Presently there is growing interest in dynamic stochastic general equilibrium (DSGE) models that have more parameters, endogenous variables, exogenous shocks, and observables than the Smets and Wouters (2007) model, and substantial additional complexities from non-Gaussian distributions and the incorporation of time-varying volatility. The popular DYNARE software package, which has proved useful for small and medium-scale models is, however, not capable of handling such models, thus inhibiting the formulation and estimation of more realistic DSGE models. A primary goal of this paper is to introduce a user-friendly MATLAB software program designed to reliably estimate high-dimensional DSGE models. It simulates the posterior distribution by the tailored random block Metropolis-Hastings (TaRB-MH) algorithm of Chib and Ramamurthy (2010), calculates the marginal likelihood by the method of Chib (1995) and Chib and Jeliazkov (2001), and includes various post-estimation tools that are important for policy analysis, for example, functions for generating point and density forecasts. Another goal is to provide pointers on the prior, estimation, and comparison of these DSGE models. An extended version of the new Keynesian model of Leeper, Traum and Walker (2017) that has 51 parameters, 21 endogenous variables, 8 exogenous shocks, 8 observables, and 1,494 non-Gaussian and nonlinear latent variables is considered in detail.
Bayesian Estimation of Macro-Finance DSGE Models with Stochastic Volatility
Rapach, David E.,
and Tan, Fei
revised and resubmitted at
Journal of Applied Econometrics,
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.