The lorenz curve and gini coefficient are applied here to measure and graph disproportionality in outcomes for multiseat elections held in 2017. It is the ratio of the area between the lorenz curve and the line of absolute equality numerator and the whole area under the line of absolute equality denominator. A second look at measuring inequality in south africa. In this lesson on lorenz curve and gini coefficient, you will learn the following. Whereas the gini coefficient is a measure of relative poverty, and it is use to measure the distribution of wealth at the world level. Pdf the estimation of the lorenz curve and gini index. Jun 26, 2018 the gini coefficient is used to express the extent of inequality in a single figure. Creating a lorenz curve from excel university of washington. A lorenz curve is a plot of two distributions in welfare economics, the vertical axis gives the.
Two conditions for the application of lorenz curve and gini. Complete lesson on the lorenz curve and gini coefficient. Jakus smith college abstract we argue that the lorenz curve for income is wellmodelled by a member of the oneparameter family of functions. The lorenz curve is a graphical representation of the distribution of some measure income, consumption, education, etc. Estimation of the gini coefficient for the lognormal. We provide a description of the gini coefficient and some. That technique is the use of the lorenz curve and its associated gini coefficient. 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. If there is a completely equal distribution of income, the g0 and the lorenz curve is a diagonal line.
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. Quantile group shares, cumulative shares lorenz ordinates. 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. 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. In this assignment, we study income inequality in the united states using the gini coefficient. Lorenz curve and gini coefficient teaching resources. The lorentz curve is a graphical representation of this inequality which is intimately related to the gini coefficient. We propose that the gini coefficient can be used to enhance students understanding of. Alevel economics the lorenz curve and gini coefficient. In this case, the gini coefficient is 0 and it means there is perfect distribution of income everyone earns the same amount. The information in a lorenz curve may be summarized by the gini coefficient and the lorenz asymmetry coefficient. 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. If a 0, it means the lorenz curve is actually the line of equality. Pdf estimation of gini coefficients using lorenz curves.
Lorenz curve and ginicoefficientginiconcentration ratio. Data are based on primary household survey data obtained from government statistical agencies and world bank country departments. This model interpolates between selfsimilar behavior at the low and high ends of the income. The gini coefficient is used to express the extent of inequality in a single figure. Jan 15, 2017 lorenz curve and gini index ha markovich. The second curve is the line y x which is the lorenz curve for a population which shares the resource equally. Gini index measures the extent to which the distribution of income or consumption expenditure among individuals or households within an economy deviates from a perfectly equal distribution. 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. Equivalently, a higher concentration of income corresponds to a larger area between the lorenz curve and the 45 reference line. Two conditions for the application of lorenz curve and. In france the first preferences of voters for political parties show. The ratio between the areas x and y on the graph is known as 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. Feb 05, 2017 an introduction for as level pupils to the lorenz curve and the gini coefficient, with examples and tasks to complete.
Gini coefficient and the lorentz curve file exchange. Income distribution is described by a twoparameter model for the lorenz curve. The gini coefficient is defined using the lorenz function. What is the relationship between a lorenz curve and a gini. Gini index is equals to area a divided by area a and b 4. Let us label the areas in the graph of a lorenz curve, in this case for an exponential distribution. The gini coefficient summarizes the entire lorenz curve income distribution into a single value. Feb, 2020 complete lesson on the lorenz curve and gini coefficient. 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.
The econometrics of inequality and poverty chapter 4. A gini of one represents perfect inequality, where one household has all of the income. The discussion compares proportional representation pr in holland pr gini 3. The lorenz curve cannot rise above the line of perfect equality. The same diagram lorenz curve is used to show the relative inequality in the distribution of income at the world level. Lorenz curve coincides with the diagonal in figure 2 and 1 perfect inequality. This paper stems from work done by the authors at the mathematics for social justice workshop held in june of 2007 at middlebury college. If the variable being measured cannot take negative values, the lorenz curve. A lorenz curve plots the cumulative percentages of total income received against the cumulative number of recipients, starting. Gini index world bank estimate world bank, development research group. How do you figure the gini coefficient and what does it represent. The bigger it is, the more unequally income is distributed. X is the area between the lorenz curve and the diagonal and y is the area above the diagonal.
The gini coefficient is defined as a ratio of the areas on the lorenz curve diagram. This correspondence between areas on the graph of the lorenz curve the concentration of income is the idea behind the gini coefficient. Thus g will lie between 0 and 1, and the greater it is, the more the inequality. Louisiana distribution of income lorenz curve and gini. The gini coefficient can be interpreted as the percentage of inequality represented in the population with respect to the given resource. 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. Estimation of gini coefficients using lorenz curves johan fellman1,2 abstract primary income data yields the most exact estimates of the gini coefficient. Gini index calculation from a lorenz function youtube. Use excel to produce the lorenz curve and calculate gini coefficient duration. The higher the gini coefficient, the more unequally income is distributed.
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. 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. Estimation of gini coefficients using lorenz curves. Based on figure four, it can be seen that the gini coefficient. Jul 28, 2016 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. Jun 30, 2010 the gini coefficient is a measure of the inequality of a distribution often used for income or wealth distributions. 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 a complementary way of presenting information about inequality. 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.