A Bayesian local likelihood method for modelling parameter time variation in DSGE models

DSGE models have recently received considerable attention in macroeconomic analysis and forecasting. They are usually estimated using Bayesian methods, which require the computation of the likelihood function under the assumption that the parameters of the model remain fixed throughout the sample. This paper presents a Local Bayesian Likelihood method suitable for estimation of DSGE models that can accommodate time variation in all parameters of the model. There are two advantages in allowing the parameters to vary over time. The first is that it enables us to assess the possibilities of regime changes, caused by shifts in the policy preferences or the volatility of shocks, as well as the possibility of misspecification in the design of DSGE models. The second advantage is that we can compute predictive densities based on the most recent parameters' values that could provide us with more accurate forecasts. The novel Bayesian Local Likelihood method applied to the Smets and Wouters (2007) model provides evidence of time variation in the policy parameters of the model as well as the volatility of the shocks. We also show that allowing for time variation improves considerably density forecasts in comparison to the fixed parameter model and we interpret this result as evidence for the presence of stochastic volatility in the structural shocks.