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Learning Parameters in Non Linear Ecological Models


  • W. Davis Dechert

    (University of Wisconsin)

  • Sharon I. O'Donnell

    (Baylor College of Medicine)

  • William A. Brock

    (University of Wisconsin)


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

Suggested Citation

  • W. Davis Dechert & Sharon I. O'Donnell & William A. Brock, 2006. "Learning Parameters in Non Linear Ecological Models," Computing in Economics and Finance 2006 258, Society for Computational Economics.
  • Handle: RePEc:sce:scecfa:258

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. 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.
    4. John Rust, 1997. "Using Randomization to Break the Curse of Dimensionality," Econometrica, Econometric Society, vol. 65(3), pages 487-516, May.
    5. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    6. 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.
    7. Ludwig,D. & Carpenter,S. & Brock,W., 2002. "Optimal phosphorus loading for a potentially eutrophic lake," Working papers 9, Wisconsin Madison - Social Systems.
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    More about this item


    Learning; pollution; stochastic dynamic programming;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - 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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