Evidence for the Gompertz Curve in the Income Distribution of Brazil 1978-2005

TL;DR

This study analyzes Brazil's income distribution from 1978 to 2005, revealing a two-class system with the majority following a Gompertz curve and the top 1% following a Pareto law, suggesting growth dynamics influence income patterns.

Contribution

It provides empirical evidence that Brazil's income distribution can be modeled by a Gompertz curve for 99% of the population and a Pareto law for the top 1%, indicating a two-class structure.

Findings

Income distribution follows a Gompertz curve for 99% of the population.

The top 1% income follows a Pareto power law.

Income share components exhibit a 4-year cyclical pattern.

Abstract

This work presents an empirical study of the evolution of the personal income distribution in Brazil. Yearly samples available from 1978 to 2005 were studied and evidence was found that the complementary cumulative distribution of personal income for 99% of the economically less favorable population is well represented by a Gompertz curve of the form $G(x)=\exp [\exp (A-Bx)]$, where $x$ is the normalized individual income. The complementary cumulative distribution of the remaining 1% richest part of the population is well represented by a Pareto power law distribution $P(x)= \beta x^{-\alpha}$. This result means that similarly to other countries, Brazil's income distribution is characterized by a well defined two class system. The parameters $A$, $B$, $\alpha$, $\beta$ were determined by a mixture of boundary conditions, normalization and fitting methods for every year in the time span of this study. Since the Gompertz curve is characteristic of growth models, its presence here suggests that these patterns in income distribution could be a consequence of the growth dynamics of the underlying economic system. In addition, we found out that the percentage share of both the Gompertzian and Paretian components relative to the total income shows an approximate cycling pattern with periods of about 4 years and whose maximum and minimum peaks in each component alternate at about every 2 years. This finding suggests that the growth dynamics of Brazil's economic system might possibly follow a Goodwin-type class model dynamics based on the application of the Lotka-Volterra equation to economic growth and cycle.