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Second-order approximation of dynamic models without the use of tensors

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  • Gomme, Paul
  • Klein, Paul

Abstract

Several approaches to finding the second-order approximation to a dynamic model have been proposed recently. This paper differs from the existing literature in that it makes use of the Magnus and Neudecker (1999) definition of the Hessian matrix. The key result is a linear system of equations that characterizes the second-order coefficients. No use is made of multi-dimensional arrays or tensors, a practical implication of which is that it is much easier to transcribe the mathematical representation of the solution into usable computer code. Matlab code is available from http://paulklein.se/newsite/codes/codes.php; Fortran 90 code is available from http://alcor.concordia.ca/~pgomme/.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 35 (2011)
Issue (Month): 4 (April)
Pages: 604-615

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Handle: RePEc:eee:dyncon:v:35:y:2011:i:4:p:604-615

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Web page: http://www.elsevier.com/locate/jedc

Related research

Keywords: Solving dynamic models Second-order approximation;

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  1. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
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  7. King, Robert G & Watson, Mark W, 2002. "System Reduction and Solution Algorithms for Singular Linear Difference Systems under Rational Expectations," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 57-86, October.
  8. Tauchen, George & Hussey, Robert, 1991. "Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models," Econometrica, Econometric Society, vol. 59(2), pages 371-96, March.
  9. Giovanni Lombardo & Alan Sutherland, 2005. " Computing Second-Order-Accurate Solutions for Rational Expectation Models Using Linear Solution Methods," CDMA Conference Paper Series 0504, Centre for Dynamic Macroeconomic Analysis.
  10. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, January.
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