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

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-period 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 converges to that of the Cox, Ingersoll, and Ross model (1985). In addition, I consider the behavior of nominal bond prices 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 nuetrality" assumption underlying Cox, Ingersoll, and Ross's nominal bond prices and related empirical studies, such as Gibbons and Ramaswamyu (1992), Heston(1991), and Pearson and Sun (1991). Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.