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A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily
| Citations: | 216 - 2 self |
BibTeX
@MISC{Uhlig_atoolkit,
author = {Harald Uhlig},
title = {A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily},
year = {}
}
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Abstract
Often, researchers wish to analyze nonlinear dynamic discrete-time stochastic models. This chapter 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 coefficients. This chapter contains nothing substantially new. Instead, the chapter simplifies and unifies 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 coefficients for models with a vector of endogenous state variables, to provide a general solution by characterizing 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-filtered 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 chapter are made available. This chapter should be useful for researchers and Ph.D. students alike.
Keyphrases
nonlinear dynamic stochastic model easily undetermined coefficient chapter simplifies necessary equation wide audience frequency-domain technique endogenous state variable social planner problem nonlinear dynamic discrete-time stochastic model explicit di erentiation matrix quadratic equation matlab program second order property distortionary taxation additional problem recursive equilibrium law nonlinear equation general solution hp-filtered version
