Solving DSGE models with perturbation methods and a change of variables

This paper explores the application of the changes of variables technique to solve the stochastic neoclassical growth model. We use the method of Judd [2003. Perturbation methods with nonlinear changes of variables. Mimeo, Hoover Institution] to change variables in the computed policy functions that characterize the behavior of the economy. We report how the optimal change of variables reduces the average absolute Euler equation errors of the solution of the model by a factor of three. We also demonstrate how changes of variables correct for variations in the volatility of the economy even if we work with first-order policy functions and how we can keep a linear representation of the laws of motion of the model if we use a nearly optimal transformation. We discuss how to apply our results to estimate dynamic equilibrium economies.