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The use of interval arithmetic in solving a non-linear rational expectation based multiperiod output-inflation process model: The case of the IN/GB method

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  • Stradi-Granados, Benito A.
  • Haven, Emmanuel

Abstract

The use of interval mathematics to solve non-linear problems is an attractive alternative to traditional real-number techniques. It was demonstrated in a previous paper [Stradi, B., Haven, E., 2005. Optimal investment strategy via interval arithmetic. International Journal of Theoretical and Applied Finance 8(2), 185-205] that interval arithmetic in the form of the Interval-Newton Generalized Bisection (IN/GB) method is effective in solving highly non-linear problems. In this paper we solve a rational expectations models with the help of the IN/GB method. This method is capable of (i) rapidly eliminating no solution sections of the multidimensional space and (ii) concentrate computational efforts on those areas of multidimensional space where there may be a solution.

Suggested Citation

  • Stradi-Granados, Benito A. & Haven, Emmanuel, 2010. "The use of interval arithmetic in solving a non-linear rational expectation based multiperiod output-inflation process model: The case of the IN/GB method," European Journal of Operational Research, Elsevier, vol. 203(1), pages 222-229, May.
    • Handle: RePEc:eee:ejores:v:203:y:2010:i:1:p:222-229
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    1. Fuller, J. David & Chung, William, 2008. "Benders decomposition for a class of variational inequalities," European Journal of Operational Research, Elsevier, vol. 185(1), pages 76-91, February.
    2. Douglas Laxton & Guy Meredith & David Rose, 1995. "Asymmetric Effects of Economic Activity on Inflation: Evidence and Policy Implications," IMF Staff Papers, Palgrave Macmillan, vol. 42(2), pages 344-374, June.
    3. Fair, Ray C & Taylor, John B, 1983. "Solution and Maximum Likelihood Estimation of Dynamic Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 51(4), pages 1169-1185, July.
    4. Gilli, Manfred & Kellezi, Evis & Pauletto, Giorgio, 2002. "Solving finite difference schemes arising in trivariate option pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 26(9-10), pages 1499-1515, August.
    5. Juillard, Michel, 1996. "Dynare : a program for the resolution and simulation of dynamic models with forward variables through the use of a relaxation algorithm," CEPREMAP Working Papers (Couverture Orange) 9602, CEPREMAP.
    6. Benito Stradi & Emmanuel Haven, 2005. "Optimal Investment Strategy Via Interval Arithmetic," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(02), pages 185-206.
    7. Jean-Pierre Laffargue, 1990. "Résolution d'un modèle macroéconomique avec anticipations rationnelles," Annals of Economics and Statistics, GENES, issue 17, pages 97-119.
    8. Jiang, Jian-Lin & Yuan, Xiao-Ming, 2008. "A heuristic algorithm for constrained multi-source Weber problem - The variational inequality approach," European Journal of Operational Research, Elsevier, vol. 187(2), pages 357-370, June.
    9. Boucekkine, Raouf, 1995. "An alternative methodology for solving nonlinear forward-looking models," Journal of Economic Dynamics and Control, Elsevier, vol. 19(4), pages 711-734, May.
    10. Gelman, Irit Askira, 2005. "Addressing time-scale differences among decision-makers through model abstractions," European Journal of Operational Research, Elsevier, vol. 160(2), pages 325-335, January.
    11. Fernandez, Jose & Pelegri'n, Blas & Plastria, Frank & Toth, Boglarka, 2007. "Solving a Huff-like competitive location and design model for profit maximization in the plane," European Journal of Operational Research, Elsevier, vol. 179(3), pages 1274-1287, June.
    12. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-1311, July.
    13. Zilinskas, Julius & Bogle, Ian David Lockhart, 2006. "Balanced random interval arithmetic in market model estimation," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1367-1378, December.
    14. repec:adr:anecst:y:1990:i:17:p:04 is not listed on IDEAS
    15. Juillard, Michel & Laxton, Douglas & McAdam, Peter & Pioro, Hope, 1998. "An algorithm competition: First-order iterations versus Newton-based techniques," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1291-1318, August.
    16. Gilli, Manfred & Pauletto, Giorgio, 1998. "Krylov methods for solving models with forward-looking variables," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1275-1289, August.
    17. Gilli, Manfred & Pauletto, Giorgio, 1997. "Sparse direct methods for model simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(6), pages 1093-1111, June.
    18. Hallett, A. Hughes & Ma, Y. & Yin, Y. P., 1996. "Hybrid algorithms with automatic switching for solving nonlinear equation systems," Journal of Economic Dynamics and Control, Elsevier, vol. 20(6-7), pages 1051-1071.
    19. Andrew P. Blake, 2004. "Analytic Derivatives for Linear Rational Expectations Models," Computational Economics, Springer;Society for Computational Economics, vol. 24(1), pages 77-96, August.
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