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. 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. In france the first preferences of voters for political parties show. A second look at measuring inequality in south africa. However, i do not aim to get lower marks, so, im looking for a research question or topic which would help me to get most of this ia. Countries ranked by gini index world bank estimate africa. It was developed by the italian statistician and sociologist corrado gini and published in his 1912 paper. Lorenz curve and gini index are important tools to measure the income distribution of the residents.
Reff economics lecturer university of arizona 2007 2016 the 2015 university of arizona fivestar faculty award. Plotted as a lorenz curve, complete equality would be a straight diagonal line with a slope of 1 the area between this curve and itself is 0, so the gini coefficient is 0. The same diagram lorenz curve is used to show the relative inequality in the distribution of income at the world level. From table 1, all the p values of the kolmogorovsmirnov tests of the various regions, rural and urban areas, male and female family heads are greater than 0. Two conditions for the application of lorenz curve and. May 25, 2016 lorenz curve and gini coefficient measures of income inequality duration. Normally lorenz curve is defined on the interval0,1and it is increasing, convex, continuous curve. If the variable being measured cannot take negative values, the lorenz curve.
The conventional formula for estimating the extended gini coefficient is a covariance formula provided by lerman and yitzhaki 1989. Jul 20, 2008 the lorenz curve and gini coefficient have also been used to explore the distribution of health professionals in relation to the population distribution of patients. Lorenz curve and gini coefficient measures of income inequality duration. Lorenz curve and gini coefficient genstat knowledge base. The lorenz curve cannot rise above the line of perfect equality. Gini coefficients of education world bank documents. In this assignment, we study income inequality in the united states using the gini coefficient. Calculus i introduction to the gini coefficient the gini coefficient or gini index is a commonlyused measure of inequality devised by italian economist corrado gini in 1912. Lorenz curve and ginicoefficientginiconcentration ratio. The gini coefficient is the area between the line of equality and the lorenz curve area, divided by the area under the line of equality. This paper analyzes the gini coefficients normative significance in welfare comparisons evaluating income distributions according to yaari dual social welfare function. The gini coefficient is a measure of the inequality of a distribution often used for income or wealth distributions. Gini coefficients of income are calculated on market income as well as disposable income basis. If there is a completely equal distribution of income, the g0 and the lorenz curve is.
Estimation of gini coefficients using lorenz curves johan fellman1,2 abstract primary income data yields the most exact estimates of the gini coefficient. Jul 28, 2016 future research could use other newtoncotes methods such as boole and weddle applied to other lorenz curve functions such as gupta and ortega et al. Whereas the ginicoefficient is a measure of relative poverty, and it is use to measure the distribution of wealth at the world level. Macroeconomics economic growth and equity in the distribution of income. A second look at measuring inequality in south africa 3 z z z i g. The two estimators are identical for the original gini coefficient, where the inequality. Biased and unbiased forms of the gini coefficient and the lorenz asymmetry coeffcient as described. The lorenz curve shows the degree of income inequality in a given economy or population. Estimation of the gini coefficient for the lognormal. Estimating the empirical lorenz curve and gini coefficient in. As is well known, the use of the gini coefficient in comparisons is inconsistent with an utilitarian approach. A lorenz curve plots the cumulative percentages of total income received against the cumulative number of. This paper analyzes the gini coefficient s normative significance in welfare comparisons evaluating income distributions according to yaari dual social welfare function.
From the result obtained, we discovered that there is a disturbing income inequality in nigeria. Suppose that n observations patient visits are dispersed among n experimental units physicians. The regression result shows that 1 percent increase in the literacy rate increase the gini coefficient by 3 percent meaning that. The lorenz curve is a graphical representation of the proportionality of a distribution the cumulative percentage of the values. So you take economics hl, so youve definitely studied it in class. If you would prefer to view this interaction in a new web window, then please follow the link below. Another limitation of the gini coefficient is that it is not additive across groups, i. In economics, the lorenz curve is a graphical representation of the distribution of income or of wealth. Dominican republic gini index world bank estimate the value for gini index world bank estimate in dominican republic was 45. If there is a completely equal distribution of income, then g0 x0 and xy must be 0and the lorenz curve is a diagonal line. Estimating lorenz curve of income in china by cubic spline. The asymmetry coefficient assesses the amount of asymmetry of the lorenz curve. The lorenz curve and gini coefficient are applied here to measure and graph disproportionality in outcomes for multiseat elections held in 2017. Intersecting generalized lorenz curves and the gini index.
The gini coefficient is equal to the area below the line of perfect equality 0. The area, a, between the lorenz curve and the straight line is called the area of concentration. When generalized lorenz curves cross once, the gini coefficient is decisive in determining welfare rankings if. The gini coefficient of nigeria lies between 46 and 60 percent. Thus, countrylevel gini coefficients cannot be aggregated into regional or global ginis, although a. Data are based on primary household survey data obtained from government statistical agencies and world bank country departments. We propose that the gini coefficient can be used to enhance students understanding of. Development strategy and policy analysis unit department.
X is the area between the lorenz curve and the diagonal and y is the area above the diagonal. Gini coefficient and the lorentz curve file exchange. Also from table 1, the estimates of the gini index for lognormal distribution was found to be between 0. In this case, the gini coefficient is 0 and it means there is perfect distribution of. May 03, 2019 the gini coefficient is the area between the line of equality and the lorenz curve area, divided by the area under the line of equality. An alternative formula for the gini index, g, is based on the mean difference, a, of the. A lorenz curve and a gini coefficent are ways of measuring the degree of income inequality in a society. A data science based standardized gini index as a lorenz. A higher gini coefficient represents a more unequal distribution. The information in a lorenz curve may be summarized by the gini coefficient and the lorenz asymmetry coefficient. Primary income data yields the most exact estimates of the gini coefficient.
The bigger it is, the more unequally income is distributed. It ranges from 0, when all units are equal, to a theoretical maximum of 1 in an infinite population in which all units but one yield 0. Thus g will lie between 0 and 1, and the greater it is, the more the inequality. Estimating the empirical lorenz curve and gini coefficient.
Estimation of gini coefficients using lorenz curves. It is calculated as the quotient of the area which the cap curve and diagonal enclose and the corresponding area in an ideal rating procedure. A comparative study of the gini coefficient estimators based on the. It ranges from 0, when all units are equal, to a theoretical maximum of 1 in an infinite population in which all units but one yield 0 weiner and solbrig, 1984. The gini coefficient g quantifies the area between the lorenz curve and the line of perfect equality expressed as a fraction of the area under the yx line. In economics, the gini coefficient sometimes called the gini index or gini ratio, is a measure of.
As the graph below shows, over the past 30 years this indicator reached a maximum value of 52. The farther away a countrys curve is from the line of absolute equality, the more unequal the distribution of income. 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. This model interpolates between selfsimilar behavior at the low and high ends of the income. Explain how the gini coefficient is derived and interpreted. The gini coefficient is the summary statistic of the cumulative accuracy profile cap chart. The gini coefficient is defined using the lorenz function. Two conditions for the application of lorenz curve and gini. When generalized lorenz curves cross once, the gini coefficient is decisive in determining welfare rankings if we. The gini coefficient on market incomesometimes referred to as a pretax gini coefficientis calculated on income before taxes and transfers, and it measures inequality in income without considering the effect of taxes and social spending already in place in a country. Data are based on primary household survey data obtained from government statistical agencies and. Use of lorenz curves and gini coefficients to assess yield.
Using lorenz curves, the gini coefficient is defined as the ratio of the area between the diagonal and the lorenz curve. A lorenze curve shows a countrys income distribution on a graph. The curve is a graph showing the proportion of overall income or wealth assumed by the bottom x% of the people and so forth. Whereas the gini coefficient is a measure of relative poverty, and it is use to measure the distribution of wealth at the world level. The lorenz curve is a graphical representation of the distribution of some measure income, consumption, education, etc. 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. The discussion compares proportional representation pr in holland pr gini 3. Our interest lies in studying the concentration or distribution of a feature of each of the n observations across the n members of the population. We suggest an alternative estimator obtained by approximating the lorenz curve by a series of linear segments. Jun 26, 2018 plotted as a lorenz curve, complete equality would be a straight diagonal line with a slope of 1 the area between this curve and itself is 0, so the gini coefficient is 0.
The second curve is the line y x which is the lorenz curve for a population which shares the resource equally. So, a value close to zero indicates near equality, while a value near to one shows a high amount of inequality. Gini index, which are ustatistics and linearization for some income distri. The closer the coefficient is to 1, the more unequal the distribution. It is defined as a ratio with values between 0 and 1. It is also recommended to investors, policy makers, financial analysts and. A simple easy to understand powerpoint explaining the lorenz curve. Gini coefficient, dissimilarity index and lorenz curve for.
The gini coefficient represents the area of concentration between the lorenz curve and the line of perfect equality as it expresses a proportion of the area enclosed by the triangle defined by the line of perfect equality and the line of perfect inequality. Pdf r code to calculate the gini coefficient and plot. The econometrics of inequality and poverty chapter 4. Normally lorenz curve is defined on the interval0,1 and it is increasing, convex, continuous curve.
My only concern is that there is already a formula for the gini coefficient of the lorenz curve, which is just a straightforward integration since real lorenz curves arent perfectly straight. This r code writes the function to plot the lorenz curves and calculate the following statistics. The gini index is a measure of the inequality of a distribution that can be derived from. The same value may result from many different distribution curves. The gini coefficient is a ratio between 0 and 1, where 0 implies that each. Joseph gastwirth reza modarres efstathia bura the use of. How do you figure the gini coefficient and what does it represent. An introduction for as level pupils to the lorenz curve and the gini coefficient, with examples and tasks to complete.
Income distribution is described by a twoparameter model for the lorenz curve. Chang and halfon 4 examined the pediatriciantochild ratios in the 50 states and showed a fourfold difference between the states with the highest maryland and lowest idaho. If a 0, it means the lorenz curve is actually the line of equality. Gini index world bank estimate world bank, development research group. Gini index g, is the ratio of the area between the lorenz curve lp and the 450 line see figure 1 to the area under the 450 line which is 112. Another is chinas gini coefficient calculated with cstpcd. Lorenz curves can also be used to illustrate wealth inequality. The gini coefficient is a numerical measure of inequality, which. Pdf r code to calculate the gini coefficient and plot the. According to world bank data, between 1981 and 20, the gini index ranged between 0. The ratio between the areas x and y on the graph is known as the gini coefficient. I have finally settled on a topic of inequality using the lorenz curve for my maths ia.
Income distribution function, pdfx, gini coefficient. In this case, the gini coefficient is 0 and it means there is perfect distribution of income everyone earns the same amount. In the hypothetical extreme where one person earned all the money and everyone else obtained nothing, the area below the lorenz curve would disappear and g would be very near to 1. The lorentz curve is a graphical representation of this inequality which is intimately related to the gini coefficient. A clear pattern of an education kuznets curve exists education gini index and generate a quinquennial data if the standard deviation of education is used. Income distribution, lorenz curves and gini coefficients. We represent the number of observations for each experimental unit as m k, k 1, n. The lorenz curve and gini coefficient business tutor2u. The lorenz curve, income shares and the gini coefficient. Pdf estimation of gini coefficients using lorenz curves. If there is a completely equal distribution of income, the g0 and the lorenz curve is a diagonal line. I have used the usual blink and dortonpages 250257 to help with this but have also found a few other resources which may be of use. The higher the gini coefficient, the more unequally income is distributed.
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