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Optimal regime switching and threshold effects

Author

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  • Raouf Boucekkine

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

  • Aude Pommeret

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

  • Fabien Prieur

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement)

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 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.

Suggested Citation

  • Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2013. "Optimal regime switching and threshold effects," Post-Print hal-01498249, HAL.
  • Handle: RePEc:hal:journl:hal-01498249
    Note: View the original document on HAL open archive server: https://hal-amu.archives-ouvertes.fr/hal-01498249
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    References listed on IDEAS

    as
    1. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2013. "Technological vs. Ecological Switch and the Environmental Kuznets Curve," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 95(2), pages 252-260.
    2. 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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    4. Pommeret, Aude & Schubert, Katheline, 2009. "Abatement Technology Adoption Under Uncertainty," Macroeconomic Dynamics, Cambridge University Press, vol. 13(4), pages 493-522, September.
    5. 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.
    6. Valente, Simone, 2011. "Endogenous Growth, Backstop Technology Adoption, And Optimal Jumps," Macroeconomic Dynamics, Cambridge University Press, vol. 15(3), pages 293-325, June.
    7. Tahvonen, Olli & Withagen, Cees, 1996. "Optimality of irreversible pollution accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1775-1795.
    8. Olli Tahvonen, 1997. "Fossil Fuels, Stock Externalities, and Backstop Technology," Canadian Journal of Economics, Canadian Economics Association, vol. 30(4), pages 855-874, November.
    9. Larry Karp & Jiangfeng Zhang, 2012. "Taxes versus quantities for a stock pollutant with endogenous abatement costs and asymmetric information," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(2), pages 371-409, February.
    10. Costas Azariadis & Allan Drazen, 1990. "Threshold Externalities in Economic Development," The Quarterly Journal of Economics, Oxford University Press, vol. 105(2), pages 501-526.
    11. Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-985, July.
    12. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
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    Citations

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    Cited by:

    1. Raouf Boucekkine & Carmen Camacho & Benteng Zou, 2020. "Optimal switching from competition to cooperation: a preliminary exploration," PSE Working Papers halshs-02434786, HAL.
    2. Bonneuil, N. & Boucekkine, R., 2016. "Optimal transition to renewable energy with threshold of irreversible pollution," European Journal of Operational Research, Elsevier, vol. 248(1), pages 257-262.
    3. Supratim Das Gupta, 2015. "Dynamics of Switching from Polluting Resources to Green Technologies," International Journal of Energy Economics and Policy, Econjournals, vol. 5(4), pages 1109-1124.
    4. Raouf Boucekkine & Blanca Martinez & Ramon Ruiz-Tamarit, 2013. "Optimal Sustainable Policies under Pollution Ceiling: The Demographic Side," AMSE Working Papers 1354, Aix-Marseille School of Economics, France, revised 04 Nov 2013.
    5. David de la Croix & Aude Pommeret, 2017. "Childbearing Postponement, its Option Value, and the Biological Clock," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2017016, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    6. Fouad El Ouardighi & Konstantin Kogan & Giorgio Gnecco & Marcello Sanguineti, 2020. "Transboundary pollution control and environmental absorption efficiency management," Annals of Operations Research, Springer, vol. 287(2), pages 653-681, April.
    7. Prudence Dato, 2017. "Energy Transition Under Irreversibility: A Two-Sector Approach," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 68(3), pages 797-820, November.
    8. Ngo Van Long & Fabien Prieur & Klarizze Puzon & Mabel Tidball, 2013. "Markov Perfect Equilibria in Differential Games with Regime Switching Strategies," Working Papers 13-06, LAMETA, Universtiy of Montpellier, revised Jan 2014.
    9. Fouad El Ouardighi & Hassan Benchekroun & Dieter Grass, 2016. "Self-regenerating environmental absorption efficiency and the $$\varvec{ soylent~green~scenario}$$ s o y l e n t g r e e n s c e n a r i o," Annals of Operations Research, Springer, vol. 238(1), pages 179-198, March.
    10. Robert J. R. Elliott & Ingmar Schumacher & Cees Withagen, 2020. "Suggestions for a Covid-19 Post-Pandemic Research Agenda in Environmental Economics," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(4), pages 1187-1213, August.
    11. Fouad El Ouardighi & Eugene Khmelnitsky & Marc Leandri, 0. "Production-based pollution versus deforestation: optimal policy with state-independent and-dependent environmental absorption efficiency restoration process," Annals of Operations Research, Springer, vol. 0, pages 1-26.
    12. Daria Onori, 2015. "Optimal Growth and Debt Dynamics under GDP-Based Collaterals," Working Papers halshs-01251352, HAL.
    13. Seidl, Andrea, 2019. "Zeno points in optimal control models with endogenous regime switching," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 353-368.
    14. Stefan Wrzaczek & Michael Kuhn & Ivan Frankovic, 2020. "Using Age Structure for a Multi-stage Optimal Control Model with Random Switching Time," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 1065-1082, March.
    15. Raouf Boucekkine & Fabien Prieur & Klarizze Puzon, 2014. "On the Timing of Political Regime Changes: Theory and Application to the Arab Spring," Working Papers 2014.104, Fondazione Eni Enrico Mattei.
    16. Long, Ngo Van & Prieur, Fabien & Tidball, Mabel & Puzon, Klarizze, 2017. "Piecewise closed-loop equilibria in differential games with regime switching strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 264-284.
    17. Fouad El Ouardighi & Eugene Khmelnitsky & Marc Leandri, 2020. "Production-based pollution versus deforestation: optimal policy with state-independent and-dependent environmental absorption efficiency restoration process," Annals of Operations Research, Springer, vol. 292(1), pages 1-26, September.

    More about this item

    Keywords

    Backstop technology; Irreversibility; Multi-stage optimal control; Non-renewable resources; Threshold effects;

    JEL classification:

    • Q30 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - General
    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • O33 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Technological Change: Choices and Consequences; Diffusion Processes

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