IDEAS home Printed from https://ideas.repec.org/a/kap/compec/v41y2013i2p267-295.html
   My bibliography  Save this article

Comparing Numerical Methods for Solving the Competitive Storage Model

Author

Listed:
  • 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

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10614-012-9318-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10614-012-9318-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Angus Deaton & Guy Laroque, 1992. "On the Behaviour of Commodity Prices," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(1), pages 1-23.
    2. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871525, Enero-Abr.
    3. 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.
    4. Bruce Preston & Mauro Roca, 2007. "Incomplete Markets, Heterogeneity and Macroeconomic Dynamics," NBER Working Papers 13260, National Bureau of Economic Research, Inc.
    5. 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.
    6. 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.
    7. 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.
    8. B. L. Gardner & G. C. Rausser (ed.), 2001. "Handbook of Agricultural Economics," Handbook of Agricultural Economics, Elsevier, edition 1, volume 1, number 2.
    9. 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.
    10. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692083, Enero-Abr.
    11. 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.
    12. 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.
    13. Miranda, Mario J. & Glauber, Joseph W., 1995. "Solving Stochastic Models Of Competitive Storage And Trade By Chebychev Collocaton Methods," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 24(01), pages 1-8, April.
    14. 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.
    15. repec:hal:spmain:info:hdl:2441/c8dmi8nm4pdjkuc9g704ld0h3 is not listed on IDEAS
    16. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    17. 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.
    18. Deaton, Angus, 1991. "Saving and Liquidity Constraints," Econometrica, Econometric Society, vol. 59(5), pages 1221-1248, September.
    19. 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.
    20. 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.
    21. Albert Park, 2006. "Risk and Household Grain Management in Developing Countries," Economic Journal, Royal Economic Society, vol. 116(514), pages 1088-1115, October.
    22. Nicolas Coeurdacier & Helene Rey & Pablo Winant, 2011. "The Risky Steady State," American Economic Review, American Economic Association, vol. 101(3), pages 398-401, May.
    23. 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.
    24. Williams,Jeffrey C. & Wright,Brian D., 2005. "Storage and Commodity Markets," Cambridge Books, Cambridge University Press, number 9780521023399, Enero-Abr.
    25. 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.
    26. 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.
    27. 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.
    28. Theresa Osborne, 2004. "Market News in Commodity Price Theory: Application to the Ethiopian Grain Market," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(1), pages 133-164.
    29. 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.
    30. 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.
    31. repec:spo:wpecon:info:hdl:2441/c8dmi8nm4pdjkuc9g704ld0h3 is not listed on IDEAS
    32. 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.
    33. 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.
    34. 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.
    35. 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.
    36. 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.
    37. Judd, Kenneth L., 1992. "Projection methods for solving aggregate growth models," Journal of Economic Theory, Elsevier, vol. 58(2), pages 410-452, December.
    38. B. L. Gardner & G. C. Rausser (ed.), 2001. "Handbook of Agricultural Economics," Handbook of Agricultural Economics, Elsevier, edition 1, volume 1, number 1.
    39. 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.
    40. repec:spo:wpmain:info:hdl:2441/c8dmi8nm4pdjkuc9g704ld0h3 is not listed on IDEAS
    41. 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.
    42. Stephen P. Zeldes, 1989. "Optimal Consumption with Stochastic Income: Deviations from Certainty Equivalence," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(2), pages 275-298.
    43. José A. Scheinkman & Jack Schechtman, 1983. "A Simple Competitive Model with Production and Storage," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(3), pages 427-441.
    44. Brian D. Wright & Jeffrey C. Williams, 1984. "The Welfare Effects of the Introduction of Storage," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 99(1), pages 169-192.
    45. repec:hal:wpspec:info:hdl:2441/c8dmi8nm4pdjkuc9g704ld0h3 is not listed on IDEAS
    46. Nicholas Kaldor, 1939. "Speculation and Economic Stability," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 7(1), pages 1-27.
    47. 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.
    48. 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(01), pages 1-13, January.
    49. 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.
    50. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
    51. 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.
    52. 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.
    53. 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.
    54. 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.
    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. 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.
    2. 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.
    3. 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.
    4. V., Ernesto Guerra & H., Eugenio Bobenrieth & H., Juan Bobenrieth & Wright, Brian D., 2023. "Endogenous thresholds in energy prices: Modeling and empirical estimation," Energy Economics, Elsevier, vol. 121(C).
    5. 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.
    6. Christophe Gouel & Nicolas Legrand, 2022. "The Role of Storage in Commodity Markets: Indirect Inference Based on Grains Data," Working Papers 2022-04, CEPII research center.
    7. Guerra Vallejos, Ernesto & Bobenrieth Hochfarber, Eugenio & Bobenrieth Hochfarber, Juan & Wright, Brian D., 2021. "Solving dynamic stochastic models with multiple occasionally binding constraints," Economic Modelling, Elsevier, vol. 105(C).
    8. 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.
    9. 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.
    10. Olga Bondarenko, 2025. "Shockwaves from Ukraine: Trends and Gaps in Agricultural Commodity Prices," IHEID Working Papers 04-2025, Economics Section, The Graduate Institute of International Studies.
    11. Gouel, Christophe, 2013. "Optimal food price stabilisation policy," European Economic Review, Elsevier, vol. 57(C), pages 118-134.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Zhou, Wei, 2015. "Three essays on modeling biofuel feedstock supply," ISU General Staff Papers 201501010800005728, Iowa State University, Department of Economics.

    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. Christophe Gouel, 2012. "Agricultural Price Instability: A Survey Of Competing Explanations And Remedies," Journal of Economic Surveys, Wiley Blackwell, vol. 26(1), pages 129-156, February.
    2. Guerra Vallejos, Ernesto & Bobenrieth Hochfarber, Eugenio & Bobenrieth Hochfarber, Juan & Wright, Brian D., 2021. "Solving dynamic stochastic models with multiple occasionally binding constraints," Economic Modelling, Elsevier, vol. 105(C).
    3. Kornher, Lukas & Kalkuhl, Matthias, 2013. "Food Price Volatility in Developing Countries and its Determinants," Quarterly Journal of International Agriculture, Humboldt-Universitaat zu Berlin, vol. 52(4), pages 1-32, November.
    4. Diagne, Youssoupha S & Fall, Alsim, 2009. "La spéculation contribue- t- elle à expliquer la dynamique des prix des produits alimentaires au Sénégal ? [Does speculation explain food prices movements in Senegal?]," MPRA Paper 54880, University Library of Munich, Germany.
    5. 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.
    6. 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.
    7. 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.
    8. John Stachurski, 2009. "Economic Dynamics: Theory and Computation," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012774, December.
    9. Kenneth L. Judd & Lilia Maliar & Serguei Maliar & Inna Tsener, 2017. "How to solve dynamic stochastic models computing expectations just once," Quantitative Economics, Econometric Society, vol. 8(3), pages 851-893, November.
    10. Donald F. Larson & Julian Lampietti & Christophe Gouel & Carlo Cafiero & John Roberts, 2014. "Food Security and Storage in the Middle East and North Africa," The World Bank Economic Review, World Bank, vol. 28(1), pages 48-73.
    11. Christophe Gouel & Sébastien Jean, 2015. "Optimal Food Price Stabilization in a Small Open Developing Country," The World Bank Economic Review, World Bank, vol. 29(1), pages 72-101.
    12. Judd, Kenneth L. & Maliar, Lilia & Maliar, Serguei & Valero, Rafael, 2014. "Smolyak method for solving dynamic economic models: Lagrange interpolation, anisotropic grid and adaptive domain," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 92-123.
    13. Gouel, Christophe, 2013. "Optimal food price stabilisation policy," European Economic Review, Elsevier, vol. 57(C), pages 118-134.
    14. Colin A. Carter & Gordon C. Rausser & Aaron Smith, 2011. "Commodity Booms and Busts," Annual Review of Resource Economics, Annual Reviews, vol. 3(1), pages 87-118, October.
    15. Lilia Maliar & Serguei Maliar & John B. Taylor & Inna Tsener, 2020. "A tractable framework for analyzing a class of nonstationary Markov models," Quantitative Economics, Econometric Society, vol. 11(4), pages 1289-1323, November.
    16. Kelley, Clare & Lanot, Gauthier, 2002. "Consumption Patterns Over Pay Periods," Economic Research Papers 269469, University of Warwick - Department of Economics.
    17. Evans, Lewis & Guthrie, Graeme, 2007. "Commodity Price Behavior With Storage Frictions," Working Paper Series 3966, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    18. Serguei Maliar & John Taylor & Lilia Maliar, 2016. "The Impact of Alternative Transitions to Normalized Monetary Policy," 2016 Meeting Papers 794, Society for Economic Dynamics.
    19. Zhu, Xiaohong, 2016. "New models to estimate costs of US farm programs," ISU General Staff Papers 201601010800006209, Iowa State University, Department of Economics.
    20. repec:vuw:vuwscr:19065 is not listed on IDEAS
    21. Evans, Lewis & Guthrie, Graeme, 2007. "Commodity Price Behavior With Storage Frictions," Working Paper Series 19065, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.

    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:kap:compec:v:41:y:2013:i:2:p:267-295. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.