriateness of such a formulation.
