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Multidimensional Transitional Dynamics: A Simple Numerical Procedure

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  • TRIMBORN, TIMO
  • KOCH, KARL-JOSEF
  • STEGER, THOMAS M.

Abstract

We 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 Info

Article provided by Cambridge University Press in its journal Macroeconomic Dynamics.

Volume (Year): 12 (2008)
Issue (Month): 03 (June)
Pages: 301-319

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Handle: RePEc:cup:macdyn:v:12:y:2008:i:03:p:301-319_07

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  1. 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.
  2. Romer, Paul M, 1990. "Endogenous Technological Change," Journal of Political Economy, University of Chicago Press, vol. 98(5), pages S71-102, October.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  9. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
  10. Jonathan Temple, 2003. "The Long-Run implications of Growth Theories," Journal of Economic Surveys, Wiley Blackwell, vol. 17(3), pages 497-510, 07.
  11. 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.
  12. 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.
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