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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 - EHESS - École des hautes études en sciences sociales - Centre national de la recherche scientifique (CNRS) - Ecole Centrale Marseille (ECM) - AMU - Aix-Marseille Université, IRES-CORE - UCL - Université Catholique de Louvain)

  • Aude Pommeret

    ()

    (IREGE - Institut de Recherche en Gestion et en Economie - USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc, University of Lausanne - University of Lausanne)

  • Fabien Prieur

    ()

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - CNRS - Institut national de la recherche agronomique (INRA) - UM1 - Université Montpellier 1 - 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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Date of creation: May 2012
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Handle: RePEc:hal:wpaper:halshs-00793200
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  1. Oded Galor, 2005. "The Demographic Transition and the Emergence of Sustained Economic Growth," Journal of the European Economic Association, MIT Press, vol. 3(2-3), pages 494-504, 04/05.
  2. 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.
  3. 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.
  4. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2011. "Technological vs ecological switch and the environmental Kuznets curve," Working Papers halshs-00633024, HAL.
  5. Parente Stephen L., 1994. "Technology Adoption, Learning-by-Doing, and Economic Growth," Journal of Economic Theory, Elsevier, vol. 63(2), pages 346-369, August.
  6. Prieur, Fabien & Tidball, Mabel & Withagen, Cees, 2013. "Optimal emission-extraction policy in a world of scarcity and irreversibility," Resource and Energy Economics, Elsevier, vol. 35(4), pages 637-658.
  7. 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.
  8. Aude Pommeret & Katheline Schubert, 2009. "Abatement technology adoption under uncertainty," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00308797, HAL.
  9. 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.
  10. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
  11. repec:cor:louvrp:-2335 is not listed on IDEAS
  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. 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.
  14. Olli Tahvonen, 1997. "Fossil Fuels, Stock Externalities, and Backstop Technology," Canadian Journal of Economics, Canadian Economics Association, vol. 30(4), pages 855-74, November.
  15. Fabien Prieur, 2009. "The environmental Kuznets curve in a world of irreversibility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 57-90, July.
  16. Tahvonen, Olli & Withagen, Cees, 1996. "Optimality of irreversible pollution accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1775-1795.
  17. 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).
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