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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

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Keywords: Solving dynamic models Second-order approximation;

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  1. Henry Kim & Jinill Kim & Ernst Schaumburg & Christopher A. Sims, 2005. "Calculating and Using Second Order Accurate Solutions of Discrete Time Dynamic Equilibrium Models," Discussion Papers Series, Department of Economics, Tufts University 0505, Department of Economics, Tufts University.
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  8. Ondrej Kamenik, 2005. "Solving SDGE Models: A New Algorithm for the Sylvester Equation," Working Papers 2005/10, Czech National Bank, Research Department.
  9. Coleman, Wilbur John, II, 1990. "Solving the Stochastic Growth Model by Policy-Function Iteration," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 27-29, January.
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  11. Lombardo, Giovanni & Sutherland, Alan, 2007. "Computing second-order-accurate solutions for rational expectation models using linear solution methods," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 515-530, February.
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