The Atkinson Inequality Measure and its Sampling Properties: Bayesian and Classical Approaches

This paper examines several Bayesian methods of obtaining posterior probability density functions of the Atkinson inequality measure and its associated social welfare function, in the context of grouped income distribution data. The methods are compared with asymptotic standard errors. The role of the number of income classes is investigated using a simulated distribution. If only a small number of groups is available in published data, there is a clear gain from generating the posterior probability density function when using an explicit income distribution assumption. Even with a small number of groups, the Bayesian approach gives results that are close to the sample values obtained using the corresponding individual observations.     

Bivariate income distributions for assessing inequality and poverty under dependent samples

As indicators of social welfare, the incidence of inequality and poverty is of ongoing concern to policy makers and researchers alike. Of particular interest are the changes in inequality and poverty over time, which are typically assessed through the estimation of income distributions. From this, income inequality and poverty measures, along with their differences and standard errors, can be derived and compared. With panel data becoming more frequently used to make such comparisons, traditional methods which treat income distributions from different years independently and estimate them on a univariate basis, fail to capture the dependence inherent in a sample taken from a panel study. Consequently, parameter estimates are likely to be less efficient, and the standard errors for between-year differences in various inequality and poverty measures will be incorrect. This paper addresses the issue of sample dependence by suggesting a number of bivariate distributions, with Singh–Maddala or Dagum marginals, for a partially dependent sample of household income for two years. Specifically, the distributions considered are the bivariate Singh–Maddala distribution, proposed by Takahasi (1965), and bivariate distributions belonging to the copula class of multivariate distributions, which are an increasingly popular approach to modelling joint distributions. Each bivariate income distribution is estimated via full information maximum likelihood using data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey for 2001 and 2005. Parameter estimates for each bivariate income distribution are used to obtain values for mean income and modal income, the Gini inequality coefficient and the headcount ratio poverty measure, along with their differences, enabling the assessment of changes in such measures over time. In addition, the standard errors of each summary measure and their differences, which are of particular interest in this analysis, are calculated using the delta method.     

ACCOUNTING FOR SRI LANKA'S EXPENDITURE INEQUALITY 1980–2002: REGRESSION-BASED DECOMPOSITION APPROACHES

Sri Lanka liberalized its economy in 1977, paving the way for more rapid economic growth and higher rates of job creation. But tensions over distributional issues still plague the body politic. This paper investigates the evolution of Sri Lanka's expenditure distribution in the period 1980–2002 and uses three decomposition methodologies—the Fields, the Shapley value decomposition, and Yun's unified method—to determine underlying causes. The study finds that while average adjusted expenditure rose across strata, the rich experienced more rapid expenditure growth leading to greater inequality. Inequality change was driven by differential access to infrastructure, education, and occupation status. Demographic factors, including ethnicity, and spatial factors contributed very little. The study recommends policies that ensure more equitable access to income earning assets such as education and infrastructure services, and that contain the rise in inequality along sectoral, regional, and ethnic fault lines.     

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.     

Bayesian assessment of Lorenz and stochastic dominance

We introduce a Bayesian approach for assessing Lorenz and stochastic dominance. For two income distributions, say X and Y, estimated via Markov chain Monte Carlo, we describe how to compute posterior probabilities for: (i) X dominates Y, (ii) Y dominates X and (iii) neither Y nor X dominates. The proposed approach is applied to Indonesian income distributions using mixtures of gamma densities that ensure flexible modelling. Probability curves depicting the probability of dominance at each population proportion are used to explain changes in dominance probabilities over restricted ranges relevant for poverty orderings. They also explain some seemingly contradictory outcomes from the p-values of some sampling theory tests.     

ACCOUNTING FOR SRI LANKA'S EXPENDITURE INEQUALITY 1980–2002: REGRESSION-BASED DECOMPOSITION APPROACHES

Sri Lanka liberalized its economy in 1977, paving the way for more rapid economic growth and higher rates of job creation. But tensions over distributional issues still plague the body politic. This paper investigates the evolution of Sri Lanka's expenditure distribution in the period 1980–2002 and uses three decomposition methodologies—the Fields, the Shapley value decomposition, and Yun's unified method—to determine underlying causes. The study finds that while average adjusted expenditure rose across strata, the rich experienced more rapid expenditure growth leading to greater inequality. Inequality change was driven by differential access to infrastructure, education, and occupation status. Demographic factors, including ethnicity, and spatial factors contributed very little. The study recommends policies that ensure more equitable access to income earning assets such as education and infrastructure services, and that contain the rise in inequality along sectoral, regional, and ethnic fault lines.     

Income and Health Concentration in Australia

This paper measures the concentration of ill-health among income groups in Australia using health survey data from 1989–90 ( Australian Bureau of Statistics 1991 ) and 1995 ( Australian Bureau of Statistics 1997 ), which contain responses on self-assessed health status and gross personal income. The technique of direct standardisation is used to control for the influence on health status of gender and age. Comparisons of the concentration of ill-health over time and between males and females and persons living in rural and urban areas are reported. For both surveys and all groups, we find that ill-health is concentrated among lower income groups. Concentration measures of ill-health are higher (in absolute terms) for men than for women. In all categories apart from women, the concentration measures fell between 1989–90 and 1995 surveys.     

Averaging Income Distributions

Various inequality and social welfare measures often depend heavily on the choice of a distribution of income. Picking a distribution that best fits the data involves throwing away information and does not allow for the fact that a wrong choice can be made. Instead, Bayesian model averaging utilizes a weighted average of the results from a number of income distributions, with each weight given by the probability that a distribution is ‘correct’. In this study, prior densities are placed on mean income, the mode of income and the Gini coefficient for Australian income units with one parent (1997–8). Then, using grouped sample data on incomes, posterior densities for the mean and mode of income and the Gini coefficient are derived for a variety of income distributions. The model‐averaged results from these income distributions are obtained.     

Bayesian estimation of social welfare and tax progressivity measures

This paper examines Bayesian methods of examining posterior distributions of inequality, concentration, tax progressivity and social welfare measures. Use is made of an explicit income distribution assumption and two alternative assumptions regarding the distribution of pre-tax mean incomes within each income group. The methods are applied to a simulated distribution of individual incomes and tax payments. It is possible to identify a minimum acceptable number of income classes to be used. The results suggest support for the use of group means in practical applications, particularly where large sample sizes are available. First version received: August 2000/Final version received: July 2001 RID="*" ID="*"  This research was supported by a Melbourne University Faculty of Economics and Commerce Research Grant. We should like to thank Bill Griffiths and two referees for comments on an earlier draft.     

Carnarvon Gorge: a comment on the sensitivity of consumer surplus estimation

Beal's (1995) method of estimating the value of Carnarvon Gorge for recreational use is re-examined. When an inconsistency in her estimation procedure is corrected, the estimated value of Carnarvon Gorge for camping is found to be six times higher. The sensitivity of the estimate to the choice of functional form is examined, and standard errors and interval estimates for consumer surplus are provided. Comments are made about functional form choice and prediction in log-log models.