The aim of the work was to evaluate the dynamics of regional innovation development and compare the Russian regions according to their innovation efficiency, used resources, and achieved results. To estimate direct and indirect innovation effects, this study used the data on Russian regions according to variables of the innovative product volume, the share of high-tech products in the gross regional product (GRP) structure, the number of used patents, and investment in innovation activity for 2006–2017. To obtain a representative sample, a cluster analysis was applied as a preliminary step, which made it possible to select a group of regions that were most advanced in terms of their innovative development. Output-oriented data envelopment analysis models were applied for Malmquist Productivity Index calculation. The obtained results indicate the average growth of total factor productivity of regional innovation development over time. The main source of innovative development is largely derived from the economy of scale, while the effectiveness of regional innovation systems is basically increasing through broader resource bases, rather than through its effective utilization. The research findings can be applied to diagnose regional innovation effectiveness, justify public investment in research and development (R & D), and identify the priorities of regional innovation policy for specific regions.

The problems of current financing of innovations determine the relevance of the research allowing for quantifying and evaluating the performance of regional innovation systems in terms of the structure of innovation financing. The paper presents an approach to analyzing and evaluating the efficiency of innovation activity in Russian regions using the Data Envelopment Analysis. To estimate the efficiency of regional innovation systems, we use the ratio of a set of input parameters of sources and structure of R&D financing to a set of output parameters of the innovative goods volume in the context of 80 Russian regions. We rank the regions according to the technical efficiency index, determine the degree of their homogeneity and differentiation, reveal leading and outsider regions by the degree of efficiency of financial resources use in regional innovation systems. It is determined that the share of the leading regions makes 25% and the share of inefficient regions makes 53%. The conclusion is made on the need to spread the best practices of the leading regions and to apply a more efficient structure for financing innovative activities in outsider regions.

The paper is devoted to the development of analytical tools for assessing the dynamics of risks to the competitiveness of Russian regions within the conditions of incomplete information. The choice of analysis methods for assessing the risk dynamics was substantiated. A solution based on the implementation of homogeneous Markov models with a discrete set of states and continuous time was proposed, it allowed to assess the probability of risks affecting regional competitiveness. A hierarchical structure of factors that determine the risks of regional competitiveness was formed as a cause-and-effect graph. Corresponding systems of Kolmogorov – Chapman differential equations were obtained and solved. An example for analyzing a 3-element minimal cut set of a cause-effect graph was presented. A set of scenarios for the study of risks and their combinations in various conditions was proposed. The solution was obtained for three leading Russian regions. For a set of scenarios, numerical assessments of risk factors that significantly affect the decline in the competitiveness of regions have been fulfilled. The study results made it possible to rank the effects of critical event occurrence, to identify the most significant risk factors for the loss of sustainable development and competitiveness for the Russian Federation regions.

The purpose of this research is to develop the Data Envelopment Analysis (DEA) methodology for modeling of the assessment of the regional higher education systems effectiveness. The importance and topicality of this study is based on the increasing role of universities in the economic development of regions and countries in recent decades as well as the need to develop approaches for assessing the university effectiveness, and using mathematical models and methods for these goals. The novelty of the research is the formation of the DEA model and its application to the analysis of regional higher education systems' effectiveness. The hypothesis of uneven development of regional higher education systems was tested from the standpoint of functional approach; the higher education systems' effectiveness has been calculated and the ranking of Russian regions was performed by different DEA models. As a result of the DEA modeling, a quantitative effectiveness assessment was carried out, and a set of Russian regions was ranked according to three basic university functions: education, science, and regional partnership. Conclusions about the level of effectiveness and development strategy of regional higher education systems in Russia have been drawn.

The article presents the results of a study of innovative spillover effects using Data Envelopment Analysis (DEA) tools. The study is novel, in that an assessment methodology has been developed based on the Malmquist index and an output-oriented DEA model has been built to analyze the dynamics of the regional innovation system development. The development of innovative systems at the regional and national levels has been assessed, the Malmquist Index has been calculated, the characteristics of the regions have been determined taking into account the evaluation of spillover effects, and conclusions have been drawn on the dynamics of the development of innovative activities. The results of the study indicate the presence of positive innovative spillover effects over 2005-2017 in the Russian economy.