Taking into consideration the main foreign theories of innovation diffusion of E. Rogers and the knowledge spillover theory of Marshall-Arrow-Romer, and Anselin, the endogenous growth model of J. Grossman and E. Helpman, using the originality of the knowledge spillover model of Ph. Aghion and P. Howitt, we explored how the economic growth of territories is associated with innovation.
On the basis of factor analysis the calculations of the "Social filter" index were carried out. Those take into account a set of indicators that determine the social and economic features of the region, such as the unemployment rate, the population with higher education engaged in R&D, the share of the employed population in the region's agriculture, the share of population in the age of up to 28 years and the share of employed in industry.
The model includes indicators that measure the growth of the gross regional product of the regions of Kazakhstan. Knowledge spillovers were taken into consideration due to distance matrices between regional centers and accessibility indices. On the basis of data on innovative indicators of the regions of Kazakhstan for 2005-2015, regression models with fixed effects were estimated.
The research confirms the main theoretical provision that innovation activity, taken into account in the calculations through (research and development) R&D costs, and costs for technological innovations and knowledge spillovers, are endogenous factors that can explain differences in the economic growth of the regions of Kazakhstan.
Conclusions are made about the ability of knowledge spillovers to reduce inequality in innovation activity among regions. Innovative leaders and regions lagged behind in innovations. The calculations showed that knowledge spillover leads to the spread of knowledge to neighboring regions, and from them to other neighboring ones, forming so-called "centers of innovation". Alignment in the level of innovative activity leads to an equalization of the rates of economic growth in the regions.