An Alternative Strategy for Estimation of a Nonlinear Model of the Term Structure of Interest Rates

Abstract

This paper develops and tests a nonlinear general equilibrium model of the term structure of interest rates based on the framework of Cox, Ingersoll and Ross (CIR, 1985). The contributions of this paper to the literature are both theoretical and empirical. The theoretical advantages of the general equilibrium model developed in this paper over the CIR model are (a) the risk premium is endogenously derived as a nonlinear function of the instantaneous interest rate. The nonlinear model shows that the term premium need not be strictly increasing in maturity as in CIR's model; it can be either increasing or humped, a result that is consistent with recent findings by Fama (1984) and McCulloch (1987). A partial differential equation for valuing the discount bond price is presented, and a closed-form expression is derived. In an empirical application of the model, we develop a strategy for estimation which permits analysis of the model's temporal stability. Our model, like that of CIR, expresses the underlying stochastic process as a highly nonlinear function of two fundamental, time-invariant parameters. Many researchers have found that general equilibrium models such as CIR's provide quite poor explanations of the evolution of the term structure of interest rates. As an alternative strategy to that of fitting the fundamental parameters, we employ nonlinear system estimation of the unrestricted reduced-form parameters with a moving-window strategy in order to capture the term structure volatility caused by factors other than the instantaneous interest rate. We purposefully do not impose any law of motion on the estimated volatilities. This methodology is shown to have strong predictive power for the observed term structure of interest rates, both in-sample and out-of-sample.