The aim of this module is to illustrate the functioning and the meaning of one of the most popular tools to. For example, a lorenz curve can show that the bottom 40% of households bring in 25% of a countrys income. Lorenz curves, the gini coefficient and parametric distributions. We can give a short numerical example written in r to illustrate the performance of the. For example, above the 3rd decile of the population is shown. We now consider a threshold z and the population which is below that threshold, sometimes the. In different words, it is a graphic display that shows how wealth is distributed among the population. Theoretical foundations of lorenz curve orderings ssb.
We thus start from an income distribution with continuous density fx. On the vertical axis of the lorenz curve is shown the cumulative percentage of income or wealth. Pdf this paper explains how to build lorenz curves for income. Types of graph a lorenz curve is a graph used in economics to show inequality in income spread or wealth. Pdf a general definition of the lorenz curve researchgate. The lorenz curve in economics and econometrics edoc. Lorenz in 1905 for representing wealth distribution.
The curve is a while taking the population percentile on the xaxis and cumulative wealth on the yaxis. In terms of figure 2 below, the ginicoefficient can be defined as the ratio. In this section some definitions that will be useful hereunder, are introduced. The lorenz curve is a graphical illustration of a statistical distribution used to measure wealth distribution equality. A discussion on the use of lorenz urves to represent inequality is also c provided.
The lorenz curve is a way of showing the distribution of income or wealth within an economy. Charting income inequality food and agriculture organization. A short conceptual background, a step bystep procedure and a simple numerical example illustrate how to calculate and draw lorenz curves. They are part of the aqa unit 3 a level economics specification. Lorenz curve, named after american economist max o. This paper uses gastwirths definition of the lorenz curve which applies to a general probability distribution on 0. 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. Estimating lorenz and concentration curves in stata.
The appropriate definition of the lorenz curve for a general distribution follows easily. Given a lorenzcurve plot, we can measure the degree of inequality of the distribution of the thing in question by a onedimensional number, the socalled ginicoefficient. The lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economist max lorenz in 1905. The lorenz curve and the concentration curve request pdf. For an example of a lorenz curve, see pareto distribution. Convergence theorems for empirical lorenz curves and their. This curve shows the entire population lined up along the. A discussion on the use of lorenz curves to represent. The curve is a graph showing the proportion of overall income or wealth. The lorenz curves of the latter are proved to converge, with probability 1, uniformly to the. Lorenz, is a graphical representation of an economic inequality model. Lorenz curve definition, example what is lorenz curve. A special form of the autoregressive simulation format is developed for convected.
A data science based standardized gini index as a lorenz. The econometrics of inequality and poverty chapter 4. In economics, the lorenz curve is a graphical representation of the distribution of income or of wealth. In order to clarify the interpretation of axiom 4 consider an example with a taxtransfer intervention that. Lorenz curve and gini coefficient the lorenz curve and gini coefficient are both methods of assessing the level of income equality or inequality within an economy. Lorenz in 1905 for representing inequality of the wealth distribution.
The aim of this module is to illustrate the functioning and the meaning of one of the. The lorenz curve also called relative concentration curve is widely used for the representation and analysis of the size distribution of income or wealth. It is often used to represent income distribution, where it shows for the bottom x% of households, what percentage of the t. Bonferroni curve, inequality index, income distribution, lorenz. It relates the cumulative income wealth fraction earned by various proportions of the population to the proportion receiving this income, when the units are arranged in increasing order of their income wealth. This revision presentation takes you through plotting and calculating both the lorenz curve and gini coefficient and sets them in some historical context. Since 1970s, the lorenz curve was introduced into health economics to assess the fairness of population, geography, and economic distribution of health resource allocation 5. It represents a probability distribution of statistical values, and is often associated with income distribution calculations. The average standard of living in the total population is given by the total mean. Documents in econstor may be saved and copied for your personal and. Briefly, the lorenz curve plots the proportion of the population, in our case the. Pdf on feb 1, 1971, joseph l gastwirth and others published a.
164 511 179 952 156 560 364 1212 636 825 580 427 996 999 738 1404 1160 40 173 421 527 1244 1309 734 316 349 1203 1095 1178 666 78