Bayesian Estimation of Macro-Finance DSGE Models with Stochastic Volatility
64 Pages Posted: 23 Oct 2019
Date Written: October 9, 2019
Researchers are increasingly turning to dynamic stochastic general equilibrium (DSGE) models to analyze the structural foundations of risk premia. However, existing DSGE studies of risk premia rarely incorporate stochastic volatility, despite its popularity in empirical asset pricing and growing importance in empirical macroeconomics. We extend the existing literature by developing a Bayesian Markov chain Monte Carlo (MCMC) algorithm for estimating risk premia in DSGE models with stochastic volatility. We first propose a Bayesian procedure for estimating a stochastic volatility process in levels and then integrate the procedure into a larger MCMC algorithm that incorporates an affine model solution based on log-normality. The larger MCMC algorithm makes likelihood-based estimation of risk premia in DSGE models with stochastic volatility computationally feasible and efficient. We use the algorithm to estimate the US equity risk premium in a DSGE model with recursive preferences 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.
Keywords: Stochastic volatility, Gibbs sampler, Tailored proposal density, Affine solution, Equity risk premium, Risk-free rate, Structural shocks, Business cycle
JEL Classification: C11, C58, E32, E44, G12
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