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The sector of knowledge-intensive services is one of the fastest-growing sectors in the present-day economy of knowledge, which explains the scientific interest in developing methods of its quantitative assessment. The object of the research is the development of new approaches to the mathematical modeling of the efficiency of the regional knowledge-intensive services sector, based on a distance function approach to assess productivity changes. An approach was proposed to analyze the efficiency of this sector using data envelopment analysis and Malmquist productivity index and its components. The article presents the results of the assessment of indicators characterizing the development of knowledge-intensive services in education, innovation, and ICT obtained from 80 Russian regions for the period 2010–2020. To perform the analysis, the following input variables were used: volume of investments in fixed assets in ICT; share of personnel employed in the ICT; share of internal expenditures on R&amp;D in GRP; the number of personnel engaged in R&amp;D; share of innovative-active organizations and registered patents; funding for higher education institutions; and the number of higher education institutions graduated. Output variables were number of used advanced production technologies in the region; share of innovative goods, works, and services in GRP, and use of the intellectual property. As a result of applying the data envelopment analysis, Malmquist productivity index and its components, data were obtained on the positive dynamics of the development of the knowledge-intensive services sector in Russian regions and conclusions were drawn about the sector’s growth sources due to economies of scale.

Approaches to Efficiency Assessing of Regional Knowledge-Intensive Services Sector Development Using Data Envelopment Analysis