Multi-Dimensional Transitional Dynamics: A Simple Numberical 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 stiff differential equations and systems giving rise to a continuum of stationary equilibria. (2) The application of theprocedure 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 infinite time horizon, which usually underlies optimal control problems in economics. As an illustrative application, we simulate the transition process of the Jones (1995) and the Lucas (1988) model.
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Bibliographic InfoPaper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 1745.
Date of creation: 2006
Date of revision:
transitional dynamics; continuous time growth models; saddle-point problems; multi-dimensional 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 M. Steger, 2004. "Multi-dimensional transitional dynamics : a simple numerical procedure," CER-ETH Economics working paper series 04/35, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
- 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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