Duangkamon Chotikapanich

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 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.

Modeling income distributions and Lorenz curves

Collection of influential papers.- A New Model of Personal Income Distribution: Specification and Estimation.- A Function for Size Distribution of Incomes.- Some Generalized Functions for the Size Distribution of Income.- Efficient Estimation of the Lorenz Curve and Associated Inequality Measures from Grouped Observations.- Distribution and Mobility of Wealth of Nations.- Survey papers on Lorenz functions and the generalizations and extensions of income distributions.- A Guide to the Dagum Distributions.- Pareto and Generalized Pareto Distributions.- The Generalized Beta Distribution as a Model for the Distribution of Income: Estimation of Related Measures of Inequality.- Parametric Lorenz Curves: Models and Applications.- Current research.- Maximum Entropy Estimation of Income Distributions from Bonferroni Indices.- New Four- and Five-Parameter Models for Income Distributions.- Fuzzy Monetary Poverty Measures under a Dagum Income Distributive Hypothesis.- Modelling Lorenz Curves: Robust and Semi-parametric Issues.- Modelling Inequality with a Single Parameter.- Lorenz Curves and Generalised Entropy Inequality Measures.- Estimating Income Distributions Using a Mixture of Gamma Densities.- Inequality in Multidimensional Indicators of Well-Being: Methodology and Application to the Human Development Index.

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.

Global income distributions and inequality, 1993 and 2000: incorporating country-level inequality modeled with beta distributions

Using a method-of-moments estimator, flexible three-parameter beta distributions are fitted to aggregate country-level income data to overcome an untenable assumption of previous studies that persons within each income group receive the same income. Regional and global income distributions are derived as weighted mixtures of country-specific distributions. Analytical expressions for Gini and Theils measures of inequality at country, regional, and global levels are derived in terms of the parameters of the beta distributions. Application to data for 91 countries in 1993 and 2000 reveals a high degree of global inequality, with evidence of declining inequality, largely attributable to growth in China.

Estimating Income Distributions Using a Mixture of Gamma Densities

The estimation of income distributions is important for assessing income inequality and poverty and for making comparisons of inequality and poverty over time, countries and regions, as well as before and after changes in taxation and transfer policies. Distributions have been estimated both parametrically and nonparametrically. Parametric estimation is convenient because it facilitates subsequent inferences about inequality and poverty measures and lends itself to further analysis such as the combining of regional distributions into a national distribution. Nonparametric estimation makes inferences more difficult, but it does not place what are sometimes unreasonable restrictions on the nature of the distribution. By estimating a mixture of gamma distributions, in this paper we attempt to benefit from the advantages of parametric estimation without suffering the disadvantage of inflexibility. Using a sample of Canadian income data, we use Bayesian inference to estimate gamma mixtures with two and three components. We describe how to obtain a predictive density and distribution function for income and illustrate the flexibility of the mixture. Posterior densities for Lorenz curve ordinates and the Gini coefficient are obtained

Inference for Income Distributions Using Grouped Data

We develop a general approach to estimation and inference for income distributions using grouped or aggregate data that are typically available in the form of population shares and class mean incomes, with unknown group bounds. We derive generic moment conditions and an optimal weight matrix that can be used for generalized method-of-moments (GMM) estimation of any parametric income distribution. Our derivation of the weight matrix and its inverse allows us to express the seemingly complex GMM objective function in a relatively simple form that facilitates estimation. We show that our proposed approach, which incorporates information on class means as well as population proportions, is more efficient than maximum likelihood estimation of the multinomial distribution, which uses only population proportions. In contrast to the earlier work of Chotikapanich, Griffiths, and Rao, and Chotikapanich, Griffiths, Rao, and Valencia, which did not specify a formal GMM framework, did not provide methodology for obtaining standard errors, and restricted the analysis to the beta-2 distribution, we provide standard errors for estimated parameters and relevant functions of them, such as inequality and poverty measures, and we provide methodology for all distributions. A test statistic for testing the adequacy of a distribution is proposed. Using eight countries/regions for the year 2005, we show how the methodology can be applied to estimate the parameters of the generalized beta distribution of the second kind (GB2), and its special-case distributions, the beta-2, Singh–Maddala, Dagum, generalized gamma, and lognormal distributions. We test the adequacy of each distribution and compare predicted and actual income shares, where the number of groups used for prediction can differ from the number used in estimation. Estimates and standard errors for inequality and poverty measures are provided. Supplementary materials for this article are available online.

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 Lankas expenditure distribution in the period 1980–2002 and uses three decomposition methodologies—the Fields, the Shapley value decomposition, and Yuns 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.

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.

Poverty and income inequality measurement: Accommodating a role for owner-occupied housing

The most common method used in Australia to identify whether an income unit is in poverty is to compare the income units disposable cash income with a cash income-based poverty line adapted to each income units needs. If disposable cash income lies below the poverty threshold then the income unit is deemed to be in poverty. This approach was adopted in the Commission of Inquiry into Poverty (Henderson, 1975) and in numerous subsequent pieces of poverty-related research in Australia.