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A Homotopy Approach to Solving Nonlinear Rational Expectation Problems

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  • Jensen, Mark J

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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  • Jensen, Mark J, 1997. "A Homotopy Approach to Solving Nonlinear Rational Expectation Problems," Computational Economics, Springer;Society for Computational Economics, vol. 10(1), pages 47-65, February.
    • Handle: RePEc:kap:compec:v:10:y:1997:i:1:p:47-65
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    1. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(1), pages 3-17.
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    Cited by:

    1. William A. Barnett & Yi Liu & Haiyang Xu & Mark Jensen, 1996. "The CAPM Risk Adjustment Needed for Exact Aggregation over Financial Assets," Econometrics 9602003, University Library of Munich, Germany.
    2. Javier J. Pérez, 2004. "A Log-Linear Homotopy Approach to Initialize the Parameterized Expectations Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 24(1), pages 59-75, August.

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    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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