An Evaluation of Alternative Empirical Models of the Term Structure of Interest Rates*

Abstract

NUMEROUS EMPIRICAL STUDIES of the term structure of interest rates have been published in recent years. Yet despite the considerable interest in the field, little effort has been devoted to a careful comparison and evaluation of the alternative hypotheses, alternative specifications, and diverse results which have been reported in the literature.' In general, the authors of empirical studies have remained content to estimate the parameters of their models and to test them for broad consistency with the data under examination. Unfortunately, it is not possible to compare these alternative models directly by examining the published statistical results since each author has chosen to examine a different sample of data. Their studies span different time periods. Moreover, some have used yearly data while others have employed quarterly, monthly or weekly observations. Most of the empirical studies have concentrated upon the bond markets in the United States, though English and Canadian data have also been analyzed. The studies have dealt with both corporate and government securities and have drawn from a variety of sources for their time series of observations. It is the purpose of this study to evaluate the alternative models and specifications by re-estimating each hypothesis using a consistent body of data. Of course, it will not be possible to prove the "correctness" of any given formulation, since a model that explains one set of observations may fail to explain another set in some subsequent experiment. On the other hand, it will be possible, as we shall see, to reject a number of formulations as inconsistent with our observations of the world and to choose among those remaining the model that best explains the data. I. THE RoLE OF EXPECTATIONSWith few exceptions there appears to be a basic agreement that expectations of

State space approach to the term structure of interest rates

“…In any case, it is difficult to verify it in the absence of explicit relationships on the co's. However, Dobson et al (1976) proved that on the assumptions of model (I) a certain recursiveness must hold among the weights wj(k) in order to ensure intertemporal consistency of the forecasts. Consistency requires that, in order to predict k periods ahead, the same sequence of weights must be shifted forward k times and the missing or future observations must be replaced by their best estimates.…”

“…If agents have observed a constant '9"'"' at all past times, they should expect 'r.IH = r. Indeed, for an unbiased forecast the following stationarity condition must hold (see Dhrymes 1981, Dobson et al 1976 …”

“…Going from the forecast r, to r,+ I a new infinite sum must be evaluated and necessarily approximated (see, for instance, Dobson et al 1976). Model (4,5), on the contrary, permits us to update the information recursively.…”

“…One of the most general descriptions of expectations formation is the infinite distributed lag model. As shown by Dobson et al (1976) a model of this kind subsumes twelve hypotheses commonly formulated in the study of term structure. We show in this paper that expectations of this kind implicitly define a scheme for recursively updating past information.…”

Finance

“…(See Dobson, Sutch and Vanderford ( 1976) for a survey of the forecasting models.) For example, consider the model of in which the short rate tends to return to a 'normal level', measured by a geometric average of past interest rates…”