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Estimating DSGE Models: Recent Advances and Future Challenges

We review the current state of the estimation of dynamic stochastic general equilibrium (DSGE) models. After introducing a general framework for dealing with DSGE models, the state-space representation, we discuss how to evaluate moments or the likelihood function implied by such a structure. We discuss, in varying degrees of detail, recent advances in the field, such as the tempered particle filter, approximated Bayesian computation, Hamiltonian Monte Carlo, variational inference, and machine learning. These methods show much promise but have not been fully explored by the DSGE community yet. We conclude by outlining three future challenges for this line of research.