Multi-dimensional transitional dynamics : a simple numerical procedure
AbstractWe propose the relaxation algorithm as a simple and powerful method for simulating the transition process in growth models. This method has a number of important advantages: (1) It can easily deal with a wide range of dynamic systems including multi-dimensional systems with stable eigenvalues that di.er drastically in magnitude. (2) The application of the procedure is fairly user friendly. The only input required consists of the dynamic system. (3) The variant of the relaxation algorithm we propose exploits in a natural manner the in.nite time horizon, which usually underlies optimal control problems in economics. Overall, it seems that the relaxation procedure can easily cope with a large number of problems which arise frequently in the context of macroeconomic dynamic models. As an illustrative application, we simulate the transition process of the well-known Jones (1995) model.
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Bibliographic InfoPaper provided by CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich in its series CER-ETH Economics working paper series with number 04/35.
Length: 24 pages
Date of creation: Dec 2004
Date of revision:
saddlepoint problems; transitional dynamics; economic growth; multidimensional stable manifolds;
Other versions of this item:
- Trimborn, Timo & Koch, Karl-Josef & Steger, Thomas M., 2008. "Multidimensional Transitional Dynamics: A Simple Numerical Procedure," Macroeconomic Dynamics, Cambridge University Press, vol. 12(03), pages 301-319, June.
- Timo Trimborn & Karl-Josef Koch & Thomas Steger, 2006. "Multi-Dimensional Transitional Dynamics: A Simple Numberical Procedure," CESifo Working Paper Series 1745, CESifo Group Munich.
- Karl-Josef Koch & Timo Trimborn & Thomas M. Steger, 2005. "Multi-Dimensional Transitional Dynamics: A Simple Numerical Procedure," Volkswirtschaftliche DiskussionsbeitrÃ¤ge 121-05, Universität Siegen, Fakultät Wirtschaftswissenschaften, Wirtschaftsinformatik und Wirtschaftsrecht.
- C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- O40 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General
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- Jonathan Temple, 2003. "The Long-Run implications of Growth Theories," Journal of Economic Surveys, Wiley Blackwell, vol. 17(3), pages 497-510, 07.
- Benhabib Jess & Perli Roberto, 1994. "Uniqueness and Indeterminacy: On the Dynamics of Endogenous Growth," Journal of Economic Theory, Elsevier, vol. 63(1), pages 113-142, June.
- Thomas M. Steger, 2005. "Welfare Implications of Non-scale R&D-based Growth Models," Scandinavian Journal of Economics, Wiley Blackwell, vol. 107(4), pages 737-757, December.
- Brunner, Martin & Strulik, Holger, 2002.
"Solution of perfect foresight saddlepoint problems: a simple method and applications,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 26(5), pages 737-753, May.
- Martin Brunner & Holger Strulik, 2002. "Code for "Solution of Perfect Foresight Sattlepoint Problems: A Simple Method and Applications"," QM&RBC Codes 93, Quantitative Macroeconomics & Real Business Cycles.
- Paul M Romer, 1999.
"Endogenous Technological Change,"
Levine's Working Paper Archive
2135, David K. Levine.
- Mercenier, Jean & Michel, Philippe, 1994. "Discrete-Time Finite Horizon Appromixation of Infinite Horizon Optimization Problems with Steady-State Invariance," Econometrica, Econometric Society, vol. 62(3), pages 635-56, May.
- Eicher, Theo S & Turnovsky, Stephen J, 1999. " Convergence in a Two-Sector Nonscale Growth Model," Journal of Economic Growth, Springer, vol. 4(4), pages 413-28, December.
- Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
- Casey B. Mulligan & Xavier Sala-i-Martin, 1991. "A Note on the Time-Elimination Method For Solving Recursive Dynamic Economic Models," NBER Technical Working Papers 0116, National Bureau of Economic Research, Inc.
- Juillard, Michel & Laxton, Douglas & McAdam, Peter & Pioro, Hope, 1998. "An algorithm competition: First-order iterations versus Newton-based techniques," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1291-1318, August.
- Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
- Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-84, August.
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