2 edition of Poverty measures and the generalized Lorenz curve for grouped data found in the catalog.
Poverty measures and the generalized Lorenz curve for grouped data
Dissertation (M.A.) - University of Warwick, 1988.
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Grouped data depicts sparse points of the Lorenz curve and hence, to estimate inequality measures, it is essential to de ne a method to link such points.
Much of the academic literature on the estimation of income inequality from grouped data deploy nonparametric techniques to approximate the shape of the Lorenz curve. While various discrete poverty measures can be applied directly to data in this limited form, they typically require an arbitrary approach to within-group interpolation.
This problem can be overcome by fitting either a parametric income distribution or a Lorenz curve to the grouped data and computing the required quantities from estimated Cited by: 9.
The primary aim of this paper is to show how can we construct poverty measures from grouped data, that is, to show how can we derive poverty measures from parameterized Lorenz curve.
The most common data source on income distribution in China is grouped data. When income data is in grouped form, some acceptable Lorenz model is needed to approximate the Poverty measures and the generalized Lorenz curve for grouped data book Lorenz curve.
inequality and poverty measures implied by the chosen Lorenz model. The outline of the paper is as follows. Section 2 presents the mathematical structure of the Lorenz curve and explains the parameterization process based on the general quadratic model.
The section also includes a discussion of the normative underpinnings of Lorenz dominance. Lorenz curves and associated measures of poverty and inequality.
To this end, we use (i) household survey data from four countries (China, Nicaragua, Tanzania and Vietnam), (ii) data drawn from several theoretical distributions (Weibull, Pareto, Log-normal and Generalized Beta II) with parameter values assigned on the basis of previous empirical.
While various discrete poverty measures can be applied directly to data in this limited form, they typically require an arbitrary approach to within‐group interpolation. This problem can be overcome by fitting either a parametric income distribution or a Lorenz curve to the grouped data and computing the required quantities from estimated.
Generalized Lorenz curves and social welfare • Generalized Lorenz curve is the Lorenz curve scaled up at each point by population mean income, i.e. a plot of pµp (‘cumulative mean’) against p, where units are ordered in ascending order of income • Class of social welfare functions, W 2 with W ∈W 2.
The econometrics of inequality and poverty Chapter 4: Lorenz curves, the Gini coefﬁcient and parametric distributions Michel Lubrano 6 Lorenz curve and other inequality measures () in his book on the history of high incomes in France makes an extensive use of quantiles to study the French income distribution and particularly its.
The advantages of using group means in estimating the Lorenz curve and Gini index from grouped data. Stat. 70(1), 25–32 () MathSciNet CrossRef Google Scholar McDonald, J.B.: Some generalized functions for the size distribution of income. The estimation of poverty and inequality often requires the use of grouped data as complete household surveys are neither always available to researchers nor easy to analyze.
This study assesses the performance of two functional forms for the Lorenz curve proposed by Kakwani () and Villasenor and Arnold (). The methods are implemented using the computational tool POVCAL, developed. Household Poverty Using Gross and Net Income: Malaysia, – 71 Poverty Proﬁ les: Malaysia, 72 Extreme Poverty Rates: Malaysia, – 73 Probability of Poverty by Household Characteristics 75 Hypothetical Lorenz Curve Calculations 85 Calculation of the Gini and poverty measurement, especially ad hoc poverty measures and generalised poverty gap measures.
If their background is weak or missing, the trainer may consider delivering other EASYPol Modules beforehand, as highlighted in the 1 EASYPol Module Charting Income Inequality: The Lorenz Curve. Downloadable (with restrictions). The most common data source on income distribution in China is grouped data.
When income data is in grouped form, some acceptable Lorenz model is needed to approximate the underlying Lorenz curve. This paper presents a new family of Lorenz curves and applies the main model in our proposed family of Lorenz curves to income data for rural China over.
Downloadable (with restrictions). Poverty and inequality are often estimated from grouped data as complete household surveys are neither always available to researchers nor easy to analyze. In this study we assess the performance of functional forms proposed by Kakwani (a) and Villasenor and Arnold() to estimate the Lorenz curve from grouped data.
A graph of the data may be used directly as a Lorenz curve, or economists and statisticians may fit a curve that represents a continuous function to fill in any gaps in the observed data. Details. Lc(x) computes the empirical ordinary Lorenz curve of x as well as the generalized Lorenz curve (= ordinary Lorenz curve * mean(x)).
The result can be interpreted like this: p* percent have L(p)* percent of x. If n is changed to anything but the default x is interpreted as a vector of class means and n as a vector of class frequencies: in this case Lc will compute the minimal.
The Lorenz curves employed by the World Bank are the general quadratic (Villasenor and Arnold, ) and the beta Lorenz curve (Kakwani, ). We have chosen the beta distribution as an alternative to Lorenz curve estimation for calculating poverty measures because (a) use of a distribution. Unfortunately, Lorenz and generalized Lorenz curves may cross, in which case, Atkinson's and Shorrock's theorems do not apply.
Distributions whose Lorenz curves cross require a specific social welfare function to determine which has higher social welfare because different values of e (≠ 0) can generate different social welfare rankings.
Fig. illustrates for the standard Lorenz curve. The Lorenz curve, introduced more than years ago, remains as one of the main tools for analysis of inequality. International institutions such as the World Bank collect and publish grouped income data in the form of population and income shares for a large number of countries.
A Uniﬁ ed Approach to Measuring Poverty and Inequality. Theory and Practice. James Foster Suman Seth Michael Lokshin Zurab Sajaia. STREAMLINED ANALYSIS WITH ADePT SOFTWARE. This essay aims at a broad, main-stream account of the literature on inequality and poverty measurement in the space of income and, additionally, deals with measures of disparity and deprivation in the more expanded domain of capabilities and functionings.
In addition to an introductory and a concluding part, the paper has four sections. The first of these, on measurement of income inequality.
The Lorenz Curve and Lorenz Dominance. Atkinson’s theorem. The Generalized Lorenz Curve and Generalized Lorenz Dominance. Generalization ofAtkinson’s theorem. The four basic properties of unidimensional inequality measures.
Lorenz consistent inequality measures. Other properties (Transfer Sensitivity, Consistency and Decomposability). Generalized Lorenz curves and social welfare • ‘Social welfare’ assessments incorporate the idea of a trade-off between increases in inequality and increases in real income levels (sufficient rise in latter offset former) • Generalized Lorenz curve: Lorenz curve scaled up at.
Efﬁcient Estimation of the Lorenz Curve and Associated Inequality Measures from Grouped Observations. Fuzzy Monetary Poverty Measures under a Dagum Income Distributive Hypothesis. Modelling Lorenz Curves Robust and Semiparametric Issues. Modelling Inequality with a Single Parameter.
Lorenz Curves and Generalised Entropy Reviews: 1. As an example, we apply our method to the publicly available grouped data of the National Survey of Family Income and Expenditure in Japan. The test accepts the null hypothesis that income distribution in Japan improved from to 2.
Generalized Lorenz dominance Generalized Lorenz curves. Let X be a positive random variable. Health Equity and Financial Protection: Streamlined Analysis with ADePT Software () by Adam Wagstaff, Marcel Bilger, Zurab Sajaia, and Michael Lokshin Assessing Sector Performance and Inequality in Education: Streamlined.
Quantile Function and Generalized Lorenz Curve Generalized Lorenz Curve Growth Incidence Curves Growth Rate of Lower Partial Mean Income General Mean Growth Curves Lorenz Curve Poverty Incidence Curve and Headcount Ratio Poverty Deficit Curve and the Poverty Gap Measure In recent years, especially since the mid s, there have been debates and commentaries exploring the concept, types, sizes and economic implications of income inequalities.
This study carried out a quantitative measure of the size and the core determinant of income inequality in Nigeria. The study used standard traditional measurement approach: the Lorenz Curve and Gini Co.
On a class of poverty measures’, (). On the Estimation of Lorenz Curves from Grouped Observations’, (). Poor results and poorer policy: A comparative ananlysis of estimates of global inequality and poverty’, Some Generalized Functions for the Size Distribution of Income’.
a common measurement of poverty. the ratio between the total amount of income that the poor fall short of the poverty line and the total income the poor would have if all the poor had incomes equal to the poverty threshold number.
measures how bad the poverty is. The primary drawback to this approach is that it measures relative poverty (as opposed to absolute poverty). This criticism spans across most poverty measurement systems (Thiel entropy, the ratio, and the Palma ratio to name a few), and ultimately implies that much of what is measured as inequality does not take into account absolute gains.
is a method used to measure changes in absolute poverty. shows the value judgement implications of using the change in income per capita as a measure of the change in development.
is a method used to measure changes in inequality. is a method used to measure the growth rate of GDP. 5 of long-term trends in global poverty, it is essential to determine whether the statistical techniques employed are indeed reliable. Kernel density estimation is one of two methods that have been used extensively in poverty analysis from grouped data.
Kakwani, T. and N. Podder () Efficient Estimation of the Lorenz Curve and Associated Inequality Measures from Grouped Observations, Econometrica,CrossRef Google Scholar Kleiber, C. () Dagum vs.
Singh-Maddala Income Distributions, Economics Letters, 53, Global data and statistics, research and publications, and topics in poverty and development It is based on the Lorenz curve, a cumulative frequency curve that compares the distribution of a specific variable (for example, income) with the uniform distribution that represents equality.
Generalized Entropy Measures: Among the most widely. Gastwirth, J.L. & M. Glauberman () The interpolation of the Lorenz curve and Gini index from grouped data. Econometr – Giorgi, G.-M. () Bibliographic portrait of the Gini concentration ratio.
In economics, the Lorenz curve is a graphical representation of the distribution of income or of was developed by Max O. Lorenz in for representing inequality of the wealth distribution.
The curve is a graph showing the proportion of overall income or wealth assumed by the bottom x% of the people, although this is not rigorously true for a finite population (see below). 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.
Gini Coefficient Lorenz Curve (2) Area below Lorenz Curve (B) If B0 then G1 (complete inequality). 31 Gini Coefficient Lorenz Curve (3) Gini coefficient (G) is the ratio of the area between the line of total equality and the Lorenz curve (A) to the area below the line of total equality (AB) A.
32 Lorenz Curve and Gini Coefficient e. Figure illustrates the greater inequality of the U.S. income distribution between and because the Lorenz curve for is farther from the degree line than for The Lorenz curve is a useful way of presenting the quintile data that provides an image of all the quintile data at once.Survey papers on Lorenz functions and the generalizations and extensions of income distributions --A guide to the dagum distributions / Christian Kleiber --Pareto and generalized Pareto distributions / Barry C.
Arnold --The generalized beta distribution as a model for the distribution of income: estimation of related measures of inequality. The greater inequality of the U.S. income distribution between and is illustrated in because the Lorenz curve for is farther from the degree line than the Lorenz curve for The Lorenz curve is a useful way of presenting the quintile data that provides an image of all the quintile data at once.