Non-linear DSGE Models, The Central Difference Kalman Filter, and The Mean Shifted Particle Filter

This paper shows how non-linear DSGE models with potential non-normal shocks can be estimated by Quasi-Maximum Likelihood based on the Central Difference Kalman Filter (CDKF). The advantage of this estimator is that evaluating the quasi log-likelihood function only takes a fraction of a second. The second contribution of this paper is to derive a new particle filter which we term the Mean Shifted Particle Filter (MSPFb). We show that the MSPFb outperforms the standard Particle Filter by delivering more precise state estimates, and in general the MSPFb has lower Monte Carlo variation in the reported log-likelihood function.