A comparative study of the gini coefficient estimators based on the. Mathematically, the gini index is defined based on the lorenz curve. Estimation of gini coefficients using lorenz curves johan fellman1,2 abstract primary income data yields the most exact estimates of the gini coefficient. One way to visualize the income distribution in a population is to draw a lorenz curve.
This is followed by an introduction of our case and the associated data. Gini index for the united states sipovginiusa fred. Gini coefficient is a tool to measure income inequality in the country. In figure 1, as op is the equidistribution line, orp is the area defined by the lorenz curve of the standard income distribution and the equidistribution line, what we. Gini coefficient definition, formula how to calculate. Raotam simplified lorenz curves the gini coefficient is 1 s 1 g.
The actual lorenz curve is calculated as a polynomial approximation using lagrange interpolation method with calculated coordinates. The lorenz curve of income distribution b is an extreme case where all incomes are equal. The gini coefficient can then be thought of as the ratio of the area that lies between the line of equality and the lorenz curve marked a in the diagram over the total area under the line of equality marked a and b in the diagram. The shape of the lorenz curve based on income distribution a is the standard lorenz curve we find you find when analysing actual income distributions. Those analysts who seek a complete cardinal comparison of the inequali ties of two. Axiomatic characterization of the gini coefficient and. Zealand commercial fishing using conditional lorenz curves. Lorenz curves and gini coefficients for example, a situation where a small fraction of the population lives in lorenz curve a graphical luxury and everybody else struggles to survive may be efficient, but few representation of inequality of people would say it is desirable due to the vast inequality between the rich some quantity such as wealth or and.
In this case, the gini coefficient is 0 and it means there is perfect distribution of income everyone earns the same amount. A second look at measuring inequality in south africa. Alternatively, the gini coefficient can also be calculated as the half of the relative mean absolute difference. The gini index is calculated as the ratio of the area between the perfect equality line and the lorenz. This revision presentation takes you through plotting and calculating both the lorenz curve and gini coefficient and sets them in some historical context. If youre seeing this message, it means were having trouble loading external resources on our website. If a 0, it means the lorenz curve is actually the line of equality. In this tutorial, well talk about what the gini coefficient measures, and how its calculated. Comparing the gini coefficients of income computed from the polynomial. If x k, yk are the known points on the lorenz curve, with the x k indexed in increasing. The gini coefficient gini 1912 is a popular measure of statistical dispersion, especially used for analyzing inequality or concentration of income, wealth or sales turnover of competing firms. A simple method for measuring inequality humanities and social. The bigger it is, the more unequally income is distributed. However, users may print, download, or email articles.
The income distribution corresponding to the rt model can be found. When a countrys lorenc curve is identical to the line of equality and so, there is perfect income equality of all in the country. Wealth distribution dynamics quantitative economics with. Furthermore it is possible for the gini coefficient of a developing country to rise due to increasing inequality of income while the number of people in absolute poverty decreases. In economics, the lorenz curve is a graphical representation of the distribution of income or of. The gini coefficient is used to express the extent of inequality in a single figure. Using the data below the household incomes for the following people, plot the income quintile bar chart for the following group of people. Finally, the lorenz curve of income distribution c is another extreme case where all incomes are zero except for the last one. The gini index measures the area between the lorenz curve and a hypothetical line of absolute equality, expressed as a percentage of the maximum area under the line.
Joseph gastwirth reza modarres efstathia bura the use of. The x and y values for this curve are in the range of 0 to 1. An application of the gini coefficients usda forest service. Sometimes the entire lorenz curve is not known, and only values at certain intervals are given. Other examples of interest are the lorenz curve and the gini coefficient in the case of wealth exchange models. The gini coefficient is the ratio of the area between the line of perfect equality and the observed lorenz. The coefficient g varies between 0 no inequalityconcentration and 1 complete inequalityconcentration. Moreover, the gini coefficient is recognized to be rationalizable under both axiom sets. Changing income inequality and panel income changes. Lorenz curves and the gini coefficient free download as powerpoint presentation. A reply by anthony koo, nguyen quan, and robert rasche e appreciate and welcome the comments b y thon. Specifically, the gini coefficient is the ratio of.
The gini coefficient g is twice the area between lorenz curve and line y x. Demonstrating lorenz curve distribution and increasing gini coefficient with the iterating koch snowflake fractal attractor. Lorenz curve gini coefficient quintile groups task full with. Estimation of gini coefficients using lorenz curves. If we are measuring income, for example, then if z max is the maximum income that anyone in the population earns and 0 is the theoretical minimum earnings, then for any income amount z between 0 and z max, if x is the percentage of the population that has income less than or. Lorenz curve coincides with the diagonal in figure 2 and 1 perfect inequality. A then you have to determine what fraction of the triangle is made up of area a. Nov 01, 2001 by introducing appropriate preference relations on the set of lorenz curves, two alternative axiomatic characterizations of lorenz curve orderings are proposed. The figure shows the cumulative percentage of total income received on the vertical axis. 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. The gini coefficient measures the area between the lorenz curve and a hypothetical line of absolute equality, expressed as a percentage of the maximum area under the line of perfect equality. And when lorenz curves cross, the lorenz criterion cannot render a verdict.
Gini coefficient definition, calculation and indias. A complete handout about the lorenz curve including various applications, including an excel spreadsheet graphing lorenz curves and calculating gini coefficients as well as coefficients of variation. In a group of 24, discuss and answer the following questions on lorenz curves and gini coefficients. If x k, yk are the known points on the lorenz curve. Lorenz curve gives an idea of distribution of income in an economy. Lorenz curves from three hypothetical income distributions, labelled a, b and c.
The gini coefficient was developed by the italian statistician corrado gini and published in his 1912 paper variability and mutability italian. The gini index is related to the lorenz curve y lx. Mar 22, 2021 a lorenz curve plots the cumulative percentages of total income received against the cumulative number of recipients, starting with the poorest individual or household. You will need internet access in order to answer question 5. Introductionthe gini coefficient gini 1912 is the most common measure of distributional concentration for income data. To know further about how a lorenz curve is plotted and what it represents, read the full article. Using lorenz curves, the gini coefficient is defined as the ratio of the area between the diagonal and the lorenz curve and the area of the whole triangle under the diagonal. Wealth distribution dynamics quantitative economics with python. The lorenz curves for various values are given in figure 2. The program then calculates the gini coefficient by integrating x minus the lorenz function. Gini index for the united states sipovginiusa fred st.
Lorenz curves and gini coefficient answers directions. Gini coefficient was first introduced by italian statistician corrado gini in 1912 in his book variability and mutability and several formulations and representations existed in the literature over the years. The gini coefficient requires you to construct a lorenz curve that would look like this. Free app get all of the videos on this channel on your phone. In that case, the gini coefficient can be approximated by using various techniques for interpolating the missing values of the lorenz curve. From the lorenz curve, the jose javier caloca martinez 22 income inequality and economic growth gini coefficient can be obtained which is the ratio of the area between the 45. By way of reference, the united states has a gini coefficient of 0. Lorenz curve and gini coefficient of income using polynomial function with degree 5. Mar 07, 2011 the coefficients are thus normalized to run from zero in a perfectly egalitarian society, to one in a society in which the wealthiest person held all the wealth.
The lorenz curve is a graphical representation of the distribution of wealthincome. Lorenz curve and gini coefficient the lorenz curve was developed by an american statistician and economist named max lorenz when he was a graduate student at the university of wisconsin the cumulative percentage of income can be plotted against the cumulative percentage of the population, producing a socalled lorenz curve see the figure. Estimating croatias gini coefficient using lagrange. A higher gini coefficient means greater inequality. Also known as gini index or gini ratio, is a popular and widely used summary measure of income. The main purpose of the lorenz is to graphically present collected data about all household income. We examine consolidation using all three methods lorenz, gini, and hhi in the new zealand commercial fishing industry.
Mathematically, the gini coefficient is defined based on the lorenz curve. Graphical representation of the gini index lorenz curve. Higher the value of an index, more dispersed is the data. Pdf estimation of gini coefficients using lorenz curves. As always, my key terms are in red, and examples are in green.
Lorenz curves to show the entire distribution of income in a country. The gini coefficient or gini index measures the inequality among the values of a variable. Two other methods are added to calculate gini coefficient, but only for comparison. Identification of the lorenz curve by lorenz coefficient. Based entirely on the relative position of the lorenz curve of a certain income distribution with respect to both an equalincome distribution and a concentrated distribution, it has a natural geometric interpretation as a relative area. Estimation of the gini coefficient for the lognormal. This curve shows the entire population lined up along the horizontal axis from the poorest to the richest. For details, see any statistics textbook for economists or 1. How the gini coefficient and lorenz curves are used to measure income inequality. This module explains how to build lorenz curves for income distributions and discusses their. Youll understand how the lorenz curve relates to the gini coefficients. To learn more about how the gini coefficient is calculated from differ. Pdf the estimation of the lorenz curve and gini index.
Household income you may be asked to work out and or plot quintile and decile groups. Draw a model of a lorenz curve representing a nation with a very small degree of income inequality, like norway. Learn how the gini coefficient can be used to interpret income inequality in this video. The definition and interpretation of the gini coefficient can be found on the corresponding wikipedia page a value of 0 indicates perfect equality corresponding the case where the lorenz curve matches the 45 degree line and a value of 1 indicates complete inequality all wealth held by the richest household. Lorenz curves and the gini coefficient gini coefficient. T h e y give us w an opportunity to clarify our position for we believe t h a t thon s skepticism is due to a misinterpretation. A lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economist max lorenz in 1905. Pdf demonstrating lorenz wealth distribution and increasing. The lorenz curve is the most common presentation of income inequality. Lorenz curves and gini indices for the considered models. Gini coefficients, and the inequality possibility frontier. If one resident earned all of the income in a nation and the rest earned zero, the gini coefficient would be 1. They are part of the aqa unit 3 a level economics specification.
Mathematics, quantitative literacy, inequality, gini coefficient, calculus, social justice, inequity, lorenz. Gini coefficient and lorenz curve video khan academy. Gini coefficient is useful because it projects negative values for income and wealth which standard measures of. Axiomatic characterization of the gini coefficient and lorenz curve. Lorenz curve is also called the equidistribution line. Equitable and even distribution of wealth is one of the macroeconomic targets of countries. It is possible for two different lorenz curves to give rise to the same gini coefficient. Building on the work of american economist max lorenz, gini proposed that the difference between the hypothetical straight line depicting perfect equality, and the actual line depicting peoples incomes, be used.
Gini coefficients of education world bank document. The lorenz curve lorenz 1905, though developed independently, can be. Feb 24, 2010 the gini coefficient ranges between 0 and 1 or it can also be expressed as a number from 0 to 100 and is given by the ratio of the areas. If youre behind a web filter, please make sure that the domains. The line at 450 represents perfect equality of incomes and the area between this line and the lorenz curve is called concentration area. Measuring the inequality of accessible trams in melbourne. If every resident of a nation had the same income, the gini coefficient would be zero. Then, we will use the gini coefficient and other measures to look at other dimensions of inequality, such as healthrelated outcomes and gender participation in education. Axiomatic characterization of the gini coefficient and lorenz.
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