The Term Structure with Highly Persistent Interest Rates

Abstract

If yields are assumed to have an exact unit-root, it has previously been shown that the rational expectations hypothesis of the term structure (REHTS) has been rejected by single-equation tests. However, small deviations from exact unit-root produce substantial changes in the small sample distributions of those tests and the normal approximation is no longer satisfactory. We assume that the yield of 1-period zero-coupon bond follows a local-to-unity process with parameter c (c=0 for exact unit root) and use asymptotics to derive alternative distributions, which are far better approximations to finite sample distributions. Those asymptotic distributions depend crucially on c, and that allows us to analyze the impact of small deviations from unit-root on the distribution of the tests. Interestingly, for small values of c, the results obtained in the data do not imply a rejection of the REHTS. The above results are useful only when c is known or consistently estimable. Thus, the REHTS is cast into a triangular representation, where the cointegrating vectors are a function of c. Consistent and asymptotically unbiased estimators of c are proposed. A Wald test for the restrictions imposed by the REHTS on the cointegrating relationship is derived. The relevance of the asymptotic results for samples of practical sizes is investigated with Monte Carlo simulations. The methods are applied to the yield data of McCulloch and Kwon (1993). Although the REHTS is statistically rejected, the results are encouraging and suggest interesting directions for further research.

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