On Calculation of the Extended Gini Coefficient.

The conventional formula for estimating the extended Gini coefficient is a covariance formula provided by Lerman and Yitzhaki (1989). We suggest an alternative estimator obtained by approximating the Lorenz curve by a series of linear segments. In a Monte Carlo experiment designed to assess the relative bias and efficiency of the two estimators, we find that, when using grouped data with 20 or less groups, our new estimator has less bias and lower mean squared error than the covariance estimator. When individual observations are used, or the number of groups is 30 or more, there is little or no difference in the performance of the two estimators.ESTIMATORS ; COEFFICIENTS ; EFFICIENCY

Estimating Lorenz Curves Using a Dirichlet Distribution.

The Lorenz curve relates the cumulative proportion of income to the cumulative proportion of population. When a particular functional form of the Lorenz curve is specified it is typically estimated by linear or nonlinear least squares, estimation techniques that have good properties when the error terms are independently and normally distributed. Observations on cumulative proportions are clearly neither independent nor normally distributed. This paper proposes and applies a new methodology that recognises the cumulative proportional nature of the Lorenz curve data by assuming that the income proportions are distributed as a Dirichlet distribution. Five Lorenz-curve specifications are used to demonstrate the technique. Maximum likelihood estimates under the Dirichlet distribution assumption provide better-fitting Lorenz curves than nonlinear least squares and another estimation technique that has appeared in the literature.Gini coefficient; maximum likelihood estimation

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

Global inequality: Recent evidence and trends

This paper examines the nature and extent of global and regional income distribution and inequality using the most recent country level data on income distribution drawn from World Bank and UNU-WIDER studies for the period 1993-2000. The methodology used is a recently developed technique to fit flexible income distributions to limited aggregated data. Empirical results show a very high degree of global inequality, but with some evidence of inequality decreasing between the two years

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

A New Semiparametric Approach to Analysing Conditional Income Distributions

In this paper we explore the application of Generalised Additive Models of Location, Scale and Shape for the analysis of conditional income distributions in Germany following the reunification. We find that conditional income distributions can generally be modelled using the three parameter Dagum distribution and our results hint at an even more pronounced effect of skill-biased technological change than can be observed by standard mean regression

Estimating and Predicting Household Expenditures and Income Distributions

A reliable prediction of unconditional welfare distributions, like income or consumption, is essential for welfare analysis, and in particular for inequality, poverty or development studies. Where observations of expenditures or income are missing, the mean prediction based on available covariates is not just a poor estimator of the unconditional distribution; it fails to predict the required information about tails and quantiles. A new estimation method is introduced which can be combined with any mean prediction model. It is used to calculate the income distribution of a survey based on subsample information, to estimate the unconditional income distribution for the non-responding households, and to predict the household expenditures of a future panel wave. It allows for imputing welfare distributions for a census from a survey or for synthetic populations under specific scenarios. Further inference is straight-forward, including prediction of Lorenz curves, indexes like the Gini, or distribution quantiles, including confidence intervals