lorenz: Lorenz curve
In REAT: Regional Economic Analysis Toolbox

Description Usage Arguments Details Value Author(s) References See Also Examples

Calculating and plotting the Lorenz curve

lorenz(x, weighting = NULL, z = NULL, na.rm = TRUE,
lcx = "% of objects", lcy = "% of regarded variable", 
lctitle = "Lorenz curve", le.col = "blue", lc.col = "black",
lsize = 1.5, ltype = "solid", bg.col = "gray95", bgrid = TRUE, 
bgrid.col = "white", bgrid.size = 2, bgrid.type = "solid",
lcg = FALSE, lcgn = FALSE, lcg.caption = NULL, lcg.lab.x = 0, 
lcg.lab.y = 1, add.lc = FALSE, plot.lc = TRUE)

`x`	A numeric vector (e.g. dataset of household income, sales turnover or supply)
`weighting`	A numeric vector containing the weighting data (e.g. size of income classes when calculating a Lorenz curve for aggregated income data)
`z`	A numeric vector for (optionally) comparing the cumulative distribution
`na.rm`	logical argument that indicates whether NA values should be excluded before computing results
`lcx`	defines the x axis label
`lcy`	defines the y axis label
`lctitle`	defines the overall title of the Lorenz curve plot
`le.col`	defines the color of the diagonale (line of equality)
`lc.col`	defines the color of the Lorenz curve
`lsize`	defines the size of the lines (default: 1)
`ltype`	defines the type of the lines (default: `"solid"`)
`bg.col`	defines the background color of the plot (default: `"gray95"`)
`bgrid`	logical argument that indicates if a grid is shown in the plot
`bgrid.col`	if `bgrid = TRUE` (background grid), `bgrid.col` defines the color of the background grid (default: "white")
`bgrid.size`	if `bgrid = TRUE` (background grid), `bgrid.size` defines the size of the background grid (default: 2)
`bgrid.type`	if `bgrid = TRUE` (background grid), `bgrid.type` defines the type of lines of the background grid (default: `"solid"`)
`lcg`	logical argument that indicates if the non-standardized Gini coefficient is displayed in the Lorenz curve plot
`lcgn`	logical argument that indicates if the standardized Gini coefficient is displayed in the Lorenz curve plot
`lcg.caption`	specifies the caption above the coefficients
`lcg.lab.x`	specifies the x coordinate of the label
`lcg.lab.y`	specifies the y coordinate of the label
`add.lc`	specifies if a new Lorenz curve is plotted (`add.lc = "FALSE"`) or the plot is added to an existing Lorenz curve plot (`add.lc = "TRUE"`)
`plot.lc`	logical argument that indicates if the Lorenz curve itself is plotted (if `plot.lc = FALSE`, only the line of equality is plotted))

The Gini coefficient (Gini 1912) is a popular measure of statistical dispersion, especially used for analyzing inequality or concentration. The Lorenz curve (Lorenz 1905), though developed independently, can be regarded as a graphical representation of the degree of inequality/concentration calculated by the Gini coefficient (G) and can also be used for additional interpretations of it. In an economic-geographical context, these methods are frequently used to analyse the concentration/inequality of income or wealth within countries (Aoyama et al. 2011). Other areas of application are analyzing regional disparities (Lessmann 2005, Nakamura 2008) and concentration in markets (sales turnover of competing firms) which makes Gini and Lorenz part of economic statistics in general (Doersam 2004, Roberts 2014).

The Gini coefficient (G) varies between 0 (no inequality/concentration) and 1 (complete inequality/concentration). The Lorenz curve displays the deviations of the empirical distribution from a perfectly equal distribution as the difference between two graphs (the distribution curve and a diagonal line of perfect equality). This function calculates G and plots the Lorenz curve optionally. As there are several ways to calculate the Gini coefficient, this function uses the formula given in Doersam (2004). Because the maximum of G is not equal to 1, also a standardized coefficient (G*) with a maximum equal to 1 can be calculated alternatively. If a Lorenz curve for aggregated data (e.g. income classes with averaged incomes) or the Lorenz curve has to be weighted, use a weighting vector (e.g. size of the income classes).

A plot of the Lorenz curve.

Thomas Wieland

Aoyama, Y./Murphy, J. T./Hanson, S. (2011): “Key Concepts in Economic Geography”. London : SAGE.

Bahrenberg, G./Giese, E./Mevenkamp, N./Nipper, J. (2010): “Statistische Methoden in der Geographie. Band 1: Univariate und bivariate Statistik”. Stuttgart: Borntraeger.

Cerlani, L./Verme, P. (2012): “The origins of the Gini index: extracts from Variabilita e Mutabilita (1912) by Corrado Gini”. In: The Journal of Economic Inequality, 10, 3, p. 421-443.

Doersam, P. (2004): “Wirtschaftsstatistik anschaulich dargestellt”. Heidenau : PD-Verlag.

Gini, C. (1912): “Variabilita e Mutabilita”. Contributo allo Studio delle Distribuzioni e delle Relazioni Statistiche. Bologna : Cuppini.

Lessmann, C. (2005): “Regionale Disparitaeten in Deutschland und ausgesuchten OECD-Staaten im Vergleich”. ifo Dresden berichtet, 3/2005. https://www.ifo.de/DocDL/ifodb_2005_3_25-33.pdf.

Lorenz, M. O. (1905): “Methods of Measuring the Concentration of Wealth”. In: Publications of the American Statistical Association, 9, 70, p. 209-219.

Nakamura, R. (2008): “Agglomeration Effects on Regional Economic Disparities: A Comparison between the UK and Japan”. In: Urban Studies, 45, 9, p. 1947-1971.

Roberts, T. (2014): “When Bigger Is Better: A Critique of the Herfindahl-Hirschman Index's Use to Evaluate Mergers in Network Industries”. In: Pace Law Review, 34, 2, p. 894-946.

cv, gini.conc, gini.spec, herf, hoover

# Market concentration (example from Doersam 2004):
sales <- c(20,50,20,10)
# sales turnover of four car manufacturing companies
lorenz (sales, lcx = "percentage of companies", lcy = "percentrage of sales", 
lctitle = "Lorenz curve of sales", lcg = TRUE, lcgn = TRUE)
# plots the Lorenz curve with user-defined title and labels 
# including Gini coefficent

# Income classes (example from Doersam 2004):
income <- c(500, 1500, 2500, 4000, 7500, 15000)
# average income of 6 income classes
sizeofclass <- c(1000, 1200, 1600, 400, 200, 600)
# size of income classes
lorenz (income, weighting = sizeofclass, lcg = TRUE, lcgn = TRUE)
# plots the Lorenz curve with user-defined title and labels
# including Gini coefficent

# Regional disparities in Germany:
gdp <- c(460.69, 549.19, 124.16, 65.29, 31.59, 109.27, 263.44, 39.87, 258.53, 
645.59, 131.95, 35.03, 112.66, 56.22, 85.61, 56.81)
# GDP of german regions 2015 (in billion EUR)
lorenz (gdp, lcg = TRUE, lcgn = TRUE)
# plots the Lorenz curve with user-defined title and labels
# including Gini coefficent