Efficient estimation of conditionally linear and Gaussian state space models

•An estimation procedure for nonlinear state space models is proposed.•Efficiency gains are obtained integrating out linear states analytically.•Nonlinear states are integrated out using Efficient Importance Sampling.•The procedure compares favorably to the particle filter.•An inflation forecasting application highlights the strengths of the approach.

An efficient estimation procedure for conditionally linear and Gaussian state space models is developed. Efficient importance sampling together with a Rao-Blackwellization step are used to construct a highly efficient estimation method that produces continuous approximations to the likelihood function, greatly enhancing simulated maximum likelihood estimation. An application where the unobserved component stochastic volatility model is used to model inflation is proposed and parameter estimates for all G7 countries are shown to be statistically different from calibrated values used in the literature. The estimated model is used to forecast inflation of these countries.