A Homotopy Approach to Solving Nonlinear Rational Expectation Problems
AbstractMany 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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Bibliographic InfoArticle provided by Society for Computational Economics in its journal Computational Economics.
Volume (Year): 10 (1997)
Issue (Month): 1 (February)
Other versions of this item:
- Mark J. Jensen, 1995. "A Homotopy Approach to Solving Nonlinear Rational Expectation Problems," Computational Economics 9506002, EconWPA.
- C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Den Haan, Wouter J & Marcet, Albert, 1994.
"Accuracy in Simulations,"
Review of Economic Studies,
Wiley Blackwell, vol. 61(1), pages 3-17, January.
- 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.
- Javier J. Pérez, 2004. "A Log-Linear Homotopy Approach to Initialize the Parameterized Expectations Algorithm," Computational Economics, Society for Computational Economics, vol. 24(1), pages 59-75, 08.
- William A. Barnett & Yi Liu & Haiyang Xu & Mark Jensen, 1996.
"The CAPM Risk Adjustment Needed for Exact Aggregation over Financial Assets,"
- William Barnett & Yi Liu & Haiyang Xu & Mark Jensen, 2012. "The CAPM Risk Adjustment Needed for Exact Aggregation over Financial Assets," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201215, University of Kansas, Department of Economics, revised Sep 2012.
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