IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v34y2010i7p1248-1259.html
   My bibliography  Save this article

Steady-state invariance in high-order Runge-Kutta discretization of optimal growth models

Author

Listed:
  • Ragni, Stefania
  • Diele, Fasma
  • Marangi, Carmela

Abstract

This work deals with infinite horizon optimal growth models and uses the results in the Mercenier and Michel (1994a) paper as a starting point. Mercenier and Michel (1994a) provide a one-stage Runge-Kutta discretization of the above-mentioned models which preserves the steady state of the theoretical solution. They call this feature the "steady-state invariance property". We generalize the result of their study by considering discrete models arising from the adoption of s-stage Runge-Kutta schemes. We show that the steady-state invariance property requires two different Runge-Kutta schemes for approximating the state variables and the exponential term in the objective function. This kind of discretization is well-known in literature as a partitioned symplectic Runge-Kutta scheme. Its main consequence is that it is possible to rely on the well-stated theory of order for considering more accurate methods which generalize the first order Mercenier and Michel algorithm. Numerical examples show the efficiency and accuracy of the proposed methods up to the fourth order, when applied to test models.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:34:y:2010:i:7:p:1248-1259
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(10)00063-1
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mercenier, Jean & Michel, Philippe, 2001. "Temporal aggregation in a multi-sector economy with endogenous growth," Journal of Economic Dynamics and Control, Elsevier, pages 1179-1191.
    2. Peter Kunkel & Oskar von dem Hagen, 2000. "Numerical Solution of Infinite-Horizon Optimal-Control Problems," Computational Economics, Springer;Society for Computational Economics, vol. 16(3), pages 189-205, December.
    3. 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.
    4. 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.
    5. Alemdar, Nedim M. & Sirakaya, Sibel & Husseinov, Farhad, 2006. "Optimal time aggregation of infinite horizon control problems," Journal of Economic Dynamics and Control, Elsevier, vol. 30(4), pages 569-593, April.
    6. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, December.
    7. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Diele, F. & Marangi, C. & Ragni, S., 2011. "Exponential Lawson integration for nearly Hamiltonian systems arising in optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 1057-1067.
    2. repec:eee:apmaco:v:273:y:2016:i:c:p:290-307 is not listed on IDEAS

    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:eee:dyncon:v:34:y:2010:i:7:p:1248-1259. 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: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/jedc .

    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 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.

    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.