Users of any of the software, ideas, data, or other materials published in the stata journal or the supporting. Estimation of gini coefficients using lorenz curves. Generalized lorenz curves and related graphs the stata journal. Estimating lorenz and concentration curves in stata.
The lorenz curve is not defined if the mean of the probability distribution is zero or infinite. However, lorenz curves representing discontinuous functions can be constructed as the limit of lorenz curves of. Estimation of gini coefficients using lorenz curves johan fellman1,2 abstract primary income data yields the most exact estimates of the gini coefficient. Stata module to estimate and display lorenz curves and concentration curves, statistical software components s4583, boston college department of economics, revised 15 jun 2018. Pdf estimating lorenz and concentration curves in stata. The reason your line of perfect equality does not pass through 0,0 is because the values for your variable do not contain 0. 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.
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. The lorenz command supports relative, generalized, absolute, unnormalized, customnormalized lorenz, and concentration curves. It is frequently the case that the measure of interest used to rank experimental units when estimating the empirical. 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 estimate lorenz and concentration curves, statistical software components s456515, boston college department of economics. Free online software calculator computes the gini coefficient, plots the lorenz curve, and computes many other measures of concentration for any dataset. It focuses on how to construct a lorenz curve from raw da. Cox helped with updating the code for our program from stata 7 glcurve7. For example, a lorenz curve can show that the bottom 40% of households bring in 25% of a countrys income. Appropriate software previously unavailable but is now for many of the.
The step from lorenz curve to distribution function is more difficult than the step from distribution function to lorenz curve. Thanks nick, it worked like a charm when i added the 7 to graph7 but i was not able to the get the visual that was shown in the stata journal 7. I have to construct a single graph whit lorenz curve of varname, lorenz curve of varname where population are ordered in descending order of. Quantile group shares, cumulative shares lorenz ordinates. Charting income inequality food and agriculture organization. A lorenz curve is a plot of two distributions in welfare economics, the vertical axis gives the. The lorenz curve for a probability distribution is a continuous function. Cox helped with updating the code for our program from stata 7 glcurve7 to stata 8. 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. Jun 26, 2018 the lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economist max lorenz in 1905. Compare the lorenz curves for the populations 10, 20, 35, 35 and 15, 15, 30, 40. The gini coefficient requires you to construct a lorenz curve that would look like this. David demery, owen odonnell, shehzad ali made useful bug reports. A lorenz curve is a plot of two distributions in welfare.
Estimating the empirical lorenz curve and gini coefficient. The econometrics of inequality and poverty chapter 4. Stata module to estimate and display lorenz curves and concentration curves, statistical software components s4583, boston. Sep 23, 2014 there is an earlier video titled lorenz curve in excel.
Sampling distribution of gini coefficient rbloggers. To do this, imagine lining people or households, depending on context in an economy up in order of income from smallest to largest. We can find some functions, in different software languages, addressing the analysis of income distributions via generalized lorenz curves and their associated. A lorenz curve always starts at 0,0 and ends at 1,1. For example, the ordinary lorenz curve lp glpmeanx. Is it possible that there isnt such option on this version. Cox helped with updating the code for our program from stata 7 glcurve7 to. Comments by zhuo adam chen lead to introduction of sort stable estimation. 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. 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. The lorenz curve is a graphical tool that is widely used to characterize the concentration of a measure in a population, such as wealth. Generalized lorenz curves and social welfare generalized lorenz curve is the lorenz curve scaled up at each point by population mean income, i.
In this paper i present a new stata command called lorenz that estimates lorenz and. For future reference, you might want to use scsomersd rather than somersd to calculate the gini coefficient with confidence limits. The lorentz curve is a graphical representation of this inequality which is intimately related to the gini coefficient. Goodness of fit and empirical results are discussed in sections 5 and 6. In sections 3 and 4 estimation methods are outlined. I have seen the following code from stata help but i was not sure how to create eqinc or chpay variables were created in the original dataset. Statistical software components s366002, department of economics. Lorenz and concentration curves are widely used tools in inequality research. Stata, lorenz, lorenz curve, concentration curve, inequality, income. Generalized lorenz curves and related graphs sage journals. Estimation and interpretation of measures of inequality. Gini comments the gini index ranges between 0 and 1, with inequality increasing with an increasing index. Creating a lorenz curve from excel university of washington. We have found that students who work though the exercises in this appendix acquire the necessary mastery, and are ready to.
Figure 3, below, shows the shape of lorenz curves in the case of the three income distributions a, b and. Stata module to derive generalised lorenz curve ordinates. Their gini coefficients are the same, but i think that this is a weakness of the indexi think the latter is a more equitable income distribution. 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. It represents a probability distribution of statistical values, and is often associated with income distribution calculations. Sep 02, 2012 what is lorenz curve the lorenz curve is a graphical representation of the cumulative distribution function of the empirical probability distribution of wealth to measure wealth inequality. Calculating gini coefficient of world income inequality with.
A value of 0 means there is a completely equal distribution of income. In particular, im interested in what happens to the sampling distributions as sample size changes of the following summary statistics. Fx, glcurve either draws its generalised lorenz curve or generates two new variables containing the generalised lorenz ordinates for x, i. Lorenz curve coincides with 45 ray through origin inequality is greater, the further the lorenz curve from the 45ray. The concentration curve is the bivariate analogue of the lorenz curve. The program works very much like the official programs cumul or kdensity. Ben jann no 15, university of bern social sciences working papers from university of bern, department of social sciences. 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. Lorenz curves instead of generalized lorenz curves. 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. Although this value will asymptotically approach 0, it will never actually reach 0. Hello, is it possible to construct a lorenz curve of a varname computed whit a population ordered in descending order of varname. As an alternative, some have built models for 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.
Stata module to estimate and display lorenz curves. The lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economist max lorenz in 1905. Query on plotting lorenz curves on stata stack overflow. Although i did not explain it during my lectures, calculating a gini index or displaying the lorenz curve can be done very easily with r. I could find it under chart wizard in another version. Charting income inequality 5 the lorenz curve table 2 calculating lorenz curves 1 individual 1 3 5 discussion 5. Jun 30, 2010 the gini coefficient is a measure of the inequality of a distribution often used for income or wealth distributions.
Coordinates of curves can be listed or saved in a new stata file. In jenkins and van kerm 1999, we presented glcurve, a program to draw general. Munich personal repec archive cointegration analysis of oil prices and consumer price index in south africa using stata software sukati, mphumuzi. Gini coefficient and the lorentz curve file exchange. A then you have to determine what fraction of the triangle is made up of area a. 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.
Focus here on estimation of lorenz curve and related concepts using sumdist and. If i want to calculate the gini coefficient and lorenz curve how should i proceed. If you type, in stata, findit lorenz then you will find a choice of programs to plot a lorenz curve. 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. Estimating lorenz and concentration curves ben jann, 2016. Estimating the empirical lorenz curve and gini coefficient in. The lorenz curve is a simple way to describe income distribution using a twodimensional graph. Lorenz and concentration curves for child benefits. Estimating lorenz and concentration curves in stata ben jann institute of sociology university of bern ben. What happens to the gini coefficient as i add many higherincome people. More software in statistical software components from boston college department of economics boston college. The glcurve command is updated to a stata 7 version, glcurve7, which is described and illustrated. Nov 18, 2010 i presume that you want to produce a lorenz curve.
You can do anything pretty easily with r, for instance, calculate concentration indexes such as the gini index or display the lorenz curve dedicated to my students. 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. Stata provides ado files that will calculate the gini coefficient as well as several other inequality indices. Stata module to estimate and display lorenz curves and. Lorenz curves models, including the one proposed by abdalla and hassan 2004 are presented. 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. In this paper i present a new stata command called lorenz that estimates. The lorenz command supports relative as well as generalized, absolute, unnormalized, or customnormalized lorenz or concentration. Users of this routine for stata 5 or 6 should use glcurve5. Pdf the estimation of the lorenz curve and gini index.
The graph plots percentiles of the population on the. The lorenz curve can give a clear graphic interpretation of the gini coefficient. Calculating gini coefficient of world income inequality. Maximum likelihood estimation of lorenz curves using. Cointegration analysis of oil prices and consumer price. Statistical software components from boston college department of economics. What is lorenz curve the lorenz curve is a graphical representation of the cumulative distribution function of the empirical probability distribution of wealth to measure wealth inequality. Stata module to produce pens parade, lorenz and generalised lorenz curve, statistical software components s456749, boston college department of economics, revised apr 2020. Working with household data sets requires a solid mastery of appropriate statistical and data management software, such as stata or spss. Can some one provide pointers on how to make the lorenz concentration curves. Gini coefficient and lorenz curve video khan academy.
Please consult the help included in the file for an extensive description of the two concepts and how to use the program. Exercises introduction working with household data sets requires a solid mastery of appropriate statistical and data management software, such as stata or spss. To construct the loren curve where population are ordered in descending order of varname i typed. He proposed what is now known as the lorenz curve in 1905. The lorenz command supports relative as well as generalized, absolute, unnormalized, or customnormalized lorenz or. Hello there, actually i am trying to compare lorenz curves 3 different incomes and i want to construct the line of 45 grades.
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