IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v35y2011i1p25-39.html
   My bibliography  Save this article

Thinning and harvesting in stochastic forest models

Author

Listed:
  • Helmes, Kurt L.
  • Stockbridge, Richard H.

Abstract

This paper analyzes a stochastic forest growth model in which the manager is able to first thin the forest to promote better growth before harvesting. Both Wicksell single thinning and harvesting cycle and Faustmann on-going rotation problems are considered. The Wicksell problem is analyzed by first restricting the class of decision times to (thinning, harvesting) pairs that bound the growth away from infinity and imbedding the problem in an infinite-dimensional linear program on a space of triplets of measures. These measures capture the thinning and harvesting decisions along with the behavior of the growth process prior to harvest. An auxiliary linear program then leads to a nonlinear optimization problem for which an optimal value and solution are determined. The values of all the problems are be related through a set of inequalities. The solution of the nonlinear problem determines (random) thinning and harvesting times for the single thinning and harvesting cycle which demonstrate the equality of the values of these various problems. Finally for the Wicksell problem, the unrestricted class of thinning and harvest times is shown to give the same value as the restricted class. The Faustmann on-going thinning and harvesting rotation problem is reduced to a Wicksell problem which then allows for the characterization of the value as the solution to a different nonlinear optimization problem. The effects of the opportunity to thin the forest are illustrated on a mean-reverting stochastic model.

Suggested Citation

  • Helmes, Kurt L. & Stockbridge, Richard H., 2011. "Thinning and harvesting in stochastic forest models," Journal of Economic Dynamics and Control, Elsevier, vol. 35(1), pages 25-39, January.
  • Handle: RePEc:eee:dyncon:v:35:y:2011:i:1:p:25-39
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(10)00235-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. Richard R. Lumley & Mihail Zervos, 2001. "A Model for Investments in the Natural Resource Industry with Switching Costs," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 637-653, November.
    3. Willassen, Yngve, 1998. "The stochastic rotation problem: A generalization of Faustmann's formula to stochastic forest growth," Journal of Economic Dynamics and Control, Elsevier, vol. 22(4), pages 573-596, April.
    4. Newman, D.H., 2002. "Forestry's golden rule and the development of the optimal forest rotation literature," Journal of Forest Economics, Elsevier, vol. 8(1), pages 5-27.
    5. Dixit, Avinash K, 1989. "Entry and Exit Decisions under Uncertainty," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 620-638, June.
    6. Miller, Robert A. & Voltaire, Karl, 1983. "A stochastic analysis of the tree paradigm," Journal of Economic Dynamics and Control, Elsevier, vol. 6(1), pages 371-386, September.
    7. Alvarez, Luis H. R. & Koskela, Erkki, 2005. "Wicksellian theory of forest rotation under interest rate variability," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 529-545, March.
    8. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    9. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    10. Brennan, Michael J & Schwartz, Eduardo S, 1985. "Evaluating Natural Resource Investments," The Journal of Business, University of Chicago Press, vol. 58(2), pages 135-157, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tahvonen, Olli & Suominen, Antti & Malo, Pekka & Viitasaari, Lauri & Parkatti, Vesa-Pekka, 2022. "Optimizing high-dimensional stochastic forestry via reinforcement learning," Journal of Economic Dynamics and Control, Elsevier, vol. 145(C).
    2. Alvarez E., Luis H.R. & Hening, Alexandru, 2022. "Optimal sustainable harvesting of populations in random environments," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 678-698.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kurt L. Helmes & Richard H. Stockbridge, 2010. "Thinning and harvesting in stochastic forest models," Post-Print hal-00753039, HAL.
    2. Luis H. R. Alvarez & Erkki Koskela, 2002. "Irreversible Investment under Interest Rate Variability: New Results," CESifo Working Paper Series 640, CESifo.
    3. Chladna, Zuzana, 2007. "Determination of optimal rotation period under stochastic wood and carbon prices," Forest Policy and Economics, Elsevier, vol. 9(8), pages 1031-1045, May.
    4. Nostbakken, Linda, 2006. "Regime switching in a fishery with stochastic stock and price," Journal of Environmental Economics and Management, Elsevier, vol. 51(2), pages 231-241, March.
    5. Adkins, Roger & Paxson, Dean, 2019. "Rescaling-contraction with a lower cost technology when revenue declines," European Journal of Operational Research, Elsevier, vol. 277(2), pages 574-586.
    6. Insley, Margaret, 2017. "Resource extraction with a carbon tax and regime switching prices: Exercising your options," Energy Economics, Elsevier, vol. 67(C), pages 1-16.
    7. Iraj J. Fooladi & Nargess K. Kayhani, 2003. "Is Entrepreneurship Only About Entering A New Business," Journal of Entrepreneurial Finance, Pepperdine University, Graziadio School of Business and Management, vol. 8(2), pages 1-11, Summer.
    8. Moon, Yongma & Baran, Mesut, 2018. "Economic analysis of a residential PV system from the timing perspective: A real option model," Renewable Energy, Elsevier, vol. 125(C), pages 783-795.
    9. Di Corato, Luca & Moretto, Michele, 2011. "Investing in biogas: Timing, technological choice and the value of flexibility from input mix," Energy Economics, Elsevier, vol. 33(6), pages 1186-1193.
    10. Kou, Ying & Luo, Meifeng, 2018. "Market driven ship investment decision using the real option approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 118(C), pages 714-729.
    11. Steven R. Grenadier, 2003. "An Equilibrium Analysis of Real Estate," NBER Working Papers 9475, National Bureau of Economic Research, Inc.
    12. Grenadier, Steven R. & Wang, Neng, 2005. "Investment timing, agency, and information," Journal of Financial Economics, Elsevier, vol. 75(3), pages 493-533, March.
    13. Grenadier, Steven R. & Wang, Neng, 2007. "Investment under uncertainty and time-inconsistent preferences," Journal of Financial Economics, Elsevier, vol. 84(1), pages 2-39, April.
    14. Caren Sureth, 2002. "Partially Irreversible Investment Decisions and Taxation under Uncertainty: A Real Option Approach," German Economic Review, Verein für Socialpolitik, vol. 3(2), pages 185-221, May.
    15. Sødal, Sigbjørn & Koekebakker, Steen & Aadland, Roar, 2008. "Market switching in shipping -- A real option model applied to the valuation of combination carriers," Review of Financial Economics, Elsevier, vol. 17(3), pages 183-203, August.
    16. Isik, Murat & Coble, Keith H. & Hudson, Darren & House, Lisa O., 2003. "A model of entry-exit decisions and capacity choice under demand uncertainty," Agricultural Economics, Blackwell, vol. 28(3), pages 215-224, May.
    17. Gamba, Andrea & Tesser, Matteo, 2009. "Structural estimation of real options models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 798-816, April.
    18. Miao, Jianjun & Wang, Neng, 2011. "Risk, uncertainty, and option exercise," Journal of Economic Dynamics and Control, Elsevier, vol. 35(4), pages 442-461, April.
    19. GAHUNGU, Joachim & SMEERS, Yves, 2011. "A real options model for electricity capacity expansion," LIDAM Discussion Papers CORE 2011044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    20. Alvarez, Luis H.R., 2011. "Optimal capital accumulation under price uncertainty and costly reversibility," Journal of Economic Dynamics and Control, Elsevier, vol. 35(10), pages 1769-1788, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:35:y:2011:i:1:p:25-39. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jedc .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.