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Learning Parameters in Non Linear Ecological Models

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Author Info
W. Davis Dechert (University of Wisconsin)
Sharon I. O'Donnell (Baylor College of Medicine)
William A. Brock (University of Wisconsin)

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Abstract

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

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Publisher Info
Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 258.

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Date of creation: 04 Jul 2006
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Handle: RePEc:sce:scecfa:258

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Related research
Keywords: Learning; pollution; stochastic dynamic programming;

Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling
Q57 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Ecological Economics

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  1. 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. [Downloadable!] (restricted)
  2. repec:att:wimass:192029 is not listed on IDEAS
  3. repec:att:wimass:1920210 is not listed on IDEAS
  4. John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
    Other versions:
  5. Karl-Göran Mäler & Anastasios Xepapadeas & Aart de Zeeuw, 2003. "The Economics of Shallow Lakes," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 26(4), pages 603-624, December. [Downloadable!] (restricted)
    Other versions:
  6. 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. [Downloadable!] (restricted)
  7. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-39, May. [Downloadable!] (restricted)
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