Steady-state invariance in high-order Runge-Kutta discretization of optimal growth models
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.
References listed on IDEAS
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.:
- 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.
- repec:cup:cbooks:9780521331586 is not listed on IDEAS
- Lucas, Robert Jr., 1988. "On the mechanics of economic development," Journal of Monetary Economics, Elsevier, vol. 22(1), pages 3-42, July.
- 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.
- repec:cup:cbooks:9780521337465 is not listed on IDEAS
- 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.
- 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.
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: (Zhang, Lei)
If references are entirely missing, you can add them using this form.