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A Homotopy Approach to Solving Nonlinear Rational Expectation Problems

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  • Mark J. Jensen

    (Southern Illinois Univ. at Carbondale)

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 preformed slowly, homotopy theory will also help 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 improves the computing speed and global convergence properties of this algorithm.

Suggested Citation

  • Mark J. Jensen, 1995. "A Homotopy Approach to Solving Nonlinear Rational Expectation Problems," Computational Economics 9506002, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpco:9506002
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    References listed on IDEAS

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    1. Wouter J. Den Haan & Albert Marcet, 1994. "Accuracy in Simulations," Review of Economic Studies, Oxford University Press, vol. 61(1), pages 3-17.
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    Cited by:

    1. 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.
    2. 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.

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    JEL classification:

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

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