Inflation, Fisher Equation, and the Term Structure of Inflation Risk Premia: Theory and Evidence from Tips

Abstract

In this paper, we study inflation risk and the term structure of inflation risk premia in the U.S. nominal interest rates through the Treasury Inflation Protection Securities (TIPS) and an analytical two-factor Cox-Ingersoll-Ross (CIR) model with correlated real rate and inflation. The analytical formula facilitates the estimation of the model parameters and improves the accuracy of the valuation of nominal rates and TIPS, and especially enables us to estimate the term structure of inflation risk premia.

We use the two-factor model to evaluate the inflation-index bonds and study the relationship between the real rate and the expected inflation rate implied by the nominal Constant Maturity Treasury (CMT) rates for the period of January 1998 through December 2004. We use the Unscented Kalman Filter (UKF) to estimate the model and the inflation risk premium. The empirical evidence indicates that the expected inflation rate, as opposed to those derived from the consumer price indexes, is very stable and the inflation risk premia demonstrate a steep term structure.

Keywords: CIR term structure model of interest rates, TIPS, Unscented Kalman Filter, Inflation Risk Premium

JEL Classification: C51, G12, E43