Learning Parameters in Non Linear Ecological Models
This paper builds on our previous work that used a non linear stochastic dynamic programming problem to solve for the optimal level of phosphorus discharged into a watershed. Typically, there is a trade off between profits from agriculture and environmental damage due to excessive levels of phosphorus (from farm animal wastes) in the watershed of a freshwater lake. The optimal management of the level of phosphorus depends not only on the costs and benefits, but also on the physical properties of the lake and on random shocks. Some lakes are more susceptible to damage from excess levels of phosphorus than others. To determine the optimal level of phosphorus for a given lake, it is necessary to learn the physical nature of the lake and its watershed. We adapted the method of optimal control with Bayes' learning of Easley and Kiefer (Econometrica 1988) to this problem. We show that in the context of the dynamic model for the flow of phosphorus in a lake, there is complete learning, i.e., there is no bandit problem in this context. We numerically solve the model and use Monte Carlo methods to solve for the mean time to learn and to determine the sensitivity of the speed of learning with respect to changes in the variance of the shocks
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.:
- Peterson,G.D. & Carpenter,S.R. & Brock,W.A., 2002. "Uncertainty and the management of multi-state ecosystems : an apparently rational route to collapse," Working papers 10, Wisconsin Madison - Social Systems.
- Karl-Göran Mäler & Anastasios Xepapadeas & Aart de Zeeuw, 2003.
"The Economics of Shallow Lakes,"
Environmental & Resource Economics,
Springer;European Association of Environmental and Resource Economists, vol. 26(4), pages 603-624, December.
- Mäler, K-G. & Xepapadeas, A. & de Zeeuw, A.J., 2000. "The Economics of Shallow Lakes," Discussion Paper 2000-69, Tilburg University, Center for Economic Research.
- Mäler, K-G. & Xepapadeas, A. & de Zeeuw, A.J., 2003. "The economics of shallow lakes," Other publications TiSEM 368f83ad-bc2f-4ad4-b603-8, Tilburg University, School of Economics and Management.
- John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
- John Rust & Department of Economics & University of Wisconsin, 1994. "Using Randomization to Break the Curse of Dimensionality," Computational Economics 9403001, EconWPA, revised 04 Jul 1994.
- Rust, J., 1994. "Using Randomization to Break the Curse of Dimensionality," Working papers 9429, Wisconsin Madison - Social Systems.
- Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
- Dechert, W.D. & O'Donnell, S.I., 2006. "The stochastic lake game: A numerical solution," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1569-1587.
- Ludwig,D. & Carpenter,S. & Brock,W., 2002. "Optimal phosphorus loading for a potentially eutrophic lake," Working papers 9, Wisconsin Madison - Social Systems.
- Wagener, F. O. O., 2003. "Skiba points and heteroclinic bifurcations, with applications to the shallow lake system," Journal of Economic Dynamics and Control, Elsevier, vol. 27(9), pages 1533-1561, July. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:sce:scecfa:258. 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: (Christopher F. Baum)
If references are entirely missing, you can add them using this form.