IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_1745.html
   My bibliography  Save this paper

Multi-Dimensional Transitional Dynamics: A Simple Numberical Procedure

Author

Listed:
  • Timo Trimborn
  • Karl-Josef Koch
  • Thomas Steger

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 stiff differential equations and systems giving rise to a continuum of stationary equilibria. (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 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.

Suggested Citation

  • Timo Trimborn & Karl-Josef Koch & Thomas Steger, 2006. "Multi-Dimensional Transitional Dynamics: A Simple Numberical Procedure," CESifo Working Paper Series 1745, CESifo.
  • Handle: RePEc:ces:ceswps:_1745
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp1745.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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 635-656, May.
    4. Jones, Charles I, 1995. "R&D-Based Models of Economic Growth," Journal of Political Economy, University of Chicago Press, vol. 103(4), pages 759-784, August.
    5. 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.
    6. 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.
    7. Eicher, Theo S & Turnovsky, Stephen J, 1999. "Convergence in a Two-Sector Nonscale Growth Model," Journal of Economic Growth, Springer, vol. 4(4), pages 413-428, December.
    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. 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.
    10. Jonathan Temple, 2003. "The Long‐Run implications of Growth Theories," Journal of Economic Surveys, Wiley Blackwell, vol. 17(3), pages 497-510, July.
    11. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Posch, Olaf & Trimborn, Timo, 2013. "Numerical solution of dynamic equilibrium models under Poisson uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2602-2622.
    2. Olaf Posch & Timo Trimborn, 2010. "Numerical solution of continuous-time DSGE models under Poisson uncertainty," Economics Working Papers 2010-08, Department of Economics and Business Economics, Aarhus University.
    3. Mário Amorim Lopes & Fernando A. C. C. Fontes & Dalila A. C. C. Fontes, 2013. "Optimal Control of Infinite-Horizon Growth Models — A direct approach," FEP Working Papers 506, Universidade do Porto, Faculdade de Economia do Porto.
    4. Trimborn, Timo, 2007. "Anticipated Shocks in Continuous-time Optimization Models: Theoretical Investigation and Numerical Solution," Hannover Economic Papers (HEP) dp-363, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    5. 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.
    6. Stephen J. Turnovsky, 2000. "Growth in an open economy: some recent developments," Working Paper Research 05, National Bank of Belgium.
    7. Benjamin Montmartin & Nadine Massard, 2015. "Is Financial Support For Private R&D Always Justified? A Discussion Based On The Literature On Growth," Journal of Economic Surveys, Wiley Blackwell, vol. 29(3), pages 479-505, July.
    8. Simon Wiederhold, 2012. "The Role of Public Procurement in Innovation: Theory and Empirical Evidence," ifo Beiträge zur Wirtschaftsforschung, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 43.
    9. Klarl, Torben, 2016. "Pollution externalities, endogenous health and the speed of convergence in an endogenous growth model," Journal of Macroeconomics, Elsevier, vol. 50(C), pages 98-113.
    10. Dirk Bethmann & Markus Reiß, 2012. "Simplifying numerical analyses of Hamilton–Jacobi–Bellman equations," Journal of Economics, Springer, vol. 107(2), pages 101-128, October.
    11. Reiß, Markus & Bethmann, Dirk, 2003. "Transitional Dynamics in the Uzawa-Lucas Model of Endogenous Growth," SFB 373 Discussion Papers 2003,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    12. Nickel, Christiane & Rother, Philipp & Theophilopoulou, Angeliki, 2008. "Population ageing and public pension reforms in a small open economy," Working Paper Series 863, European Central Bank.
    13. Gómez Manuel A. & Sequeira Tiago Neves, 2012. "The Transitional Dynamics of an Endogenous Growth Model: Generalizing Production Functions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(5), pages 1-27, December.
    14. Volker Grossmann & Thomas M. Steger & Timo Trimborn, 2016. "Quantifying Optimal Growth Policy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(3), pages 451-485, June.
    15. De, Supriyo, 2014. "Intangible capital and growth in the ‘new economy’: Implications of a multi-sector endogenous growth model," Structural Change and Economic Dynamics, Elsevier, vol. 28(C), pages 25-42.
    16. Ragni, Stefania & Diele, Fasma & Marangi, Carmela, 2010. "Steady-state invariance in high-order Runge-Kutta discretization of optimal growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(7), pages 1248-1259, July.
    17. Eicher, Theo S. & Turnovsky, Stephen J., 2001. "Transitional dynamics in a two-sector non-scale growth model," Journal of Economic Dynamics and Control, Elsevier, vol. 25(1-2), pages 85-113, January.
    18. Ben Fine, 1998. "Endogenous Growth Theory: A Critical Assessment," Working Papers 80, Department of Economics, SOAS University of London, UK.
    19. Maria João Ribeiro, 2003. "Endogenous Growth: Analytical Review of its Generating Mechanisms," NIPE Working Papers 4/2003, NIPE - Universidade do Minho.
    20. Perez-Sebastian, Fidel, 2000. "Transitional dynamics in an R&D-based growth model with imitation: Comparing its predictions to the data," Journal of Monetary Economics, Elsevier, vol. 45(2), pages 437-461, April.

    More about this item

    Keywords

    transitional dynamics; continuous time growth models; saddle-point problems; multi-dimensional stable manifolds;
    All these keywords.

    JEL classification:

    • 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, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ces:ceswps:_1745. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/cesifde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.