“Estimating a Model of Real and Nominal Term Structures using Treasury Yields, Inflation Forecasts, and Inflation Swap Rates” by George G. PENNACCHI
George G. PENNACCHI
University of Illinois
Federal Reserve Bank of Cleveland
Case Western Reserve University
This paper develops and estimates an equilibrium model of the term structures of nominal and real interest rates. The factors include the short term real interest rate, expected inflation, and inflation's central tendency. Additional factors are GARCH volatility processes that drive actual inflation, expected inflation, the real rate, and the central tendency. We derive analytical solutions for the prices of nominal bonds and inflation-indexed bonds that have an indexation lag, such as U.S. Treasury Inflation-Protected Securities (TIPS). Solutions for expected inflation rates and rates on inflation swaps also are derived. The model's parameters are estimated using data on nominal Treasury yields, survey forecasts of inflation, and inflation swap rates. We find that allowing for GARCH effects is particularly important for real interest rate and expected inflation processes, but that long-horizon real and inflation risk premia are relatively stable. Comparing our model prices of inflation indexed bonds to those of TIPS suggests that TIPS were underpriced prior to 2004 but subsequently were valued fairly. We also find that unexpected increases in both short run and longer run inflation implied by our model have a negative impact on stock market returns.