Construction of an aggregated production function with implementation based on the example of the regions of the Central Federal District of the Russian Federation

A three-dimensional case is considered on the basis of a method developed for estimating the parameters of the aggregated production function used to calculate dynamic standards and build integral indicators of the performances of the functioning of socio-economic systems. The aggregated production function is determined by the quadratic convolution of the production functions of the results of the functioning of the elements of the subsystem and their correlation matrix. The parameters of the aggregated production function are determined from solving the problem of maximizing the likelihood function of a random variable – the residuals of production functions aggregated according to a similar rule. On the example of a project subsystem within the framework of the Kleiner’s spatial-temporal classification of socio-economic systems we obtained adjusted values of the parameters of a function that includes power-law multiplicative models of the relationship between the volume of gross domestic product by region for sections F (construction), G (wholesale and retail trade), K (financial activity) according to NACE 2 and the cost of fixed assets (total for section K, for sections F and G), the average annual number of employees (for sections F and G) and the average annual population (for section K), based on data for 2015–2020 (sections G, K) and 2018–2020 (section F) for the regions of the Central Federal District. The EFRA software package and Python’s project were used as tools. The results obtained can be used by regional authorities in assessing the functioning of the regions and the formation of appropriate standards in the short term.