Calculating and Using Second Order Accurate Solutions of Discrete Time

We describe an algorithm for calculating second order approximations to the solutions to nonlinear stochastic rational expectation models. The paper also explains methods for using such an approximate solution to generate forecasts, simulated time paths for the model, and evaluations of expected welfare differences across different versions of a model. The paper gives conditions for local validity of the approximation that allow for disturbance distributions with unbounded support and allow for non-stationarity of the solution process.