Extracting Inflation Expectations from the Term Structure: the Fisher Equation in a Multivariate SDF Framework

We propose a new way of extracting inflation information from the term structure, by setting the Fisher equation in the context of the stochastic discount factor (SDF) asset pricing theory. We develop a multivariate estimation framework which models the term structure of interest rates in a manner consistent with the SDF theory while generating and including an often omitted time varying risk component in the Fisher equation. The joint distribution of excess bond returns and fundamental macroeconomic factors is modelled on the basis of the consumption CAPM, using multivariate GARCH with conditional covariances in the mean to capture the term premia. We apply this methodology to the US economy and find it offers substantial evidence in support of the Fisher equation, greatly improving its goodness of fit at horizons of up to one year.