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

We develop a nonlinear state-space model that captures the joint dynamics of consumption, dividend growth, and asset returns. Our model consists of an economy containing a common predictable component for consumption and dividend growth and multiple stochastic volatility processes. The estimation is based on annual consumption data from 1929 to 1959, monthly consumption data after 1959, and monthly asset return data throughout. We maximize the span of the sample to recover the predictable component and use high-frequency data, whenever available, to efficiently identify the volatility processes. Our Bayesian estimation provides strong evidence for a small predictable component in consumption growth (even if asset return data are omitted from the estimation). Three independent volatility processes capture different frequency dynamics; our measurement error specification implies that consumption is measured much more precisely at an annual than monthly frequency; and the estimated model is able to capture key asset-pricing facts of the data.