This paper proposes a new function, linear in the parameters, to deal with lorenz curves. Inference for lorenz curves requires its rigorous definition and good specifications. We take in account mainly two cases a the transformed variable lorenz dominates the initial one and b the initial lorenz dominates the transformed one. The lorenz curve lp is defined as a function of the proportion p of the. Lorenz in 1905 for representing wealth distribution. And so, this curve right over here, which you could view as describing the reality for a certain nation, this is known as a lorenz curve, lorenz curve, and what gini said is, well the difference between the lorenz curve and this line right over here, that that would be a measure of income inequality. The area between curves suppose we want to nd the area between two curves fx and. To display a lorenz curve like that below, select the lorenz curve option from the world map, lorenz curve, gini, histogram form and choose the same variable you displayed in the world map. Lorenz curve definition of lorenz curve by merriamwebster. The lorenz curve concentrates on disposable income money left for spending after the payment of taxes. A second look at measuring inequality in south africa. The purpose of this note is to present an alternative definition of the lorenz curve in terms of the inverse of the theoretical distribution function. The lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economistmax lorenz in 1905. 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.
Creating a lorenz curve from excel university of washington. In the hypothetical example shown in figure 5, the cumulated. The lorenz curve represents a concave curve starting at point 0 and ending at point a, as shown in the following diagram. As there is a direct relationship between lorenz curves and cap curves, the measure may be regarded as a cap based measure. The lorenz curve lc is an important instrument for analyzing the size of distribution. A lorenz curve always starts at 0,0 and ends at 1,1. Second, in order to measure the distribution of income for any country, the gini coefficient is used in order to quantify the lorenz curve. However, lorenz curves representing discontinuous functions can be constructed as the limit of lorenz curves of. Lorenz curve a graph which is used in the study of social stratification in order to show the extent to which the actual distribution of a particular good usually income, earnings, or wealth deviates from a condition of perfect equality. The fitted function allows us to compute the lorenz curve, the income probability density function, and the gini coefficient, as well as their uncertainties. Joseph gastwirth reza modarres efstathia bura the use of. The lorenz curve is a probability plot a pp plot comparing the distribution of a parameter in a population against a hypothetical.
Lorenz curves are the basis of a concentration theory and related acceptable. Lorenz curve is an analytical technique that is used to display inequalities mathematically, it is a cumulative distribution function, it is always convex. The lorenz curve l p is defined as a function of the proportion p of the. Provides a picture of the income distribution within the population, and is used to construct the gini coefficient. To do this, imagine lining people or households, depending on context in an economy up in order of income from smallest to largest. World map, lorenz curve, gini, histogram university of denver. Relative as well as generalized, absolute, unnormalized, or customnormalized lorenz or concentration curves are supported, and tools for computing contrasts between different subpopulations or outcome variables are provided.
In order to effectively select the optimal breakpoint to break the circular histogram, the. If x k, yk are the known points on the lorenz curve. The lorenz curve is often accompanied by a straight diagonal line with a slope of 1, which represents perfect equality in income or wealth distribution. Lorenz in 1905 for representing inequality of the wealth distribution. Lorenz curve and gini coefficient measure distribution of thing your interested in. As an alternative, some have built models for lorenz curves. Understanding what is lorenz curve global finance school. It represents a probability distribution of statistical values, and is often associated with income distribution calculations. Join s of fellow economics teachers and students all getting the tutor2u economics teams latest resources and support delivered fresh in their inbox. Summary this tool addresses the most popular inequality index, the gini index. The aim of this module is to illustrate the functioning and the meaning of one. Joseph gastwirth reza modarres efstathia bura the use. While it may be used in ecology as well as some other fields, it is frequently used in economics to represent social inequality. Applications of lorenz curves in economic analysis english.
Alevel economics the lorenz curve and gini coefficient. The aim of this module is to illustrate the functioning and the meaning of one of the. In economics, the lorenz curve is a graphical representation of the distribution of income or of wealth. Shifting lorenz curve mcq revision question economics tutor2u. Pdf on feb 1, 1971, joseph l gastwirth and others published a general definition of the lorenz curve find, read and cite all the research you need on researchgate. The degree of inequality in a country can be obtained by calculating the ratio of the area between the diagonal and the lorenz curve as compared to the total, area of the half square in which the curve lies. In economics, the lorenz curve is a graphical representation of the distribution of income or of. Lorenz curves can also be used to illustrate wealth inequality. Pdf application of lorenz curves in economic analysis. Lorenz curve article about lorenz curve by the free dictionary. Gini coefficient and lorenz curve video khan academy. The ratio of the shaded area ea to the total area of the triangle bcd. Pdf a general definition of the lorenz curve researchgate.
The gini statistic is a measure of predictive power based on the lorenz curve. This study considers analyses of other properties of the transformed lorenz curves, especially its limits. A graph showing what percentage of a population possesses a certain percentage of a thing. In a perfectly equal society, the poorest 25% of the population would earn 25% of the total income, the poorest 50% of the population would earn 50% of the total income and the lorenz curve would. The gini index or gini coefficient is a statistical measure of distribution which was developed by the italian. Applications of lorenz curves in economic analysis english abstract. Extended version of the gini index with different weighting schemes are also discussed. The lorenz curve is a simple way to describe income distribution using a twodimensional graph. A lorenz curve is a plot of two distributions in welfare economics, the vertical axis gives the. The gini coefficient is equal to the area below the line of perfect equality 0. A decrease in inequality can be shown on the lorenz curve by the line of income distribution moving closer to the line of complete equality.
Pdfs, cdfs, quantile functions, and lorenz curves the purpose of chapter 2 is to lay a foundation for the connection between distributional properties such as the central tendency, dispersion, skewness, and kurtosis of a population attribute and inequality measures in a broad sense. The use of the lorenz curve, gini index and related measures of relative inequality and uniformity in securities law. It is proportionate to the area between the random line and the model curve. The purpose of this paper is to propose and justify the use of a few measures of inequality for summarizing the basic information provided by the lorenz curve.
Lorenz curve definition is a curve formed by plotting the cumulative distribution of the amount of a variable against the cumulative frequency distribution of the individuals having the amount as for indicating the degree of concentration of salary income among a number of individuals. By exploiting the fact that the lorenz curve can be considered analogous to a cumulative distribution function it is demonstrated that the moments of the lorenz curve generate a convenient family of inequality measures, called the. In that case, the gini coefficient can be approximated by using various techniques for interpolating the missing values of the lorenz curve. The lorenz curve relates the cumulative proportion of income units to the cumulative proportion of income received when units are arranged in ascending order of their income. Save it in an easily accessible location, such as a folder on your desktop. The gini index is defined as the area under the lorenz curve. It relates the cumulative income wealth fraction earned by various proportions of the population to the proportion receiving this income, when the units are arranged in increasing order of their income wealth. The lorenz curve shows the degree of income inequality in a given economy or population. Share of largest firms in an oligopolistic industry, e. Modelling lorenz curve johan fellman1,2 abstract there has been a large number of studies in which the scientists have built models for income distributions.
The more concave the curve, then the higher the degree of income inequality in the country. Jun 26, 2018 the lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economist max lorenz in 1905. Charting income inequality 5 the lorenz curve table 2 calculating lorenz curves 1 individual 1 3 5 discussion 5. This post briefly discusses alternative definitions and ways of specifying lorenz curves.
These principles are illustrated with two examples. I also describe some difficulties with using it as a way to track income inequality. Introduction the lorenz curve is a graphical display of the distribution of the cumulative percent of events by the cumulative percent of people in the population. Changing income inequality and panel income changes. Pdfs, cdfs, quantile functions, and lorenz curves sage. A graph for showing the concentration of ownership of economic quantities such as wealth and income. Lorenz curve and ginicoefficientginiconcentration ratio. The lorenz curve shows the percentage of total income earned by cumulative percentage of the population. Data uncertainties were estimated from yeartoyear variations of the income share. Lorenz curve article about lorenz curve by the free. The lorenz curve is a probability plot a pp plot comparing the distribution of a parameter in a population against a hypothetical uniform distribution of that parameter.
The econometrics of inequality and poverty chapter 4. A free powerpoint ppt presentation displayed as a flash slide show on id. The more the lorenz curve slopes away from the line of complete equality the more unequal a society is. Lorenz curves for five countries sketching the lorenz curve. Let and denote income level, cdf, pdf and inversecdf functions respectively. Pdf the use of the lorenz curve, gini index and related. The lorenz curve lc is an important instrument for analyzing the size of. The lorenz curve is a way of showing the distribution of income or wealth within an economy. Lorenz curvethe goal of this curve is to measure the level of income inequality in a country, as compared with other countries. The lorenz curve is not defined if the mean of the probability distribution is zero or infinite. Similar to an edgeworth box, max lorenz created the lorenz curve in 1905 in order to show the percentage of income the yaxis in figure 1 held by a certain percentage of the population the xaxis in. Figure 3, below, shows the shape of lorenz curves in the case of the three income distributions a, b and.
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. The graph plots percentiles of the population on the. Lorenz curve wikipedia economics a graph that shows the proportion of overall income or wealth of the bottom percentage of people, often used to represent economic inequality. A data science based standardized gini index as a lorenz. The results presented in this paper will enable banks to quantify, how well a model is able to. Figure 1 the lorenz curve and the equidistribution.
The theory behind the gini index relies on the difference between a theoretical. Characterizations of lorenz curves and income distributions. Sometimes the entire lorenz curve is not known, and only values at certain intervals are given. Stata module to estimate and display lorenz curves.
The lorenz curve also called relative concentration curve is widely used for the representation and analysis of the size distribution of income or wealth. If x k, yk are the known points on the lorenz curve, with the x k indexed in increasing. In the next sections a step by step procedure to work out a lorenz curve, a simple numerical example and a discussion on how to benckmark lorenz curves against the equidistribution line are presented. A discussion on the use of lorenz curves to represent. Charting income inequality food and agriculture organization. For example, a lorenz curve can show that the bottom 40% of households bring in 25% of a countrys income. Lorenz curve method has been proposed by american statistician lorenz. Properties of lorenz curves for transformed income. Lorenz curves article about lorenz curves by the free.
Mar 06, 2019 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. Lorenz curve the graph of the percent of income owned by the poorest x percent of the population, for all x. The estimation of the lorenz curve and gini index joseph l. 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. Lorenz curve, gini coefficient, income held by top 10%. However, the previous formula can still apply by generalizing the definition of xf xf1.
It discusses its characteristics and the link with another popular graphical tool of representing inequality, the lorenz curve. The symbol used to represent the curve is the letter l. The following diagrams display five lorenz curves, each relating to a different country. For example, a lorenz curve may show that the top five percent of the people in a country control 40% of the wealth. The graph plotspercentiles of the population on the. In our work below, we emphasize lorenz curve comparisons and lorenz. Gastwirth i introduction m ost of the measures of income inequality are derived from the lorenz curve. The lorenz curve can then be contrasted with the line of perfect equality to show the scale of income and wealth inequality in a country.
In the hypothetical example shown in figure 5, the cumulated percentage of income recipients is plotted against the cumulated percentage of total income, for. The gini index is the area between the tradeoff curve and the obtained curve multiplied. Draw the lorenz curve of a group whose annual incomes in thousands of dollars are given by the. The further away the lorenz curve from the line of absolute equality the 45 line, the greater the degree of income inequality.
Article information, pdf download for anything lorenz curves can do, top shares can do. The lorenz curve for a probability distribution is a continuous function. There are a number of ways in which one can depict the distribution of some magnitude e. The graph of the percent of income owned by the poorest x percent of the population, for all x. Usually the lorenz curve generated by a theoretical distribution function is defined in terms of two equations l, p. The step from lorenz curve to distribution function is more difficult than the step from distribution function to lorenz curve. Gini coefficient and lorenz curve explained towards data. Pdf this paper explains how to build lorenz curves for income distributions and discusses their use for inequality measurement. Gini coefficient and lorenz curve explained towards data science. The lorenz curve shows the cumulative share of income from different sections of the population.
In this video i introduce the ideas of the lorenz curve and gini coefficient for measuring income 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 area between the line of equality and the actual lorenz curve is the area of inequality. Ideal lorenz curve is a straight line from the start under the angle of 45 degrees.