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