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Using Numerical Dynamic Programming to Compare Passive and Active Learning in the Adaptive Management of Nutrients in Shallow Lakes

  • Bond, Craig A.
  • Loomis, John B.

This paper illustrates the use of dual/adaptive control methods to compare passive and active adaptive management decisions in the context of an ecosystem with a threshold effect. Using discrete-time dynamic programming techniques, we model optimal phosphorus loadings under both uncertainty about natural loadings and uncertainty regarding the critical level of phosphorus concentrations beyond which nutrient recycling begins. Active management is modeled by including the anticipated value of information (or learning) in the structure of the problem, and thus the agent can perturb the system (experiment), update beliefs, and learn about the uncertain parameter. Using this formulation, we define and value optimal experimentation both ex ante and ex post. Our simulation results show that experimentation is optimal over a large range of phosphorus concentration and belief space, though ex ante benefits are small. Furthermore, realized benefits may critically depend on the true underlying parameters of the problem.

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Paper provided by Colorado State University, Department of Agricultural and Resource Economics in its series Working Papers with number 108720.

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Date of creation: Dec 2008
Date of revision:
Handle: RePEc:ags:csdawp:108720
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  1. Klumpp, Tilman, 2006. "Linear learning in changing environments," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2577-2611, December.
  2. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
  3. Graham, Daniel A, 1981. "Cost-Benefit Analysis under Uncertainty," American Economic Review, American Economic Association, vol. 71(4), pages 715-25, September.
  4. Yaakov Bar-Shalom & Edison Tse, 1976. "Caution, Probing, and the Value of Information in the Control of Uncertain Systems," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 3, pages 323-337 National Bureau of Economic Research, Inc.
  5. Miller, Jon R & Lad, Frank, 1984. "Flexibility, learning, and irreversibility in environmental decisions: A bayesian approach," Journal of Environmental Economics and Management, Elsevier, vol. 11(2), pages 161-172, June.
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  7. Craig Bond & Y. Farzin, 2008. "Alternative Sustainability Criteria, Externalities, and Welfare in a Simple Agroecosystem Model: A Numerical Analysis," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 40(3), pages 383-399, July.
  8. Kaplan, Jonathan D. & Howitt, Richard E. & Farzin, Y. Hossein, 2003. "An information-theoretical analysis of budget-constrained nonpoint source pollution control," Journal of Environmental Economics and Management, Elsevier, vol. 46(1), pages 106-130, July.
  9. Kelly, David L. & Kolstad, Charles D., 1999. "Bayesian learning, growth, and pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 23(4), pages 491-518, February.
  10. Giovanni Immordino, 2003. "Looking for a Guide to Protect the Environment: The Development of the Precautionary Principle," Journal of Economic Surveys, Wiley Blackwell, vol. 17(5), pages 629-644, December.
  11. Wieland, Volker, 2000. "Learning by doing and the value of optimal experimentation," Journal of Economic Dynamics and Control, Elsevier, vol. 24(4), pages 501-534, April.
  12. Jean-Paul Chavas & Daniel Mullarkey, 2002. "On the Valuation of Uncertainty in Welfare Analysis," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 84(1), pages 23-38.
  13. Cunha-e-Sa, Maria A. & Santos, Vasco, 2008. "Experimentation with accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 32(2), pages 470-496, February.
  14. Fisher, Anthony C. & Hanemann, W. Michael, 1987. "Quasi-option value: Some misconceptions dispelled," Journal of Environmental Economics and Management, Elsevier, vol. 14(2), pages 183-190, June.
  15. Kendrick, David A., 2005. "Stochastic control for economic models: past, present and the paths ahead," Journal of Economic Dynamics and Control, Elsevier, vol. 29(1-2), pages 3-30, January.
  16. P. Mercado & David Kendrick, 2006. "Parameter Uncertainty and Policy Intensity: Some Extensions and Suggestions for Further Work," Computational Economics, Society for Computational Economics, vol. 27(4), pages 483-496, June.
  17. Bond, Craig A., 2008. "On the Potential Use of Adaptive Control Methods for Improving Adaptive Natural Resource Management," Working Papers 108721, Colorado State University, Department of Agricultural and Resource Economics.
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