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Approximate Solutions to Dynamic Models - Linear Methods

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  • Harald Uhlig

Abstract

Linear Methods are often used to compute approximate solutions to dynamic models, as these models often cannot be solved analytically. Linear methods are very popular, as they can easily be implemented. Also, they provide a useful starting point for understanding more elaborate numerical methods. It shall be described here first for the example of a simple real business cycle model, including how to easily generate the log-linearized equations needed before solving the linear system. For a general framework, formulas are provided for calculating the recursive law of motion. The algorithm described here is implemented with the "toolkit" programs available per

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Bibliographic Info

Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2006-030.

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Length: 12 pages
Date of creation: Apr 2006
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Handle: RePEc:hum:wpaper:sfb649dp2006-030

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Keywords: numerical methods; linear solution method; loglinearization; dynamic stochastic general equilibrium methods; recursive law of motion;

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  1. Taylor, John B & Uhlig, Harald, 1990. "Solving Nonlinear Stochastic Growth Models: A Comparison of Alternative Solution Methods," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 8(1), pages 1-17, January.
  2. Binder, M. & Pesaran, H., 1996. "Multivariate Linear Rational Expectations Models: Characterisation of the Nature of the Solutions and Their Fully Recursive Computation," Cambridge Working Papers in Economics, Faculty of Economics, University of Cambridge 9619, Faculty of Economics, University of Cambridge.
  3. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, Econometric Society, vol. 48(5), pages 1305-11, July.
  4. Roger E. A. Farmer, 1999. "Macroeconomics of Self-fulfilling Prophecies, 2nd Edition," MIT Press Books, The MIT Press, The MIT Press, edition 2, volume 1, number 0262062038, December.
  5. Sims, Christopher A, 2002. "Solving Linear Rational Expectations Models," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 1-20, October.
  6. King, Robert G & Plosser, Charles I & Rebelo, Sergio T, 2002. "Production, Growth and Business Cycles: Technical Appendix," Computational Economics, Society for Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 87-116, October.
  7. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, Econometric Society, vol. 50(6), pages 1345-70, November.
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