Income Distributions, Inequality, and Poverty in Asia, 1992–2010

Income distributions for developing countries in Asia are modeled using beta-2 distributions, which are estimated by a method of moments procedure applied to grouped data. Estimated parameters of these distributions are used to calculate measures of inequality, poverty, and pro-poor growth in four time periods over 1992–2010. Changes in these measures are examined for 11 countries, with a major focus on the People’s Republic of China (PRC), India, and Indonesia, which are separated into rural and urban regions. We find that the PRC has grown rapidly with increasing inequality accompanying this growth. India has been relatively stagnant. Indonesia has grown rapidly after suffering an initial set back from the Asian financial crisis in 1997

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

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.Comment: 22 pages, 15 figures, 4 tables. LaTeX. Accepted for publication in "The European Physical Journal B

Estimating Income Inequality in China Using Grouped Data and the Generalized Beta Distribution

There are two main types of data sources of income distributions in China: household survey data and grouped data. Household survey data are typically available for isolated years and individual provinces. In comparison, aggregate or grouped data are typically available more frequently and usually have national coverage. In principle, grouped data allow investigation of the change of inequality over longer, continuous periods of time, and the identification of patterns of inequality across broader regions. Nevertheless, a major limitation of grouped data is that only mean (average) income and income shares of quintile or decile groups of the population are reported. Directly using grouped data reported in this format is equivalent to assuming that all individuals in a quintile or decile group have the same income. This potentially distorts the estimate of inequality within each region. The aim of this paper is to apply an improved econometric method designed to use grouped data to study income inequality in China. A generalized beta distribution is employed to model income inequality in China at various levels and periods of time. The generalized beta distribution is more general and flexible than the lognormal distribution that has been used in past research, and also relaxes the assumption of a uniform distribution of income within quintile and decile groups of populations. The paper studies the nature and extent of inequality in rural and urban China over the period 1978 to 2002. Income inequality in the whole of China is then modeled using a mixture of province-specific distributions. The estimated results are used to study the trends in national inequality, and to discuss the empirical findings in the light of economic reforms, regional policies, and globalization of the Chinese economy

Global and regional inequality in the distribution of income: Estimation with limited and incomplete data

The paper examines the nature and extent of global and regional inequality using the most recent country level data on inequality drawn from World Bank studies, and real per capita income from the Penn World Tables, for the period 1980–1990. The methodology employed in the paper is based on a mixture of parametric and non-parametric approaches to inequality measurement. It is designed to handle the limited and incomplete nature of income distribution data from different countries. Empirical results show a very high degree of global inequality, but with some evidence of catch-up and convergence between regions

Estimating and Combining National IncomeDistributions using Limited Data

RESEARCH PAPER NUMBER 926, ISSN 0819-2642, ISBN 0 7340 2582 3A major problem encountered in studies of income inequality at regional and globallevels is the estimation of income distributions from data that are in a summary form.In this paper we estimate national and regional income distributions within a generalframework that relaxes the assumption of constant income within groups. A techniqueto estimate the parameters of a beta-2 distribution using grouped data is proposed.Regional income distribution is modelled using a mixture of country-specificdistributions and its properties are examined. The techniques are used to analysenational and regional inequality trends for eight East Asian countries and twobenchmark years, 1988 and 1993