This article focuses on the assessment of the size of the public sector, which goes back to the assessment of the degree of state participation in the domestic economy and remains controversial. Such assessments are often carried out without the presentation of threshold criteria and without evaluation of its effectiveness and combination with other institutional sectors. At the same time, it is obvious that the ratio between the public and other (non-state) sectors refers to the issue of strategic importance, to the issue of the effectiveness of the country's economic system in its integrity, and therefore requires theoretical, methodological and practical resolution.

The objectives of the research are: (1) to determine the relative scale and efficiency of the public sector functioning in the national economy, to establish minimum necessary and maximum possible values of its scale; (2) to determine the size and establish a measure of harmonious combination of institutional components of the domestic economy aimed at maximizing its efficiency.

Materials and methods. Theoretical foundations of the research have been developed on the basis of the authors' preferences regarding the results of conceptual and applied developments of domestic scientists in the field of philosophy, mathematics, economics and sociology, as well as the practice of structural and spectral analysis in their subject areas. The analysis of parameters (indicators) of the state and other institutional sectors of the national economy was carried out (mainly) on the basis of statistical data of ROSSTAT for 2006-2016, materials of official reports and developments of analytical centers. The methodological basis of the research is formed by works on modular theory of society, public sector economy, and structural harmony of systems. Tabular methods of visualization of research results and statistical methods of source data processing were used. Standard packages of Microsoft Office application programs were used for solving research tasks.

Results. It is shown that against the background of a decrease in relative resource capacity, the public sector over the period under review does not show an increase in the degree of government participation in the Russian economy. At the same time, performance indicators of the public sector did not show not only worse, but also worsening values, both as compared with the private sector and the economy as a whole. Criteria of minimum required and maximum possible scale of the public sector have been defined and it is shown that as of 2016 the integral indicator of the scale of the public sector of the Russian economy does not reach the minimum required value. A quantitative model for optimizing the sectoral composition of the national economy has been constructed. System solutions are proposed and a method for determining the share of institutional sectors in the structure of the national economy is given.

Conclusion. The article deals with the issues of state participation in the economy, defines the scale and efficiency of the public sector in the national economy. It is noted that within the limits of maximally liberal and maximally ethical ideological statements the task of optimization of neither the size of the public sector of the national economy nor the harmonious combination of its sectoral composition find a satisfactory solution. The analysis of institutional composition of the national economy has been carried out and the way of optimization of its structure has been shown, the direction of the state economic policy on optimization of institutional structure of the national economy has been determined. Orientation of economic policy towards achievement of optimal structure (harmony) of economic system (as well as the very movement towards it) will create conditions not only for increase of its efficiency, but also will allow to satisfy economic needs of socially-professional groups to the fullest extent, and society as a whole will successfully develop.

Purpose of the study. The research materials continue the author's series of articles devoted to the problems of the stakeholder approach. The social responsibility of business acts as a launching pad for fruitful cooperation and interaction between business structures and authorities. The concept of corporate social responsibility is very dynamic, characterized by constant transformation, change and enrichment with new ideas. So, if in the middle of the XX century it developed rather slowly, not finding a response in the business environment, then in the XXI century it is “preached” as the main business philosophy by most of the advanced countries. At the same time, a characteristic feature of existing scientific approaches is the emphasis on technocratic and economic positions and the complete absence of approaches based on the relationship between business and stakeholders. However, such approaches from the author's point of view are insufficient for the entire range of requirements imposed by the external and internal environment on modern business. The ambiguity of the interpretation of the concept under study made it possible to state the complexity of this category and its multidimensional nature. In this regard, there is a need for a comprehensive statistical assessment of the degree of business socialization and the choice of appropriate tools for this.

Materials and methods. The statistical assessment of the degree of business social responsibility is based on local criteria, combined into five blocks. The presented system of criteria characterizes the activities of the business taking into account the requirements of the stakeholders. At the same time, the list of criteria can be adjusted when socio-economic trends and problems of society change. The information base of the study was the annual and financial reports of regional enterprises, the results of expert assessments. The hierarchy analysis method and the graphical polygon (radar) method were used as a tool for assessing the degree of business socialization.

Results. The article concretizes the concept of social and economic responsibility of business. The author's approach covers the idea of a responsible partnership based on the interaction of business with a wide range of interested groups involved in active and passive forms of participation in its operations. The variety of interests of stakeholders representing various subjects of market interaction emphasizes the multi-criteria nature of the category of “social and economic responsibility of business”. Statistical tools are fully capable of providing an assessment of the entire spectrum of signs of corporate social responsibility. The integral indicator of the degree of social responsibility, built on the basis of the hierarchy analysis method, made it possible to distinguish four degrees of business socialization: low, moderate, noticeable and high. For each degree of socialization, characteristic features are determined. The results of the study showed that as the degree of social responsibility grows, business performance indicators increase and its well-being in the long term depends on the coordination of the interests of key participants in corporate relations. An integral assessment of the degree of business socialization was carried out according to twenty-six local criteria. As a result of calculating the private and local ranks of the values of the corresponding criteria, fifteen polygons of the degree of socialization of the regional business were built, included in the sample. The results obtained make it possible to ascertain the existence of a high degree of heterogeneity of regional enterprises in terms of the investigated integral indicator. The leaders in terms of social responsibility are JSC “Teplichnoye”, OJSC “Mordovcement”, OJSC “Elektrovypryamitel”, OJSC “Lato”. Outsiders include OJSC Cheese-Making Plant “Ichalkovsky”, Ltd “Lisma”, OJSC “Stankostroitel”, OJSC “RubEx”. Among the features of regional enterprises, one can single out the heterogeneity in the distribution of indicators along the radial straight lines. JSC “Teplichnoye” is characterized by sharp fluctuations in rank values, which is most active in interaction with consumers, its own personnel, but also stands out as one of the smallest values of the block associated with relationships with business partners. A similar situation is observed among outsider enterprises. The proposed methodology can be used as a tool for a comprehensive study of existing trends in the practice of socially responsible business behavior, characteristics of the results achieved, as well as identifying problem areas that focus additional attention.

The aim of the research is to develop theoretical and methodological approaches to market value forecasting in the real estate market. The relevance of the research is determined by the system-forming place that the real estate market occupies in the economy of the country and regions, affecting the interests of owners of various forms of ownership, construction and development companies, insurance companies, banks. Another aspect that determines the actuality of the study is the discrepancy between well-structured cadastral databases and market data dispersed between different owners of information resources, and the unstructured nature of market data, which in most cases is focused on advertising, rather than on analytical market research.

Materials and methods. The study uses a model of a multidimensional logarithmically normal distribution law of the ensemble of prices for residential real estate at equidistant points of time and cadastral value, the ARIMA model for predicting market value, taking into account the features of the logarithmically normal distribution of prices, as a distribution with positive asymmetry. As a statistical material, we used market data on residential real estate published in the periodical press in the period from the end of 2012 to 2018. The volume of samples of weekly publications is 15000-20000 objects; data for 21 quarters (more than five years) was used. As a comparison base, we used data from cadastral registration of real estate objects in Saint Petersburg for 2018. The total volume of the cadastral database of residential real estate in Saint Petersburg (individual apartments) is 2 226734 objects with a fairly complete (and well-structured) set of price-forming factors. The authors propose a method for estimating the most likely movement of the market value for a pre-selected real estate object that has passed cadastral registration and has a cadastral value entered in the register and predicting the market value in the future period.

Results. The theoretical significance of the work is the proposed algorithm for estimating the most probable trajectory of the market value of the investigated object, based on the conditional multivariate log-normal distribution for a given value of the cadastral value. A well-developed and studied ARIMA time series forecasting model is applied to the logarithms of the obtained time series, the return from logarithmic prices to real prices is carried out taking into account the peculiarities of the logarithmically normal distribution. Results are compared with median scores and estimates, obtained by average values.

Conclusion. The paper shows that the introduction of cadastral value in the Russian Federation opens up new opportunities for analyzing and forecasting market prices, since cadastral databases contain the most complete lists of real estate objects, including the cadastral value, which now, in accordance with the law, must be updated at least once every three years and, as of 2015 and 2018, was determined as the market value, therefore, until the next cadastral assessment, can serve as a basis for constant comparison with market data, which are constantly changing, primarily in the composition of objects.

Purpose of the study. The study of the qualitative parameters of the human resources potential of the economy is necessary to describe the conditions in which digitalization processes develop, to identify the problems of training specialists. The professional education system is considered in the article as an institution that provides human resources to the digital economy of the region. Innovative processes increase the requirements not only for the system of training specialists, but also for the skills of the lecturer, individual level of mastering information and communication technologies. The purpose of this study is to diagnose the levels of digital competencies of lecturers of professional educational institutions and to identify, on the basis of statistical analysis, the impact on the level of digital competencies of a lecturer of various parameters, such as the lecturer’s age; the disciplines he/her teaches; the data of continuing education in the field of information and communication technologies.

Materials and methods. This paper provides an overview of approaches to solving the problems of staffing education in the context of informatization. Taking into account the proposed model of digital competencies of lecturers, the testing complex was approved. Methods of statistical data analysis were applied: descriptive statistics, correlation coefficients were calculated, a range diagram and scatter diagrams of lecturers' testing results were constructed. For the information processing, the qualitative indicators were converted into quantitative ones and the statistical analysis software packages were used: Microsoft Excel and STATISTICA 10.0.

Results. As a result of the lecturers’ testing of professional educational institutions and statistical analysis, data were obtained on the level of human resources in terms of the formation of knowledge and skills in the field of information and computer technologies. The relationship between the level of digital competence and various factors has been identified. The factors that were analyzed in the course of the study: age, subjects taught, the period of limitation of the advanced training in the field of information and communication technologies.

Conclusion. The introduction of the proposed model of competencies and diagnostic methods will allow diagnosing lecturers' skills in working in a digital environment and will ensure the adoption of informed managerial decisions in the development of the human resources of the vocational education system both at the level of the educational organization and at the level of public administration bodies. This model can be used to obtain information about the formation of digital competencies of different groups: employees of organizations and enterprises, state and municipal employees.

The development programs of Russian universities contain many different target indicators. Many of these indicators are focused on the development of the research activities. In the context of limited financial resources for development, the question of an effective system of target indicators is very important. To construct such a system of target indicators, three conditions must be met: 1) these target indicators do not contradict each other; 2) there are indicators with a positive effect on economic indicators; 3) subject areas are taken into account.

The aim of the research. This study is aimed to study linear correlation dependencies between the main indicators measuring the university’s publication activity and other scientometric, social and structural indicators.

Materials and methods. The study used economic, structural and scientometric data for 49 largest universities in Russia over 4 years, downloaded from monitoring the performance of educational institutions of higher education and the SciVal analytical tool.

Results. As part of the research, it was studied which variables are correlated with the taken scientometric variables. Due to the large number of variables involved in the primary analysis, the table contains only those variables that correlate with the variables under consideration with a correlation coefficient of more than 0.3 modulus.

Conclusion. The results obtained allow both to resolve the contradiction of the simultaneous increase in the number and quality of publications, and to highlight a number of links between scientometric indicators and indicators of university economics, internationalization and quality of admission. Knowledge of these dependencies is useful for compiling university development programs that do not contain internal contradictions. The conclusions obtained make it possible to increase the efficiency of construction a system of university target indicators in the research field in three areas: compiling the university development program with consistent target indicators, the inclusion of indicators with a positive impact on economic indicators, taking into account the peculiarities of the field of science and education in which the university operates.

Purpose of the study. The rapidly developing processes of the formation of the digital economy affect various spheres of human life in modern society, inevitably changing the educational environment. The aim of the work is to analyze the main development trends and emerging transformation processes in the field of higher education under the influence of growing digitalization and digital transformation of various aspects of human life.

Materials and methods. In the course of the work, a dynamic, structural analysis of analytical and statistical information about the processes taking place in this area was used, as well as methods of theoretical research: analysis and generalization.

Results. The pace of development of the digital economy in the modern world is very rapid, due to which the life of a number of professions is shortened, and changes affecting the content of labor contribute to the emergence of new ones. Based on this, it is necessary to understand the main directions of development in higher education, since personnel training is one of the most important components of the digitalization of the economy. The paper formulates the main directions for the development of education using digital technologies for the training of qualified specialists who meet the requirements of the digital economy and outlines a number of problems that the educational system will face in the process of transformation.

Conclusion. The spread of digital and information technologies contributes to significant transformations in various fields of human activity and the sphere of higher education is no exception. The format of the digital economy is quite mobile, which leads to the fact that some specialties will emerge, others will lose their importance and disappear more or less rapidly, and also under the influence of constant and fairly rapid changes, the requirements for training will change. Considering the high mobility and variability of the current situation both in the economy and in the field of higher education, there is a need for constant adjustment of educational programs taking into account the ongoing changes. The rapid development of new knowledge and technologies, and many other reasons, contribute to significant transformations of higher education systems around the world. At the same time, considering the speed of changes, it is quite difficult at the present time to assess the entire range of challenges and problems that face the sphere of higher education. Separate sections of the work have been published earlier in a number of articles by the author devoted to this problem.

The purpose of the research is to develop a generalized structural scheme of organizational and technical systems based on the general theory of management, which contains the necessary and sufficient number of modules and formalize on this basis the main management tasks that act as goals of the behavior of the management object. The main modules that directly implement the management process are the status assessment module of organizational and technical systems and the management module. It is shown that in traditional organizational and technical systems, including the decision-maker, the key module is the state assessment module of organizational and technical systems. In this regard, the key aspect of the work is to study the optimal algorithms for evaluating the state of processes occurring in the organizational and technical systems and develop on this basis the principles of mathematical formalization and algorithmization of the status assessment module. The research method is the application of the principles of the theory of statistical estimates of random processes occurring in the organizational and technical systems against the background of interference and the synthesis of algorithms for the functioning of the status assessment module on this basis. It is shown that a characteristic feature of random processes occurring in organizational and technical systems is their essentially discrete nature and Poisson statistics. A mathematical description of the statistical characteristics of point random processes is formulated, which is suitable for solving the main problems of process evaluation and management in organizational and technical systems. The main results were the definition of state space of the organizational and technical systems, the development of a generalized structural scheme of the organizational and technical systems in state space that includes the modules forming the state variable of the module assessment and module management. This mathematical interpretation of the organizational and technical systems structure allowed us to formalize the main problems solved by typical organizational and technical systems and consider optimal algorithms for solving such problems. The assumption when considering the problems of synthesis of optimal algorithms is to optimize the status assessment module of organizational and technical systems and the control module separately, while the main attention is paid to the consideration of optimal estimation algorithms. The formalization and algorithmization of the organizational and technical systems behavior is undertaken mainly in terms of the Bayesian criterion of optimal statistical estimates. Various methods of overcoming a priori uncertainty typical for the development of real organizational and technical systems are indicated. Methods of adaptation are discussed, including Bayesian adaptation of the decision-making procedure under conditions of a priori uncertainty. Using a special case of the Central limit theorem, an asymptotic statistical relationship between the mentioned point processes and traditional Gaussian processes is established. As an example, a nontrivial problem of optimal detection of Poisson signal against a background of Poisson noise is considered; graphs of the potential noise immunity of this algorithm are calculated and presented. The corresponding references are given to the previously obtained results of estimates of Poisson processes. For automatic organizational and technical systems, the generally accepted criteria for the quality of management of such systems are specified. The result of the review is a classification of methods for formalization and algorithmization of problems describing the behavior of organizational and technical systems.