Steady-state invariance in high-order Runge-Kutta discretization of optimal growth models
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Dynamics and Control.
Volume (Year): 34 (2010)
Issue (Month): 7 (July)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jedc
Optimal growth models Steady-state invariance Partitioned symplectic Runge-Kutta methods;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Martin Brunner & Holger Strulik, 2002. "Code for "Solution of Perfect Foresight Sattlepoint Problems: A Simple Method and Applications"," QM&RBC Codes 93, Quantitative Macroeconomics & Real Business Cycles.
- 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.
- Mercenier, Jean & Michel, Philippe, 2001. "Temporal aggregation in a multi-sector economy with endogenous growth," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1179-1191, August.
- Mercenier, J. & Michel, P., 1995. "Temporal Aggregation in a Multi-Sector Economy with Endogenous Growth," Cahiers de recherche 9540, Universite de Montreal, Departement de sciences economiques.
- Jean Mercenier & Philippe Michel, 1995. "Temporal aggregation in a multi-sector economy with endogenous growth," Working Papers 554, Federal Reserve Bank of Minneapolis.
- 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.
- 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.
- Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
- 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.
- Léonard,Daniel & Long,Ngo van, 1992.
"Optimal Control Theory and Static Optimization in Economics,"
Cambridge University Press, number 9780521331586, October.
- Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521337465, October.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
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 references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link 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 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.