This paper shows how to use the Kalman filter (Kalman 1960) to back out the shocks of a dynamic stochastic general equilibrium model. In particular, we use the smoothing algorithm as described in Hamilton (1994) to estimate the shocks of a sticky-prices and sticky-wages model using all the...

This paper introduces a nonlinear certainty-equivalent approximation method for dynamic stochastic problems. We first introduce a novel, stable, and efficient method for computing the decision rules in deterministic dynamic economic problems. We use the results as nonlinear and global...

We highlight a state variable misspecification with one accepted method to implement stochastic volatility (SV) in DSGE models when transforming the nonlinear state-innovation dynamics to its linear representation. Although the technique is more efficient numerically, we show that it is not...

We derive recursive representations of nonlinear moving average (NLMA) perturbations of DSGE models. As the stability of higher order NLMA representations follows directly from stability at first order, these recursive representations provide rigorous support for the practice of pruning that is...

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...

We show how to use a simple perturbation method to solve non-linear rational expectation models. Drawing from the applied mathematics literature we propose a method consisting of series expansions of the non-linear system around a known solution. The variables are represented in terms of their...

I provide a solution method in the frequency domain for multivariate linear rational expectations models. The method works with the generalized Schur decomposition, providing a numerical implementation of the underlying analytic function solution methods suitable for standard DSGE estimation and...

We establish the standard procedures in solving a class of dynamic stochastic general equilibrium models with a second-order approximation to the policy function. The innovation is that the means of exogenous shocks vary with the variances. The numerical results show that second-order...