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The aim of this research work is to analyze growth and convergence processes in the service sector and its large groups, market, and non-market services, at the regional level in Ecuador by taking the labor productivity variable as a reference. The methodology used is an analysis of distributive dynamics of the data, applying the non-parametric method of Kernel density functions from a mathematical economics approach. The results obtained show that the service sector has non-alarming levels of inequality, its trend over time is increasing. When disaggregating the data, it was observed that non-market services show a rapid growth in inequality. In contrast, market services show greater stability during the period analyzed. Regarding intra-distribution dynamics for the service sector and its subsectors, in the long term, poor regions improve, while rich regions deteriorate. However, deterioration of advanced regions is less intense in non-market services.

Application of the Kernel Density Function for the Analysis of Regional Growth and Convergence in the Service Sector through Productivity