Method for assessing the results of hierarchical socio-economic systems’ functioning based on the aggregated production function

Abstract

The article presents a method that develops a methodology for assessing the functioning of hierarchical socio-economic systems. The methodology includes formalized description of the object of research and the construction of partial and integral performance indicators. Performance indicators are calculated using production functions. The method is based on an algorithm for constructing an aggregated production function, which is used to calculate the normative (expected) value of the result of the functioning of the object of research. Using the example of the regions in Central Federal District and data for 2007–2016 testing and comparative analysis of four algorithms for estimating the parameters of the aggregate production function in the construction of the integral indicator are carried out. The gross regional product for the NACE sections (C, D and E) was chosen as effective indicators. The scientific novelty of the study is as follows. Three algorithms for constructing the distribution density of an aggregated random variable, which is a combination of residuals from econometric equations that describe the particular results of the functioning of elements of a hierarchical socio-economic system, are proposed and tested. The distribution density is used to find the parameters of the aggregated production function. For the two-dimensional case, analytical expression of the corresponding probability distribution density is obtained. The conclusion about the possibility of using the method to evaluate the results of the functioning of hierarchical socio-economic systems is substantiated.