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A Review of Tipping Points and Precaution using HJB equations

Author

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  • Aart Zeeuw

    (Tilburg University
    Royal Swedish Academy of Sciences)

Abstract

This paper analyzes three models in environmental economics with the property that tipping can occur in the ecological part of the model: the pollution control model where tipping suddenly shifts up the damage, the fishery model where tipping suddenly lowers the carrying capacity, and the Ramsey growth model where tipping suddenly decreases the total factor productivity. The question is whether the possibility of tipping gives rise to precaution in the sense of lower production, lower harvest, or higher accumulation of capital, respectively. The paper shows that precaution always results in the pollution control model but in the other two models, it depends on the elasticity of intertemporal substitution. In these models, the tipping point is uncertain, and the analysis employs a hazard rate that can be constant or state dependent. The paper shows that the Hamilton-Jacobi-Bellman equations are the appropriate framework to implement this hazard rate. The results are mostly known, but this paper puts the results together in a transparent way, using the HJB equations consistently. In this way, it pays tribute to this technique in optimal control that proves to be useful when tipping points can occur. Extensions to differential games are discussed at the end of each section.

Suggested Citation

  • Aart Zeeuw, 2024. "A Review of Tipping Points and Precaution using HJB equations," Dynamic Games and Applications, Springer, vol. 14(1), pages 253-270, March.
  • Handle: RePEc:spr:dyngam:v:14:y:2024:i:1:d:10.1007_s13235-023-00505-y
    DOI: 10.1007/s13235-023-00505-y
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    References listed on IDEAS

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    1. Ren, Bijie & Polasky, Stephen, 2014. "The optimal management of renewable resources under the risk of potential regime shift," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 195-212.
    2. Derek Lemoine & Christian Traeger, 2014. "Watch Your Step: Optimal Policy in a Tipping Climate," American Economic Journal: Economic Policy, American Economic Association, vol. 6(1), pages 137-166, February.
    3. Polasky, Stephen & de Zeeuw, Aart & Wagener, Florian, 2011. "Optimal management with potential regime shifts," Journal of Environmental Economics and Management, Elsevier, vol. 62(2), pages 229-240, September.
    4. Wirl, Franz, 2007. "Do multiple Nash equilibria in Markov strategies mitigate the tragedy of the commons?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3723-3740, November.
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    More about this item

    Keywords

    Tipping points; Precaution; Pollution control; Fishery; Growth; Climate;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O44 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Environment and Growth
    • Q22 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Fishery
    • Q52 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Pollution Control Adoption and Costs; Distributional Effects; Employment Effects
    • Q54 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Climate; Natural Disasters and their Management; Global Warming

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