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Optimal regime switching and threshold effects

Author

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  • Boucekkine, R.
  • Pommeret, A.
  • Prieur, F.

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

  • Boucekkine, R. & Pommeret, A. & Prieur, F., 2013. "Optimal regime switching and threshold effects," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2979-2997.
  • Handle: RePEc:eee:dyncon:v:37:y:2013:i:12:p:2979-2997
    DOI: 10.1016/j.jedc.2013.08.008
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    References listed on IDEAS

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    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.
    3. 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.
    4. 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.
    5. Pommeret, Aude & Schubert, Katheline, 2009. "Abatement Technology Adoption Under Uncertainty," Macroeconomic Dynamics, Cambridge University Press, vol. 13(04), pages 493-522, September.
    6. 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.
    7. Michel, Philippe, 1982. "On the Transversality Condition in Infinite Horizon Optimal Problems," Econometrica, Econometric Society, vol. 50(4), pages 975-985, July.
    8. Hamilton, James D., 1990. "Analysis of time series subject to changes in regime," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 39-70.
    9. 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.
    10. Valente, Simone, 2011. "Endogenous Growth, Backstop Technology Adoption, And Optimal Jumps," Macroeconomic Dynamics, Cambridge University Press, vol. 15(03), pages 293-325, June.
    11. Tahvonen, Olli & Withagen, Cees, 1996. "Optimality of irreversible pollution accumulation," Journal of Economic Dynamics and Control, Elsevier, vol. 20(9-10), pages 1775-1795.
    12. 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.
    13. Olli Tahvonen, 1997. "Fossil Fuels, Stock Externalities, and Backstop Technology," Canadian Journal of Economics, Canadian Economics Association, vol. 30(4), pages 855-874, November.
    14. Costas Azariadis & Allan Drazen, 1990. "Threshold Externalities in Economic Development," The Quarterly Journal of Economics, Oxford University Press, vol. 105(2), pages 501-526.
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    Citations

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    Cited by:

    1. 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.
    2. 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).
    3. 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.
    4. Daria Onori, 2015. "Optimal Growth and Debt Dynamics under GDP-Based Collaterals," Working Papers halshs-01251352, HAL.
    5. Raouf BOUCEKKINE & Blanca MARTINEZ & José Ramon RUIZ-TAMARIT, 2013. "Optimal sustainable policies under pollution ceiling: the demographic side," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 2013028, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    6. 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.
    7. repec:spr:annopr:v:238:y:2016:i:1:d:10.1007_s10479-015-2096-x is not listed on IDEAS
    8. 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.
    9. 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.
    10. 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.

    More about this item

    Keywords

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

    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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