Computational Economics

, Volume 41, Issue 2, pp 267–295 | Cite as

Comparing Numerical Methods for Solving the Competitive Storage Model

  • Christophe Gouel


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.


Binding constraint Nonlinear rational expectations models Numerical methods 


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  1. Aruoba S. B., Fernández-Villaverde J., Rubio-Ramírez J. F. (2006) Comparing solution methods for dynamic equilibrium economies. Journal of Economic Dynamics and Control 30(12): 2477–2508CrossRefGoogle Scholar
  2. Barillas F., Fernández-Villaverde J. (2007) A generalization of the endogenous grid method. Journal of Economic Dynamics and Control 31(8): 2698–2712CrossRefGoogle Scholar
  3. Barsky R. B., Mankiw N. G., Zeldes S. P. (1986) Ricardian consumers with Keynesian propensities. The American Economic Review 76(4): 676–691Google Scholar
  4. Cafiero C., Bobenrieth E. S. A., Bobenrieth J. R. A., Wright B. D. (2011) The empirical relevance of the competitive storage model. Journal of Econometrics 162(1): 44–54CrossRefGoogle Scholar
  5. Cafiero C., Wright B. D. (2006) Is the storage model a ‘closed’ empirical issue? The empirical ability of the storage model to explain price dynamics. In: Sarris A., Hallam D. (eds) Agricultural commodity markets and trade. New approaches to analyzing market structure and instability  Chap. 4. FAO/Edward Elgar, Northampton, pp 89–114Google Scholar
  6. Carroll C. D. (2001) A theory of the consumption function, with and without liquidity constraints. The Journal of Economic Perspectives 15(3): 23–45CrossRefGoogle Scholar
  7. Carroll C. D. (2006) The method of endogenous gridpoints for solving dynamic stochastic optimization problems. Economics Letters 91(3): 312–320CrossRefGoogle Scholar
  8. Carter C. A., Revoredo Giha C. L. (2007) The Working curve and commodity storage under backwardation. American Journal of Agricultural Economics 89(4): 864–872CrossRefGoogle Scholar
  9. Chambers M. J., Bailey R. E. (1996) A theory of commodity price fluctuations. The Journal of Political Economy 104(5): 924–957CrossRefGoogle Scholar
  10. Christiano L. J., Fisher J. D. M. (2000) Algorithms for solving dynamic models with occasionally binding constraints. Journal of Economic Dynamics and Control 24(8): 1179–1232CrossRefGoogle Scholar
  11. Coeurdacier, N., Rey, H., & Winant, P. (2011). The risky steady state. American Economic Review, 101(3), 398–401. Papers and proceedings of the one hundred and twenty-third annual meeting of the American Economic Association, Denver, CO, January 6–9, 2011.Google Scholar
  12. Deaton A. (1991) Saving and liquidity constraints. Econometrica 59(5): 1221–1248CrossRefGoogle Scholar
  13. Deaton A., Laroque G. (1992) On the behaviour of commodity prices. Review of Economic Studies 59(1): 1–23CrossRefGoogle Scholar
  14. Deaton A., Laroque G. (1995) Estimating a nonlinear rational expectations commodity price model with unobservable state variables. Journal of Applied Econometrics 10: S9–S40CrossRefGoogle Scholar
  15. Deaton A., Laroque G. (1996) Competitive storage and commodity price dynamics. The Journal of Political Economy 104(5): 896–923CrossRefGoogle Scholar
  16. den Haan, W. J., & de Wind, J. (2009). How well-behaved are higher-order perturbation solutions? DNB Working Paper 240. De Nederlandsche Bank.Google Scholar
  17. den Haan W. J., Marcet A. (1990) Solving the stochastic growth model by parameterizing expectations. Journal of Business & Economic Statistics 8(1): 31–34Google Scholar
  18. Dirkse S. P., Ferris M. C. (1995) The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems. Optimization Methods and Software 5: 123–156CrossRefGoogle Scholar
  19. Fackler P. L. (2005) A MATLAB solver for nonlinear rational expectations models. Computational Economics 26(2): 173–181CrossRefGoogle Scholar
  20. Feigenbaum J. (2005) Second-, third-, and higher-order consumption functions: A precautionary tale. Journal of Economic Dynamics and Control 29(8): 1385–1425CrossRefGoogle Scholar
  21. Gardner B. L. (1979) Optimal stockpiling of grain. Lexington Books, Lexington, MAGoogle Scholar
  22. Gustafson, R. L. (1958). Carryover levels for grains: A method for determining amounts that are optimal under specified conditions. Technical Bulletin 1178. US Dept. of Agriculture.Google Scholar
  23. Heer B., Maußner A. (2008) Computation of business cycle models: A comparison of numerical methods. Macroeconomic Dynamics 12(5): 641–663CrossRefGoogle Scholar
  24. Judd K. L. (1992) Projection methods for solving aggregate growth models. Journal of Economic Theory 58(2): 410–452CrossRefGoogle Scholar
  25. Judd K. L. (1998) Numerical methods in economics. MIT Press, Cambridge, MAGoogle Scholar
  26. Judd K. L., Maliar L., Maliar S. (2011) Numerically stable and accurate stochastic simulation approaches for solving dynamic economic models. Quantitative Economics 2(2): 173–210CrossRefGoogle Scholar
  27. Kaldor N. (1939) Speculation and economic stability. The Review of Economic Studies 7(1): 1–27CrossRefGoogle Scholar
  28. Kanzow C., Petra S. (2004) On a semismooth least squares formulation of complementarity problems with gap reduction. Optimization Methods and Software 19(5): 507–525CrossRefGoogle Scholar
  29. Kanzow C., Petra S. (2007) Projected filter trust region methods for a semismooth least squares formulation of mixed complementarity problems. Optimization Methods and Software 22: 713–735CrossRefGoogle Scholar
  30. Kim S. H., Kollmann R., Kim J. (2010) Solving the incomplete market model with aggregate uncertainty using a perturbation method. Journal of Economic Dynamics and Control 34(1): 50–58CrossRefGoogle Scholar
  31. Krusell P., Smith A. A. Jr. (2006) Quantitative macroeconomic models with heterogeneous agents. In: Blundell R., Newey W., Persson T. (eds) Advances in economics and econometrics: Theory and Applications, Ninth World Congress  Econometric Society Monographs, Chap. 8. Cambridge University Press, New York, pp 298–340CrossRefGoogle Scholar
  32. Lence S. H., Hayes D. J. (2002) U.S. farm policy and the volatility of commodity prices and farm revenues. American Journal of Agricultural Economics 84(2): 335–351CrossRefGoogle Scholar
  33. Michaelides A., Ng S. (2000) Estimating the rational expectations model of speculative storage: A Monte Carlo comparison of three simulation estimators. Journal of Econometrics 96(2): 231–266CrossRefGoogle Scholar
  34. Miranda M. J. (1997) Numerical strategies for solving the nonlinear rational expectations commodity market model. Computational Economics 11(1–2): 71–87CrossRefGoogle Scholar
  35. Miranda M. J., Fackler P. L. (2002) Applied computational economics and finance. MIT Press, CambridgeGoogle Scholar
  36. Miranda M. J., Glauber J. W. (1995) Solving stochastic models of competitive storage and trade by Chebychev collocation methods. Agricultural and Resource Economics Review 24(1): 70–77Google Scholar
  37. Miranda M. J., Helmberger P. G. (1988) The effects of commodity price stabilization programs. The American Economic Review 78(1): 46–58Google Scholar
  38. Newbery D. M. G., Stiglitz J. E. (1982) Optimal commodity stock-piling rules. Oxford Economic Papers 34(3): 403–427Google Scholar
  39. Osborne T. (2004) Market news in commodity price theory: Application to the Ethiopian grain market. The Review of Economic Studies 71(1): 133–164CrossRefGoogle Scholar
  40. Park A. (2006) Risk and household grain management in developing countries. Economic Journal 116(514): 1088–1115CrossRefGoogle Scholar
  41. Plato G., Gordon D. (1983) Dynamic programming and the economics of optimal grain storage. Journal of Agricultural Economics Research 35(1): 10–22Google Scholar
  42. Preston, B., & Roca, M. (2007). Incomplete Markets, Heterogeneity and Macroeconomic Dynamics. Working Paper 13260. National Bureau of Economic Research.Google Scholar
  43. Rust J. (1996) Numerical dynamic programming in economics. In: Amman H. M., Kendrick D. A., Rust J. (eds) Handbook of Computational Economics (Vol. 1, Chap. 14). Elsevier, Amsterdam, pp 619–729CrossRefGoogle Scholar
  44. Scheinkman J. A., Schechtman J. (1983) A simple competitive model with production and storage. The Review of Economic Studies 50(3): 427–441CrossRefGoogle Scholar
  45. Williams J. C., Wright B. D. (1991) Storage and commodity markets. Cambridge University Press, New YorkCrossRefGoogle Scholar
  46. Winschel V., Krätzig M. (2010) Solving, estimating, and selecting nonlinear dynamic models without the curse of dimensionality. Econometrica 78(2): 803–821CrossRefGoogle Scholar
  47. Working H. (1948) Theory of the inverse carrying charge in futures markets. Journal of Farm Economics 30(1): 1–28CrossRefGoogle Scholar
  48. Wright B. D. (2001) Storage and price stabilization. In: Gardner B. L., Rausser G. C. (eds) Marketing, distribution and consumers, Vol. 1B, Part 2 of Handbook of agricultural economics  Chap. 14. Elsevier, Amsterdam, pp 817–861CrossRefGoogle Scholar
  49. Wright B. D., Williams J. C. (1982) The economic role of commodity storage. The Economic Journal 92(367): 596–614CrossRefGoogle Scholar
  50. Wright B. D., Williams J. C. (1984) The welfare effects of the introduction of storage. The Quarterly Journal of Economics 99(1): 169–192CrossRefGoogle Scholar
  51. Zeldes S. P. (1989) Optimal consumption with stochastic income: Deviations from certainty equivalence. The Quarterly Journal of Economics 104(2): 275–298CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  1. 1.Development Research Group, Agriculture and Rural DevelopmentThe World BankWashingtonUSA
  2. 2.CEPIIParisFrance

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