Lorenz and concentration curves are widely used tools in inequality. Variable v1 has a range 010 where higher values indicate poorer performance. Charting income inequality 5 the lorenz curve table 2 calculating lorenz curves 1 individual 1 3 5 discussion 5. If x is a random variable, for any positive number c the random variable c x has the same lorenz curve as x. Query on plotting lorenz curves on stata stack overflow. The lorenz command supports relative as well as generalized, absolute, unnor malized, or. This module should be installed from within stata by typing ssc install alorenz. 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. I am interested not only in the mean value of v1 but also the. This replaces the relative percentage of total income on the vertical axis by the absolute total income per head, so that it is now denominated in currency.
A matlab inequality package, including code for computing gini, atkinson, theil indexes and for plotting the lorenz curve. Section 5 applies the method to uk data and section 6 concludes. Stata module to derive generalised lorenz curve ordinates. Stata module to estimate and display lorenz curves. 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. Intersecting generalized lorenz curves and the gini index. Lorenz curves and generalised entropy ge measures are popular tools for analyzing income inequality. Stata, lorenz, lorenz curve, concentration curve, inequality, income distribution, wealth. If g is a generalized lorenz curve, then there is a unique distribution f yielding g as its generalized lorenz curve.
The graph plots percentiles of the population on the. When generalized lorenz curves cross once, the gini coefficient is decisive in. 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. Stata module to derive generalised lorenz curve ordinates given variable varname, call it x with c. Figure 1, below, illustrates the shape of a typical lorenz urve. Derivation of generalised lorenz curve ordinates with unit record data. 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. Joao pedro azevedo and samuel franco additional contact information samuel franco. This module should be installed from within stata by typing ssc install lorenz. Lorenz curve definition of lorenz curve by merriamwebster. Frequency histogram an overview sciencedirect topics. Our interest lies in studying the concentration or distribution of a feature of each of the n observations across the n members. The lorenz curve is invariant under positive scaling. The step from lorenz curve to distribution function is more difficult than the step from distribution function to lorenz curve.
To download and install the jenkins and van kerm glcurve command from the internet, for instance. Modeling bivariate lorenz curves with applications to. For future reference, you might want to use scsomersd rather than somersd to calculate the gini coefficient with confidence limits. The lorenz command supports relative, generalized, absolute, unnormalized, customnormalized lorenz, and concentration curves.
Figure 3, below, shows the shape of lorenz curves in the case of the three income distributions a, b and. The lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economist max lorenz in 1905. The lorenz curve is a simple way to describe income distribution using a twodimensional graph. Article information, pdf download for estimating lorenz and concentration curves. We represent the number of observations for each experimental unit as m k, k 1, n. Stata module to estimate and display lorenz curves and. As is well known, the use of the gini coefficient in comparisons is inconsistent with an utilitarian approach. 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. Creating a lorenz curve from excel university of washington.
Estimating lorenz and concentration curves stata journal article. 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. The lorenz curves are usually defined for five quintiles or for 10 deciles. I am attempting to compare the performance of companies for the country as a whole and to that at the local level metropolitan statistical area. 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. Where distributions differ in their mean incomes, as where comparing different countries, we may use the generalized 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. Shorrocks and kakwani both show that, regardless of mean. Incontrast,theordinatesofthegeneralized lorenz curve, gl xp,refertothe cumulative outcome average. 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. Fx, glcurve draws its generalised lorenz curve andor generates two new variables. Nov 18, 2010 i presume that you want to produce a lorenz curve. Since the lorenz urve records cumulative proportions, it c.
A publication to promote communication among stata users. Pdf generalized lorenz curves and related graphs researchgate. Working with household data sets requires a solid mastery of appropriate statistical and data management software, such as stata or spss. Estimating the empirical lorenz curve and gini coefficient. The glcurve command is updated to a stata 7 version, glcurve7, which is described and illustrated. Hello there, actually i am trying to compare lorenz curves 3 different incomes and i want to construct the line of 45 grades. Ipea statistical software components from boston college department of economics. One quick yet very crude fix to force the lorenz curve to start at the origin if it doesnt already is.
A generalized lorenz curve facilitates a comparison of distributions based on both these preferences. Stata module to produce pens parade, lorenz and generalised. Dear all, i am analyzing the performance of companies indicated by a variable v1. Statistical software components from boston college department of economics. 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. Pens parade, lorenz, generalized lorenz oai identifier. Produces the difference between the following curve with confidence.
The lorenz command supports relative, generalized, absolute, unnormalized, customnormalized lorenz, and. Thus, the height of the generalized lorenz curve reflects the level of incomes, while the convexity of the generalized lorenz curve reflects degree of income inequality. Lorenz curves and generalised entropy inequality measures. Estimation of gini coefficients using lorenz curves.
It also provides tools for computing contrasts between different subpopulations or outcome variables. Estimating the empirical lorenz curve and gini coefficient in. Fx, glcurve either draws its generalised lorenz curve or. This paper seeks to connect these techniques by demonstrating that ge inequality measures may be derived directly from the lorenz curve. The generalized lorenz curve is based on the notion that greater inequality can be compensated by higher average income if the differences between the lorenz curves tend to be relatively small compared with variations in mean incomes. 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.
Suppose that n observations patient visits are dispersed among n experimental units physicians. Stata program atkinson, inequal, lorenz, relsgini these four adofiles provide a variety of measures of inequality. Modeling bivariate lorenz curves with applications to multidimensional inequality in wellbeing jos e mar a sarabia1, vanesa jord a department of economics, university of cantabria, 39005santander, spain updated version 10th june 20 abstract the extension of the univariate lorenz curve to higher dimensions is not an obvious task. If you type, in stata, findit lorenz then you will find a choice of programs to plot a lorenz curve.
The lorenz curve cumulates the population in increasing order of income, and shows on the vertical axis their cumulative share in total income. This paper analyzes the gini coefficients normative significance in welfare comparisons evaluating income distributions according to yaari dual social welfare function. The duality relationship hinges on the use of the gastwirthtype definition of the generalized lorenz curve 10, and the properties of the order function. Generalized lorenz curves for household incomes by head of. Produces the following curves with confidence interval. 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 lorenz curve is equivalent, up to the division by mean income, to other representations of the data, but it allows a ready comparison of two or more distributions. Sep 02, 2012 stata program atkinson, inequal, lorenz, relsgini these four adofiles provide a variety of measures of inequality. Stata module to produce pens parade, lorenz and generalised 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. Estimating lorenz and concentration curves in stata. Estimating lorenz and concentration curves ben jann, 2016. Lorenz curve 0 10 20 30 40 50 60 70 80 90 100 0 1020 3040 5060 708090 100 cumulative % population cumulative % income. Section 3 develops the semiparametric approach to modelling lorenz curves and section 4 discusses the practical problem of parameter choice in implementing the method. Stata module to produce pens parade, lorenz and generalised lorenz curve, statistical software components s456749, boston college department of economics, revised apr 2020. Charting income inequality food and agriculture organization. Lorenz and concentration curves are widely used tools in inequality research. Quantile group shares, cumulative shares lorenz ordinates.
The command dfgts decomposes the allevation of fgt poverty by income components and provides standard errors on elements of the decompositions. Generalized lorenz curves and social welfare generalized lorenz curve is the lorenz curve scaled up at each point by population mean income, i. Jun 26, 2018 the lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economist max lorenz in 1905. Produces the following curve with confidence interval. The scsomersd package is downloadable from ssc, and calculates the. We have found that students who work though the exercises in this appendix acquire the necessary mastery, and are ready to tackle almost any chal. The generalized lorenz curve is the lorenz curve scaled up at each point by mean income, and is often used for welfare dominance comparisons cowell 1995, lambert 1993. In economics, the lorenz curve is a graphical representation of the distribution of income or of wealth. As an alternative, some have built models for lorenz curves. Stata module to calculate summary statistics for income distributions.