Exploring the Innovative Development of Russian Regions: A Spatial Regression Analysis Using the Cobb-Douglas Model

Relevance. Extensive research has focused on evaluating and modeling innovative processes in territorial systems. However, an underexplored aspect is the assessment of spatial effects resulting from neighboring territories and the modeling of inter-territorial interactions in enterprise innovation. The existing regression models have limitations in accounting for spatial effects, indicating the presence of unaccounted factors. Research objective. This study aims to develop a methodological approach to evaluate the influence of factors on the dynamics of shipped innovative goods in Russian regions, taking into account spatial effects. Additionally, it aims to test the hypothesis that territories located near innovatively developing regions exhibit faster progress. Data and methods. The study utilizes regression analysis of panel data, employing combined least squares, fixed effects, and random effects methods to evaluate the influence of enterprise costs on innovation, the number of research personnel (researchers and technicians), advanced production technologies developed and used, the number of research organizations, as well as the internal costs of fundamental and applied research and development on the volume of shipped innovative goods in Russian regions from 2000 to 2021. To account for spatial effects, spatial econometrics techniques such as Spatial Autoregressive (SAR) models considering spatial lag and Spatial Autoregressive Conditional Heteroscedasticity (SAC) models considering both spatial lag and spatial error are employed. The Generalized Method of Moments (GMM) with the White period weight matrix is used to address heteroscedasticity, and data transformation techniques including orthogonal deviations and the inclusion of dummy variables for each spatial unit and time period are applied. Results. The study reveals deepening spatial heterogeneity in innovation processes during economic downturns, which smooth out during economic recovery. Regions with high and low concentrations of shipped innovative goods are identified. Regression analysis establishes the impact of various factors on shipped innovative goods. Spatial models utilizing the Cobb-Douglas SAR and SAC frameworks demonstrate positive spatial effects, wherein neighboring regions exert influence on innovative development. Regions with high enterprise innovation activity, including Moscow, St. Petersburg, and others, exhibit the highest spatial effects. Conclusions. The innovative development of a single region depends not only on its own production factors but also on the innovative activity of enterprises in the surrounding regions. These findings highlight the importance of considering spatial effects in assessing and modeling regional innovation dynamics.