The economic complexity index defines the basis of the modern theory of economic complexity and reflects the level of knowledge embedded in the production structure of the economy. This study examines the direct relationship between the economic complexity index and gross regional product (GRP) while taking into account other factors of the GRP production function in its generalized representation. As a result, we can isolate the impact of the economic complexity index from other phenomena. The non-linear nature of the relationship between economic complexity and GRP is revealed, and the direct relationship is manifested only at sufficiently high values of economic complexity, exceeding a certain threshold, which is found endogenously using econometric methods. In addition, the paper studies the relationship between economic complexity and indices of sectoral specialization. We found that there is a direct relationship between economic complexity and the extractive industry index and no relationship with the level of development of manufacturing industry. We obtained a clarification of the generalized production function of GRP, in which the threshold effect of the influence of economic complexity manifested itself as a factor of nonlinear dependence describing the elasticity of labor: a high level of economic complexity provides greater labor productivity. Overall, the results of the study of the dependence of GRP on economic complexity lead to the conclusion that increasing economic complexity can be an effective way to stimulate economic growth and development, but only starting from a certain threshold level. This suggests that an economy must reach a minimum level of diversity and complexity in its industrial activities before it can experience the productivity gains necessary for substantial GRP growth.