Markov-Chain Approximation and Estimation of Nonlinear, Non-Gaussian State Space Models

I develop a new method for approximating and estimating nonlinear, non-Gaussian state space models. I show that any such model can be well approximated by a discrete-state Markov process and estimated using techniques developed in Hamilton (1989). Through Monte Carlo simulations, I demonstrate that my method outperforms popular existing methods both in terms of accuracy and computational efficiency for empirically relevant sample sizes. This finding has important implications for the estimation of nonlinear dynamic economic models, many of which are computationally intractable using exisiting methods. I illustrate an empirical application of my method by re-estimating the Wu and Xia shadow rate term structure model. When I calculate the shadow rate using the parameter estimates from my proposed filter, I find that it was as much as 2.2 percentange points lower in July 2012 than previous estimates imply