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. We have some set of people who are very rich whose living standards are relatively high. The gini coefficient is defined as a ratio of the areas on the lorenz curve diagram. 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.
Intuitively, the further away the lorenz curve is from the perfect equality line. This model interpolates between selfsimilar behavior at the low and high ends of the income. This paper analyzes the gini coefficient s normative significance in welfare comparisons evaluating income distributions according to yaari dual social welfare function. Indicators of distribution and poverty build on production and flows. In case a is a very large area and b is a small area, the gini coefficient is large. This results in a smaller gini coefficient for the country since income is more evenly distributed in society if there is a progressive tax. Please consult the help included in the file for an extensive description of the two concepts and how to use the program. To confirm this, we compute the gini coefficient 16 and plot the lorenz curve 17 in the gini coefficient encodes the degree of inequality in the interaction distribution over pairs. Gini index gini coefficient 100 calculation the ginicoefficient is calculated as a ratio of areas on the lorenz curve diagram. 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 recipients, starting with the poorest individual or household. Then lp is convex and its derivative, lp, equals one at p f. The same diagram lorenz curve is used to show the relative inequality in the distribution of income at the world level.
This paper analyzes the gini coefficients normative significance in welfare comparisons evaluating income distributions according to yaari dual social welfare function. 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. We thus start from an income distribution with continuous density fx. It shows for the bottom p1% of households, what percentage p2% of the total income they have.
Graph the lorenz curve, and find the gini coefficient for this income distribution. Graphing a lorenz curve and calculating the gini coefficient 1 lorenz curves and gini coefficients directions. Gini coefficient and lorenz curve pdf download, cambridge international as and alevel chemistry course book free download ae94280627 estimation of the gini coefficient for the lognormal distribution of income using the. As inequality increases, so does area a, the gini coefficient rises. Gini coefficient of inequality the most widely used single measure of inequality is the gini coefficient. 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. Gini coefficient and the lorentz curve file exchange. Rau3,4 1department of plant science, pennsylvania state university, university park, pa, usa, 2department of agricultural and. Gini coefficient are aggregate inequality measure and can vary anywhere from 0 perfect equality to 1 perfect inequality. If income is totally equally distributed so that the lorenz curve follows the 450 line, the gini coefficient is zero. In particular, it measures the ratio of the area between the lorenz curve and the equidistribution line henceforth, the concentration area to the area of maximum concentration.
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. Creating a lorenz curve from excel university of washington. A second look at measuring inequality in south africa. Extended version of the gini index with different weighting schemes are also discussed. 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 income received. The information in a lorenz curve may be summarized by the gini coefficient and the lorenz asymmetry coefficient. Pdf the estimation of the lorenz curve and gini index. Jun 30, 2010 the lorentz curve is a graphical representation of this inequality which is intimately related to the gini coefficient. In a group of 24, discuss and answer the following questions on lorenz curves and gini coefficients.
A longknown index that is more comprehensive than the 1%measure is the gini index, named after italian. Variation in income is highly visible in most part of the economies of the third world nations especially nigeria. If the area between the line of perfect equality and lorenz curve is a, and. The closer the lorenz curve is to the line of equality, the smaller area a is. A lorenz curve is a plot of two distributions in welfare economics, the vertical axis gives the. It plots the cumulative share of income y axis earned by the poorest x% of the population, for all possible values of x see the illustration on page 1 for a practical example. Lorenz curves and gini coefficient answers directions. The lorenz curve is a measure of the distribution of wealth or income or other factors in a society. The gini coefficient ranges from 0 complete equality to 1 complete inequality. The lorentz curve is a graphical representation of this inequality which is intimately related to the gini coefficient. Xis the cumulative distribution of the population variable, for i 0,z with x 00 and x 11. The gini coefficient, which is derived from the lorenz curve, can be used as an indicator of economic development in a country. Pdf estimation of gini coefficients using lorenz curves. Lorenz curve coincides with the diagonal in figure 2 and 1 perfect inequality.
Joseph gastwirth reza modarres efstathia bura the use. Global income has increased exponentially over the last two hundred years. Alevel economics the lorenz curve and gini coefficient. The lorenz curve is a common graphical method of representing the degree of income inequality in a country 9. Describe the three theories of how income should be distributed and. It discusses its characteristics and the link with another popular graphical tool of representing inequality, the lorenz curve. Louisiana distribution of income lorenz curve and gini. Gini coefficient definition, formula how to calculate. Contd it is defined as a ratio and can range from 0 and 1 0% to 100% the gini index is the gini coefficient expressed as a percentage. You will need internet access in order to answer question 5. When generalized lorenz curves cross once, the gini coefficient is decisive in determining welfare rankings if we. The gini coefficient is calculated as the ratio of the area that lies between the straight 45degree line and the lorenz curve marked area a in figure 1. The lorenz curve is a graphical representation of the distribution of some measure income, consumption, education, etc. It was developed by the italian statistician and sociologist corrado gini and published in his 1912 paper.
Intersecting generalized lorenz curves and the gini index. Lorenz curve and gini coefficient reveal hot spots and hot. Summary this tool addresses the most popular inequality index, the gini index. As is well known, the use of the gini coefficient in comparisons is inconsistent with an utilitarian approach. 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. Estimation of the gini coefficient for the lognormal. The gini coefficient can vary from 0 perfect equality to 1 perfect inequality. Income distribution is described by a twoparameter model for the lorenz curve. Inequality analysis food and agriculture organization.
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 and ginicoefficientginiconcentration ratio. Lorenz curves and the gini coefficient gini coefficient. Within countries, ifs computes a gini coefficient from a lorenz curve tied to the relative shares of income that skilled and unskilled households. 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. If the variable being measured cannot take negative values, the lorenz curve. This family was rst proposed in 11, but our derivation, interpretation, and analysis is new. Mar 07, 2011 the lorenz curve is a measure of the distribution of wealth or income or other factors in a society.
The value of the curve corresponds to a percentile of the population ordered according to the characteristic in question. The gini index was developed by gini, 1912, and it is strictly linked to the representation of income inequality through the lorenz curve. The lorenz curve can be used to calculate the gini coefficient another measure of inequality. The gini coefficient is a measure of the inequality of a distribution often used for income or wealth distributions. Joseph gastwirth reza modarres efstathia bura the use of. If there is a high degree of inequality, then area a will be a bigger percentage of the total area. The income and the wealth of the country seem to be unevenly distributed. Oct 22, 2019 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. The gini coefficient measures the degree of income equality in a population. The value of the curve represents that portion of the total value of the characteristic in question held by people no wealthier than the a. A second look at measuring inequality in south africa 3 z z z i g.
The bigger it is, the more unequally income is distributed. The econometrics of inequality and poverty chapter 4. Pdf demonstrating lorenz curve distribution and increasing. It indicates there is huge incomewealth inequality. What is the relationship between a lorenz curve and a gini. The gini coefficient requires you to construct a lorenz curve that would look like this. We chose the gini index as the indicator of inequality because it is widely reported in official sources that are based on. Draw a model of a lorenz curve representing a nation with a very small degree of income inequality, like norway. It is also recommended to investors, policy makers, financial analysts and.
The lorenz curve cannot rise above the line of perfect equality. The gini coefficient can vary from 0 perfect equality, also represented as 0% to 1 perfect inequality, also represented as 100%. Compute the gini coefficient for the societies in problem 4. The gini coefficient is a numerical measure of inequality, which. The most common measure of inequality, the 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. The gini coefficient is a ratio between 0 and 1, where 0 implies that each. The formula for the gini coefficient can be calculated. 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. Complete lesson on the lorenz curve and gini coefficient. Suppose the lorenz curve for a society is given by s r r 100 2. When generalized lorenz curves cross once, the gini coefficient is decisive in determining welfare rankings if. Various attempts have been made to obtain accurate estimates.
833 1016 754 1060 920 1380 439 440 960 112 173 346 435 350 1036 351 485 524 1205 468 11 1095 1394 1359 938 718 1464 992 6 261 724 1005 954 547 1475 576 499 636 376 409