Using trapezoidal rule for the area under a curve calculation shitao yeh, glaxosmithkline, collegeville, pa. Ipea statistical software components from boston college department of economics. To construct the loren curve where population are ordered in descending order of varname i typed. 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. This module should be installed from within stata by typing ssc install lorenz. If you type, in stata, findit lorenz then you will find a choice of programs to plot a lorenz curve. Estimating lorenz and concentration curves in stata boris.
Statistical software components s366002, department of economics. Lorenz curves and inequality a lorenz curve is a plot of the cumulative income share of the poorest 100p% against cumulative population share p, where units are ordered in ascending order of income complete equality. Furthermore, every application of a lorenz curve ive seen looks at univariate data e. The lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economist max lorenz in 1905. I know gini 2auc1, but im not actually sure how to calculate it on its own. Lorenz curve coincides with 45 ray through origin inequality is greater, the further the lorenz curve from the 45ray. In economics, the lorenz curve is a graphical representation of the distribution of income or of wealth. We introduce a userwritten stata command conindex which provides point estimates and standard errors of a range of concentration indices. In this paper i present a new stata command called lorenz that estimates lorenz and concentration curves from individuallevel data and, optionally, displays the results in a graph. Estimating lorenz and concentration curves in stata. Lorenz curve and gini coefficient for measuring classifier.
Usage and importance of dasp in stata abdelkrim araar, jeanyves duclos and luis huesca comparisons of stata to other software or use of stata together with other software. In this paper i present a new stata command called lorenz that estimates lorenz and. Charting income inequality food and agriculture organization. The lorenz curve is a simple way to describe income distribution using a twodimensional graph. Query on plotting lorenz curves on stata stack overflow. The reason your line of perfect equality does not pass through 0,0 is because the values for your variable do not contain 0. Lorenz and concentration curves are widely used tools in inequality research. Estimation of gini coefficients using lorenz curves johan fellman1,2 abstract primary income data yields the most exact estimates of the gini coefficient. Although this value will asymptotically approach 0, it will never actually reach 0. The lorenz command supports relative as well as generalized, absolute, unnormalized, or customnormalized lorenz or concentration. Gini coefficient and the lorentz curve file exchange. In a similar manner, i would like to be able to plot the lorenz curve and calculate the gini coefficient for my classifier. The decomposition is performed using the shapley value. The module is made available under terms of the gpl v3.
Pdf estimating lorenz and concentration curves in stata. Estimating the empirical lorenz curve and gini coefficient. Van kerm and jenkins, 2001, svylorenz jenkins, 2006, clorenz araar, 2005, alorenz azevedo and franco, 2006 and lorenz. Stata module to estimate and display lorenz curves and. The lorenz curve functionality of roctab, which provides an alternative to standard roc. To do this, imagine lining people or households, depending on context in an economy up in order of income from smallest to largest. 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. The lorentz curve is a graphical representation of this inequality which is intimately related to the gini coefficient. Stata, lorenz, lorenz curve, concentration curve, inequality, income distribution, wealth. As an alternative, some have built models for lorenz curves. The concentration curve is the bivariate analogue of the lorenz curve. Stata module to estimate and display lorenz curves. Suppose that n observations patient visits are dispersed among n experimental units physicians. For future reference, you might want to use scsomersd rather than somersd to calculate the gini coefficient with confidence limits.
Focus here on estimation of lorenz curve and related concepts using. The gini coefficient requires you to construct a lorenz curve that would look like this. The data set to be used is the same from the problem set 4. Quantile group shares, cumulative shares lorenz ordinates.
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. Stata module to estimate lorenz and concentration curves. In this article, i present a new command, lorenz, that estimates lorenz and concentration curves from individuallevel data and, optionally, displays the results in a graph. Trying to compare distribution over this period using absolute lorenz curves. Coordinates of curves can be listed or saved in a new stata file. Figure 1, below, illustrates the shape of a typical lorenz urve. He proposed what is now known as the lorenz curve in 1905. Hello lakshmikanth, the variable cdfinc, which is represented in the horizontal axis of the lorenz curve in the resolution that you quoted resolution 18022, is defined in step 6 of the overview section of the resolution. Inequality analysis food and agriculture organization. We will suggest some basic methods to calculate the hill estimator, the lorenz curve, and the gini coefficient. Since the lorenz urve records cumulative proportions, it c. The software is available free of charge from the world banks site.
Estimating lorenz and concentration curves ben jann, 2016. Finally, the lorenz curve of income distribution c is another extreme case where all incomes are zero except for the last one. The scsomersd package is downloadable from ssc, and calculates the gini coefficient in one line, as. Estimating lorenz and concentration curves sage journals. The lorenz command supports relative, generalized, absolute, unnormalized, customnormalized lorenz, and concentration curves. The integration of a, b from a functional form is divided into n equal pieces, called a trapezoid. Estimation of gini coefficients using lorenz curves. The lorenz command supports relative as well as generalized, absolute, unnormalized, or customnormalized lorenz or. 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. Sampling distribution of gini coefficient rbloggers. 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. 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 particular, im interested in what happens to the sampling distributions as sample size changes of the following summary statistics. Lorenz and concentration curves are widely used tools in inequality.
Pepe has posted stata datasets and programs used to. Xi with ia as an indicator function being equal to 1 if a is true and 0 otherwise. More software in statistical software components from boston college department of economics boston college. Despite their frequent use in inequality research literature, stata does not offer. Calculating gini coefficient of world income inequality. Estimating lorenz and concentration curves in stata ben jann institute of sociology university of bern ben. Stata program atkinson, inequal, lorenz, relsgini these four adofiles provide a variety of measures of inequality. Please consult the help included in the file for an extensive description of the two concepts and how to use the program. Calculating gini coefficient of worldincome inequality with stata replicating and extending arrighidrangel findings with stata software related issues. Gini coefficient ie the area between a lorenz curve and the line of perfect equality p90p10 ie income at the 90% richest percentile divided by that at the 10% percentile p80p20 as above, but the 80 and.
Stata module to plot lorenz curve type findit glcurve or ssc install glcurve in stata prompt to install free addon to stata to compute inequality and poverty measures free online software calculator computes the gini coefficient, plots the lorenz curve, and computes many other measures of concentration for any dataset. Statistical software components s456515, department of economics, boston college. Abstract the trapezoidal rule is a numerical integration method to be used to approximate the integral or the area under a curve. 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 step from lorenz curve to distribution function is more difficult than the step from distribution function to lorenz curve. Estimation and interpretation of measures of inequality. Hello, is it possible to construct a lorenz curve of a varname computed whit a population ordered in descending order of varname. Title plotting lorenz curve with the blessing of ggplot2 version 0. The command dfgts decomposes the allevation of fgt poverty by income components and provides standard errors on elements of the decompositions.
A then you have to determine what fraction of the triangle is made up of area a. Generalized lorenz curves with confidence intervals stata. Use the rank procedure to store the empirical cumulative distribution function cdf result of income in the new variable cdfinc. The econometrics of inequality and poverty chapter 4. Estimation using sample survey data means that estimates.
Lorenz curves and concentration curves, statistical software components. Lorenz curve is also called the equidistribution line. Hello there, actually i am trying to compare lorenz curves 3 different incomes and i want to construct the line of 45 grades. The command also graphs concentration curves and lorenz curves and performs statistical inference for the comparison of inequality between groups.
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