In economics, the lorenz curve is a graphical representation of the distribution of income or of wealth. Here we will learn how to calculate gini coefficient with examples, calculator and downloadable excel template. When there are n equal intervals on the xaxis, equation 6. More simply, it tells us how evenly the variable is spread. The gini index or gini coefficient is a statistical measure of distribution developed by the italian statistician corrado gini in 1912. Lorenz curves, the gini coefficient and parametric distributions. Inequality measures members of the generalised entropy class of measures have the general formula as follows. Methodology the data used in this study are obtained from the educational statistics year book from the period of 19862005. I will discuss the gini coefficient and relate it to the relative mean difference. Lorenz curve coincides with the diagonal in figure 2 and 1 perfect inequality. Gini coefficient formula calculator examples with excel. 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.
They obtained statistically significant coefficients of 2. The closer the lorenz curve is to the line of equality, the smaller area a is. A popular measure of inequality is the gini coefficient, which ranges from 0 per fect equality to. But the fact that income data, unemployment data, as well as the estimates of the severity of recessions, all point in the same direction does. Notes on how to compute gini coefficient suppose you are given data like this. Imf says australia has one of the fastest rising income inequality rates. Oct 22, 2019 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 coefficient is the gini index expressed as a number between 0 and 1. A simple way to calculate the gini coefficient, and some. The standard definition of the lorenz curve is in term of two equations. The land gini coefficient and its application for land use.
It discusses its characteristics and the link with another popular graphical tool of representing inequality, the lorenz curve. Piketty 2000 in his book on the history of high incomes in france makes an extensive use. In economics, the gini coefficient sometimes called the gini index or gini ratio, is a measure of. In a lorenz curve, a measure of the difference between a given distribution of some variable, like population or income, and a perfectly even distribution. Insights from machine learning june 2016 abstract in the literature on inequality and economic development, the overwhelming focus is on the gini coefficient, a single statistic for the entire income distribution. When i asked peter lambert, a professor at the university of oregon and the author of several books on the gini coefficient and income distribution, why the gini methodology is still relevant today, he listed the usual reasons, but one point surprised me. From wikibooks, open books for an open world economics. If there is a perfectly equal distribution of income the whole area will be b, hence aa. Imf says australia has one of the fastest rising income. Gini coefficient is also known as the gini index is the statistical measure which is used in order to measure the distribution of the income among the population of the country i. The econometrics of inequality and poverty chapter 4. School quality, educational inequality and economic growth. As with other inequality coefficients, the gini coefficient is influenced by the granularity of the measurements. In a 2person economy, the owner of a firm pays 20% of the total output to the worker.
Following is the example to understand the lorenz curve with the help of a graph. The gini coefficient is usually a number between 0 and 1 or 0 to 100. About the exact and asymptotic distribution of the gini coefficient. Nearly all of those links refer to the gini coefficient as a measure in economics. The direct method uses the following formula to calculate gini coefficient deaton 1997. 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. We do however also present formula for the atkinson class of inequality measures, which are ordinally equivalent to the ge class, and the popular gini coefficient. Gini coefficients of education world bank documents. 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. What is the gini coefficient and what is its formula. In the quest for developing the best underwriting model possible we believe that there is a need for an objective and quantifiable way to measure with a number the quality of a model. The gini index or gini coefficient measures the percentage that a real lorenz curve is below the ideal curve. Jun 19, 2017 the gini coefficient is used to measure inequality of a region.
Gini coefficient is widely used by economist to show the inequality in a population king, et. Why equality is better for everyone, penguin books, london. A gini coefficient of one 100 on the percentile scale expresses maximal inequality among values for example where only one person has all the income. Gini coefficient simple english wikipedia, the free. In economics, the gini coefficient, also known as 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. In other words, even small changes in the overall distribution of inequality can lead to sizeable changes in the incidence of poverty. The coefficient measures the dispersion of income or distribution of wealth among the members of a population to understand this, we must. 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. Pdf the gini index and measures of inequality researchgate. The gini coefficient is used in a wide range of fields including psychology, economics, and agriculture. One of the measures that is often used is the gini coefficient. They present two methods direct and indirect for calculating an education gini index, and generate a quinquennial data set on education gini indexes for the over15population in 85 countries 196090. Mcnelis january 2014 abstract this paper examines the relationships of the gini coe.
A gini coefficient of zero expresses perfect equality where all values are the same for example, where everyone has an exactly equal income. 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. So if everyone in a country had the same income, the number would be 0, and if one person made all the money and everyone else made. The industry gini index is based on the gini coefficient, a commonlyused measure of inequality across a group. Gini index frees preliminaries industry and academia gini index ratemaking homeowners data ordered lorenz curve and gini index ordered lorenz curve statistical inference gini interpretations concluding remarks the gini index the 45 degree line is known as the line of equality in welfare economics, this represents the situation where each. In this assignment, we study income inequality in the united.
The gini index is one of the most accepted and established methods to measure income inequality. Gini coefficientthe gini coefficient is a measure of inequality in an economy the higher the value, the greater the inequality. The power of the gini index the formula pacific standard. A rise in the gini coefficient shows a rise in inequality it shows. It is equal to the difference between the gini index for the social. Any lorenz curve we find for a real population will be below this curve. Ultimately, the economics article should be kept here without a disambiguation page since economics is the most common application of the term gini coefficient. We provide a description of the gini coefficient and some. 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. Here, the cost of an extra worker is equal to the revenue generated by the extra unit that he or she produces. Oecd 2011, causes of growing income inequality in oecd countries, oecd publishing, paris, forthcoming. Also this textbook intends to practice data of labor force survey. Apr 25, 2017 the gini coefficient of the whole world ranges from 0. In some cases, this equation can be applied to calculate the gini coefficient without direct reference to the lorenz.
This is because the lorenz curves can have different shapes and yet still yield the same gini coefficient. In this case, the gini coefficient is 0 and it means there is perfect distribution of income everyone earns the same amount. Lorenz curve and gini coefficient are examples of new entities, their purpose being. The area between the two lines expressed as a ratio to the area under the straight line gives a representation of the inequality and is called the gini coefficient developed by the italian statistician corrado gini in the year 1912. This is a list of countries or dependencies by income inequality metrics, including gini coefficients.
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 how does the gini coefficient work. For example, five 20% quantiles low granularity will yield a lower gini coefficient than twenty 5% quantiles high granularity taken from the same distribution. 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. 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. We deduce the integration by part formula by simply rearranging the terms. Developed in 1912 by corado gini an italian statistician the gini coefficient is most prominently used as a measure of inequality of income or wealth distribution. Like the relative mean difference, there does not exist a sample statistic that is in general an unbiased estimator of the population gini coefficient.
The gini coefficient, originally used for quantifying differences in income, was reintroduced as the lgc to analyze the rationality of land use structure. The bigger it is, the more unequally income is distributed. Lorenz curve definition, example what is lorenz curve. The gini coefficient can vary from 0 perfect equality, also represented as 0% to 1 perfect inequality, also represented as 100%. If x is a random variable with lorenz curve l x f, then. Gini coefficients refer to mid2000s for greece and switzerland. The kakwani index is a measure of the progressivity of a social intervention, and is used by social scientists, statisticians, and economists. The cia world f actbook 4 reports that the gini index of u. Alvareto, a note on the relationship between top income. This is video 5 of 8 videos in the equity in the distribution of income series. The gini coefficient is used to measure inequality of a region. It converts the lorenz curve into a number between 0 and 1.
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. Modeling income distribuions and lorenz curves, volume 5 of economic. The index, he said, allows people to care about each other, which is quite unusual in. Published in 1912 by corrado gini, the gini coefficient is best known for uses in economic studies that measure income inequality within nations, and the underlying mechanics make it. 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 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 also known as the gini index or gini ratio is a measure of differences in income. Confidence intervals for the population gini coefficient can be calculated using bootstrap techniques. Then according to the holmes definition the dollar income received by. As the gini index approaches 1, income inequality increases. Ib economicsmacroeconomics wikibooks, open books for an. Many people are familiar with the gini coefficient for inequality. Measuring education inequality gini coefficients of education. As compared to other countries in figure 1, we see that the u.
The major advantage of the gini coefficient is that it can quantify differences, and it is very intuitive because it is based on the lorenz curve. Gini coefficient hl gross domestic product gdp gross national product gnp human development index hdi indirect taxation. Pdf the gini index is a summary statistic that measures how. From wikibooks, open books for an open world gini coefficient gini coefficient the gini coefficient gini index or gini ratio is a statistical measure of economic inequality in a population. Extended version of the gini index with different weighting schemes are also discussed. It is named after the economist who first proposed and used it, nanak chand kakwani. If there is a high degree of inequality, then area a will be a bigger percentage of the total area. The lorenz curve is invariant under positive scaling.
From the classical gini index of income inequality to a new zenga. Mathematically, the gini coefficient is defined as a ratio of the areas on the lorenz curve diagram see figure 8. Relative to the lognormal distribution with a similar value of the gini coefficient, the singhmaddala distribution has a. Gini coefficient definition, calculation and indias. Gini coefficient definition, formula how to calculate. The alertness line level of gini coefficient arxiv. Rongxing guo, in understanding the chinese economies, 20. Definition of the gini coefficient economics online. The gini coefficient is derived from the lorenz curve, which sorts the population from poorest to richest, and shows the cumulative proportion. If a 0, it means the lorenz curve is actually the line of equality. If mathy lxmath is the equation of a lorentz curve, then the inequality in the corresponding distribution of wealth is measured by the gini index, which is given by the formula. Income distribution function, pdfx, gini coefficient. In education, gini coefficient is used to estimate the level of inequality in education for the given population.
The kakwani index uses the gini framework to measure how progressive a social intervention is. If x is a random variable, for any positive number c the random variable c x has the same lorenz curve as x. 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. It is defined as a ratio with values between 0 and 1. Gini coefficient of inequality the most widely used single measure of inequality is the gini coefficient. In rural tanzania, average incomes increased substantially between 1983. Panel data estimates are provided for the overall data set. This paper stems from work done by the authors at the mathematics for social justice workshop held in june of 2007 at middlebury college. Setups 3 and 4 have relatively low inequality with approximate gini coefficients ofg2 0. If playback doesnt begin shortly, try restarting your device. How to find the gini index of this lorenz curve using. Pdf about the exact and asymptotic distribution of the gini. Summary this tool addresses the most popular inequality index, the gini index.
The gini coefficient is a number between 0 and 1, where 0 corresponds with perfect equality where everyone has the same income and 1 corresponds with perfect inequality where one person has all the incomeand everyone else has no income. It can be derived by comparing areas on a lorenz curve, as follows. In this paper, we question this singular focus on the gini coefficient and evaluate. A simple way to calculate the gini coefficient, and some implications branko milanovic world bank, washington, d. The level at which the marginal cost of labor is equal to the marginal revenue product. The answer is supposed to be 35 but i end up getting 310 ins. The authors use a gini index to measure inequality in educational attainment. Alvareto, a note on the relationship between top income shares and gini coefficients, economics letters 2011. The formula reveals why the gini index sometimes appears in calculus books in the. It was developed by the italian statistician corrado gini in 1912.
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