# Intersecting Generalized Lorenz Curves And The Gini Index

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### Quantile Treatment E ects Estimation and Stochastic Dominance

Ranking intersecting lorenz curves, Social Choice and Welfare 33: 235{259. Intersecting generalized Lorenz curves and the Gini index, Social Choice and Welfare 16

### Three 'I's of Poverty Curves, with an Analysis of UK Poverty

The forte of generalized Lorenz curves (Shorrocks, 1983) and poverty deficit curves (Atkinson, 1987) is that they permit the checking of poverty dominance criteria.3 But TIP curves also have this property, as we shall show. 3. Poverty dominance Given the poverty line z, denote a typical index in the class P by P(xlz), and a

### Inequality measures for intersecting Lorenz curves: an

transfers ), that is, the higher of two non-intersecting Lorenz curves can be obtained from the lower one by an iteration of income transfers from richer to poorer individuals (the so called elementary transfers or T-transforms, Marshall et al., 2009, p.

### EXTENDED BI-POLARIZATION AND

However, as with Lorenz curves, it is possible to have intersecting polariza­ tion curves. As do Lorenz curves, polarization curves induce only a partial or­ dering over income distributions, while the shaded area under the polarization curve in Figure 1 (P. 0) induces a complete ordering (like the Gini coefficient).

### 1 Introduction - unisi.it

Key words: Bezier curves, Generalized Lorenz curves, Bernstein polynomials, Legendre transform, Newton-Raphson method, Gini index, Skewness coeﬃcient, De Casteljau s algorithm. 1 Introduction The most widely used measure of inequality is the Gini index, which is twice the area between the Lorenz curve and the line of perfect equality.

Sep 08, 2000 The Robin Hood Index 89 Generalized Lorenz Curve 89 5.2 Calculation of the Gini 88 3.11 Intersecting TIP Curves 57 4.1 Pen s Parade: Malaysia, 1995 2004

### ces-hoy-lect1

Cases of Intersecting Lorenz curves are empirically distribution ' 'A Lorenz dommates distribution B (A B). This reflects the general acceptance of the Pigou-Dalton prmciple as central to inequality analysis. transters, tne Lorenz curve tor A Will Ile above qweaKIY at least) that for B at all points.

### The Dual Theory of Measuring Social Welfare and Inequality

Yitzhaki, S. (1983): On an extension of the Gini inequality index, International Economic Review, 24, 617-628. Zoli, C. (1999): Intersecting generalized Lorenz curves and the Gini index, Social Choice and Welfare, 16, 183-196. Zoli, C. (2002): Inverse stochastic dominance, inequality measurement and Gini indices, Journal of

### The Impact of Taxes and Transfer Payments on the Distribution

The introduction of a third parameter allows for intersecting Lorenz curves. Some three-parameter models which have been used to model the size distribution of income include the generalized gamma (Amoroso, 1924-25 and Taille, 1981) and beta (Thurow, 1970) as well as two

### 607 Public Economics Seminar Peter Lambert, Fall 2014

4. The principle of diminishing transfers and intersecting Lorenz and generalized Lorenz curves Shorrocks A.F. and J. Foster (1987). Transfer sensitive inequality measures. Review of Economic Studies, vol. 54, pp. 485-497. Dardanoni, V. and Lambert, P.J. (1988). Welfare rankings of income distributions: a rôle for the variance

### DEPARTMENT OF ECONOMICS

from information on the Gini coefficients and mean income for each country, it is known to be restrictive in that it implies symmetric and non-intersecting Lorenz curves. A large number of less restrictive alternative distributions have been suggested in the literature. See, for example, McDonald and Ransom (1979),

### Making Socioeconomic Health Inequality Comparisons When

a (health achievement) socioeconomic health inequality index if and only if the (generalized) health concentration curve of the former distribution lies above that of the other one.4 However, when the (generalized) health concentration curves intersect each other, their condition cannot help rank the health distributions.

### Measuring the citation impact of journals with generalized

in particular, its integral namely, the generalized Lorenz curve (GLC, Shorrocks, 1983). The GLC provides an attractive representation of the overall impact as well as the shape of the citation distribution. For a given journal with ὐpublications, the GLC evaluated in ∈0,1ὑ determines an

### The statistical legacy of Corrado Gini

The statistical legacy of Corrado Gini 143 be generated by either objective and/or subjective causes. Therefore, such a component should be taken into account to avoid bias in estimation, interpretation and prediction.

### Inverse Stochastic dominance, inequality measures and Gini index

transfers with intersecting Lorenz curves; in Section 7 we present the Generalized Lorenz curve and positive monotone dependence.; in Section 8 we make some concluding remarks and some comments 2 The Lorenz curve and Gini index. The seminal work of Gini on the measurement of concentration of income distribution has

### (y:502asd oa ank-lor.doc) 28. august 1997

Ranking Intersecting Lorenz Curves Rolf Aaberge. 1. Research Department, Statistics Norway, P.O. Box 8131 Dep., N-0033 Oslo, Norway (Social Choice and Welfare, 33, 235 259, 2009) Abstract This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz

### The Economic Theory of Income Inequality

B. Generalized Gini Indices 28. John A. Weymark (1981), 'Generalized Gini Inequality Indices', Mathematical Social Sciences, 1 (4), August, 409-30 457 29. Shlomo Yitzhaki (1983), 'On an Extension of the Gini Inequality Index', International Economic Review, 24 (3), October, 617-28 479 C. Axiomatics and Generalized Inequality Measures 30.

### SHORT CV Professor Claudio Zoli Department of Economics

Intersecting generalized Lorenz curves and the Gini index. Social Choice and Welfare, vol. 16, the Gini-Exposure index, WP Number: 30, December 2015, Dipartimento

### Introduction - Science Publishing Group

For intersecting Lorenz curves alternative inequality measures have to be defined. The most frequently used is the Gini coefficient, G (Gini, 1914). Using the Lorenz curves, this coefficient is the ratio between the area between the diagonal and the Lorenz curve and the whole area under the diagonal. The formula is ³ 1 0 G 1 2 L(p)dp

### Regression Analyses of Income Inequality Indices

The estimated Gini index based on this polynomial is Gˆ =0.3 15750 , and the agreement with the theoretical value is acceptable. The Lorenz curves for the Pareto, and Gupta models are pre

### Tommaso Lando - Curriculum vitae

Intersecting Lorenz Curves: Analysis of income distribution in European countries. Pro-ceedings of the 35th International Conference on Mathematical Methods in Economics, pp. 402-407. ISBN 978-80-7435-678-0. WOS:000427151400069 4.LANDO, T; BERTOLI BARSOTTI, L. (2017) Comparing inequality of distributions on the basis of mixed Lorenz curves.

### Mathematical Analysis of Distribution and Redistribution of

For intersecting Lorenz curves alternative inequality measures have to be defined. The most frequently used is the Gini coefficient, G (Gini, 1914). Using the Lorenz curves, this coefficient is the ratio between the area between the diagonal and the Lorenz curve and the whole area under the diagonal. The formula is ³ 1 0 G 1 2 L(p)dp

### Soc Choice Welfare (1999) 16: 183-196 ~ Social Choice máWtttt

Intersecting generalized Lorenz curves and the Gini index Claudio Zoli1 2 1 Department of Economics, University of Bologna, Bologna, Italy 2 Department of Public Economics, University of Pavia, Pavia, Italy Received: 28 August 1996 /Accepted: 22 October 1997 Abstract. As is well known, the use of the Gini coefficient in comparisons is

### SHORT CV Professor Claudio Zoli Posizione Professionale Attuale

Intersecting generalized Lorenz curves and the Gini index. Social Choice and Welfare, vol. 16, 183-196. the Gini-Exposure index, WP Number: 30, December 2015

### INEQUALITY MEASURES: THE KOLKATA INDEX IN COMPARISON WITH

the Gini coe cient or index (see [16]) and the Pietra index (see [17]). The Gini index is the ratio of the area between the 45 line and the Lorenz curve to the total area under the 45 line. Equivalently, the Gini index is twice the area between the Lorenz curve and the line of perfect equality. The Pietra index is the maximum value of the gap

### INTERNATIONAL COMPARISONS OF EARNINGS

Both the Gini and Theil indices, however, have a common disadvantage. If they are derived from distributions with intersecting Lorenz curves, that is, curves showing the relationship between the cumulated percentage of earnings and the cumulated percentage of earners, meaningful comparisons of the indices become problematic (Braun, 1988).

### Increasingly Unequal Yet Similar 21st Century Constituent

2. They are related to the Absolute Gini and associated Lorenz and Generalized Lorenz curves as measures of wellbeing together with the introduction of an Ambiguity Index for complete orderings in a given class in Section 3. After the Canadian background for interest in these issues is outlined in section 4, the