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

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Author Info
Paul Gomme () (Concordia University)
Paul Klein () (University of Western Ontario)
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://www.ssc.uwo.ca/economics/faculty/klein; Fortran 90 code is available from http://alcor.concordia.ca/~pgomme/.

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File URL: http://alcor.concordia.ca/~pgomme/secondorder.pdf
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Publisher Info
Paper provided by Concordia University, Department of Economics in its series Working Papers with number 09004.

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Length: 24 pages
Date of creation: 17 Feb 2009
Date of revision: 25 Mar 2009
Handle: RePEc:crd:wpaper:09004

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Related research
Keywords: Solving dynamic models; second-order approximation;

Find related papers by JEL classification:
E0 - Macroeconomics and Monetary Economics - - General
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques

References listed on IDEAS
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  1. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
    Other versions:
  3. Christiano, Lawrence J, 2002. "Solving Dynamic Equilibrium Models by a Method of Undetermined Coefficients," Computational Economics, Springer, vol. 20(1-2), pages 21-55, October. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
  5. King, Robert G & Watson, Mark W, 2002. "System Reduction and Solution Algorithms for Singular Linear Difference Systems under Rational Expectations," Computational Economics, Springer, vol. 20(1-2), pages 57-86, October. [Downloadable!]
  6. 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. [Downloadable!]
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  7. Schmitt-Grohe, Stephanie & Uribe, Martin, 2004. "Solving dynamic general equilibrium models using a second-order approximation to the policy function," Journal of Economic Dynamics and Control, Elsevier, vol. 28(4), pages 755-775, January. [Downloadable!] (restricted)
    Other versions:
  8. King, Robert G & Plosser, Charles I & Rebelo, Sergio T, 2002. "Production, Growth and Business Cycles: Technical Appendix," Computational Economics, Springer, vol. 20(1-2), pages 87-116, October. [Downloadable!]
    Other versions:
  9. 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. [Downloadable!] (restricted)
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