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. So y lx is the lorenz curve if the poorest 100x percent of the population owns 100y percent of the wealth here, 0. In this paper i present a new stata command called lorenz that estimates lorenz and. But for any stata 8, those commands are no longer state of the art, about a decade behind the stata times. A value of 0 means there is a completely equal distribution of income. The graph plots percentiles of the population on the. The lorenz curve for a probability distribution is a continuous function. Jenkins iser, university of essex colchester co4 3sq, uk email. May 18, 2017 for the conclusion of the series on the lorenz curve, here is the curve for actual u.
A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. The lowest 10% of earners make 2% of all wages the next 40% of earners make 18% of all wages the next 40% of earners make 30% of all wages the highest 10% of earners make 50% of all wages. Estimation of gini coefficients using lorenz curves. As an alternative, some have built models for lorenz curves. Generalized lorenz curves for household incomes by head of. Charting income inequality food and agriculture organization. Creating a lorenz curve from excel university of washington. The orange curve is a bit below the cyan curve, indidating a slight increase in inequality over this decade. However, lorenz curves representing discontinuous functions can be constructed as the limit of lorenz curves of. The lorenz curve is not defined if the mean of the probability distribution is zero or infinite. Lorenz curve the lorenz curve is a tool used to represent wealth distributions as proposed by lorenz 1905. Graphing concentration curves in stata can be done using the command glcurve. Pdf generalized lorenz curves and related graphs researchgate.
For users of stata, there is a fastginicommand that can be downloaded and used directly see. The glcurve command is updated to a stata 7 version, glcurve7, which is described and illustrated. 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. Estimating lorenz and concentration curves sage journals. Inequality measures summary inequality is a broader concept than poverty in that it is defined over the entire population, and does not only focus on the poor. The graphics commands you are using are for stata 7. Income inequality can be measured graphically by a lorenz curve or mathematically using the gini coefficient. Estimation and interpretation of measures of inequality. Fieldwork data may be used but it is more common to use secondary sources e. Hello there, actually i am trying to compare lorenz curves 3 different incomes and i want to construct the line of 45 grades.
To construct the gini coefficient, graph the cumulative percentage of households from poor to rich on the horizontal axis and the cumulative per. Lorenz curve assignment help lorenz curve homework help online. Income, 1968 and 2010 that the lorenz curve for the united states became more bowed out between 1968 and 2010. In this case, the gini coefficient is 0 and it means there is perfect distribution of income everyone earns the same amount.
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. If a 0, it means the lorenz curve is actually the line of equality. Stata module to produce pens parade, lorenz and generalised lorenz curve, statistical software components s456749, boston college department of economics, revised apr 2020. As philippe suggested, there is more than one way to do lorenz curves. Identify the main sources of changes in inequality using theils l. However, instead of ending up with income shares, the lorenz curve relates the cumulative proportion of income to the cumulative proportion of individuals. Quantile group shares, cumulative shares lorenz ordinates. The lorenz curve functionality of roctab, which provides an alternative. Jun 17, 20 income inequality can be measured graphically by a lorenz curve or mathematically using the gini coefficient. The module is made available under terms of the gpl v3 s. Pdf the estimation of the lorenz curve and gini index. Focus here on estimation of lorenz curve and related concepts using. I could find it under chart wizard in another version. Hello, is it possible to construct a lorenz curve of a varname computed whit a population ordered in descending order of varname.
Nov 12, 2014 a look at how income inequality is measured. 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. This module should be installed from within stata by typing ssc install alorenz. He proposed what is now known as the lorenz curve in 1905. For the conclusion of the series on the lorenz curve, here is the curve for actual u. Lorenz curve it is one of the simplest representations of inequality. The step from lorenz curve to distribution function is more difficult than the step from distribution function to lorenz curve.
Estimation using sample survey data means that estimates. Development strategy and policy analysis unit department of. Summary this tool addresses the most popular inequality index, the gini index. This model interpolates between selfsimilar behavior at. Stata january 1995 technical stb23 bulletin stata press. The lorenz curve corresponding to any random variable x with cumulative distribution function fx and finite mean p f x dfx is defined to be 2 lp p1 f lt dt, o lorenz curves given a population, the lorenz curve shows the distribution of wealth among the constituents. Estimating lorenz and concentration curves in stata ben jann institute of sociology university of bern ben. As far as i can recall, glcurve tends to drop zero obserations philippe is the author, he should know better. Calculus i introduction to the gini coefficient the gini coefficient or gini index is a commonlyused measure of inequality devised by italian. The more bowed out the curve, the less equal the distribution. Quantile group shares, cumulative shares lorenz ordinates, and generalized lorenz ordinates. If i want to calculate the gini coefficient and lorenz curve how should i proceed. 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.
To construct the loren curve where population are ordered in descending order of varname i typed. 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. Feb 24, 2010 the gini coefficient ranges between 0 and 1 or it can also be expressed as a number from 0 to 100 and is given by the ratio of the areas. It is most often used in economics to measure how far a countrys wealth or income distribution deviates from a totally equal distribution. The gini coefficient ranges between 0 and 1 or it can also be expressed as a number from 0 to 100 and is given by the ratio of the areas.
Estimation of agricultural resource inequality in india using. For future reference, you might want to use scsomersd rather than somersd to calculate the gini coefficient with confidence limits. A lorenz curve always starts at 0,0 and ends at 1,1. Can some one provide pointers on how to make the lorenz concentration curves. Charting income inequality 5 the lorenz curve table 2 calculating lorenz curves 1 individual 1 3 5 discussion 5. To do this, imagine lining people or households, depending on context in an economy up in order of income from smallest to largest. The gini coefficient is a single number aimed at measuring the degree of inequality in a distribution.
Stata, pshare, percentile shares, lorenz curve, concentration curve, inequality, income distribution, wealth distribution, graphics. 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. Estimation of gini coefficients using lorenz curves johan fellman1,2 abstract primary income data yields the most exact estimates of the gini coefficient. The lorenz curve is a simple way to describe income distribution using a twodimensional graph. Figure 3, below, shows the shape of lorenz curves in the case of the three income distributions a, b and. 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. Lorenz curve coincides with 45 ray through origin inequality is greater, the further the lorenz curve from the 45ray. Lorenz curve assignment help lorenz curve homework help. For users of stata, there is a gini command that may be downloaded and used directly see appendix 3. Query on plotting lorenz curves on stata stack overflow. The command is available online for installation in netaware stata. 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. Estimating lorenz and concentration curves in stata. There are a number of ways in which one can depict the distribution of some magnitude e.
Is it possible that there isnt such option on this version. Generalized lorenz curves and related graphs the stata journal. Estimation of agricultural resource inequality in india using lorenz curve and gini coefficient approach mada melkamu1 and richard kwasi bannor2. Plotting lorenz curve with ggplot2 description the package provides statistical transformations for plotting empirical ordinary lorenz curve and generalized lorenz curve. It discusses its characteristics and the link with another popular graphical tool of representing inequality, the lorenz curve.
The closer a lorenz curve lies to the 45degree line, the more equal the distribution. Despite their frequent use in inequality research literature, stata does not offer. On the horizontal axis is the cumulative number of income recipients ranked from the poorest to the richest individual or. Suppose the lorenz curve for a society is given by s r r.
This model interpolates between selfsimilar behavior at the low and high ends of the income. Jun 26, 2018 the lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economist max lorenz in 1905. Stata module to estimate and display lorenz curves. Gini comments the gini index ranges between 0 and 1, with inequality increasing with an increasing index.
Extended version of the gini index with different weighting schemes are also discussed. The simplest measurement of inequality sorts the population from poorest to richest and shows the. Xi with ia as an indicator function being equal to 1 if a is true and 0 otherwise. Income distribution is described by a twoparameter model for the lorenz curve. The lorenz curve is a graphical representation of income inequality or wealth inequality developed by american economist max lorenz in 1905. The generalized lorenz curve is the lorenz curve scaled up at each point by mean income.
Estimating lorenz and concentration curves in stata boris. 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. The standard relative lorenz curve illustrates the shape of a distribution and. Srinivasulu rajendran centre for the study of regional development csrdjawaharlal nehru university jnu new delhi india r. Notes on how to compute gini coefficient suppose you are given data like this. Generalized lorenz curves and social welfare generalized lorenz curve is the lorenz curve scaled up at each point by population mean income, i. The lorenz curve is a graphical method used to display the concentration of activities within an area e. Jun 15, 2018 lorenz estimates lorenz and concentration curves from individuallevel data and, optionally, displays the results in a graph. The concentration curve is the bivariate analogue of the lorenz curve. Characterizations of lorenz curves and income distributions. If you type, in stata, findit lorenz then you will find a choice of programs to plot a lorenz curve. 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. The econometrics of inequality and poverty chapter 4.
723 322 907 852 1294 1087 183 576 782 649 759 605 460 1567 351 275 464 234 1313 433 17 1364 1211 1153 244 373 1443 1137 231