Estimating Nonlinear Economic Models Using Surrogate Transitions

We propose a novel combination of algorithms for jointly estimating parameters and unobservable states in a nonlinear state space system. We exploit an approximation to the marginal likelihood to guide a Particle Marginal Metropolis-Hastings algorithm. While this algorithm seemingly targets reduced dimension marginal distributions, it draws from a joint distribution of much higher dimension. The algorithm is demonstrated on a stochastic volatility model and a Real Business Cycle model with robust preferences.