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

Abstract

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