This paper introduces a quasi maximum likelihood approach based on the central difference Kalman filter to estimate non-linear dynamic stochastic general equilibrium (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. These properties are verified in a Monte Carlo study for a DSGE model solved to second and third order with structural shocks that are Gaussian, Laplace distributed, or display stochastic volatility.
