Affine Term Structure Modeling and Macroeconomic Risks at the Zero Lower Bound

Abstract

We propose the first affine term structure model able to include observable macroeconomic variables while being consistent with the zero lower bound. Using a blend of gamma processes and linear-quadratic combinations of Gaussian processes, our model-implied short-rate is non-negative and can stay extensively at its lower bound. When the nominal stochastic discount factor is given by an exponential-quadratic combination of the state variables, both physical and risk-neutral dynamics are affine. The model therefore produces nominal and real interest rates levels and forecasts as closed-form functions of the yield factors and the macroeconomy. We provide an empirical exercise on U.S. data incorporating inflation and three latent factors. We show the performance of the model in terms of fit, moments, and of the consistency of the decomposition of nominal rates in real and inflation risk premia. We illustrate the model by revisiting the results of the inflation risk premium literature. We provide a study of its dynamic behavior, of the U-shape of the pricing kernel with respect to inflation, and an analysis of the effect of the liftoff through an impulse-response exercise.