Assessment of the Regions Functioning Based on Production Functions with the Above Cost Factors

When modeling the growth of a regional economy by means of production functions, a problem arises of choosing models, factors and methods for adjusting cost characteristics in order to obtain adequate and accurate models, as well as the formation of integral and partial indicators of performance that provide a correct assessment and analysis of the performance of the regions of Russia. Such a problem becomes especially significant if the models are adequate and accurate, and, consequently, the process under study is invariant with respect to the models, factors and calculation methods used. The aim of the study is to estimate the results of the regions' performance on the basis of production functions, provided that the process of changing the volume of GDP by region is invariant with respect to models, factors and methods of bringing them to a comparable form when modeling the growth of the Russia regional economy. The hypothesis of the investigation is the invariance of the process of the change of the volume of GDP by region relative to the models, factors and methods used to bring the cost indicators to a comparable form. The study used data on the CFD regions (2007–2020). As a result, five models were constructed, the factors of which were calculated in five different ways, taking into account both price changes and average annual characteristics. It was determined that partial indicators have similar dynamics. At the same time, statistical tests and the author's methodology for choosing a model that would take into account the priorities of regional development did not allow for identifying the best of them. This allowed us to conclude that the process under study is invariant with respect to the models and correction techniques used. To solve the problem of choosing models for evaluating the regions' performance results, it is proposed that an integral performance indicator should be applied that summarizes the calculation methods used. This would reduce the influence of subjectivity of such a choice. The theoretical significance lies in the possibility of applying the methodology to form integral and partial indicators of performance for arbitrary socio-economic systems. The practical significance of the conducted research lies in the fact that the results obtained can be used to design activities that would be aimed at ensuring the CFD regions' sustainable development.