Quasi-Bayesian estimation of time-varying volatility in DSGE models

We propose a novel quasi‐Bayesian Metropolis‐within‐Gibbs algorithm that can be used to estimate drifts in the shock volatilities of a linearized dynamic stochastic general equilibrium (DSGE) model. The resulting volatility estimates differ from the existing approaches in two ways. First, the time variation enters non‐parametrically, so that our approach ensures consistent estimation in a wide class of processes, thereby eliminating the need to specify the volatility law of motion and alleviating the risk of invalid inference due to mis‐specification. Second, the conditional quasi‐posterior of the drifting volatilities is available in closed form, which makes inference straightforward and simplifies existing algorithms. We apply our estimation procedure to a standard DSGE model and find that the estimated volatility paths are smoother compared to alternative stochastic volatility estimates. Moreover, we demonstrate that our procedure can deliver statistically significant improvements to the density forecasts of the DSGE model compared to alternative methods.