An alternative formula for the gini index, g, is based on the mean difference, a, of the. Finance and economics discussion series divisions of research. We measure the distribution of income and wealth by using concepts such as the lorenz curve and the gini coefficient the lorenz curve. 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. Summary this tool addresses the most popular inequality index, the gini index. Data are based on primary household survey data obtained from government statistical agencies and. Lorenz curves can also be used to illustrate wealth inequality. Primary income data yields the most exact estimates of the gini coefficient. The gini coefficient is a numerical measure of inequality, which. Gini coefficients of education world bank documents. It is also recommended to investors, policy makers, financial analysts and.
A hypothetical lorenz curve is drawn in figure 1 for the case n 8, k 5. Complete lesson on the lorenz curve and gini coefficient. 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. A simple correction to remove the bias of the gini coefficient due. The discussion compares proportional representation pr in holland pr gini 3. What is the relationship between a lorenz curve and a gini.
A data science based standardized gini index as a lorenz. Estimation of the gini coefficient for the lognormal. My only concern is that there is already a formula for the gini. If you would prefer to view this interaction in a new web window, then please follow the link below. The lowest 10% of earners make 2% of all wages the next 40% of earners make 18% of all wages the next 40% of earners make 30% of all wages the highest 10% of earners make 50% of all wages. As is well known, the use of the gini coefficient in comparisons is inconsistent with an utilitarian approach.
Comparing the gini coefficients of income computed from the polynomial function with degree 5 for the trapezium, simpson and. Rotterdam using data files made available by the netherlands central bureau of. 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. Inequality analysis food and agriculture organization. Y is the cumulative distribution of the income variable, for i 0,z with y 00 and y 11. The gini coefficient is defined using the lorenz function. The conventional formula for estimating the extended gini coefficient is a covariance formula provided by lerman and yitzhaki 1989. Notes on how to compute gini coefficient suppose you are given data like this. 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. Romania gini index world bank estimate the value for gini index world bank estimate in romania was 35. The lorenz curve shows the degree of income inequality in a given economy or population. The lorentz curve is a graphical representation of this inequality which is intimately related to the gini coefficient.
Louisiana distribution of income lorenz curve and gini. It discusses its characteristics and the link with another popular graphical tool of representing inequality, the lorenz curve. X is the area between the lorenz curve and the diagonal and y is the area above the diagonal. 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. As a matter of fact, if p1 p2, the lorenz curve is a straight line which says for instance that. Because 100% is equal to 100100 1, and the two axes in the lorenz curve goes from 0% to 100%, the area of the entire box must be 1. From the result obtained, we discovered that there is a disturbing income inequality in nigeria. Two conditions for the application of lorenz curve and. Estimating lorenz curve of income in china by cubic spline. If there is a completely equal distribution of income, then g0 x0 and xy must be 0and the lorenz curve is a diagonal line. Pdf r code to calculate the gini coefficient and plot. I have finally settled on a topic of inequality using the lorenz curve for my maths ia. It was developed by the italian statistician and sociologist corrado gini and published in his 1912 paper.
The gini coefficient is defined as a ratio of the areas on the lorenz curve diagram. A lorenz curve and a gini coefficent are ways of measuring the degree of income inequality in a society. Included in the slides is also a number of mcqs and 15 mark exam question from aqa alevel economics with a suggested plan, sample student responses and mark scheme. I need to find the equation of the lorenz curve so i can use integration to find the area between the line of absolute equality and the lore. The econometrics of inequality and poverty chapter 4. If there is a completely equal distribution of income, the g0 and the lorenz curve is. The lorenz curve attempts to show the extent of the inequality of income in an economy as no economy has ever sustained a system of an equaldistribution of income, the aim is to achieve equity in the distribution of income. The two estimators are identical for the original gini coefficient, where the inequality.
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. If a 0, it means the lorenz curve is actually the line of equality. A geometrical interpretation can be made by linking the gini coefficient with the lorenz curve. The gini index is a measure of the inequality of a distribution that can be derived from. Income distribution function, pdfx, gini coefficient. Cubic spline interpolation, lorenz curve, gini index, lorenz curve aggregation. I will discuss the gini coefficient and relate it to the relative mean difference. So, a value close to zero indicates near equality, while a value near to one shows a high amount of inequality.
Xis the cumulative distribution of the population variable, for i 0,z with x 00 and x 11. Normally lorenz curve is defined on the interval0,1and it is increasing, convex, continuous curve. A map showing gini coefficients by country for 2017. It is defined as a ratio with values between 0 and 1. In economics, the gini coefficient sometimes called the gini index or gini ratio, is a measure of. 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. The asymmetry coefficient assesses the amount of asymmetry of the lorenz curve. Abstractwe propose a firstorder bias correction term for the gini index to. Extended version of the gini index with different weighting schemes are also discussed. I need to find the gini coefficient in 2014 for canada. Gini index world bank estimate world bank, development research group.
The lorenz curve and gini coefficient are applied here to measure and graph disproportionality in outcomes for multiseat elections held in 2017. 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 regression result shows that 1 percent increase in the literacy rate increase the gini coefficient by 3 percent meaning that. Estimating the empirical lorenz curve and gini coefficient. Development strategy and policy analysis unit department. How to find the equation of the lorenz curve quora. 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. This r code writes the function to plot the lorenz curves and calculate the following statistics. 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. Lorenz curves, the gini coefficient and parametric distributions. The gini coefficient is a ratio between 0 and 1, where 0 implies that each. Intersecting generalized lorenz curves and the gini index.
In this case, the gini coefficient is 0 and it means there is perfect distribution of. When generalized lorenz curves cross once, the gini coefficient is decisive in determining welfare rankings if. Quantile group shares, cumulative shares lorenz ordinates. This paper analyzes the gini coefficients normative significance in welfare comparisons evaluating income distributions according to yaari dual social welfare function. A higher gini coefficient represents a more unequal distribution. Gini coefficient and the lorentz curve file exchange. We represent the number of observations for each experimental unit as m k, k 1, n. The gini coefficient of nigeria lies between 46 and 60 percent. In france the first preferences of voters for political parties show.
We suggest an alternative estimator obtained by approximating the lorenz curve by a series of linear segments. Income distribution, lorenz curves and gini coefficients. The gini coefficient is a commonlyused measure of income inequality that condenses the entire income distribution for a country into a single number between 0 and 1. The gini index or gini coefficient is a statistical measure of distribution developed by the italian statistician corrado gini in 1912. Alevel economics the lorenz curve and gini coefficient. Biased and unbiased forms of the gini coefficient and the lorenz asymmetry coeffcient as described. The same value may result from many different distribution curves. A lorenze curve shows a countrys income distribution on a graph. Whereas the ginicoefficient is a measure of relative poverty, and it is use to measure the distribution of wealth at the world level. A lorenz curve plots the cumulative percentages of total income received against the cumulative number of. Please consult the help included in the file for an extensive description of the two concepts and how to use the program. 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. The main objective of the study is to compare the newtoncotes methods such as the trapezium rule, simpson rule and simpson 38 rule to estimate the area under the lorenz curve and gini coefficient of income using polynomial function with degree 5.
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. The lorenz curve, income shares and the gini coefficient. A second look at measuring inequality in south africa 3 z z z i g. According to world bank data, between 1981 and 20, the gini index ranged between 0. The bigger it is, the more unequally income is distributed. Lorenz in 1905 for representing inequality in the wealth distribution. Suppose that n observations patient visits are dispersed among n experimental units physicians. How do you figure the gini coefficient and what does it represent. Lorenz curve and ginicoefficientginiconcentration ratio. The gini coefficient, gini index, or coefficient of concentration is a concept that comes up for example in economics, when looking at the distribution of incomes.
Using lorenz curves, the gini coefficient is defined as the ratio of the area between the diagonal and the lorenz curve. 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. In economics, the lorenz curve is a graphical representation of the distribution of income or of wealth. Lorenz curve and gini index are important tools to measure the income distribution of the residents. Lorenz curve and gini coefficient teaching resources. Since the n families are ordered according to increasing income shares, the lorenz curve does not cross the horizontal axis until positive incomes have balanced negative. Lorenz curve and gini coefficient measures of income inequality duration.
Pdf estimation of gini coefficients using lorenz curves. A second look at measuring inequality in south africa. Lorenz curve and gini coefficient genstat knowledge base. Reff economics lecturer university of arizona 2007 2016 the 2015 university of arizona fivestar faculty award. In this assignment, we study income inequality in the united states using the gini coefficient. Use of lorenz curves and gini coefficients to assess yield. As the graph below shows, over the past 26 years this indicator reached a maximum value of 39. 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. An introduction for as level pupils to the lorenz curve and the gini coefficient, with examples and tasks to complete. What links here related changes upload file special pages permanent link page information.