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We propose a nonparametric estimator of the Lorenz curve that satisfies its theoretical properties, including monotonicity and convexity. We adopt a transformation approach that transforms a constrained estimation problem into an unconstrained one, which is estimated nonparametrically. We utilize the splines to facilitate the numerical implementation of our estimator and to provide a parametric representation of the constructed Lorenz curve. We conduct Monte Carlo simulations to demonstrate the superior performance of the proposed estimator. We apply our method to estimate the Lorenz curve of the U.S. household income distribution and calculate the Gini index based on the estimated Lorenz curve.

Dominance techniques are used to analyze and rank inequality, welfare, and poverty across regions in Thailand in the 1990s. Inference-based dominance methods are applied to consumption expenditure microdata from the Household Socio-Economic Surveys (SES) of 1992, 1994, 1996, 1998 and 2000. Attention is focused on the period immediately before and after the economic contraction of 1996–1997. Lorenz dominance is employed to assess inequality, while first-order Engel food share dominance is applied to rank welfare across time and among regions. Poverty is evaluated by comparing truncated food-share quantile functions. The evidence reveals that the economic crisis in 1997 seems to affect inequality in Bangkok (the richest region) more than the Northeast (the poorest region), and most dramatic changes occur in the North and South. Welfare in Bangkok is unambiguously higher than in other regions before and after economic contraction. In fact, the great economic contraction changes the rankings of economic well-being and poverty only in the North, South, and Northeast.

This note formally investigates the applicability of stochastic dominance (Lorenz dominance) to ordinal data such as self-reported health status. We confirm that for ordinal data distributions, stochastic dominance has limited applicability in ranking social welfare, while it has no applicability in ranking inequality.

The growth incidence curve of Ravallion and Chen (2003) is based on the quantile function. Its distribution-free estimator behaves erratically with usual sample sizes leading to problems in the tails. The authors propose a series of parametric models in a Bayesian framework. A first solution consists in modeling the underlying income distribution using simple densities for which the quantile function has a closed analytical form. This solution is extended by considering a mixture model for the underlying income distribution. However, in this case, the quantile function is semi-explicit and has to be evaluated numerically. The last solution consists in adjusting directly a functional form for the Lorenz curve and deriving its first-order derivative to find the corresponding quantile function. The authors compare these models by Monte Carlo simulations and using UK data from the Family Expenditure Survey. The authors devote a particular attention to the analysis of subgroups.

This paper examines the gender differences of expenditure distribution within the last decade in Spain. In particular, the Lorenz dominance is tested using expenditure distributions as approximated by the Dagum model. The sensitivity of the results to some conceptual choices, such as the equivalence scale or the gender reference, is also analysed.

Labor markets for unskilled and low-wage workers in the United States stagnated in the last quarter of the 20th century. The collapse in the low-wage labor market has been well documented¹ and numerous research initiatives have investigated the causes. Despite some geographical mismatches between buyers and sellers low-paying jobs are generally available but forces are at work on both the demand and supply sides of unskilled labor markets that make it increasingly difficult for working families at or near the bottom of the income distribution to earn enough to meet basic needs. Welfare reform effectively increased the supply of unskilled workers, which placed added pressures on wages and earnings of low-income families.

In a period of political change in the European Union, when the European Constitution is in the centre of the debate, the social convergence among European Union countries is a crucial issue. However, the measurement of welfare, inequality and poverty and the comparisons among countries are issues of great controversy. One of the main reasons for this is that implicit or explicit value judgements have to be made, and it is not easy to determine which of these value judgements are the most appropriate ones. In this paper we apply inference-based stochastic dominance methods to study welfare, inequality and poverty in European Union countries in 2000, applying purchasing power parities from the OECD. There are two main advantages of the methods and data used in this work: on the one hand, the stochastic method uses explicit and widely, though not universally, accepted assumptions, and if this small number of assumptions is accepted, the welfare and poverty ranking that the method provides is unambiguous. On the other hand, the use of the European Community Household Panel permits the comparisons in welfare, inequality and poverty among different countries using harmonised data. In addition, the use of inference tests permits a more precise ranking.

This paper develops criteria for an alternative concept of inequality dominance and shows how they relate to criteria for comparing relative poverty. The results warn inter alia against the use of some popular indices of inequality. They do, however, provide an ethical basis for the use of other popular indices of (restricted) inequality as potential relative poverty indices. The results also suggest an interesting extension of the Schutz coefficient as well as a use of Lorenz curves for the analysis of relative poverty and restricted inequality. A graphical illustration shows how the new criteria of restricted inequality dominance extend the ranking power of previously proposed inequality dominance criteria.

This paper aims to evaluate the progressivity of health-care financing in Egypt by assessing all five financing sources individually and then combining them to analyze the equity of the whole financing system.

Lorenz dominance analysis and Kakwani progressivity index were applied on data from 2010/2011 Household Income, Expenditure, and Consumption Survey and the National Health Accounts 2011 using Stata to evaluate the progressivity of each source of health-care finance and the financing system overall.

The data show that Egypt’s health-care system, which is largely financed by out-of-pocket (OOP) payments, is slightly regressive, with an overall Kakwani index of −0.079. The overall regressive effect was the result of three regressive sources (OOP payments, an earmarked cigarette tax and direct taxes), one proportional finance source (social health insurance) and two slightly progressive sources (indirect taxes and private health insurance). This shows that the burden of financing health care falls more on the poor. These results signal the need for reform of health-care financing in Egypt to reduce dependence on OOP payments to achieve more equitable financing.

The paper seeks to augment the literature on health-care financing in Egypt by calculating specific progressivity estimates for all five sources of financing the Egyptian health-care system and analyzing the overall equity of this financing system. It will, therefore, provide a benchmark for monitoring the equity of finance in the Egyptian health-care system in future studies and allow one to assess the impact of implemented financing reforms in the future on the level of progressivity of health system financing.