International Journal of Economics and Finance; Vol. 13, No. 11; 2021 ISSN 1916-971X E-ISSN 1916-9728 Published by Canadian Center of Science and Education 57 Knowledge Economy in Brazil: Analysis of Sectoral Concentration and Production by Region Jose Antonio de Franca 1 & Wilfredo Sosa Sandoval 2 1 PhD in Accountancy and Economics, University of Brasilia (UnB), Brazil 2 PhD in Mathematics, Catholic University of Brasilia (UCB), Brazil Correspondence: Jose Antonio de Franca, PhD in Accountancy and Economics, University of Brasilia (UnB), Brazil. Received: August 29, 2021 Accepted: October 10, 2021 Online Published: October 12, 2021 doi:10.5539/ijef.v13n11p57 URL: https://doi.org/10.5539/ijef.v13n11p57 Abstract The research presented in this article investigates and analyzes the concentration of knowledge production in Brazil, in the context of a public policy, at postgraduate level, by using the spectral methods grounded on the LQ (location quotient) and CI (concentration index) indicators, in three dimensions, from 2013 to 2018. The dimensions are economics, geography, and time. Economics is represented by Fields and Major Fields of knowledge production. Geography corresponds to the regions identified by each Federation unit (FU). Time is a chronological unit of the timeline in which knowledge is produced. The research then evaluates knowledge concentration in the income performance of the families by FU. The results are robust and indicate significant evidence that sectorial knowledge production in Brazil is regionally unequal and impacts on family incomes, but those family incomes evolve regardless of the knowledge concentration level produced. The research contributions are relevant to assist public policy regulators and monitoring managers, as well as to encourage future discoveries in regional economics applications. Keywords: knowledge economy, knowledge Concentration Index (CI), LQ Regional Matrix (LQRM), local and global percentages 1. Introduction This article investigates and analyzes the concentration of knowledge produced in Brazil at postgraduate level, in the context of agglomerations, grounded on the quantitative data of master theses and doctoral dissertations, by Field and Major Field of knowledge, by federation unit (FU), within the timeline from 2013 to 2018, and investigates the contribution of knowledge concentration produced in the income performance of families. Field is the aggregate of all knowledge produced within the geography represented by a FU. Major Field aggregates the knowledge produced by all related Fields, in the same timeline unit. Knowledge concentration is a non-negative neutral measure that, when orbiting near zero, suggests that a FU is developed. Thus, there are three variables to evaluate the concentration of the knowledge economy: FU, which is equivalent to a geographical territory unit, named Region; Field and Major Field, which correspond to the sectors in which the economy produces knowledge; and time, which is a chronological unit of the timeline in which knowledge is produced. With these variables, a local and global analysis of knowledge concentration is produced. To investigate the degree of knowledge concentration, the article introduces the concentration index (CI), which uses spectral analysis metrics, in the context of linear algebra theory, applied to the study of agglomerations, guided by the location quotient (LQ) model in three dimensions: economics, geography and time. These metrics indicate how equal or unequal knowledge production is in terms of regional development, and how concentrated or dispersed the knowledge produced by each region is. To evaluate knowledge concentration performance in the average household income (AHI) of families and the statistical significance of this performance, the Data Envelopment Analysis (DEA) deterministic model and the quantile linear regression model are used. In the LQ specification for the three dimensions, the S sectors (k) of the economy represented by the Fields are identified, totaling 81; by Major Fields, totaling 9; by geographic R regions (i) identified by each FU, totaling 27; and by the T timeline composed of time units (t), totaling 6, divided in periods p of four P units (t), so that P=4t and each period p is defined by T-P+1 T timeline unit. Thus, an economic variable V is defined, observed in the