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

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  • Ragni, Stefania
  • Diele, Fasma
  • Marangi, Carmela
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

    Volume (Year): 34 (2010)
    Issue (Month): 7 (July)
    Pages: 1248-1259

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

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    Web page: http://www.elsevier.com/locate/jedc

    Related research

    Keywords: Optimal growth models Steady-state invariance Partitioned symplectic Runge-Kutta methods;

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    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. Mercenier, J. & Michel, P., 1995. "Temporal Aggregation in a Multi-Sector Economy with Endogenous Growth," Cahiers de recherche 9540, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. 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.
    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 635-56, May.
    5. Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
    6. Peter Kunkel & Oskar von dem Hagen, 2000. "Numerical Solution of Infinite-Horizon Optimal-Control Problems," Computational Economics, Society for Computational Economics, vol. 16(3), pages 189-205, December.
    7. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, October.
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