Habilitation Thesis
DOI
https://doi.org/10.11606/T.11.1971.tde-12012021-173034
Document
Author
Full name
Rodolfo Hoffmann
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
Piracicaba, 1971
Committee
Nobre, Érico da Rocha (President)
Nogueira, Izaias Rangel
Paniago, Euter
Schuh, G Edward
Vieira, Dorival Teixeira
Title in Portuguese
Contribuição à análise da distribuição da renda e da posse da terra no Brasil
Keywords in Portuguese
Distribuição de renda
Posse da terra
Abstract in Portuguese
Title in English
Not available
Keywords in English
Not available
Abstract in English
The objectives of this research are, on one hand, to contribute to the improvement of the methods of measurement of degree of concentration of income and of wealth and, on the other hand, to furnish subsidies for the analysis of income distribution and of land tenancy in Brazil. In respect to the methods of analysis of income distribution (or of wealth), the principal aspects of this research are the following: a) Using Simpson´s method of approximate integration, we sought to establish a means of calculating Gini's index which would not underestimate the degree of inequality of the Lorenz curve which occours when one applies the usual means of calculation. Keeping in mind that the use of trinomial of the second degree presented certain problems, we instead chose to utilize arcs of a power function (Y =a . Xb with X being the accumulated fraction of number of people and Y the accumulated fraction of income) and then, by integration, to determine the area of inequality delineated by the Lorenz curve and the line of perfect equality. b) We used the redundancy and Theil`s index as measurements of the degree of concentration. The great advantage of redundancy is that it permits, when data is available by regions (or sectors), division into interregional and intraregional components (or intersectorial and intrasectorial components). e) We utilized Pareto's equation with three parameters: (See Theses). d) We established that, when income distrioution is adjusted to Pareto`s function with three parameters, the Lorenz curve is given by the following equation: (See Theses). e) We established a process of adjusting Pareto's curve with three parameters using the method of least squares regression. We also presented the formulas for calculation of the estimates of standard deviation of the estimated parameters. An analysis of distribution of land tenancy in Brazil was made using data from the agricultural census of 1920, 1940, 1950, and 1960, and the property registry of IBRA (Brazilian Institute of Agrarian Reform) for 1967. In relation to this subject the most important aspects analyzed in this research are as follows: (See Theses)