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Optimal Regime Switching and Threshold Effects: Theory and Application to a Resource Extraction Problem under Irreversibility

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  • Raouf Boucekkine

    ()
    (AMSE - Aix-Marseille School of Economics - Aix-Marseille Univ. - Centre national de la recherche scientifique (CNRS) - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - Ecole Centrale Marseille (ECM), IRES-CORE - Université Catholique de Louvain)

  • Aude Pommeret

    ()
    (IREGE - Institut de Recherche en Gestion et en Economie - Université de Savoie, University of Lausanne - University of Lausanne)

  • Fabien Prieur

    ()
    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - Université Montpellier I - CNRS : UMR5474 - Institut national de la recherche agronomique (INRA) : UR1135 - Centre international de hautes études agronomiques méditerranéennes [CIHEAM])

Abstract

We consider a general control problem with two types of optimal regime switch. The first one concerns technological and/or institutional regimes indexed by a finite number of discrete parameter values, and the second features ecological-like regimes relying on given threshold values for given state variables. We propose a general optimal control framework allowing to derive the first-order optimality conditions and in particular to characterize the geometry of the shadow prices at optimal switching times (if any). We apply this new optimal control material to address the problem of the optimal management of natural resources under ecological irreversibility, and with the possibility to switch to a backstop technology.

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Paper provided by HAL in its series Working Papers with number halshs-00793200.

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Date of creation: May 2012
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Handle: RePEc:hal:wpaper:halshs-00793200

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Keywords: Multi-stage optimal control; threshold effects; irreversibility; non-renewable resources; backstop technology;

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References

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  1. Olli Tahvonen, 1997. "Fossil Fuels, Stock Externalities, and Backstop Technology," Canadian Journal of Economics, Canadian Economics Association, vol. 30(4), pages 855-74, November.
  2. Tomiyama, Ken, 1985. "Two-stage optimal control problems and optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 9(3), pages 317-337, November.
  3. Oded Galor, 2004. "The Demographic Transition and the Emergence of Sustained Economic Growth," GE, Growth, Math methods 0409005, EconWPA.
  4. Boucekkine, Raouf & Saglam, Cagri & Vall Ee, Thomas, 2004. "Technology Adoption Under Embodiment: A Two-Stage Optimal Control Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 8(02), pages 250-271, April.
  5. Fabien Prieur & Mabel Tidball & Cees Withagen, 2012. "Optimal Emission-Extraction Policy in a World of Scarcity and Irreversibility," OxCarre Working Papers 077, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
  6. Karp, Larry & Zhang, Jiangfeng, 2008. "Taxes Versus Quantities for a Stock Pollutant with Endogenous Abatement Costs and Asymmetric Information," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt84q0s8tb, Department of Agricultural & Resource Economics, UC Berkeley.
  7. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2011. "Technological vs ecological switch and the environmental Kuznets curve," Working Papers halshs-00633024, HAL.
  8. Tahvonen, Olli & Withagen, Cees, 1996. "Optimality of irreversible pollution accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1775-1795.
  9. Pommeret, Aude & Schubert, Katheline, 2009. "Abatement Technology Adoption Under Uncertainty," Macroeconomic Dynamics, Cambridge University Press, vol. 13(04), pages 493-522, September.
  10. BOUCEKKINE, Raouf & KRAWCZYK, Jacek B. & VALLEE, Thomas, . "Environmental quality versus economic performance: a dynamic game approach," CORE Discussion Papers RP -2335, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  11. Zampolli, Fabrizio, 2006. "Optimal monetary policy in a regime-switching economy: The response to abrupt shifts in exchange rate dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1527-1567.
  12. Simone Valente, 2009. "Endogenous Growth, Backstop Technology Adoption and Optimal Jumps," CER-ETH Economics working paper series 09/104, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
  13. Fabien Prieur, 2007. "The Environmental Kuznets Curve in a World of Irreversibility," Working Papers 2007.57, Fondazione Eni Enrico Mattei.
  14. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
  15. Makris, Miltiadis, 2001. "Necessary conditions for infinite-horizon discounted two-stage optimal control problems," Journal of Economic Dynamics and Control, Elsevier, vol. 25(12), pages 1935-1950, December.
  16. repec:cor:louvrp:2335 is not listed on IDEAS
  17. Parente Stephen L., 1994. "Technology Adoption, Learning-by-Doing, and Economic Growth," Journal of Economic Theory, Elsevier, vol. 63(2), pages 346-369, August.
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Cited by:
  1. Ngo Van Long & Fabien Prieur & Klarizze Puzon & Mabel Tidball, 2014. "Markov Perfect Equilibria in Differential Games with Regime Switching Strategies," CESifo Working Paper Series 4662, CESifo Group Munich.
  2. Nævdal, Eric & Vislie, Jon, 2013. "Resource Depletion and Capital Accumulation under Catastrophic Risk: Policy Actions against Stochastic Thresholds and Stock Pollution," Memorandum 24/2013, Oslo University, Department of Economics.

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