Bayesian Estimation of Macro-Finance DSGE Models with Stochastic Volatility

We develop a Bayesian Markov chain Monte Carlo algorithm for estimating risk premia in dynamic stochastic general equilibrium (DSGE) models with stochastic volatility. Our approach is fully Bayesian and employs an affine solution strategy that makes estimation of large-scale DSGE models computationally feasible. We use our algorithm to estimate the US equity risk premium in a DSGE model that includes time-preference, technology, investment, and volatility shocks. Time-preference and technology shocks are primarily responsible for the sizable equity risk premium in the estimated DSGE model. The estimated historical stochastic volatility and equity risk premium series display pronounced countercyclical fluctuations.