For more information and methodology, please see povcalnet. If the variable being measured cannot take negative values, the lorenz curve. Mathematically, the gini coefficient is defined as a ratio of the areas on the lorenz curve diagram see figure 8. Developed by corrado gini in 1912 gini 1912, the gini coefficient is an inequality measure based on the lorenz curve.
Combining this result with equation a1, we obtain the first equation of. The gini coefficient for a country is often displayed visually using a graph called the lorenz curve, as depicted below. This correspondence between areas on the graph of the lorenz curve the concentration of income is the idea behind the gini coefficient. Lorenz curves showing two different distributions of income can in fact have the same gini coefficient d. Gini coefficient and lorenz curve explained towards data. The bigger it is, the more unequally income is distributed. 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. Jul 28, 2016 the lorenz curve and gini index of income for the lognormal distribution is given as.
Gini coefficient and lorenz curve and poverty poverty rates, at country and. As is well known, the use of the gini coefficient in comparisons is inconsistent with an utilitarian approach. The higher the gini coefficient, the more unequally income is distributed. Jun 30, 2010 the gini coefficient is a measure of the inequality of a distribution often used for income or wealth distributions. The lorenz curve lt is then the fraction of total income held by. 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 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. The gini coefficient subject give clear graphic illustrations of how to measure absolute equality given the linear and area pictures in gini coefficient and lorenz curve. The lorenz curve is a graphical representation of the cumulative income distribution. We propose that the gini coefficient can be used to enhance students understanding of. Draw lorenz curves and gini coefficients the first set of numbers represent incomes and. Generalizing the result of proposition 1, well impose that all the poverty indicators.
Thus g will lie between 0 and 1, and the greater it is, the more the inequality. Quantile group shares, cumulative shares lorenz ordinates. The gini coefficient is equal to the area below the line of perfect equality 0. The lorenz curve cannot rise above the line of perfect equality. Lorenz curve with gini coefficient how to draw the lorenz curve with gini coefficient theory video. Gini index frees outline 1 preliminaries industry and academia gini index 2 ratemaking homeowners data 3 ordered lorenz curve and gini index ordered lorenz curve statistical inference 4 gini.
It shows for the bottom p1% of households, what percentage p2% of the total income they have. Inequality, lorenz, gini coefficient, voting paradox, arrows. The lorentz curve is a graphical representation of this inequality which is intimately related to the gini coefficient. Jul 20, 2008 in section 3, we define the lorenz curve and gini coefficient and discuss the potential bias in more detail. 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. In that case, the gini coefficient can be approximated by using. This paper analyzes the gini coefficient s normative significance in welfare comparisons evaluating income distributions according to yaari dual social welfare function. We chose the gini index as the indicator of inequality because. Mar 20, 2020 a lorenz curve plots the cumulative percentages of total income received against the cumulative number of recipients, starting with the poorest individual or household. Jun 26, 2018 the gini coefficient is used to express the extent of inequality in a single figure. Ebert 12 demonstrated that by combining these two orderings a social. 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. Sometimes the entire lorenz curve is not known, and only values at certain intervals are given.
Intersecting generalized lorenz curves and the gini index. 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. Lorenz curve and ginicoefficientginiconcentration ratio. Pdf the estimation of the lorenz curve and gini index. The gini coefficient can vary from 0 perfect equality, also represented as 0% to 1 perfect inequality, also represented as 100%. Gastwirth i introduction m ost of the measures of income inequality are derived from the lorenz curve. Development strategy and policy analysis unit department. Pdf estimation of gini coefficients using lorenz curves. In economics, the gini coefficient, sometimes called the gini index or gini ratio, is a measure of statistical dispersion intended to represent the income or wealth distribution of a nations residents, and is the most commonly used measurement of inequality. The gini index is often represented graphically through the lorenz curve, which shows income or wealth distribution by plotting the population percentile by income on the horizontal axis and cumulative income on the vertical axis. 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 gini coefficient is the shaded area between the lorenz curve that would exist in a perfectly egalitarian society the dashed line and the lorenz curve that does exist, divided by the area under the lorenz curve that would exist in a perfectly egalitarian society. The gini coefficient is a statistic that indicates the degree of inequality by looking at how far the lorenz curve is from the 45degree line. A gini coefficient of 1 represents an economy where a single individual generates all income, whereas a gini coefficient. In particular, the gini index has been widely used by economists and. X is the area between the lorenz curve and the diagonal and y is the area above the diagonal.
Two conditions for the application of lorenz curve and gini. You will need internet access in order to answer question 5. 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. Extended version of the gini index with different weighting schemes are also discussed. Is south africa the most unequal society in the world.
Poverty and inequality analysis within the lorenz framework. Confidence intervals for the population gini coefficient can be calculated using bootstrap techniques. Moreover, the gini coefficient is recognized to be rationalizable under. Gini index world bank estimate world bank, development research group. 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. On the xaxis the percentage of the population is displayed that earns what. If a 0, it means the lorenz curve is actually the line of equality. Use excel to produce the lorenz curve and calculate gini coefficient duration. The gini coefficient of nigeria lies between 46 and 60 percent. Manual on household income definition and data collection and to improve data. Ordinary gini is a member of an extended family based on a focal parameter that is interpreted as an indicator of inequality. The extended gini family the ordinary gini coefficient is equal to the area between the lorenz curve and the line of complete equality also known as the 45degree line divided by the whole area under the 45degree line. Pdf on feb 1, 1972, joseph l gastwirth and others published the estimation of the lorenz curve and gini index find, read and cite all the.
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. Examples of parametric distributions with such pdfs can be found in, e. Estimating gini coefficient based on hurun report and. In this lesson on lorenz curve and gini coefficient, you will learn the following. Estimating gini coefficient based on hurun report and poverty line. The lorenz curve shows the income distribution in a population where. Although the lorenz curve plots the fraction of the total income concentrated in a fraction of the population ranked by income, cc plots the fraction of the total sum of a health variable that is concentrated in a fraction of the population ranked by a socioeconomic variable e. What is the relationship between lorenz curve and the gini. Whereas the gini coefficient is a measure of relative poverty, and it is use to measure the distribution of wealth at the world level. If we measure the centralization of market capitalization across the top 100 cryptocurrencies, the gini coefficient is 0. The gini coefficient is equal to the area between the actual income distribution curve and the line of perfect income equality, scaled to a number between 0 and 100. 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. The ratio between the areas x and y on the graph is known as the gini coefficient. The lorenz model of the size distribution of income.
From the classical gini index of income inequality to a new zenga. We provide a description of the gini coefficient and some. Section 5 contains the results of a simulation study evaluating these methods. 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. May 26, 2016 lorenz curve with gini coefficient how to draw the lorenz curve with gini coefficient theory video. Measures of poverty and inequality in the countries and.
The gini coefficient is defined using the lorenz function. For the computation of these measures, datt uses mathematical expressions derived from a parameterization of either the beta lorenz curve kakwani 1980 or the general quadratic lorenz curve villasenor and arnold 1984. The information in a lorenz curve may be summarized by the gini coefficient and the lorenz asymmetry coefficient. Feb 05, 2017 an introduction for as level pupils to the lorenz curve and the gini coefficient, with examples and tasks to complete. Two conditions for the application of lorenz curve and. A lorenz curve plots the cumulative percentages of total income received against the cumulative number of recipients, starting. If the calculation is zero the implication is that income distribution is perfect i. Axiomatic characterization of the gini coefficient and lorenz curve. The lorenz curve is a very useful way to calculate income inequality. Lorenz curve coincides with the diagonal in figure 2 and 1 perfect inequality.
In a group of 24, discuss and answer the following questions on lorenz curves and gini coefficients. Gini coefficients, and the inequality possibility frontier. The gini coefficient is the gini index expressed as a number between 0 and 1. The same diagram lorenz curve is used to show the relative inequality in the distribution of income at the world level. Estimation of the gini coefficient for the lognormal. In the literature are proposed many others gini index extensions. Applying the gini coefficient to measure inequality of water use in the olifants river water management area, south africa james cullis and barbara van koppen introduction benefits of water use. If there is a high degree of inequality, then area a will be a bigger percentage of the total area. Lorenz curve and gini coefficient teaching resources. 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. Using lorenz curve and gini coefficient to reflect the.
Lorenz curve and gini coefficient 1 lorenz curve lc and income distribution households hh persons cumulative % income cumulative % 0 100 100 lc explanations xaxis. It was developed by the italian statistician and sociologist corrado gini and published in his 1912 paper variability and mutability. 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. The lorenz curve and gini coefficient are applied here to measure and graph disproportionality in outcomes for multiseat elections held in 2017. Estimating the empirical lorenz curve and gini coefficient in. In this assignment, we study income inequality in the united states using 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. The concentration gini coefficient versus a polarization index 45 remark 2. Sep 30, 2015 it is often said that south africa is the most unequal society in the world. 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. The estimation of the lorenz curve and gini index joseph l. A lorenz curve is a plot of two distributions in welfare economics, the vertical axis gives the. It is, however, recommended that more indepth studies are conducted to develop this concept further and to address some of the issues raised in this. Summary this tool addresses the most popular inequality index, the gini index.
It discusses its characteristics and the link with another popular graphical tool of representing inequality, the lorenz curve. Data are based on primary household survey data obtained from government statistical agencies and world bank country departments. Estimation of gini coefficients using lorenz curves. A popular measure of inequality is the gini coefficient, which ranges from 0 perfect equality to 1 perfect inequality, but is typically in the range of 0. Nortey, and anani lotsi department of statistics, school of physical and mathematical sciences, college of basic and applied sciences, university of ghana, accra, ghana. Joseph gastwirth reza modarres efstathia bura the use of. The discussion compares proportional representation pr in holland pr gini 3. Employing the gini coefficient to measure participation. The higher the coefficient, the more unequal the distribution is. Estimation of the gini coefficient for the lognormal distribution of income using the lorenz curve kwasi a. It was developed by the italian statistician and sociologist corrado gini and published in his 1912 paper. How do you figure the gini coefficient and what does it represent. This paper stems from work done by the authors at the mathematics for social justice workshop held in june of 2007 at middlebury college. The closer the lorenz curve is to the line of equality, the smaller area a is.
A given households position in the distributions of income, wealth, and consumption changes over time. The gini coefficient is the ratio of the area between the line of perfect equality and the observed lorenz curve to the area between the line of perfect equality and the line of perfect inequality. A then you have to determine what fraction of the triangle is made up of area a. In this case, the gini coefficient is 0 and it means there is perfect distribution of income everyone earns the same amount. A lorenz curve plots the cumulative percentages of total income received against the cumulative. When generalized lorenz curves cross once, the gini coefficient is decisive in determining welfare rankings if we. According to world bank data, between 1981 and 20, the gini. Let us label the areas in the graph of a lorenz curve, in this case for an exponential distribution. The gini coefficient of income is obtained for both the market income and disposable income basis while the coefficient of market income is obtained from pre. A higher gini coefficient represents a more unequal distribution. Householdspersons are arranged in ascending order of income cumulative percentage. Gini coefficient and the lorentz curve file exchange. The lorenz curve is a graphical representation of the distribution of some measure income, consumption, education, etc.
The lorenz curve can be used to calculate the gini coefficient another measure of inequality. Relationship between lorenz curve and gini coefficient is the more the lorenz line curves away from the line of equality, the greater the degree of inequality represented. These findings illustrate the value of combining aggregate measures of inequal. Graphing a lorenz curve and calculating the gini coefficient 1 lorenz curves and gini coefficient answers directions. Apr 25, 2017 the gini coefficient can be represented mathematically on a lorenz curve which plots the proportion of populations income earned cumulatively by a bottom percentage of the population. This fits our intuition as about 70% of the market capitalization as of july 2017 is held by the top two cryptocurrencies, namely bitcoin and. The econometrics of inequality and poverty chapter 4. The gini coefficient is derived from the lorenz curve, which sorts the population from poorest to richest, and shows the cumulative proportion. Various attempts have been made to obtain accurate estimates.
In section 4, we present several different analytic strategies that can be used to estimate the lorenz curve and gini coefficient. If there is a completely equal distribution of income, the g0 and the lorenz curve is a diagonal line. Pdf the use of the lorenz curve, gini index and related measures. A lorenz curve plots the cumulative percentages of total income received against the cumulative number of recipients, starting with. The lorenz curve and gini coefficient are applied here to measure and graph. The gini coefficient requires you to construct a lorenz curve that would look like this.
319 1023 1198 1635 1626 44 332 1468 25 1588 535 857 1369 82 1563 787 582 1285 349 1456 56 1580 951 870 241 983 827 263 1031 103 1425 384 1280 924 238 45 47 1259 703