Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function

14 Pages Posted: 28 Sep 2001

See all articles by Stephanie Schmitt-Grohé

Stephanie Schmitt-Grohé

Centre for Economic Policy Research (CEPR); National Bureau of Economic Research (NBER)

Martín Uribe

Columbia University - Graduate School of Arts and Sciences - Department of Economics; National Bureau of Economic Research (NBER)

Multiple version iconThere are 3 versions of this paper

Date Written: September 2001

Abstract

Since the seminal paper of Kydland and Prescott (1982) and King, Plosser and Rebelo (1988), it has become commonplace in macroeconomics to approximate the solution to nonlinear, dynamic general equilibrium models using linear methods. Linear approximation methods are useful to characterize certain aspects of the dynamic properties of complicated models. First-order approximation techniques are not however, well suited to handle questions such as welfare comparisons across alternative stochastic of policy environments. The problem with using linearized decision rules to evaluate second-order approximations to the objective function is that some second-order terms of the objective function are ignored when using a linearized decision rule. Such problems do not arise when the policy function is approximated to second-order or higher. In this paper we derive a second order approximation to the policy function of a dynamic, rational expectations model. Our approach follows the perturbation method described in Judd (1998) and developed further by Collard and Juillard (2001). We follow Collard and Juillard closely in notation and methodology. An important difference separates this Paper from the work of Collard and Juillard. Namely, Collard and Juillard apply what they call a bias reduction procedure to capture the fact that the policy function depends on the variance of the underlying shocks. Instead, we explicitly incorporate a scale parameter for the variance of the exogenous shocks as an argument of the policy function. In approximating the policy function, we take a second order Taylor expansion with respect to the state variables as well as this scale parameter. To illustrate its applicability, the method is used to solve the dynamics of a simple neoclassical model. The Paper closes with a brief description of a set of MATLAB programs designed to implement the method.

Keywords: Solving dynamic general equilibrium models, second order approximation, MATLAB code

JEL Classification: C63, E00

Suggested Citation

Schmitt-Grohe, Stephanie and Uribe, Martin, Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function (September 2001). Available at SSRN: https://ssrn.com/abstract=285504

Stephanie Schmitt-Grohe (Contact Author)

Centre for Economic Policy Research (CEPR) ( email )

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National Bureau of Economic Research (NBER)

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Martin Uribe

Columbia University - Graduate School of Arts and Sciences - Department of Economics ( email )

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