Template-Type: ReDIF-Paper 1.0
Author-Name: Viktors Ajevskis
Author-X-Name-First: Viktors
Author-X-Name-Last: Ajevskis
Author-Workplace-Name: Bank of Latvia
Title: Non-Local Solutions to Dynamic Equilibrium Models: the Approximate Stable Manifolds Approach 
Abstract: This paper presents a method to construct a sequence of approximate policy functions of increasing accuracy on non-local domains. The method is based upon the notion of stable manifold originated from dynamical systems theory. The approximate policy functions are constructed employing the contraction mapping theorem and the fact that solutions to rational expectations models converge to a steady state. The approach allows us to derive the accuracy of the approximations and their domain of definition. The method is applied to the neoclassical growth model and compared with the perturbation method. Just the second approximation of the proposed approach yields very high accuracy of the approximate solution on a global domain. In contrast to the Taylor series expansions, the solutions of the method inherit globally the properties of the true solution such as monotonicity and concavity.
Creation-Date: 2013-12-28
File-URL: https://www.bank.lv/images/stories/pielikumi/publikacijas/petijumi/WP_3_2013_Ajevskis.pdf
File-Format: Application/pdf
File-URL: https://www.macroeconomics.lv/sites/default/files/wp_3_2013_ajevskis_0.pdf
File-Format: Application/pdf
Number: 2013/03
Classification-JEL: C62, C63, D9, D58
Keywords: dynamic equilibrium, rational expectations, non-linear perfect foresight models, stable manifold, perturbation method, extended path, neoclassical growth model
X-File-Ref: https://repec.bank.lv/refs/wpaper201303.txt
Handle: RePEc:ltv:wpaper:201303