A Toolkit for Analysing Nonlinear Dynamic Stochastic Models Easily

Abstract

An extensive treatment is provided of methods that use log‐linear approximations to solve nonlinear dynamic discrete‐time stochastic models. These methods, based on their linear counterparts, have been extensively used in the macroeconomic literature, and Uhlig simplifies, integrates, and compares them. He shows how to log‐linearize the necessary equations characterizing the equilibrium without explicit differentiation, provides a general solution to a linearized system using the method of undetermined coefficients, allowing in particular for a vector of endogenous states, and provides a simulation‐free frequency‐domain method to calculate the model implications in its Hodrick–Prescott filtered version. These methods are easy to use if a numerical package such as MATLAB is available. Examples of the approach taken are presented in an appendix, which looks at Hansen's (1985) real business cycle model for the case of saddle‐point stability (using the Blanchard–Kahn approach) and the case where equilibria may be undetermined; the appendix also describes the MATLAB programs needed to carry out the calculations.