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A Homotopy Approach to Solving Nonlinear Rational Expectation Problems

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Author Info
Jensen, Mark J

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Abstract

Many numerical methods have been developed in an attempt to find solutions to nonlinear rational expectations models. Because these algorithms are numerical in nature, they rely heavily on computing power and take sizeable cycles to solve. In this paper we present a numerical tool known as homotopy theory that can be applied to these methods. Homotopy theory reduces the computing time associated with an iterative algorithm by using a rational expectation problem with known solutions and transforming it into the problem at hand. If this transformation is performed slowly, homotopy theory also helps the global convergence properties of the numerical algorithm. We apply homotopy theory to Den Haan and Marcet's Parameterized Expectation Approach to show how homotopies improve the computing speed and global convergence properties of this algorithm. Citation Copyright 1997 by Kluwer Academic Publishers.

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Article provided by Springer in its journal Computational Economics.

Volume (Year): 10 (1997)
Issue (Month): 1 (February)
Pages: 47-65
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Handle: RePEc:kap:compec:v:10:y:1997:i:1:p:47-65

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  1. Wouter J. den Haan & Albert Marcet, 1993. "Accuracy in Simulations," Economics Working Papers 42, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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  1. Javier J. Pérez, 2001. "A Log-linear Homotopy Approach to Initialize the Parameterized Expectations Algorithm," Economic Working Papers at Centro de Estudios Andaluces E2001/02, Centro de Estudios Andaluces. [Downloadable!]
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This page was last updated on 2009-10-15.

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