You will need internet access in order to answer question 5. M ost of the measures of income inequal ity are derived from the lorenz curve. This video tutorial shows, how to draw the lorenz curve in microsoft excel and afterwards, its shown how to calculate the gini coefficient. However, the use of the lorenz curve in the way it is usually used by economists would give misleading results as a measure of inequalities in school finance. Lorenz curve models and demonstrates how to build efficient models for the lorenz curve using our proposed singleparametric forms. The gini coefficient ranges from 0 complete equality to 1 complete inequality.
Estimation of gini coefficients using lorenz curves johan fellman1,2 abstract primary income data yields the most exact estimates of the gini coefficient. Lorenz curve coincides with 45 ray through origin inequality is greater, the further the lorenz curve from the 45ray gini coefficient. The gini coefficient is a measure of inequality of a distribution. The income distribution corresponding to the rt model can be found. It is calculated by dividing the area between the lorenz curve and the perfect equality line, by the total area underneath the perfect equality line. The figure shows the cumulative percentage of total income received on the vertical axis. Joseph gastwirth reza modarres efstathia bura the use of. A lorenz curve is a plot of the cumulative income share of the poorest 100p% against cumulative population share p, where units are ordered in ascending order of income complete equality. Moreover, a ten percent increase in everyones income will not impact the gini coefficient. Next, we present the lorenz curve and the concentration curve for the continuous case see yitzhaki and schechtman, 20. In addition, the tax data analysis is a more casual analysis working with limited sets of data of different sizes.
The gini coefficient is a measure of statistical dispersion most prominently used as a measure of inequality of income distribution or inequality of wealth. Almost thirty years ago, the author of this brief attended a lecture addressing the economics of inequality. 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. Pdf the estimation of the lorenz curve and gini index. In economics, the lorenz curve is a graphical representation of the distribution of income or of wealth. Gini coefficient as a measure of inequality is widely used in various contexts such as energy, credit availability, income, health care and wealth. In a group of 24, discuss and answer the following questions on lorenz curves and gini coefficients. Draw a model of a lorenz curve representing a nation with a very small degree of income inequality, like norway.
Figure 3 also shows a possible consequence of the use of this technique. 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. These different measures behave differently when there are negative values of wealth which is not a concern in the analysis of income inequality so we study which measures can be used for wealth distributions and under what conditions. The econometrics of inequality and poverty chapter 4. Lorenz in 1905 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. Raotam simplified lorenz curves the gini coefficient is 1 s 1 g. Scholars have devised over a dozen variants of the gini coefficient source. The lorenz curve and the gini coefficient are used to evaluate equity in the distribution of health or income in a population. In the 1830s, almost a century before lorenz and gini, the belgian astronomer adolphe quetelet, one of a few ambitious quantifiers porter, 2001, p. The use of the lorenz curve, gini index and related measures of. A higher gini coefficient means greater inequality.
A second look at measuring inequality in south africa. May 08, 2020 the gini coefficient is equivalent to the region beneath the line of impeccable uniformity 0. Lorenz curves, the gini coefficient, and two entropy measures of inequality. Gini index gi and a related measure of relative inequality, the coefficient of dispersion cd can be used to examine. The area between the two lines expressed as a ratio to the area under the straight line gives a representation of the inequality and is called the gini coefficient developed by the italian statistician corrado gini in the year 1912. Gini coefficient, dissimilarity index and lorenz curve for the. The gini coefficient or gini index measures the inequality among the values of a variable. Louisiana distribution of income lorenz, gini, and palma. A comparative study of the gini coefficient estimators based on the. Lorenz curves and gini coefficient answers directions. Lorenz curves and gini coefficients core economics.
Gini coefficient and lorenz curve around the world. If one uses the lorenz curve, 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. This is twice the grey area in the previous picture. The more equal the distribution of income, the closer the curve is to the diagonal line. Lorenz curve definition, example what is lorenz curve. Gini coefficient is one of the most efficient and commonly used measurement of income inequality in the world. Let us denote the income of a randomly chosen individual from each population by x, y. The gini coefficient is usually defined mathematically based on the lorenz curve, which plots the proportion of the total income of the population y axis that is cumulatively earned by the bottom x% of the population see diagram. Please consult the help included in the file for an extensive description of the two concepts and how to use the program. The lorenz curve allows for conditional specification over stratified groupings, which yields straightforward interpretation and illustration of overall inequality for more nuanced interpretations.
The relationship between gini terminology and the roc curve. But this is a virtue of this variation of the technique. Figure 2 presents the average of all three year pools up to the most recent pool, 20162018. Which test is better to evaluate equity lorenz curve or. Then the gini index of inequality is a measure of the difference. Figures 1 and 2 present the one year and threeyear lorenz curves and gini coefficients.
At the start, the class was invited to imagine the. If the calculation is zero the implication is that income distribution is perfect i. The comparison of lorenz curves for two or more populations is a graphical way to compare their distributions of wealth, income. Following is the example to understand the lorenz curve with the help of a graph.
Key words lorenz curves, gini coefficient, herfindahl hirschman index hhi, consolidation, individual transferable. The geometric relationship with the lorenz curve is immediate, as is the geometric interpretation of the gini coefficient via the leimkuhler curve, see burrell 1991. A popular representation of income inequality, the gini coefficient is based on the lorenz curve, which plots the share of population against the share of. Estimation of the gini coefficient for the lognormal. Definition 1 the distribution function fx gives the proportion of individuals of the population having a standard of living below or equal to x. Jun 02, 2012 tic lorenz curve lies between these extremes, as in figure 2. Pdf the lorenz curve and the measurement of inequality in. The empirical applications are presented in the sixth section. When a countrys lorenc curve is identical to the line of equality and so, there is perfect income equality of all in the country. The povcal procedure fits a parametric lorenz curve general quadratic or beta through the available distributional data. The lorenz curves are usually defined for five quintiles or for 10 deciles. Graphical representation of the gini index lorenz curve.
Here ill always convert the resource into money, usually dollars. This curve is defined on the interval 0,1 and is referred to as the lorenz curve of the resource distribution. The gini coefficient is defined as a ratio of the areas on the lorenz curve diagram. The bigger it is, the more unequally income is distributed. Ap microeconomics lorenz and gini practice questions 1.
Gini coefficient and the lorentz curve file exchange. Quantile group shares, cumulative shares lorenz ordinates. It is therefore natural that we dene as a measure of inequality the area between the diagonal and the lorenz curve, as a percentage of the entire area between the two extremes which is 1 2. Lorenz curve coincides with the diagonal in figure 2 and 1 perfect inequality. It was developed by the italian statistician and sociologist corrado gini the gini coefficient measures the inequality among values.
Alternatively, the gini coefficient can also be calculated as the half of the relative mean absolute difference. Mathematically, the gini coefficient is defined based on the lorenz curve. Please also comment if you like it or find it useful. We thus start from an income distribution with continuous density fx. We provide a description of the gini coefficient and some discussion of how it. The lorenz curve plots the percentiles of the population on the graphs horizontal axis according to income or wealth, whichever is being measured. Pdf on feb 1, 1972, joseph l gastwirth published the estimation of the lorenz curve and gini index find, read and cite all the research. If wealth were equally distributed, the lorenz curve would be a straight line. The lorenz curves for various values are given in figure 2.
If a 0, it means the lorenz curve is actually the line of equality. A lorenz curve plots the cumulative percentages of total income received against the cumulative percentages of recipients, starting with the poorest individual or. Pdf estimation of gini coefficients using lorenz curves. That technique is the use of the lorenz curve and its associated gini coefficient. View notes calculate gini coefficient using lorenz curve. Lorenz curves and gini indexes to measure income inequality in a country and compare this phenomenon among countries more accurately, economists use lorenz curves and gini indexes. Zealand commercial fishing using conditional lorenz curves. 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. At the end of the day, it is twofold the region between the lorenz bend and the line of immaculate uniformity. Mar 27, 2020 a lorenz curve plots the cumulative percentages of total income received against the cumulative number of recipients, starting with the poorest individual or household. A lorenz curve for wealth in a population tells, for example, that the least wealthy 50% of the population owns 10% of the wealth. If you are interested in evaluating equity in the distribution of. To learn more about how the gini coefficient is calculated from differ.
The estimated gini coefficients according to the trapezium rule are inaccurate and show. Lorenz curve definition, example what is lorenz curve in. 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. We examine consolidation using all three methods lorenz, gini, and hhi in the new zealand commercial fishing industry. The predictive values of the indicators are calculated by the authors using the approximations for 2017 and 2018 only based o n the. Jun 30, 2010 the lorentz curve is a graphical representation of this inequality which is intimately related to the gini coefficient. 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. How the gini coefficient and lorenz curves are used to measure income inequality. Introduction this note seeks to quantify inequality in the distribution of 2000 and 2001 agricultural subsidies for france, great britain, the european union and the united states using gini coefficients and associated lorenz curves. The main purpose of the lorenz is to graphically present collected data about all household income. The line at 450 represents perfect equality of incomes and the area between this line and the lorenz curve is called concentration area. Gini index, which is relevant to our paper, is the gmd divided by twice the mean.
The estimation of the lorenz curve and gini index jstor. Lorenz curve and gini coefficient of income using polynomial function with degree 5. Lorenz curve a graphical representation of inequality of some quantity such as wealth or income. Where the estimated curve is valid, we use it to approximate the income shares obtained by different quintiles. The lorenz curve is the most common presentation of income inequality. Figure 1 presents lorenz curves for 1 for an overview of the derivation of the gini coefficient for a discrete distribution by estimating lower and upper bounds, and a compromise measure, see cowell 1995, chapter 5. Measuring relative equality of concentration between. Pdf the use of the lorenz curve, gini index and related measures. It is computed as twice the region between a lorenz curve and the egalitarian line. The construct of lorenz curves and of the ginicoeficient to depict. Higher the value of an index, more dispersed is the data. Zealand commercial fishing using conditional lorenz curves to. If one resident earned all of the income in a nation and the rest earned zero, the gini coefficient would be 1.
A smaller number means that there is less inequality in income distribution. The gini index is twice the area between the line of inequality y x and the lorenz curve y lx. 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. Lorenz curves showing two different distributions of income can in fact have the same gini coefficient d. Lorenz curve and gini coefficient are examples of new entities, their purpose being to measure the degree of dispersion of a set of figures. Comparing the gini coefficients of income computed from the polynomial. If every resident of a nation had the same income, the gini coefficient would be zero. The gini coefficient measures the area between the. Lorenz curves, the gini coefficient and parametric distributions. 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. A biparametric lorenz curve we call l with p p 0,1 a lorenz curve if it satisfies l0 0, l, 1lc. This is followed by an introduction of our case and the associated data.
The more bent the line of the lorenz concentration curve is, the more unequal is its distribution across the population. Intuitively, the further away the lorenz curve is from the perfect equality line, the more unequal the income. The estimation of the gini coefficient in per cent applied to the lorenz curve for the pareto distributions. System by type of goods from 1960 to the year 2010 for business units. In this case, the gini coefficient is 0 and it means there is perfect distribution of income everyone earns the same amount.
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