Identifying Long-Run Risks: A Bayesian Mixed-Frequency Approach

We develop a nonlinear state-space model to capture the joint dynamics of consumption, dividend growth, and asset returns. Building on Bansal and Yaron (2004), the core of our model consists of an endowment economy that is, in part, driven by a common predictable component for consumption and dividend growth. The measurement equations of our state-space model are set up to allow the use of mixed-frequency data, i.e., annual consumption data from 1929 to 1959, monthly consumption data after 1959, and monthly asset return data throughout. Our Bayesian estimation provides strong evidence for a small predictable component in consumption growth (even if asset return data are omitted from the estimation); our measurement error specification implies that consumption is measured much more precisely at annual than monthly frequency; and the estimated model is able to capture key asset pricing facts of the data.