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Accuracy of Numerical Solution to Dynamic Programming Models

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  • King, Robert P.
  • Lohano, Heman D.

Abstract

Dynamic programming models with continuous state and control variables are solved approximately using numerical methods in most applications. We develop a method for measuring the accuracy of numerical solution of stochastic dynamic programming models. Using this method, we compare the accuracy of various interpolation schemes. As expected, the results show that the accuracy improves as number of nodes is increased. Comparison of Chebyshev and linear spline indicates that the linear spline may give higher maximum absolute error than Chebyshev, however, the overall performance of spline interpolation is better than Chebyshev interpolation for non-smooth functions. Two-stage grid search method of optimization is developed and examined with accuracy analysis. The results show that this method is more efficient and accurate. Accuracy is also examined by allocating a different number of nodes for each dimension. The results show that a change in node configuration may yield a more efficient and accurate solution.

Suggested Citation

  • King, Robert P. & Lohano, Heman D., 2006. "Accuracy of Numerical Solution to Dynamic Programming Models," Staff Papers 14230, University of Minnesota, Department of Applied Economics.
    • Handle: RePEc:ags:umaesp:14230
    DOI: 10.22004/ag.econ.14230
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    1. Manuel S. Santos, 2000. "Accuracy of Numerical Solutions using the Euler Equation Residuals," Econometrica, Econometric Society, vol. 68(6), pages 1377-1402, November.
    2. Bambenek, Jerome V. & Raup, Philip M., 1968. "The Minnesota Rural Real Estate Market In 1967," Economic Study Reports 13227, University of Minnesota, Department of Applied Economics.
    3. Olson, Kent D. & Westman, Lorin L. & Nordquist, Dale W., 1998. "1997 Annual Report Of The Southeastern Minnesota Farm Business Management Association," Staff Papers 13310, University of Minnesota, Department of Applied Economics.
    4. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    5. Judd, Kenneth L., 1996. "Approximation, perturbation, and projection methods in economic analysis," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 12, pages 509-585, Elsevier.
    6. Mario J. Miranda & Paul L. Fackler, 1999. "Hybrid Methods for Continuous Space Dynamic Programming," Computing in Economics and Finance 1999 1332, Society for Computational Economics.
    7. Burt, Oscar R. & Taylor, C. Robert, 1989. "Reduction Of State Variable Dimension In Stochastic Dynamic Optimization Models Which Use Time-Series Data," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 14(2), pages 1-10, December.
    8. Sharon A. Johnson & Jery R. Stedinger & Christine A. Shoemaker & Ying Li & José Alberto Tejada-Guibert, 1993. "Numerical Solution of Continuous-State Dynamic Programs Using Linear and Spline Interpolation," Operations Research, INFORMS, vol. 41(3), pages 484-500, June.
    9. Bera, Anil K. & Jarque, Carlos M., 1981. "Efficient tests for normality, homoscedasticity and serial independence of regression residuals : Monte Carlo Evidence," Economics Letters, Elsevier, vol. 7(4), pages 313-318.
    10. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
    11. Brekke, Jon & Tao, Hung-Lin & Raup, Philip M., 1993. "The Minnesota Rural Real Estate Market In 1992," Economic Reports 13010, University of Minnesota, Department of Applied Economics.
    12. Hans M. Amman & David A. Kendrick, . "Computational Economics," Online economics textbooks, SUNY-Oswego, Department of Economics, number comp1.
    13. 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.
    14. 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.
    15. Schnitkey, Gary D. & Taylor, C. Robert & Barry, Peter J., 1989. "Evaluating Farmland Investments Considering Dynamic Stochastic Returns And Farmland Prices," Western Journal of Agricultural Economics, Western Agricultural Economics Association, vol. 14(1), pages 1-14, July.
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    Cited by:

    1. Heman D. Lohano & Robert P. King, 2009. "A Stochastic Dynamic Programming Analysis of Farmland Investment and Financial Management," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 57(4), pages 575-600, December.

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