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Numerical analysis of non-constant pure rate of time preference: A model of climate policy

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  • Fujii, Tomoki
  • Karp, Larry

Abstract

When current decisions affect welfare in the far-distant future, as with climate change, the use of a declining pure rate of time preference (PRTP) provides potentially important modeling flexibility. The difficulty of analyzing models with non-constant PRTP limits their application. We describe and provide software (available online) to implement an algorithm to numerically obtain a Markov perfect equilibrium for an optimal control problem with non-constant PRTP. We apply this software to a simplified version of the numerical climate change model used in the Stern Review. For our calibration, the policy recommendations are less sensitive to the PRTP than widely believed.

Suggested Citation

  • Fujii, Tomoki & Karp, Larry, 2008. "Numerical analysis of non-constant pure rate of time preference: A model of climate policy," Journal of Environmental Economics and Management, Elsevier, vol. 56(1), pages 83-101, July.
    • Handle: RePEc:eee:jeeman:v:56:y:2008:i:1:p:83-101
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    1. Frederick Ploeg & Armon Rezai, 2019. "Simple Rules for Climate Policy and Integrated Assessment," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 72(1), pages 77-108, January.
    2. Francisco Cabo & Guiomar Martín-Herrán & María Pilar Martínez-García, 2020. "Non-constant Discounting, Social Welfare and Endogenous Growth with Pollution Externalities," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(2), pages 369-403, July.
    3. Maria Arvaniti & Chandra K. Krishnamurthy & Anne-Sophie Crépin, 2019. "Time-consistent resource management with regime shifts," CER-ETH Economics working paper series 19/329, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    4. Garth Heutel, 2012. "How Should Environmental Policy Respond to Business Cycles? Optimal Policy under Persistent Productivity Shocks," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 15(2), pages 244-264, April.
    5. Jindrich Matousek & Tomas Havranek & Zuzana Irsova, 2022. "Individual discount rates: a meta-analysis of experimental evidence," Experimental Economics, Springer;Economic Science Association, vol. 25(1), pages 318-358, February.
    6. Karp, Larry & Tsur, Yacov, 2011. "Time perspective and climate change policy," Journal of Environmental Economics and Management, Elsevier, vol. 62(1), pages 1-14, July.
    7. Winkler, Ralph, 2009. "Now or Never: Environmental Protection under Hyperbolic Discounting," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy, vol. 3, pages 1-22.
    8. Chen, Fubin & Yang, Zhao & Wang, Yiping & He, Hongxia & Zhang, Yong & Zhao, Yanfeng, 2025. "Comprehensive economic, environmental and social benefit assessment for refrigeration and air-conditioning equipment combined with the social cost of carbon," Energy, Elsevier, vol. 326(C).
    9. Dietz, Simon & Venmans, Frank, 2019. "The endowment effect, discounting and the environment," Journal of Environmental Economics and Management, Elsevier, vol. 97(C), pages 67-91.
    10. Da Rocha, José María & García-Cutrín, Javier & Gutiérrez Huerta, María José & Touza, Julia, 2015. "Reconciling yield stability with international fisheries agencies precautionary preferences: the role of non constant discount factors in age structured models," DFAEII Working Papers 1988-088X, University of the Basque Country - Department of Foundations of Economic Analysis II.
    11. Karp, Larry S., "undated". "Sacrifice, discounting and climate policy: five questions," CUDARE Working Papers 51612, University of California, Berkeley, Department of Agricultural and Resource Economics.
    12. Jesus Marin-Solano & Concepcio Patxot, 2009. "Discounting Arduousness," Working Papers in Economics 230, Universitat de Barcelona. Espai de Recerca en Economia.
    13. Iverson, Terrence, 2012. "Optimal Carbon Taxes with Non-Constant Time Preference," MPRA Paper 43264, University Library of Munich, Germany.
    14. Iverson, Terrence, 2013. "Minimax regret discounting," Journal of Environmental Economics and Management, Elsevier, vol. 66(3), pages 598-608.
    15. Gersbach, Hans & Hummel, Noemi, 2016. "A development-compatible refunding scheme for a climate treaty," Resource and Energy Economics, Elsevier, vol. 44(C), pages 139-168.
    16. Mota, Rui Pedro & Nichols, Rachel, 2023. "Habitat considerations in optimal fisheries recovery," Ecological Economics, Elsevier, vol. 214(C).
    17. Terrence Iverson & Scott Denning & Sammy Zahran, 2015. "When the long run matters," Climatic Change, Springer, vol. 129(1), pages 57-72, March.
    18. Lugovoy, O. & Polbin, A., 2016. "On Intergenerational Distribution of the Burden of Greenhouse Gas Emissions," Journal of the New Economic Association, New Economic Association, vol. 31(3), pages 12-39.
    19. Terrence Iverson & Larry Karp, 2021. "Carbon Taxes and Climate Commitment with Non-constant Time Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(2), pages 764-799.
    20. Breton, Michèle & Keoula, Michel Yevenunye, 2014. "A great fish war model with asymmetric players," Ecological Economics, Elsevier, vol. 97(C), pages 209-223.
    21. Kalk, Andrei & Sorger, Gerhard, 2023. "Climate policy under political pressure," Journal of Environmental Economics and Management, Elsevier, vol. 122(C).
    22. Fujii, Tomoki, 2013. "Modeling myopia: Application to non-renewable resource extraction," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 95-104.
    23. Arvaniti, Maria & Krishnamurthy, Chandra Kiran B. & Crépin, Anne-Sophie, 2023. "Time-consistent renewable resource management with present bias and regime shifts," Journal of Economic Behavior & Organization, Elsevier, vol. 207(C), pages 479-495.
    24. Gersbach, Hans & Hummel, Noemi, 2011. "Climate Policy and Developing Countries," CEPR Discussion Papers 8685, C.E.P.R. Discussion Papers.

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