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Comparing Numerical Methods for Solving the Competitive Storage Model

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  • Christophe Gouel

Abstract

This paper compares numerical methods for solving the competitive storage model. Because storage implies a nonnegativity constraint on stocks, the solution methods must be considered carefully. The model is solved using value function iteration and several projection approaches, including parameterised expectations and decision rules approximation. In considering a storage model with convenience yield, in which the inequality constraint is smoothed, perturbation methods are also applied. Parameterised expectations approximation proves to be the most accurate method, whereas perturbation techniques are shown inadequate for solving this highly nonlinear model. The endogenous grid method allows rapid solution if supply is assumed to be inelastic. Copyright Springer Science+Business Media, LLC. 2013

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  • Christophe Gouel, 2013. "Comparing Numerical Methods for Solving the Competitive Storage Model," Computational Economics, Springer;Society for Computational Economics, vol. 41(2), pages 267-295, February.
    • Handle: RePEc:kap:compec:v:41:y:2013:i:2:p:267-295
    DOI: 10.1007/s10614-012-9318-y
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    as
    1. Christiano, Lawrence J. & Fisher, Jonas D. M., 2000. "Algorithms for solving dynamic models with occasionally binding constraints," Journal of Economic Dynamics and Control, Elsevier, vol. 24(8), pages 1179-1232, July.
    2. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, February.
    3. Heer, Burkhard & Maußner, Alfred, 2008. "Computation Of Business Cycle Models: A Comparison Of Numerical Methods," Macroeconomic Dynamics, Cambridge University Press, vol. 12(5), pages 641-663, November.
    4. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-1248, September.
    5. Albert Park, 2006. "Risk and Household Grain Management in Developing Countries," Economic Journal, Royal Economic Society, vol. 116(514), pages 1088-1115, October.
    6. Williams,Jeffrey C. & Wright,Brian D., 2005. "Storage and Commodity Markets," Cambridge Books, Cambridge University Press, number 9780521023399, May.
    7. Feigenbaum, James, 2005. "Second-, third-, and higher-order consumption functions: a precautionary tale," Journal of Economic Dynamics and Control, Elsevier, vol. 29(8), pages 1385-1425, August.
    8. Colin A. Carter & Cesar L. Revoredo Giha, 2007. "The Working Curve and Commodity Storage under Backwardation," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 89(4), pages 864-872.
    9. Kim, Sunghyun Henry & Kollmann, Robert & Kim, Jinill, 2010. "Solving the incomplete market model with aggregate uncertainty using a perturbation method," Journal of Economic Dynamics and Control, Elsevier, vol. 34(1), pages 50-58, January.
    10. Kenneth L. Judd & Lilia Maliar & Serguei Maliar, 2011. "Numerically stable and accurate stochastic simulation approaches for solving dynamic economic models," Quantitative Economics, Econometric Society, vol. 2(2), pages 173-210, July.
    11. Barsky, Robert B & Mankiw, N Gregory & Zeldes, Stephen P, 1986. "Ricardian Consumers with Keynesian Propensities," American Economic Review, American Economic Association, vol. 76(4), pages 676-691, September.
    12. den Haan, Wouter J & Marcet, Albert, 1990. "Solving the Stochastic Growth Model by Parameterizing Expectations," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(1), pages 31-34, January.
    13. Miranda, Mario J, 1998. "Numerical Strategies for Solving the Nonlinear Rational Expectations Commodity Market Model," Computational Economics, Springer;Society for Computational Economics, vol. 11(1-2), pages 71-87, April.
    14. Nicolas Coeurdacier & Helene Rey & Pablo Winant, 2011. "The Risky Steady State," American Economic Review, American Economic Association, vol. 101(3), pages 398-401, May.
    15. Wright, Brian D & Williams, Jeffrey C, 1982. "The Economic Role of Commodity Storage," Economic Journal, Royal Economic Society, vol. 92(367), pages 596-614, September.
    16. Stephen P. Zeldes, 1989. "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," The Quarterly Journal of Economics, Oxford University Press, vol. 104(2), pages 275-298.
    17. Brian D. Wright & Jeffrey C. Williams, 1984. "The Welfare Effects of the Introduction of Storage," The Quarterly Journal of Economics, Oxford University Press, vol. 99(1), pages 169-192.
    18. Sergio H. Lence & Dermot J. Hayes, 2002. "U.S. Farm Policy and the Volatility of Commodity Prices and Farm Revenues," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 84(2), pages 335-351.
    19. Plato, Gerald & Gordon, Douglas, 1983. "Dynamic Programming and the Economics of Optimal Grain Storage," Journal of Agricultural Economics Research, United States Department of Agriculture, Economic Research Service, vol. 35(1), pages 1-13, January.
    20. Sergio H. Lence & Dermot J. Hayes, 2002. "U.S. Farm Policy and the Volatility of Commodity Prices and Farm Revenues," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 84(2), pages 335-351.
    21. Cafiero, Carlo & Bobenrieth H., Eugenio S.A. & Bobenrieth H., Juan R.A. & Wright, Brian D., 2011. "The empirical relevance of the competitive storage model," Journal of Econometrics, Elsevier, vol. 162(1), pages 44-54, May.
    22. Angus Deaton & Guy Laroque, 1992. "On the Behaviour of Commodity Prices," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 1-23.
    23. Carroll, Christopher D., 2006. "The method of endogenous gridpoints for solving dynamic stochastic optimization problems," Economics Letters, Elsevier, vol. 91(3), pages 312-320, June.
    24. Viktor Winschel, 2005. "Solving, Estimating and Selecting Nonlinear Dynamic Economic Models without the Curse of Dimensionality," GE, Growth, Math methods 0507014, University Library of Munich, Germany.
    25. José A. Scheinkman & Jack Schechtman, 1983. "A Simple Competitive Model with Production and Storage," Review of Economic Studies, Oxford University Press, vol. 50(3), pages 427-441.
    26. Miranda, Mario J. & Glauber, Joseph W., 1995. "Solving Stochastic Models of Competitive Storage and Trade by Chebychev Collocation Methods," Agricultural and Resource Economics Review, Cambridge University Press, vol. 24(1), pages 70-77, April.
    27. Paul Fackler, 2005. "A MATLAB Solver for Nonlinear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 26(2), pages 173-181, October.
    28. Michaelides, Alexander & Ng, Serena, 2000. "Estimating the rational expectations model of speculative storage: A Monte Carlo comparison of three simulation estimators," Journal of Econometrics, Elsevier, vol. 96(2), pages 231-266, June.
    29. Rust, John, 1996. "Numerical dynamic programming in economics," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 14, pages 619-729, Elsevier.
    30. H. M. Amman & D. A. Kendrick & J. Rust (ed.), 1996. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 1, number 1, 00.
    31. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
    32. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
    33. Christopher D. Carroll, 2001. "A Theory of the Consumption Function, with and without Liquidity Constraints," Journal of Economic Perspectives, American Economic Association, vol. 15(3), pages 23-45, Summer.
    34. Deaton, Angus & Laroque, Guy, 1995. "Estimating a Nonlinear Rational Expectations Commodity Price Model with Unobservable State Variables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(S), pages 9-40, Suppl. De.
    35. Miranda, Mario J & Helmberger, Peter G, 1988. "The Effects of Commodity Price Stabilization Programs," American Economic Review, American Economic Association, vol. 78(1), pages 46-58, March.
    36. Deaton, Angus & Laroque, Guy, 1996. "Competitive Storage and Commodity Price Dynamics," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 896-923, October.
    37. Chambers, Marcus J & Bailey, Roy E, 1996. "A Theory of Commodity Price Fluctuations," Journal of Political Economy, University of Chicago Press, vol. 104(5), pages 924-957, October.
    38. Holbrook Working, 1948. "Theory of the Inverse Carrying Charge in Futures Markets," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 30(1), pages 1-28.
    39. Viktor Winschel & Markus Kr‰tzig, 2010. "Solving, Estimating, and Selecting Nonlinear Dynamic Models Without the Curse of Dimensionality," Econometrica, Econometric Society, vol. 78(2), pages 803-821, March.
    40. Barillas, Francisco & Fernandez-Villaverde, Jesus, 2007. "A generalization of the endogenous grid method," Journal of Economic Dynamics and Control, Elsevier, vol. 31(8), pages 2698-2712, August.
    41. Nicholas Kaldor, 1939. "Speculation and Economic Stability," Review of Economic Studies, Oxford University Press, vol. 7(1), pages 1-27.
    42. Newbery, David M G & Stiglitz, Joseph E, 1982. "Optimal Commodity Stock-piling Rules," Oxford Economic Papers, Oxford University Press, vol. 34(3), pages 403-427, November.
    43. Gustafson, Robert L., 1958. "Carryover levels for grains: A method for determining amounts that are optimal under specified conditions," Technical Bulletins 157231, United States Department of Agriculture, Economic Research Service.
    44. Wright, Brian, 2001. "Storage and price stabilization," Handbook of Agricultural Economics, in: B. L. Gardner & G. C. Rausser (ed.), Handbook of Agricultural Economics, edition 1, volume 1, chapter 14, pages 817-861, Elsevier.
    45. Theresa Osborne, 2004. "Market News in Commodity Price Theory: Application to the Ethiopian Grain Market," Review of Economic Studies, Oxford University Press, vol. 71(1), pages 133-164.
    46. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
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    Cited by:

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    2. Zhou, Wei & Babcock, Bruce A., 2014. "Pricing RINs and Corn in a Competitive Storage Model," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 170581, Agricultural and Applied Economics Association.
    3. Zhou, Wei, 2015. "Three essays on modeling biofuel feedstock supply," ISU General Staff Papers 201501010800005728, Iowa State University, Department of Economics.
    4. Eugenio S.A. Bobenrieth & Juan R.A. Bobenrieth & Ernesto A. Guerra & Brian D. Wright & Di Zeng, 2021. "Putting the Empirical Commodity Storage Model Back on Track: Crucial Implications of a “Negligible” Trend," American Journal of Agricultural Economics, John Wiley & Sons, vol. 103(3), pages 1034-1057, May.
    5. Gouel, Christophe & Legrand, Nicolas, 2016. "Bayesian Estimation of the Storage Model using Information on Quantities," 2016 Annual Meeting, July 31-August 2, Boston, Massachusetts 235599, Agricultural and Applied Economics Association.
    6. Nicolas Legrand, 2019. "The Empirical Merit Of Structural Explanations Of Commodity Price Volatility: Review And Perspectives," Journal of Economic Surveys, Wiley Blackwell, vol. 33(2), pages 639-664, April.
    7. Bruce A. Babcock & Wei Zhou, 2013. "Impact on Corn Prices from Reduced Biofuel Mandates," Center for Agricultural and Rural Development (CARD) Publications 13-wp543, Center for Agricultural and Rural Development (CARD) at Iowa State University.
    8. Zhou, Wei & Babcock, Bruce A., 2017. "Using the competitive storage model to estimate the impact of ethanol and fueling investment on corn prices," Energy Economics, Elsevier, vol. 62(C), pages 195-203.
    9. Kleppe, Tore Selland & Oglend, Atle, 2017. "Estimating the competitive storage model: A simulated likelihood approach," Econometrics and Statistics, Elsevier, vol. 4(C), pages 39-56.
    10. Pfuderer, Simone, 2015. "An Experimental Approach to Testing the Competitive Storage Model," 89th Annual Conference, April 13-15, 2015, Warwick University, Coventry, UK 204297, Agricultural Economics Society.
    11. Zhou, Wei & Babcock, Bruce A., 2014. "Endogenous Price in a Dynamic Model for Agricultural Supply Analysis," 2014 Annual Meeting, July 27-29, 2014, Minneapolis, Minnesota 170584, Agricultural and Applied Economics Association.
    12. Pfuderer, Simone, 2014. "Are stockholders rational? An experimental approach to testing the competitive storage model," 88th Annual Conference, April 9-11, 2014, AgroParisTech, Paris, France 170537, Agricultural Economics Society.

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