A Toolkit for Analysing Nonlinear Dynamic Stochastic Models Easily

Abstract

Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This paper provides a toolkit for solving such models easily, building on log-linearizing the necessary equations characterizing the equilibrium and solving for the recursive equilibrium law of motion with the method of undetermined coe cients. This paper contains nothing substantially new. Instead, the paper simpli es and uni es existing approaches to make them accessible for a wide audience, showing how to log-linearizing the nonlinear equations without the need for explicit di erentiation, how to use the method of undetermined coe cients for models with a vector of endogenous state variables, to provide a general solution by c haracterizing the solution with a matrix quadratic equation and solving it, and to provide frequency-domain techniques to calculate the second order properties of the model in its HP-ltered version without resorting to simulations. Since the method is an Euler-equation based approach rather than an approach based on solving a social planners problem, models with externalities or distortionary taxation do not pose additional problems. MATLAB programs to carry out the calculations in this paper are made available. This paper should be useful for researchers and Ph.D. students alike.

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