If one uses the lorenz curve, 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. Curve fitting functions include polynomial fits and a versatile local regression loess function. Editor with autoit now also running from start to cursor position. Looking at figure 1, we can see that area a is the area between the actual income distribution and the perfect equality line. The further away the lorenz curve from the line of absolute equality the 45 line, the greater the degree of income inequality. Lorenz curve 0 10 20 30 40 50 60 70 80 90 100 0 1020 3040 5060 708090 100 cumulative % population cumulative % income. Estimation of gini coefficients using lorenz curves. To construct the loren curve where population are ordered in descending order of varname i typed. Sort order in graph box, over by previous by thread. 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. In economics, the lorenz curve is a graphical representation of the distribution of income or of.
Characterizations of lorenz curves and income distributions. Since 80% of the population has zero wealth, lx 0, 0. The gini coefficient requires you to construct a lorenz curve that would look like this. This is a small package for the famous statistical programming language r. He proposed what is now known as the lorenz curve in 1905.
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. Creating a lorenz curve from excel university of washington. The lorenz curves are usually defined for five quintiles or for 10 deciles. For future reference, you might want to use scsomersd rather than somersd to calculate the gini coefficient with confidence limits. Shifting lorenz curve mcq revision question economics.
A graph showing what percentage of a population possesses a certain percentage of a thing. Lorenz curve and gini coefficient measures of income inequality. The lorenz curve is a simple way to describe income distribution using a twodimensional graph. The gini coefficient, founded by corrado gini in 1912, is a quantitative representation of the lorenz curve. Data curve fit creator addin is an easytouse data analysis addin for microsoft excel. Stata module to derive generalised lorenz curve ordinates, statistical software components s366302, boston college department of economics, revised 24 jun 2008. The more bowed out the curve, the less equal the distribution. How to plot a nice lorenz curve for factors in r ggplot. Van kerm and jenkins, 2001, svylorenz jenkins, 2006, clorenz araar, 2005, alorenz azevedo and franco, 2006 and lorenz.
Aug 19, 2017 but my hunch was that this would underestimate inequality, because of the straight lines in the lorenz curve above which are a simplification of the real, more curved, reality. Estimating lorenz and concentration curves in stata. This module should be installed from within stata by typing ssc install lorenz. The lorenz curve for a probability distribution is a continuous function. Figure 1, below, illustrates the shape of a typical lorenz urve. Is it possible that there isnt such option on this version.
Calculating gini coefficient of worldincome inequality with stata replicating and extending arrighidrangel findings with stata software related issues. Calculating gini coefficient of world income inequality with. The step from lorenz curve to distribution function is more difficult than the step from distribution function to lorenz curve. To do this, imagine lining people or households, depending on context in an economy up in order of income from smallest to largest. In this context members of the population are ranked in terms of their wealth and the cumulative wealth is plotted on the yaxis against the cumulative proportion of the population on the xaxis. Estimating gini coefficient when we only have mean income by. Stata module to estimate and display lorenz curves and concentration curves, statistical software components s4583, boston college department of economics, revised 15 jun 2018. Lorenz curve and gini coefficient for measuring classifier. I have to construct a single graph whit lorenz curve of varname, lorenz curve of varname where population are ordered in descending order of varname and a 45 line.
In a similar manner, i would like to be able to plot the lorenz curve and calculate the gini coefficient for my classifier. Income, 1968 and 2010 that the lorenz curve for the united states became more bowed out between 1968 and 2010. The glcurve command is updated to a stata 7 version, glcurve7, which is described and illustrated. Pdf the estimation of the lorenz curve and gini index. The closer a lorenz curve lies to the 45degree line, the more equal the distribution. Furthermore, every application of a lorenz curve ive seen looks at univariate data e. Since the lorenz urve records cumulative proportions, it c.
W e can then build and draw the lorenz curves, together with the 45 degree line which corresponds to the lorenz curve for a perfectly equal distribution, with the following commands. Hello there, actually i am trying to compare lorenz curves 3 different incomes and i want to construct the line of 45 grades. Figure 3, below, shows the shape of lorenz curves in the case of the three income distributions a, b and. The values we need to plot the perfect equality line are given in cells c9 to c19 labelled perfect equality line. For example, a lorenz curve may show that the top five percent of the people in a country control 40% of the wealth. Calculating gini coefficient of world income inequality. Our interest lies in studying the concentration or distribution of a feature of each of the n observations across the n members of the population. Stata module to estimate and display lorenz curves. 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. Download32 is source for lorenz curve shareware, freeware download curve pilot for mac, data curve fit creator addin, curve editor personal, experience curve software, rcm pf curve screensaver, etc.
The lorentz curve is a graphical representation of this inequality which is intimately related to the gini coefficient. The stata code run but my problem is that the graph is wrong, because all incomes appear as straight lines i mean over y axis and those dont look as curves under line 45 that i was created. The lorenz curve is a graphical statistic that was first introduced in 1905 as a tool for exhibiting the concentration of wealth in a population. You will notice that these values are the same as those in cells a9 to a19, because the perfect equality line is where the horizontal and vertical axis. Stata module to estimate and display lorenz curves and. One quick yet very crude fix to force the lorenz curve to start at the origin if it doesnt already is to add an observation to the data after obtaining rank and yord, and then deleting it after you have your curve. For a population ordered in ascending order of x, a graph of glp against p plots the cumulative total of x divided by population size, against cumulative. Gini coefficient and the lorentz curve file exchange. Using the findit command, stata can search and install userwritten stata.
As you can see, in the c graph, the curve starts from coordinates 0,0, as a zero fraction of the population owns a zero fraction of income. As an alternative, some have built models for lorenz curves. Stack overflow for teams is a private, secure spot for you and your coworkers to find and share information. Lorenz and concentration curves are widely used tools in inequality research. You can use the instructions to download the data provided in etutorial. Query on plotting lorenz curves on stata stack overflow. We will use the lorenz curve for afghanistan in 1980 as an example. In this paper i present a new stata command called lorenz that estimates lorenz and. The lorenz command supports relative, generalized, absolute, unnormalized, customnormalized lorenz, and concentration curves.
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. Please consult the help included in the file for an extensive description of the two concepts and how to use the program. Charting income inequality food and agriculture organization. The module is made available under terms of the gpl v3. I suggest a stata dofile to compute the hill estimator mentioned in prof. The lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economist max lorenz in 1905. The area of the triangle under the lorenz curve is onehalf base times height, so twice the area under the curve is just base times height. The best way to become a millionaire in five years or less 02. The scsomersd package is downloadable from ssc, and calculates the gini coefficient in one line, as. Suppose that n observations patient visits are dispersed among n experimental units physicians. Lorenz curves can also be used to illustrate wealth inequality.
Sep 02, 2012 stata program atkinson, inequal, lorenz, relsgini these four adofiles provide a variety of measures of inequality. 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. Along with the lorenz curve, the gini coefficient gastwirth 1972 is another widely used measure of inequality. Gini coefficient is perhaps more generally known as one minus twice the area under the lorenz curve of x. Stata program atkinson, inequal, lorenz, relsgini these four adofiles provide a variety of measures of inequality. Use excel to produce the lorenz curve and calculate gini coefficient. To construct the loren curve where population are ordered in descending order of varname i. It offers the possibility to draw nice lorenz curves with hadley wickhams ggplot2 package and compute different inequality measures until now only the giniindex and the herfindahlindex are implemented.
I know gini 2auc1, but im not actually sure how to calculate it on its own. I could find it under chart wizard in another version. Interpolations include linear, cubic spline, bessel and monotonic constrained splines, as well as a flexible spline that allows. We represent the number of observations for each experimental unit as m k, k 1, n.
If one uses the lorenz curve, 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. A then you have to determine what fraction of the triangle is made up of area a. To download and install the jenkins and van kerm glcurve command from the internet, for. The econometrics of inequality and poverty chapter 4. A lorenz curve always starts at 0,0 and ends at 1,1. Jun 26, 2018 the lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economist max lorenz in 1905. Estimating the empirical lorenz curve and gini coefficient. Fx, glcurve either draws its generalised lorenz curve or generates two new variables containing the generalised lorenz ordinates for x, i. The lorenz curve is not defined if the mean of the probability distribution is zero or infinite. Jun 30, 2010 the lorentz curve is a graphical representation of this inequality which is intimately related to the gini coefficient. Hello, is it possible to construct a lorenz curve of a varname computed whit a population ordered in descending order of varname. One way to visualize the income distribution in a population is to draw a lorenz curve. Quantile group shares, cumulative shares lorenz ordinates. Oct 29, 2012 lorenz curve and gini coefficient measures of income inequality.
Charting income inequality 5 the lorenz curve table 2 calculating lorenz curves 1 individual 1 3 5 discussion 5. The data set to be used is the same from the problem set 4. If you type, in stata, findit lorenz then you will find a choice of programs to plot a lorenz curve. Dv modulo 11 modeldiag module to generate graphics after regression. For example, the stata commands 1 glcurve jenkins and van kerm, 2004. To investigate this issue, i started by creating a known population of 10,000 income observations from a burr distribution, which is a flexible, continuous nonnegative. In economics, the lorenz curve is a graphical representation of the distribution of income or of wealth. Generalized lorenz curves and social welfare generalized lorenz curve is the lorenz curve scaled up at each point by population mean income, i. Shifting lorenz curve mcq revision question economics tutor2u. I have to construct a single graph whit lorenz curve of varname, lorenz curve of. We will suggest some basic methods to calculate the hill estimator, the lorenz curve, and the gini coefficient. A lorenz curve is a plot of two distributions in welfare economics, the vertical axis gives the. The lorenz curve shows the degree of income inequality in a given economy or population. Estimating the empirical lorenz curve and gini coefficient in.
It adds curve fitting, interpolation, and data smoothing functions to excel. Stata, lorenz, lorenz curve, concentration curve, inequality, income. Stata module to plot lorenz curve type findit glcurve or ssc install glcurve in stata prompt to install. 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. Estimating lorenz and concentration curves in stata ben jann institute of sociology university of bern ben.
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