Application of differential evolution algorithm for solving the Solow model with the addition of human capital

  • S. I. Kabanikhin Institute of Computational Mathematics and Mathematical Geophysics of SB RAS
  • M. A. Bektemessov al-Farabi Kazakh National University
  • M. A. Shishlenin Institute of Computational Mathematics and Mathematical Geophysics of SB RAS
  • Xin-She Yang Middlesex University, London, United Kingdom
  • Zh. M. Bektemessov al-Farabi Kazakh National University

Abstract

This paper is devoted to a numerical study of defining of parameters of dynamical systems arisingin financial and economic problems. The importance of parameters that are difficult to measure isgreat, so defining them will help to make forecasts and a work plan for the future at the governmentallevel. An effective way to restore parameters is to solve the inverse problem. The methodof coefficient recovery using the algorithm of differential evolution, which was proposed by RainerStorn and Kenneth Price, is presented in this paper. On the example of solving the direct problemof the mathematical model of neoclassical economic growth of Robert Solow and the resultsobtained, the inverse problem was solved and unknown parameters were determined. The Solowmodel is based on the Cobb-Douglas production function, taking into account labor, capital andexogenous neutral technical progress. Also, for further calculations, the economic model proposedby Mankiw-Romer-Weil based on the Solow model was considered, but with the addition of humancapital, where the number of variables and coefficients that need to be restored has alreadyincreasing. A direct problem was also solved, results were obtained that were applied in the algorithmof differential evolution for parameters recovery.

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Published
2018-08-29
How to Cite
KABANIKHIN, S. I. et al. Application of differential evolution algorithm for solving the Solow model with the addition of human capital. Journal of Mathematics, Mechanics and Computer Science, [S.l.], v. 98, n. 2, p. 57-66, aug. 2018. ISSN 1563-0277. Available at: <http://bm.kaznu.kz/index.php/kaznu/article/view/406>. Date accessed: 10 dec. 2018. doi: https://doi.org/10.26577/jmmcs-2018-2-406.
Keywords economical model, inverse problems, optimization, differential evolution, Solow model