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

  • Raouf Boucekkine

    ()

    (AMSE - Aix-Marseille School of Economics - Aix-Marseille Univ. - Centre national de la recherche scientifique (CNRS) - École des Hautes Études 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 - Institut d'Administration des Entreprises (IAE) - Savoie Mont-Blanc, 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])

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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  1. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2011. "Technological vs ecological switch and the environmental Kuznets curve," Working Papers halshs-00633024, HAL.
  2. Oded Galor, 2004. "The Demographic Transition and the Emergence of Sustained Economic Growth," GE, Growth, Math methods 0409005, EconWPA.
  3. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
  4. 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).
  5. Fabien Prieur & Mabel Tidball & Cees A. Withagen, 2011. "Optimal Emission-Extraction Policy in a World of Scarcity and Irreversibility," CESifo Working Paper Series 3512, CESifo Group Munich.
  6. BOUCEKKINE, Raouf & SAGLAM, Cagri & VALLEE, Thomas, . "Technology adoption under embodiment: a two-stage optimal control approach," CORE Discussion Papers RP -1702, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Fabrizio Zampolli, 2006. "Optimal monetary policy in a regime-switching economy: the response to abrupt shifts in exchange rate dynamics," Bank of England working papers 297, Bank of England.
  8. 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.
  9. Tahvonen, Olli & Withagen, Cees, 1996. "Optimality of irreversible pollution accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1775-1795.
  10. repec:cor:louvrp:2335 is not listed on IDEAS
  11. repec:ner:tilbur:urn:nbn:nl:ui:12-3107026 is not listed on IDEAS
  12. 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.
  13. Pommeret, Aude & Schubert, Katheline, 2009. "Abatement Technology Adoption Under Uncertainty," Macroeconomic Dynamics, Cambridge University Press, vol. 13(04), pages 493-522, September.
  14. 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.
  15. Fabien Prieur, 2007. "The Environmental Kuznets Curve in a World of Irreversibility," Working Papers 2007.57, Fondazione Eni Enrico Mattei.
  16. Valente, Simone, 2011. "Endogenous Growth, Backstop Technology Adoption, And Optimal Jumps," Macroeconomic Dynamics, Cambridge University Press, vol. 15(03), pages 293-325, June.
  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.
  18. Olli Tahvonen, 1997. "Fossil Fuels, Stock Externalities, and Backstop Technology," Canadian Journal of Economics, Canadian Economics Association, vol. 30(4), pages 855-74, November.
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