In the framework of the modern paradigm of the existence of economic systems, the introduction of innovative technologies, elements of the digital economy in management, production, social and economic activities is recognized as the most important means of influencing the positive dynamics of productive forces, which is the basis for economic growth. Qualitative economic growth is possible only in the case of large-scale introduction of innovations and digital technologies. However, the implementation of these conditions in the Russian economy is fraught with difficulties due to the reduction of the working-age population and the lack of the necessary qualifications of the workforce. In turn, the lack of high-tech production hinders the creation of the required number of high-paying jobs. The article discusses the issues of quantitative assessment, based on the developed economic and mathematical model, the economic category «higher education and advanced training», which is the backbone for the regional economy, which is on the way to the innovative stage of development. The indicated category is studied as a macroeconomic characteristic of the subject of the Russian Federation. When researching a problem, finding and developing solutions, we used methods of comparative analysis, economic and mathematical modeling (regression analysis, correlation analysis, factor analysis), statistical data processing methods (the official data of the Federal State Statistics Service for the period 2007–2017 are taken as the basis), as well as specially developed application software. Information support of the formed economic-mathematical model was provided by economically interpreted and commented data, reduced to a comparable form. The index method was used as a tool for quantification. A fixation is made and a meaningful description of the category «higher education and advanced training» is given. Composed numerical indicators (indices) characterizing the basic aspects of the functioning of the studied category. A calculation-experimental method has been carried out to prove the adequacy of the developed model, given a quantitative assessment using examples of constituent entities of the Russian Federation that are part of the North-West and Volga Federal Districts. The obtained results develop scientific knowledge in the field of regional economy, which contributes to the development and use of innovative methods of managing the socio-economic system of the region. The practical application of the developed methodological approaches will allow us to purposefully and reasonably solve the tasks of strategic development of priority development.