Some Results on the Solution of the Neoclassical Growth Model

Jesus Fernandez-Villaverde and Juan Francisco Rubio-Ramírez
Working Paper 2003-34
December 2003

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This paper presents some new results on the solution of the stochastic neoclassical growth model with leisure. We use the method of Judd (2003) to explore how to change variables in the computed policy functions that characterize the behavior of the economy. We find a simple closed-form relation between the parameters of the linear and the loglinear solution of the model. We extend this approach to a general class of changes of variables and show how to find the optimal transformation. We thus reduce 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 model’s laws of motion if we use a nearly optimal transformation. We conclude by discussing how to apply our results to estimate dynamic equilibrium economies.

JEL classification: C63, C68, E37

Key words: dynamic equilibrium economies, computational methods, changes of variables, linear and nonlinear solution methods

The authors gratefully acknowledge Dirk Krueger and participants at SITE 2003 for useful comments. They also thank Kenneth Judd for pointing out this line of research to them. The views expressed here are the authors’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors’ responsibility.

Please address questions regarding content to Jesus Fernandez-Villaverde, University of Pennsylvania, 160 McNeil Building, 3718 Locust Walk, Philadelphia, PA 19104, 215-898-1504,, or Juan Francisco Rubio-Ramírez, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, NE, Atlanta, GA 30309-4470, 404-498-8057,