Mathematical modeling and neural network prediction of the structure and dynamics of human capital of the Russian Federation

The problem of mathematical modeling and forecasting the values, structure and dynamics of human capital using the neural network algorithm is solved. The paper is used an integrated economic and mathematical model of human capital, which includes quantitative and qualitative characteristics. A quantitative characteristic is the distribution of demographic elements by ages. Qualitative characteristics include such components of human capital as educational capital, health, and cultural capital. The forecast of the dynamics of human capital is based on the two-dimensional transport equation, which takes into account the time and age of demographic elements, as well as the forecast values of the volume of budgetary and private investments in human capital, built on a multilayer neural network model. The calculations were made on the basis of statistical information for the Russian Federation, including data on demographics, volumes of investments in human capital of the economic system of the Russian Federation, as well as indicators of directions of socio-economic development. Volumes of investments in human capital determine budget expenditures and private expenses of citizens. To forecast the dynamics of human capital, the values of the volumes of investments in it are used, the forecast of which, in turn, is built using the neural network model. The period 2000-2018 was chosen as the studied one. The adaptive neural network modeling algorithm used in the work made it possible to construct a forecast of human capital of the Russian Federation until 2025. The neural network model used in this study is a multilayer fully connected perceptron with a sigmoidal logistic activation function. Neural network modeling of investment values has been shown to be effective. The constructed forecasts satisfy the given accuracy. So, the deviation of the model values of investments from the actual in the components of human capital for the period of retrospective forecast 2015-2018. amounted to 1.6%. Calculations of the human capital of the Russian Federation in the interval 2000-2018 showed that it began to increase since 2005 with an annual average rate of 5.5%. Since that moment in time, the average annual investment rate in the components of human capital has increased: health - 3.7%, education - 3.8%, culture - 2.6%. In the future, until 2025, a slowdown in the growth of human capital of the Russian Federation to 1.0% per year is forecasted. The proposed methodology for calculating the magnitude and dynamics of human capital can be used to assess and compare the socio-economic situation of the Russian Federation regions.

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