Inflation, Rational Expectations and the Term Structure of Interest Rates

Abstract

In a number of recent papers [11] [12],2 it has been shown that, for the United States, the behaviour of the term structure of interest rates can be explained remarkably well by combining the Preferred Habitat version of the Expectation Theory with a simple and readily tractable model of the formation of expectations, a model in which expected future rates are represented by a linear function of past rates. The purpose of the present paper is to generalize that approach and to strengthen the evidence supporting it in two major directions. First, we endeavour to broaden and refine the earlier analysis by making proper allowance for one additional factor, which is entirely consistent with the spirit of the model but was not duly taken into account, namely the effect of expectations of future changes in the price level. Evidence is provided that this additional factor is empirically important and that by allowing for it one can obtain a significant improvement in fit as well as a reduction in the serial correlation of the residual error. Some further improvement can also be achieved by introducing a variable intended to measure the effect of changes in the uncertainty about the future course of interest rates on the risk premium. Our second goal is to provide independent evidence in support of both the expectation theory and of our model of expectation formation and of the determinants of the risk premium, by exploring the relation between our model and the expectation To this end we first derive expressions for the (in the least square sense) linear forecast of all future rates, conditional upon the past history of rates of interest and rates of inflation. We show that the relation between the long rate and the history of short rates and prices which is estimated in the process of fitting our term structure equation is broadly similar to the relation that would hold if, in fact, (1) the long rate were an average of expected future rates-as called for by the expectation hypothesis-and (2) the expected future rates tended to represent optimal forecasts-as called for by the rational expectation hypothesis. These results provide strong evidence in support of both hypotheses, and of our term structure model built on them. Further

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