Non-Markov Gaussian Term Structure Models: The Case of Inflation

Abstract

Standard Gaussian macro-finance term structure models impose the Markov property: the conditional mean is a function of the risk factors. We relax this assumption parsimoniously, and consider models where yields are linear in the conditional mean (but not in the risk factors). To illustrate, if inflation is one of the factors, then yields should span expected inflation but not inflation. We confirm that model forecasts match the out-of-sample accuracy of survey forecasts. Second, expected and surprise yield changes can have opposite contemporaneous effects on expected inflation. We confirm the difference empirically. Third, the inflation survey forecasts and the inflation rate can be used consistently within the state equation. These three features are inconsistent with the Markov assumption. Our results hold for the US and for Canada, and the decomposition of nominal yields differs from that of the standard specification.

Keywords: Markov, Term Structure, Inflation Risk Premium, Real Yields, Inflation Forecasts, Survey of Professional Forecasters

JEL Classification: E43, E47, G12