Real and Nominal Interest Rates: A Discrete-Time Model and Its Continuous-Time Limit

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Abstract
I provide a general equilibrium theory of the term structure of real interest rates in a discrete-time economy. I derive the prices for one-perid and two-period real bonds and a simple recursive formula for general k-period bonds, and prove that the price formula with appropriately specified parameters converses to that of the Cox, Ingersoll, and Ross model (1985). In addition, I consider the behavior of nominal bond pries in a partial equilibrium setting in which an exogenous price level process is correlated with the real economy. Finally, I provide an illustrative empirical investigation of the model. The results indicate a significant correlation between the price level and the growth rate of consumption, which does not support the 'money neutrality' assumption underlying Cox, Ingersoll and Ross's nominal bond prices and related empirical studies, such as Gibbons and Ramaswamy (1992), Heston (1991), and Pearson and Sun (1991).