Environmental and Resource Economics

, Volume 58, Issue 4, pp 627–647 | Cite as

Repeated Experimentation to Learn About a Flow-Pollutant Threshold

  • Rolf Adriaan GroeneveldEmail author
  • Michael Springborn
  • Christopher Costello


We examine in discrete time the management of a flow pollutant that causes damage when it crosses a fixed but unknown threshold. The manager sequentially chooses a pollution level that allows learning about the threshold, thereby improving future decisions. If crossed, damage can be reversed at some cost. We analyze the conditions under which experimentation is optimal, and explore how experimentation depends on restoration costs, information about the threshold, and the discount rate. Our results suggest that the level of experimentation, defined as the difference between the optimal activity with and without learning, is non-monotonic in costs and decreasing in the discount rate. We identify two stopping boundaries for the experiment, depending on cost levels compared to the lower bound of the threshold’s interval. We show that when costs are high the stopping boundary under an infinite number of decisions is the same as when there are only two decision moments. A computational extension to more than two decisions suggests that an optimal sequence of experiments can cross the same threshold several times before experimentation ceases. These results shed light on a large class of environmental decision problems that has not been examined in the literature.


Discrete time Dynamic programming Environmental catastrophes Endogenous learning Flow pollution Reversible events Threshold effects Uncertainty 



Helpful comments on earlier versions of this article by Aart de Zeeuw, Amos Zemel, and an anonymous reviewer are gratefully acknowledged. Any remaining errors are the responsibility of the authors.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Rolf Adriaan Groeneveld
    • 1
    Email author
  • Michael Springborn
    • 2
  • Christopher Costello
    • 3
    • 4
    • 5
  1. 1.Environmental Economics and Natural Resources GroupWageningen UniversityWageningenThe Netherlands
  2. 2.Department of Environmental Science and PolicyUniversity of CaliforniaDavisUSA
  3. 3.Bren School of Environmental Science and ManagementUniversity of CaliforniaSanta BarbaraUSA
  4. 4.UMR1135 LametaMontpellierFrance
  5. 5.NBERCambridgeUSA

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