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Wicksellian Theory of Forest Rotation under Interest Rate Variability

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  • Luis H. R. Alvarez
  • Erkki Koskela

Abstract

The current literature on optimal forest rotation makes the assumption of constant interest rate. However, the irreversible harvesting decisions of forest stands are typically subject to relatively long time horizons over which interest rates do fluctuate considerably. In this paper we apply the Wicksellian single rotation framework to extend the existing studies to cover the unexplored case of variable interest rate. Given the technical generality of the considered valuation problem, we provide a thorough mathematical characterization of the optimal timing problem and develop new results. We show that even in the deterministic case if the current interest rate deviates from its long-run steady state, interest rate variability changes the rotation age significantly when compared with the constant discounting case. Further, and importantly, allowing for interest rate uncertainty is shown to increase the optimal rotation period when the value of the optimal policy is a convex function of the current interest rate. In line with this finding, we also establish that increased interest rate volatility has a positive impact on the optimal rotation period.

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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 606.

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Date of creation: 2001
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Handle: RePEc:ces:ceswps:_606

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Related research

Keywords: Wicksellian rotation; variable interest rates; linear diffusions; optimal stopping; free boundary problems;

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References

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  1. Merton, Robert C, 1975. "An Asymptotic Theory of Growth under Uncertainty," Review of Economic Studies, Wiley Blackwell, vol. 42(3), pages 375-93, July.
  2. Koskela, Erkki & Ollikainen, Markku, 2001. "Forest Taxation and Rotation Age under Private Amenity Valuation: New Results," Journal of Environmental Economics and Management, Elsevier, vol. 42(3), pages 374-384, November.
  3. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1980. " An Analysis of Variable Rate Loan Contracts," Journal of Finance, American Finance Association, vol. 35(2), pages 389-403, May.
  4. Alvarez, Luis H.R. & Koskela , Erkki, 2003. "Irreversible investment under interest rate variability: new results," Research Discussion Papers 29/2003, Bank of Finland.
  5. Luis H. R. Alvarez & Erkki Koskela, 2006. "Irreversible Investment under Interest Rate Variability: Some Generalizations," The Journal of Business, University of Chicago Press, vol. 79(2), pages 623-644, March.
  6. Luis H. R. Alvarez, 2001. "Reward functionals, salvage values, and optimal stopping," Computational Statistics, Springer, vol. 54(2), pages 315-337, December.
  7. Luis H. R. Alvarez, 2001. "Solving optimal stopping problems of linear diffusions by applying convolution approximations," Computational Statistics, Springer, vol. 53(1), pages 89-99, April.
  8. Insley, Margaret, 2002. "A Real Options Approach to the Valuation of a Forestry Investment," Journal of Environmental Economics and Management, Elsevier, vol. 44(3), pages 471-492, November.
  9. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  10. Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1992. "Waiting to Invest: Investment and Uncertainty," The Journal of Business, University of Chicago Press, vol. 65(1), pages 1-29, January.
  11. Reed, William J., 1993. "The decision to conserve or harvest old-growth forest," Ecological Economics, Elsevier, vol. 8(1), pages 45-69, August.
  12. Markku Ollikainen & Erkki Koskela, 2001. "Optimal Private and Public Harvesting under Spatial and Temporal Interdependence," CESifo Working Paper Series 452, CESifo Group Munich.
  13. Hartman, Richard, 1976. "The Harvesting Decision When a Standing Forest Has Value," Economic Inquiry, Western Economic Association International, vol. 14(1), pages 52-58, March.
  14. Alvarez, Luis H. R., 2001. "On the form and risk-sensitivity of zero coupon bonds for a class of interest rate models," Insurance: Mathematics and Economics, Elsevier, vol. 28(1), pages 83-90, February.
  15. Reed, William J & Clarke, Harry R, 1990. "Harvest Decisions and Asset Valuation for Biological Resources Exhibiting Size-Dependent Stochastic Growth," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(1), pages 147-69, February.
  16. Tahvonen, Olli & Salo, Seppo & Kuuluvainen, Jari, 2001. "Optimal forest rotation and land values under a borrowing constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 25(10), pages 1595-1627, October.
  17. Samuelson, Paul A, 1976. "Economics of Forestry in an Evolving Society," Economic Inquiry, Western Economic Association International, vol. 14(4), pages 466-92, December.
  18. Morck, Randall & Schwartz, Eduardo & Stangeland, David, 1989. "The Valuation of Forestry Resources under Stochastic Prices and Inventories," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(04), pages 473-487, December.
  19. Thomas A. Thomson, 1992. "Optimal Forest Rotation When Stumpage Prices Follow a Diffusion Process," Land Economics, University of Wisconsin Press, vol. 68(3), pages 329-342.
  20. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. " General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December.
  21. Yaacov Z. Bergman & Bruce D. Grundy & Zvi Wiener, . "General Properties of Option Prices (Revision of 11-95) (Reprint 058)," Rodney L. White Center for Financial Research Working Papers 01-96, Wharton School Rodney L. White Center for Financial Research.
  22. Reed, William J., 1984. "The effects of the risk of fire on the optimal rotation of a forest," Journal of Environmental Economics and Management, Elsevier, vol. 11(2), pages 180-190, June.
  23. Swallow Stephen K. & Wear David N., 1993. "Spatial Interactions in Multiple-Use Forestry and Substitution and Wealth Effects for the Single Stand," Journal of Environmental Economics and Management, Elsevier, vol. 25(2), pages 103-120, September.
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Citations

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Cited by:
  1. Luis H.R. Alvarez & Erkki Koskela, 2004. "Irreversible investment under interest rate variability: new results," Others 0404007, EconWPA.
  2. Luis H. R. Alvarez & Erkki Koskela, 2005. "Optimal Harvesting under Resource Stock and Price Uncertainty," CESifo Working Paper Series 1384, CESifo Group Munich.
  3. Shan Chen & Margaret Insley, 2008. "Regime switching in stochastic models of commodity prices: An application to an optimal tree harvesting problem," Working Papers 08003, University of Waterloo, Department of Economics.
  4. Luis Alvarez, 2010. "Irreversible capital accumulation under interest rate uncertainty," Computational Statistics, Springer, vol. 72(2), pages 249-271, October.
  5. Brunette, Marielle & Couture, St├ęphane & Langlais, Eric, 2009. "Amenities and Risk in Forest Management," MPRA Paper 14743, University Library of Munich, Germany.
  6. 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.
  7. Alvarez, Luis H R & Koskela, Erkki, 2003. "On Forest Rotation under Interest Rate Variability," International Tax and Public Finance, Springer, vol. 10(4), pages 489-503, August.
  8. Luis H. R. Alvarez & Erkki Koskela, 2004. "Does Risk Aversion Accelerate Optimal Forest Rotation under Uncertainty?," CESifo Working Paper Series 1285, CESifo Group Munich.
  9. Alvarez, Luis H.R. & Koskela, Erkki, 2003. "Irreversible Investment under Interest Rate Variability: Some Generalizations," Discussion Papers 841, The Research Institute of the Finnish Economy.
  10. Luis H. R. Alvarez & Erkki Koskela, 2004. "Taxation and Rotation Age under Stochastic Forest Stand Value," CESifo Working Paper Series 1211, CESifo Group Munich.
  11. Luis H.R. Alvarez E., 2006. "Irreversible Investment, Incremental Capital Accumulation, and Price Uncertainty," Discussion Papers 4, Aboa Centre for Economics.
  12. Olivier Damette & Philippe Delacote, 2009. "The environmental resource curse hypothesis: the forest case," Working Papers - Cahiers du LEF 2009-04, Laboratoire d'Economie Forestiere, AgroParisTech-INRA.
  13. Sylvain Caurla & Philippe Delacote & Franck Lecocq & Ahmed Barkaoui, 2009. "Fuelwood consumption, restrictions about resource availability and public policies: impacts on the French forest sector," Working Papers - Cahiers du LEF 2009-03, Laboratoire d'Economie Forestiere, AgroParisTech-INRA.

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