Non-linear DSGE Models and The Central Difference Kalman Filter

This paper introduces a Quasi Maximum Likelihood (QML) approach based on the Central Difference Kalman Filter (CDKF) to estimate non-linear DSGE models with potentially non-Gaussian shocks. We argue that this estimator can be expected to be consistent and asymptotically normal for DSGE models solved up to third order. A Monte Carlo study shows that this QML estimator is basically unbiased and normally distributed infi?nite samples for DSGE models solved using a second order or a third order approximation. These results hold even when structural shocks are Gaussian, Laplace distributed, or display stochastic volatility.