The convergence of productivity in the regions means their sustainable development and the protection of the national economy from external challenges. Accelerating digitalization of society expands the sphere of services and exacerbates the issue of measuring the productivity of the region's economy and the impact on it of internal knowledge factors (including innovations). The spatial heterogeneity of Russian regions, when identifying interrelationships, requires taking into account the spatial aspect. The main aim of the work is to assess the conditional beta-convergence of the gross regional product per capita growth rates of the employed population and the impact of technological innovations on productivity in the regional economy on the basis of spatial-econometric models. Research hypotheses suggest that, spatial dependence contributes to the productivity growth rates convergence in the regional economy, technological innovations have a positive impact on productivity growth in the regional economy. The study uses Moran and Geary global spatial correlation indices, Moran local spatial correlation index, econometric model with spatial auto-regression lag, econometric model with spatial interaction in errors, maximum likelihood estimation. We revealed the spatial positive correlation of labor productivity, while the growth rates of real costs for technological innovations have a spatial negative correlation (strong regions "pull" innovations from weak neighbors). Authors didn't confirm the impact of the patents number for inventions and the use of the Internet in organizations on the growth rate of the gross regional product. Based on spatial-econometric models of panel data analysis, no beta-convergence of productivity growth rates in the regions was found.
