It was developed by the italian statistician corrado gini in 1912 definition. Joseph gastwirth reza modarres efstathia bura the use. 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. 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. If lorenz curve is closer to the diagonal line, the distribution of wealth is closer to perfect equality. The line at 45 degrees thus represents perfect equality of incomes. In a situation where the richest person has all the income and everyone else none, the lorenz curve is horizontal along the bottom of the chart and spikes up to 1 at the extreme right so b is 0. The lorenz ratio is derived from the lorenz curve diagram and is defined as the ratio of the area between the lorenz curve and the perfect equality line. Pdf the estimation of the lorenz curve and gini index. In a situation of perfect equality everyone has the same income, or whatever it is we are measuring inequality of the lorenz curve is the diagonal line, and a is 0 so the gini coefficient is 0. From this you get lorenz curve and calculate the gini of x. Graphical representation of the gini index lorenz curve the gini coefficient is usually defined mathematically based on the lorenz curve, which plots the proportion of the total income of the population yaxis that is cumulatively earned by the bottom x% of the 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 gini coefficient subject give clear graphic illustrations of how to measure absolute equality given the linear and area pictures in gini coefficient and lorenz curve.
This paper stems from work done by the authors at the mathematics for social justice workshop held in june of 2007 at middlebury college. 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. Macroeconomics economic growth and equity in the distribution of income. In my function, fex 19968, ginicoeff requires two variables. The gini coefficient is a measure of income equality derived from a lorenz curve of an economy by dividing the area between the straight line and the lorenz curve by the total area beneath the straight line. Lorenz curves, the gini coefficient and parametric distributions. Lorenz curve and gini coefficient teaching resources. What is the relationship between a lorenz curve and a gini.
Joseph gastwirth reza modarres efstathia bura the use of. This correspondence between areas on the graph of the lorenz curve the concentration of income is the idea behind the gini coefficient. Pdf estimation of gini coefficients using lorenz curves. A listing of the gini coefficients can be found here. If there is a high degree of inequality, then area a will be a bigger percentage of the total area. Jenkins iser, university of essex colchester co4 3sq, uk. Estimation of the gini coefficient for the lognormal. A lorenz curve is a plot of two distributions in welfare economics, the vertical axis gives the. This can cause mathematical errors from the inclusion of negative incomes. The gini coefficient is calculated as the ratio of the area between the line of equality and the lorenz curve to the area under the line of equality. Find powerpoint presentations and slides using the power of, find free presentations research about lorenz curve ppt.
The lorenz curve is a graphical representation of the distribution of some measure income, consumption, education, etc. Please consult the help included in the file for an extensive description of the two concepts and how to use the program. It discusses how the italian statistician corrado gini developed it. The econometrics of inequality and poverty chapter 4. Pdf the use of the lorenz curve, gini index and related measures. Meanwhile, and not least as a result of major contributions by atkinson 1970 and sen 1973 the traditional framework of lorenz curves and gini coefficients has retained its adherents, although theil 1967 has shown that a measure of inequality based on entropy has advantages. We suggest an alternative estimator obtained by approximating the lorenz curve by a series of linear segments. Derivation of the lorenz curve and gini coefficient for global income in 2011 cmg lee. The estimation of the lorenz curve and gini index joseph l. One of the main goals of a government is to ensure equal distribution of income.
Lorenz curve and gini coefficient 1 lorenz curve lc and income distribution households hh persons cumulative % income cumulative % 0 100 100 lc explanations xaxis. Gini coefficient of inequality the most widely used single measure of inequality is the gini coefficient. We provide a description of the gini coefficient and some. The closer the lorenz curve is to the line of equality, the smaller area a is. Gini coefficient and lorenz curve explained towards data science. The gini coefficient ranges from 0 complete equality to 1 complete inequality. Gini coefficient and the lorentz curve file exchange. The entry highlights methodological aspects to explain the various formulas that can be used to calculate the g value and to show the links with the lorenz curve and the mean.
The gini coefficient is the result of the estimated difference between the slopes along the lorenz curve. The ratio between the areas x and y on the graph is known as the gini coefficient. Gini coefficient simple english wikipedia, the free. The gini coefficient g is an index for measuring inequality. The assessment of poverty and inequality through parametric estimation of lorenz curves an evaluation. Creating a lorenz curve from excel university of washington. Estimating gini coefficient based on hurun report and. Ordered lorenz curve and gini index ordered lorenz curve statistical inference gini interpretations concluding remarks the lorenz curve we consider methods that are variations of wellknown tools in economics, the lorenz curve and the gini index. To find the gini coefficient, we find the area between the line of equality and the lorenz curve and divide it by the area of the triangular region that lies below the line of equality. It is defined as a ratio with values between 0 and 1. The area above the lorenz curve marked a is shaded differently from the area below the curve marked b. Jun 30, 2010 the lorentz curve is a graphical representation of this inequality which is intimately related to the gini coefficient.
View and download powerpoint presentations on lorenz curve ppt. Overview the personal distribution of income is the way analysts organize income by categories such as households, families, or even individuals. 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. Economists have tried to correct for these errors by using revised statistical models that limit different aspects of. The larger the gini coefficient the greater the inequality in the distribution of income tragakes 304. Lorenz curve coincides with the diagonal in figure 2 and 1 perfect inequality.
Pdf on feb 1, 1972, joseph l gastwirth and others published the estimation of the lorenz curve and gini index find, read and cite all the. Householdspersons are arranged in ascending order of income cumulative percentage. Gastwirth i introduction m ost of the measures of income inequality are derived from the lorenz curve. The gini coefficient also known as the gini index or gini ratio is a measure of differences in income. Gini coefficient diagram, based on the version by bluemoosebenfrantzdale. Convergence theorems for empirical lorenz curves and their. Gini can also be expressed in percentages gini coefficient. He described the lorenz curve, lp, for wealth within populations in the foll owing way. The gini coefficient can then be thought of as the ratio of the area that lies between the line. This file is licensed under the creative commons attributionshare alike 4. M ost of the measures of income inequal ity are derived from the lorenz curve.
The use of the lorenz curve, gini index and related measures of. Hi you have given the answer to the calculation of gini index using spss. Estimation of gini coefficients using lorenz curves johan fellman1,2 abstract primary income data yields the most exact estimates of the gini coefficient. The gini coefficient is usually a number between 0 and 1 or 0 to 100. May 26, 2016 lorenz curve with gini coefficient how to draw the lorenz curve with gini coefficient theory video. Derivation of the lorenz curve and gini coefficient for global. In economics, it is common to read in newspaper about gini coefficient gini was taken from italian sociologist who introduce this method. The small sample variance properties of the gini coefficient are not known, and large sample approximations to the variance of the coefficient are poor mills and zandvakili, 1997. Whereas the gini coefficient is a measure of relative poverty, and it is use to measure the distribution of wealth at the world level.
Feb 05, 2017 an introduction for as level pupils to the lorenz curve and the gini coefficient, with examples and tasks to complete. 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 role and robustness of the gini coefficient as an. The lorenz curve of the distribution of wealth is a graph of cumulative proportion of total wealth owned, against cumulative proportion of the population owning it. 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.
The gini coefficient as a robust measure of gene expression stability in multiple cellline data sets. In that case, the gini coefficient can be approximated by using. The gini coefficient can vary from 0 perfect equality, also represented as 0% to 1 perfect inequality, also represented as 100%. The gini coefficient, or gini index, is derived from the lorenz curve, and like the lorenz curve, it measures the degree of economic equality across a given population and simplifies this reality into a single number how does the gini coefficient work. Therefore the lorenz curves always start and end at the same places, where 0% of people make 0% of the countrys income and 100% of people make 100% of the total income. The information in a lorenz curve may be summarized by the gini coefficient and the lorenz asymmetry coefficient.
Jul 28, 2016 the lorenz curve and gini index of income for the lognormal distribution is given as. Economists often use another technique to measure describe the distribution of income, viz. The two estimators are identical for the original gini coefficient, where the inequality. A gini coefficient of one or 100% expresses maximal inequality among values for example, where only one person has all the income or consumption, and all others have none. Introduction there are many criteria that policymakers can use to assess outcomes or allocations of economic interactions, in order for them to evaluate which. The lorenz curve cannot rise above the line of perfect equality. Jul 06, 2010 the lorenz curve is constructed by plotting the cumulative share of household on the horizontal axis and cumulative share of household income on the vertical axis. Gini coefficient weakness abstract as the gap between the highest and lowest incomes increases rapidly in the united states, voters, politicians and researchers have become more aware of the importance of this difference. This can ensure most accurate lorenz curve and thus most accurate computation of the coefficient in 2003 the gini coefficient for australia was 0. Gini ranges from 0 to 1, where 0 means perfect equality everyone has the same incomewealth and 1 means absolute inequality one person gets the whole incomewealth and the others get nothing. Gini coefficient and lorenz curve explained towards data. If the variable being measured cannot take negative values, the lorenz curve. A more bowed out curves shows a less equal distribution.
Sampling distribution of weighted gini coefficient by. The lorenz curve is named after an american statistician lorenz who in 1905 devised it to depict and measure inequalities in the distribution of income. Estimation of gini coefficients using lorenz curves. Quantile group shares, cumulative shares lorenz ordinates. Gini index is equals to area a divided by area a and b 4. Quantile group shares, cumulative shares lorenz ordinates, and generalized lorenz ordinates. The gini coefficient is another method for describing the. Label each lorenz curve with its corresponding gini coefficient, and check that the coefficients are consistent with what you see in your charts. The gini index or gini coefficient is a statistical measure of distribution which was developed by the italian statistician corrado gini in 1912. However, a lorenz curve is used in the gini index due to the continuous cumulative portions of population in fig. Lorenz curve coincides with 45 ray through origin inequality is greater, the further the lorenz curve from the 45ray gini coefficient equals twice the area between the lorenz curve and the 45ray. The gini coefficient is usually defined mathematically based on the lorenz curve, which plots the proportion of the total income of the population.
Confidence intervals for the population gini coefficient can be calculated using bootstrap techniques. A second look at measuring inequality in south africa. Equivalently, a higher concentration of income corresponds to a larger area between the lorenz curve and the 45 reference line. Lorenz 4 developed it in order to analyze the distribution of income and wealth within populations. The estimation of the lorenz curve and gini index jstor. Dec 31, 20 this video shows how to calculate the gini index that corresponds to a given lorenz function, using either the fundamental theorem of calculus or the function integration fnint command on a ti83. We previously identified a number of genes in the human protein atlas hpa cell line data. Sometimes the entire lorenz curve is not known, and only values at certain intervals are given. The gini coefficient requires you to construct a lorenz curve that would look like this. The weakness of the gini coefficient in farm states. A rise in the gini coefficient shows a rise in inequality it shows the lorenz curve is. The same diagram lorenz curve is used to show the relative inequality in the distribution of income at the world level. X is the area between the lorenz curve and the diagonal and y is the area above the diagonal. A simple easy to understand powerpoint explaining the lorenz curve.
Lorenz curve and gini coefficient are examples of new entities, their purpose being to measure the degree of dispersion of a set of figures. The inequality of incomes is measured by the lorenz curve and the gini coefficient which are explained below. Gini index calculation from a lorenz function youtube. Estimating gini coefficient based on hurun report and poverty. Plot along one axis accumulated per cents of the population from poorest to. Read the discussion of the lorenz curve in chapter 14, then look up on the web the gini coefficient for your country and compare it with the gini coefficient for a couple of other countries. Jan 12, 2015 hi b, thank you for your question about a point that is often misunderstood. The origins of the lorenz curve and the gini coefficient, working papers 2004. It was noted in the introduction that lorenz curves and gini coefficients. You can think of the horizontal axis as percent of people and the vertical axis as the percent of income those people receive. A then you have to determine what fraction of the triangle is made up of area a. Lorenz curve and ginicoefficientginiconcentration ratio.
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